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on The Coexistence Problem in Smooth Dynamical Systems, I \r\n\r\n", "source_sha256": "cc0e0dac282365d0422d9174e5d1bf1de06c3d8d181e85678728c7e756c2da9c", "paper_ids": ["Paper/68961", "Paper/71498", "Paper/65759", "Paper/69361"], "id": "Session/18065"}, {"title": " COMAP Special Session on Mathematical Modeling in Action: Student and Advisor Experiences in COMAP’s Modeling Contests, II \r\n\r\n", "source_sha256": "328ff01a0a9a60c30829b99a602ec44d898a7757dff26fd65c7e4484b49d93b1", "paper_ids": ["Paper/71228", "Paper/68079", "Paper/68907", "Paper/68546", "Paper/67466", "Paper/70360", "Paper/70043", "Paper/69958"], "id": "Session/18066"}, {"title": " AMS Special Session on Crystals, Schubert Calculus, and Beyond, I \r\n\r\n", "source_sha256": "8df191470944e42283241fa375b37453cc4fc74a61f983713cbbd5d4400650ab", "paper_ids": ["Paper/68733", "Paper/65031", "Paper/69562", "Paper/69449", "Paper/66067", "Paper/67504", "Paper/66161", "Paper/69731"], "id": "Session/18067"}, {"title": " SIGMAA Contributed Paper Session on Research in Undergraduate Mathematics Education, I \r\n\r\n", "source_sha256": "e9a7eca85f6ad1d9c3d9698637589f0ba9e4234a19bba039c523e6336103b6a3", "paper_ids": ["Paper/67912", "Paper/63439", "Paper/62716", "Paper/71558", "Paper/70698", "Paper/71410", "Paper/64736", "Paper/70298", "Paper/69877", "Paper/65686"], "id": "Session/18068"}, {"title": " SIAM Minisymposium on Modern Nonsmooth Optimization: Theory, Algorithms and Applications, I \r\n\r\n", "source_sha256": "9de2b912e728b83934a1949d735946e4e983cfea912a50004e23f08ad2f4ad5d", "paper_ids": ["Paper/63557", "Paper/66943", "Paper/68361", "Paper/66216", "Paper/63702", "Paper/70253", "Paper/65747"], "id": "Session/18069"}, {"title": " JMM Panel on From Theory to Practice: Why and How to Build Mathematics Prison Education Programs \r\n\r\n", "source_sha256": "a62dc611409487f155d49712d3a14900b80a14c921d64ef330f8e797f15df4d6", "paper_ids": [], "id": "Session/18070"}, {"title": " AMS Special Session on Topological Methods: Combinatorics, Geometry, and Applications, I \r\n\r\n", "source_sha256": "697a477c2fdae61367ba3f91aee49ab5036d602af880670e68515a9ad4c5bab0", "paper_ids": ["Paper/71026", "Paper/69083", "Paper/67090", "Paper/64850", "Paper/70012", "Paper/67142"], "id": "Session/18072"}, {"title": " AMS Special Session on Cryptography and Related Fields, I \r\n\r\n", "source_sha256": "38ecbec1bb2aff3cb2251e2ac6915dba3cae9a5fb68cd806e5091cde4e984f7f", "paper_ids": ["Paper/70941", "Paper/69323", "Paper/68926", "Paper/67601", "Paper/68910", "Paper/66764", "Paper/69805", "Paper/68110"], "id": "Session/18073"}, {"title": " AMS Special Session on Mathematics and New Media, I \r\n\r\n", "source_sha256": "5b6b415c6c77e17f5e53e30f979edb6ac2b234b8d411e1c4665fbb4f844471fd", "paper_ids": ["Paper/70906", "Paper/70229", "Paper/68293", "Paper/71508", "Paper/72337", "Paper/71534", "Paper/68616"], "id": "Session/18074"}, {"title": "AWM Special Session on Arithmetic Geometry & Algebraic Groups, I", 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Scientific Workflows, I \r\n\r\n", "source_sha256": "475506fe00a345cd8ea54c83e7a40b01099170fa98fd8ff3daac0a8a003a2388", "paper_ids": ["Paper/70660", "Paper/69372", "Paper/69716", "Paper/68914", "Paper/70560", "Paper/65486", "Paper/68987", "Paper/70332"], "id": "Session/18105"}, {"title": " AMS Special Session on Graph Theory: Structure, Algorithms, and Applications, I \r\n\r\n", "source_sha256": "01677906eeb06ae077f60a786ec4e1f046360bc2ec108707712fd456cfafb63f", "paper_ids": ["Paper/67536", "Paper/66019", "Paper/65834", "Paper/66027", "Paper/69424", "Paper/64335", "Paper/70574", "Paper/66175"], "id": "Session/18106"}, {"title": " SIAM Minisymposium on Coherent Structures in Complex Systems, I \r\n\r\n", "source_sha256": "7c5856a62e90abab166db43d7d4ae4346c88f1f322317e5cbc98a24f8c243d16", "paper_ids": ["Paper/69529", "Paper/70741", "Paper/70324", "Paper/70661", "Paper/69122", "Paper/68576", "Paper/65264", "Paper/62343"], "id": "Session/18109"}, {"title": " JMM Panel on The Mapper Algorithm in Theory and Practice \r\n\r\n", "source_sha256": "1c51120af88a87d45978ecfe5b2790892e7e2fc7142a3a670c912c4c687e316a", "paper_ids": [], "id": "Session/18112"}, {"title": " SIAM Minisymposium on Recent Advances in Quantum Computing Algorithms and Applications, I \r\n\r\n", "source_sha256": "0c2d0afdca81fb1814d6ae3a3b2aafbaef14ef7d2777fd16d5a49fba65466bc0", "paper_ids": ["Paper/65875", "Paper/64614", "Paper/71589", "Paper/68740", "Paper/72008", "Paper/69175", "Paper/68873", "Paper/72009"], "id": "Session/18113"}, {"title": " AMS Special Session on Applied Topology: Finding Shape in Data, I \r\n\r\n", "source_sha256": "458f6e18d5f239eac6192b2edb11a84460a27a07c12153cd736de525b8f93ec7", "paper_ids": ["Paper/70492", "Paper/62922", "Paper/66868", "Paper/67297", "Paper/67439", "Paper/67715", "Paper/68057", "Paper/65402"], "id": "Session/18114"}, {"title": " AMS Special Session on Algebraic Statistics Across the Sciences: Models from Biology, Networks, and Learning \r\n\r\n", 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PME Contributed Session on Research by Undergraduates, VI \r\n\r\n", "source_sha256": "d61b63bbd8e97285eede238f95cf0eab7792cbde3040f218e5859c69ad3f865d", "paper_ids": ["Paper/71194", "Paper/71724", "Paper/71731", "Paper/71740", "Paper/71747", "Paper/72396", "Paper/71770", "Paper/71782", "Paper/71787", "Paper/72040", "Paper/72061", "Paper/72076", "Paper/72077", "Paper/72097", "Paper/72108", "Paper/72138"], "id": "Session/18242"}, {"title": " PME Contributed Session on Research by Undergraduates, VII \r\n\r\n", "source_sha256": "4d30d775f5e619bfca3468c6e96e38d7b9cd28124860cfd6237a7610916e4f0a", "paper_ids": ["Paper/72145", "Paper/72148", "Paper/72179", "Paper/72180", "Paper/72196", "Paper/72201", "Paper/72204", "Paper/62719", "Paper/72384", "Paper/72394", "Paper/62033", "Paper/72407", "Paper/72425", "Paper/72441", "Paper/72442", "Paper/72469"], "id": "Session/18243"}, {"title": " SIAM Minisymposium on Coherent Structures in Complex Systems, II \r\n\r\n", "source_sha256": 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Data Analysis and Computational Science, II \r\n\r\n", "source_sha256": "2ec701800dd2272d19e2e4aa5b0a8b2337667fbe29385ad07e5d57c5997abc68", "paper_ids": ["Paper/69822", "Paper/69345", "Paper/72404", "Paper/68925", "Paper/71119", "Paper/72405", "Paper/71196"], "id": "Session/18247"}, {"title": " Spectra Special Session on Research by LGBTQ+ and Allied Mathematicians, II \r\n\r\n", "source_sha256": "e72f15715602bd5cf06f77e49e79cb319d48e9fd2d3f7039bc6a58434c4a8ec0", "paper_ids": ["Paper/70276", "Paper/70573", "Paper/71052", "Paper/72936"], "id": "Session/18248"}, {"title": "TPSE Contributed Paper Session on Course Coordination: Insights from Research and Practice, II", "source_sha256": "6e342bef904c583fa01adffa31b4c13103ea596f8ef5c05207001f6a8a455570", "paper_ids": ["Paper/68939", "Paper/67652", "Paper/67653", "Paper/70010", "Paper/71801", "Paper/65932", "Paper/65800", "Paper/71802", "Paper/63332", "Paper/64575", "Paper/71803", "Paper/68114", "Paper/68446"], "id": "Session/18250"}, {"title": "AMS Special Session on Advances in Commutative Algebra and Connections with Geometry and Combinatorics, II", "source_sha256": "81c58fcc2a8255330211343d89eabe056a69e2dcd56543f4fcd664ed1ebfe407", "paper_ids": ["Paper/70487", "Paper/71094", "Paper/67843", "Paper/68553", "Paper/68703", "Paper/70071", "Paper/67380", "Paper/68863"], "id": "Session/18253"}, {"title": "AMS Special Session on Advances in Fractional Difference Equations and Dynamic Equations on Time Scales, II", "source_sha256": "17efb4c6f330cd9b54cf3be450fda2dd5e2cb013e2c814f539bb2aa3cb15cc11", "paper_ids": ["Paper/67169", "Paper/66952", "Paper/66827", "Paper/66648", "Paper/68422"], "id": "Session/18254"}, {"title": "AMS Special Session on Algebraic Methods in Graph Theory and Applications, II", "source_sha256": "e783c2b02bf058d1cd53f0972c894061026dff3055b7e0e9f97621485db347d6", "paper_ids": ["Paper/68511", "Paper/62174", "Paper/64922", "Paper/64985"], "id": "Session/18255"}, {"title": " AMS Special Session on 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AMS Contributed Papers Sessionon Graph Theory, II \r\n\r\n", "source_sha256": "037090718e001e16099083345cdc06d3399d3b5a388f4c2388fbece1f4258823", "paper_ids": ["Paper/64188", "Paper/68038", "Paper/66609", "Paper/70607", "Paper/69156", "Paper/67139", "Paper/66127", "Paper/63540", "Paper/68496", "Paper/69747", "Paper/71099", "Paper/69165"], "id": "Session/19360"}, {"title": " AMS Contributed Papers Session on Number Theory, II \r\n\r\n", "source_sha256": "76234b870209f3d6a9885cd17377479df592d2347d9086af792babc74eec8475", "paper_ids": ["Paper/70322", "Paper/69765", "Paper/70646", "Paper/68597", "Paper/70870", "Paper/66924", "Paper/68373", "Paper/68475", "Paper/63883", "Paper/65065", "Paper/71104", "Paper/70449"], "id": "Session/19361"}, {"title": " AMS Contributed Papers Session on Group Theory \r\n\r\n", "source_sha256": "3da51968658eb39878ed6d0cdbc7c2d7eb78d387bd8069226510af811704dfb3", "paper_ids": ["Paper/71513", "Paper/64778", "Paper/64906", "Paper/69073", "Paper/66606", "Paper/68358", "Paper/65147", "Paper/68207", "Paper/67642", "Paper/69174", "Paper/66886", "Paper/62312", "Paper/72715", "Paper/72771", "Paper/71411"], "id": "Session/19362"}, {"title": " AMS Contributed Papers Session on Differential Equations, I \r\n\r\n", "source_sha256": "37b2c40d3ae1537be3101f86cbbbe445542edd5b377f862f71c9313c1c1c47ef", "paper_ids": ["Paper/67657", "Paper/67890", "Paper/70910", "Paper/68816", "Paper/69541", "Paper/66417", "Paper/66967", "Paper/65638", "Paper/69317", "Paper/65846", "Paper/68242", "Paper/63183", "Paper/72793"], "id": "Session/19363"}, {"title": " AMS Contributed Papers Session on Statistics and Probability, II \r\n\r\n", "source_sha256": "32977eb3df427b54dd1818ee2ea46beba3a650960fcee3a0775c29645af7e7bc", "paper_ids": ["Paper/70641", "Paper/64761", "Paper/71380", "Paper/63588", "Paper/70590", "Paper/66156", "Paper/63068", "Paper/61826", "Paper/66966", "Paper/68916", "Paper/72951", "Paper/70149", "Paper/70576", "Paper/71602"], "id": "Session/19364"}, {"title": " AMS Contributed Papers Session on Mathematical Biology, III \r\n\r\n", "source_sha256": "33a029f548bd08cf7128fc1f3bc8d06590a9f84fc15a8eaaac77ca0e22f9c961", "paper_ids": ["Paper/70074", "Paper/67932", "Paper/71381", "Paper/69335", "Paper/63894", "Paper/66537", "Paper/70707", "Paper/70865", "Paper/72594", "Paper/65499", "Paper/68158", "Paper/70623", "Paper/68996", "Paper/71136", "Paper/68051"], "id": "Session/19365"}, {"title": " AMS Contributed Papers Session on Graph Theory, III \r\n\r\n", "source_sha256": "c5c62b54929fab4912ff73d1aaf0c8ded37ecdfb315f895577634c0baa426470", "paper_ids": ["Paper/65878", "Paper/69493", "Paper/71548", "Paper/67783", "Paper/67852", "Paper/65342", "Paper/71343", "Paper/63950", "Paper/71507", "Paper/68481", "Paper/69596", "Paper/69568", "Paper/65864", "Paper/65787", "Paper/71537"], "id": "Session/19366"}, {"title": " AMS Contributed Papers Session on Number Theory, III \r\n\r\n", "source_sha256": "1c470ad3b2d2b68bcc9be075c7455d1a02da399fabfa8deeb297a9500f444504", "paper_ids": ["Paper/69079", "Paper/70318", "Paper/67455", "Paper/70317", "Paper/68392", "Paper/68969", "Paper/70771", "Paper/70805", "Paper/63480", "Paper/70914", "Paper/64760", "Paper/70993", "Paper/71350", "Paper/68861", "Paper/71188"], "id": "Session/19367"}, {"title": " AMS Contributed Papers Session on Complex Analysis \r\n\r\n", "source_sha256": "ebc87dc6271305360ca621ae920a2049a73447611aa504bc75717b22dc212b1a", "paper_ids": ["Paper/68196", "Paper/70635", "Paper/61765", "Paper/71465", "Paper/71273", "Paper/71238", "Paper/67841", "Paper/65217", "Paper/65992", "Paper/66177", "Paper/70564", "Paper/67772", "Paper/65477", "Paper/63952", "Paper/63953", "Paper/65121"], "id": "Session/19368"}, {"title": " AMS Contributed Papers Session on Differential Equations, II \r\n\r\n", "source_sha256": "9bdc253d8881d6f4a146a42dc408f1dfc7cb49a97829a9ab1cabb510eb02ed8a", "paper_ids": ["Paper/71290", "Paper/67304", "Paper/71079", "Paper/68276", "Paper/68184", "Paper/66212", "Paper/64844", "Paper/71583", "Paper/68437", "Paper/68927", "Paper/69004", "Paper/70937", "Paper/61518"], "id": "Session/19369"}, {"title": " AMS Contributed Papers Session on Probability Theory \r\n\r\n", "source_sha256": "5b6118d55ebb6fddd114efad739264125f9b9e8ab0ab669784c2873c9b9eb0b7", "paper_ids": ["Paper/70578", "Paper/69802", "Paper/67423", "Paper/68780", "Paper/66872", "Paper/71156", "Paper/71016", "Paper/70497", "Paper/66190", "Paper/71246", "Paper/65236", "Paper/69936", "Paper/70350", "Paper/72868"], "id": "Session/19370"}, {"title": " AMS Contributed Paper Session on Mathematical Biology, IV \r\n\r\n", "source_sha256": "8f87a51a3da9398c4618533e3fa0f69a481316ea4b8802d753126b1e4318d0d6", "paper_ids": ["Paper/68589", "Paper/67769", "Paper/69685", "Paper/67464", "Paper/69758", "Paper/70447", "Paper/68037", "Paper/70801", "Paper/71551", "Paper/70927", "Paper/69469", "Paper/71580", "Paper/69628", "Paper/70951", "Paper/65467"], "id": "Session/19371"}], "schema_version": 1, "event": "JMM 2027, Chicago, January 12-15", "papers": [{"title": " Hilbert’s Sixth Problem: From Particles to Waves \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/17286"], "source_sha256": "65f0f52ebfaa3e2e609465bf2449647eb779aff80a2ed93664dcedd43acdf4b0", "withdrawn": "", "abstract": "Hilbert’s sixth problem calls broadly for the axiomatic foundation of physics. A central theme is the derivation of the macroscopic laws of statistical physics starting from the laws of dynamics (like Newton’s laws) that describe the motion at the microscopic level. In this regard, Hilbert singled out the rigorous derivation of the fundamental equations of hydrodynamics, such as the compressible Euler and Navier-Stokes equations, from Newton’s laws, and suggested using Boltzmann’s kinetic theory as an intermediate step. The crucial challenge here is the passage from the time-reversible Newtonian dynamics of a gas of particles to the irreversible dynamics of the Boltzmann kinetic equation.\n\nIf one replaces gas particles by waves, interacting according to some nonlinear wave theory, one obtains what is known as \"wave kinetic theory” (sometimes called \"wave turbulence theory\"). Here too, the central question is to give the rigorous foundations of the wave kinetic theory starting from the time-reversible wave dynamics.  \n\nIn this lecture, we shall survey the history of these problems, and discuss some major advances that were made over the past five years.", "id": "Paper/61369", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61369"}, {"title": " Finding the Hidden Circle \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/17242"], "source_sha256": "e328dee145ae88854144247a9cfb11e8a4fec10c4d86ea2ada9372933a716d38", "withdrawn": "", "abstract": "Pi shows up in many unexpected corners throughout mathematics. This talk explores a few such occurrences that initially seem completely unrelated to circles, such as the dynamics underlying the Mandelbrot set and certain convergent series. In all cases, there is a joy in hunting down the hidden circle that explains what pi was doing there in the first place.", "id": "Paper/61370", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61370"}, {"title": " Ooh ooh ooh what a little course can do: personal and institutional transformation through 1-credit ADAPT courses \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/17288"], "source_sha256": "af260b4bead80dd1ff648b09dcf0848326b1100c5c2dc39f8b95942663ac1303", "withdrawn": "", "abstract": "To meet the needs of rapid technological changes and a data-driven world, we need to rethink education. Attention spans are short. People learn best by doing things they care about. Those of us who can be flexible learners and willing to evolve our work practices will be best equipped to help our students do the same. We are tired in so many ways, but we cannot give up. As mathematical scientists, in collaboration with other foundational fields for data science and AI, we are well-positioned to lead. My education-related experiences in K-12, industry, higher education, non-profit, and government led me to serve as the inaugural Executive Director of the NC State University Data Science and AI Academy from 2021-2026. In this short time, the academy developed interdisciplinary capacity to engage data and AI across the 10 colleges of the largest public university in North Carolina, reaching students in over 175 programs of study, building data and AI literacy and fluency for students, faculty, staff, and community partners. The key to this success has been a common pedagogical approach: the All-Campus (or perhaps all-learner) Data Science and AI Project-Based Teaching and Learning Model (ADAPT Model). I look forward to sharing how this approach has infused data science and AI across the NC State campus and beyond.", "id": "Paper/61371", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61371"}, {"title": " To be announced \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/17289"], "source_sha256": "32cebe328141ffc5ef04e3951194797aaba125ec475c45827eda3e7a52441abf", "withdrawn": "w", "abstract": "To be announced", "id": "Paper/61372", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61372"}, {"title": " Mathematics of Hearing the Will of the People \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/17290"], "source_sha256": "f4bc1792b7808b0e4fa66ce1ac59433b691e61bad460f79c8bdbae1481e0a1f4", "withdrawn": "", "abstract": "I will weave three threads together to explain how a collection of mathematical and algorithmic ideas became the standard for deciding if a collection of political districts are gerrymandered. The first thread is  a personal one about how an undergraduate project in 2013 developed into one of the main methods now accepted. The second was the quest to refine the ideas to convince the lawyers and then the courts of their power. The last is the interesting mathematics that has arisen from these investigations.\n\nJust over a decade ago when we started our work, there was no consensus in the courts on how to identify gerrymandering. Now due to the work of a number of mathematicians, statisticians, computational scientists, policy advocates, and lawyers from around the country, there are legally accepted methods for answering this question.  \n\nI will talk about how these ideas entered into various court cases and let me testify in front of three-judge constitutional panels including Common Cause v. Rucho (that went to the US Supreme Court), Common Cause v. Lewis, Harper v. Lewis, and Harper v. Hall/Moore.  \n\nThe legal discussion has been increasingly informed by the mathematical framework, and the mathematics has been pushed to better include policy considerations. This back and forth has been important to finding ways to effectively inform the policymakers and courts. This experience has also sharpened my understanding of the importance of communicating mathematical ideas.  \n\nThe problem of understanding gerrymandering has also prompted the development of a number of new computational algorithms that come with new mathematical questions. I will explain the mathematical frameworks we have developed, some of the results we have, and a number of open mathematical questions that have arisen.  For more info see https://url.us.m.mimecastprotect.com/s/E-4vC1wpv8up7KZ7fLfp1sV3H08?domain=duke.is and https://url.us.m.mimecastprotect.com/s/jIbGC2kqw5ckNAmNH1h3ws5PTOC?domain=duke.is", "id": "Paper/61373", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61373"}, {"title": " Puzzles I Cannot Yet Solve \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/17291"], "source_sha256": "f92f017264bc77dab15035ba484a5066ebbf1a32f89f9c94f91ce633478090a6", "withdrawn": "", "abstract": "I spent the last two years writing a book of recreational mathematics called Puzzle Planet. I envision it as a sea of icebergs: cute little toy problems poking up above the surface, deep unknown structures lurking beneath. I will share (1) share some of my favorites, (2) confront the fact that my own iceberg-probing powers have been surpassed by certain inhuman colleagues of mine, and (3) propose that, in this strange new world of A Chatbot Already Solved My Problem, recreational mathematics may offer a renewable source of Problems I Cannot Yet Solve.", "id": "Paper/61374", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61374"}, {"title": " How Topology Shapes Quantum Information \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/17732"], "source_sha256": "13cccced475b324b4c01f7c6687cd8d45b620f9069da1d61cb24efb38d36c037", "withdrawn": "", "abstract": "Topology is usually introduced as the study of shapes that can bend and stretch but not break. Quantum information, by contrast, is famous for its fragility: small errors can destroy delicate quantum states. One of the surprises of modern mathematics and physics is that these two themes meet in a deep way. This talk will explore the role of topology in quantum information, starting with the Jones polynomial of a knot and the remarkable fact that estimating it at roots of unity is tied to the computational power of quantum computers. From there we will follow the same braid-theoretic ideas into the world of anyons, topological phases of matter, and quantum error correction. The goal is to explain, through examples, why topology provides a mathematical structure governing what can be computed, how quantum particles can move, and how quantum information might be protected. I will close with recent work showing how new ideas in low-dimensional topology can change the computational behavior of standard anyon models.", "id": "Paper/61382", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61382"}, {"title": " Are We Cooked? \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/17369"], "source_sha256": "cabe973b7933ca1ce1dc895b5a2ca9de9aad57da82c2688a2b21566faed5c5cd", "withdrawn": "", "abstract": "I'll describe some recent case studies of using AI to solve major open problems that I've cared about in quantum computing and computational complexity theory, and reflect on what mathematics might look like going forward.  I'll also talk about what I think mathematicians can contribute to AI safety and alignment.", "id": "Paper/61383", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61383"}, {"title": " Heterogeneity, Stochasticity, Uncertainty, Oh My! When variation matters in infectious disease modeling. \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/17362"], "source_sha256": "f3259d7f61f96a208a9e01d3822055c6496b2483aa7bd34d1fd42bf581a56620", "withdrawn": "", "abstract": "Two seminal models, the Susceptible-Infected-Recovered (SIR) model and the Ross-Macdonald model for malaria, have inspired myriads of mathematical models of infectious disease for over a century. Part of the beauty of these models is in their simplicity: they are mathematically tractable and provide valuable insights into disease management. As mathematics and computational tools have advanced, we are now able to tackle subtleties that were previously averaged away. In this talk I provide a few biologically-motivated examples of when variation matters in malaria modeling and the dynamical systems approaches we can use to address that variation. I conclude with a discussion about the role of uncertainty when models are confronted with data.", "id": "Paper/61384", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61384"}, {"title": " To be announced \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/17366"], "source_sha256": "b7a71906552b526bb58de25951e87e8c3d94c528cdaf4eae105bb0b9bd23bdf7", "withdrawn": "", "abstract": "To be announced", "id": "Paper/61385", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61385"}, {"title": " To be announced \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/17367"], "source_sha256": "b7af07869ecf8bfdb75b7cd94fb888853dc0ef5d27f04f1ea6f909091d4fa6e4", "withdrawn": "", "abstract": "To be announced", "id": "Paper/61386", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61386"}, {"title": " To be announced \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/17368"], "source_sha256": "9c165f43d092c5a6366a5e11ddae22f9f694c1b229699ef5665b50fb4acfed70", "withdrawn": "", "abstract": "To be announced", "id": "Paper/61387", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61387"}, {"title": " A Few Things I have Learned About Wave Turbulence \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/17360"], "source_sha256": "b0b556b6030d02e7d3dc28ae53664752449991357b05e4527f9208f61395886b", "withdrawn": "", "abstract": "Over the last few years, I have worked on several problems that fall under the broad umbrella of wave turbulence theory, or, in my simpler terms, the study of the nonlinear interactions of waves. Along the way, I have encountered phenomena that can be understood deterministically, others that occur with very high probability, and still others that are extremely rare.\nProbability is, of course, the natural language for distinguishing among these different behaviors. Yet, in the end, I always return to what I learned in graduate school and to the basic mantra of Fourier analysis: decompose into simpler pieces, understand how they interact, and then reconstruct the whole.\nIn this lecture, I will describe, in broad strokes, a few examples from my work and some of the mathematical surprises I encountered along the way. My goal is not to give a systematic introduction to wave turbulence theory, but rather to share a few ideas, phenomena, and lessons that have shaped the way I think about the subject.", "id": "Paper/61388", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61388"}, {"title": " To be announced \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/17364"], "source_sha256": "b3fb0d186f988b569b73d71a185bf004cae7b8cfae6735a9f8de58c321b454b9", "withdrawn": "w", "abstract": "To be announced", "id": "Paper/61389", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61389"}, {"title": " To be announced \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18164"], "source_sha256": "268885505904dcec068dd662760f9e78c651657ab99c62c56947d387c2c5922c", "withdrawn": "w", "abstract": "To be announced", "id": "Paper/61440", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61440"}, {"title": " To be announced \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/17472"], "source_sha256": "fd0195c9b257262e5c32ca808bb12dbf919df546b9d0841cd7f61c630cdc4fd2", "withdrawn": "w", "abstract": "To be announced", "id": "Paper/61476", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61476"}, {"title": " To be announced \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/17363"], "source_sha256": "567a3e7d4016bc4acbd83a9b0577af5a81fbd40c77cf3fd0cb0d2345e88c1bda", "withdrawn": "", "abstract": "To be announced", "id": "Paper/61477", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61477"}, {"title": " Differential Equations and Irrationality \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18434"], "source_sha256": "2a42d4d7af2f3d1a99410b081abab8a9c15522e21137a3a82d6ae1c9f9e7dff9", "withdrawn": "", "abstract": "Abstract: Recent breakthrough work of Calegari, Dimitrov, and Tang has lead to new irrationality proofs for a number of arithmetically interesting constants (for example the L-value L(2, χ_{-3})), building on earlier ideas of Apéry, Beukers, and others. I'll give an overview of some of their ideas and their general context in arithmetic geometry and number theory.", "id": "Paper/61478", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61478"}, {"title": " Particles and Waves \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18433"], "source_sha256": "6abd3c6c8303e5da064600d7efdfe992ad01b2a646b211f5861fbd9f63f76947", "withdrawn": "w", "abstract": "To be announced", "id": "Paper/61479", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61479"}, {"title": " Optimism before and after the Telescope Conjecture \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18435"], "source_sha256": "113d7705bb7572762bd858add2547001bda68b7df1a5f6809d783e42dc672cb7", "withdrawn": "", "abstract": "The stable homotopy groups of spheres encode the ways in which topological spaces can be built from spheres when we are free to add helper dimensions. Holding the secret ingredients of all spaces, it is an understatement to say that these groups are complicated. Introduced in the 1970s, chromatic homotopy theory is based on the idea that the stable homotopy groups of spheres can be effectively understood by filtering the different frequencies of periodic patterns of which they are comprised. The Telescope Conjecture was the optimistic hypothesis that these periodic patterns look the same from a geometric or an algebraic perspective. However, its recent disproof by Burklund, Hahn, Levy, and Schlank indicates that homotopy theory still holds mysteries about the abundance of possible periodicities.", "id": "Paper/61480", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61480"}, {"title": " Fibering and Pseudo-Anosovs in Higher Dimensions \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18437"], "source_sha256": "925b4ad36f63985bfee77bf30e2711ddb0320a21d701897d34050b3ebcc0a3c8", "withdrawn": "", "abstract": "Pseudo-Anosov homeomorphisms of surfaces are essential for how we understand hyperbolic 3-manifolds via fibrations over the circle. Martelli recently suggested this theory has much to say in higher dimensions too, through a beautiful 4-d pseudo-Anosov homemorphism he constructed with some stunning applications in geometric topology. This talk will survey the half-century of geometry and topology that leading up to this elegant construction, some of its applications, and some future directions it suggests.", "id": "Paper/61481", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61481"}, {"title": " The Search for New Universality Phenomena for Exponential Sums \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/17365"], "source_sha256": "18fbd0631233013872ccd5fe8e6c8cb6b040cce36f9e4d77c0903d3533fb45a9", "withdrawn": "", "abstract": "Over the past fifteen years, Fourier analysis, combined with deep geometric input from Kakeya-type phenomena, has influenced a wide range of problems in number theory, partial differential equations, harmonic analysis and spectral theory that can be reformulated in terms of exponential sums. Some of these seemingly unrelated problems are governed by a universal principle known as Fourier decoupling. At its heart lies the realization that appropriate geometric separation among frequencies, rather than a rigid lattice structure, can be sufficient to produce square-root cancellation. I will also explore the limitations of this principle and the search for new universality phenomena capable of addressing a broader range of open problems.", "id": "Paper/61482", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61482"}, {"title": " To be announced \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18472"], "source_sha256": "a3919b222ddd098eae701097a10de82e4c34b650aebf1e1d194946a03110134b", "withdrawn": "w", "abstract": "To be announced", "id": "Paper/61484", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61484"}, {"title": " To be announced \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18473"], "source_sha256": "610c293bf17b73b60f09eab924b6d61cb4151117d73c2581bfe3904dffaf6c91", "withdrawn": "w", "abstract": "To be announced", "id": "Paper/61485", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61485"}, {"title": " From Matrix to Tensor Algebra: the Value of a Matrix-mimetic Tensor Framework in Multiway Applications \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18474"], "source_sha256": "9bc2677104e85f62daa8ccae690c9a461d077c4c114436bee54bae5d055c7142", "withdrawn": "", "abstract": "Tensors, also known as multiway arrays, have become ubiquitous as representations for operators or as convenient schemes for storing data.   In this talk, we will review some of the common tensor decompositions and discuss their theoretical and practical limitations.  We then discuss a family of tensor algebras based on the so-called star-M definition of tensor-tensor products.  Unlike traditional tensor approaches, the framework based around this tensor-tensor product allows the elegant generalization of classical concepts and algorithms from linear algebra.  Specifically, tensors can be decomposed in a ‘matrix-mimetic’ way with provable approximation properties and with provable benefits over traditional matrix approximation.   Throughout the talk, we give several examples that demonstrate the value of such matrix-mimetic properties in practice.   We conclude with a survey of recent related literature including work addressing the choice of M and work by Hoyos, et al. that extends the matrix-mimetic tensor framework to the case when tensor-tensor products are determined by finite groups.", "id": "Paper/61486", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61486"}, {"title": " Modernizing Math Education to Meet the Moment \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18478"], "source_sha256": "e3363a4a70cf65c2cabdd4c6af30d8a9ac2fc8ff6c84538833aa6699ce4aa8a5", "withdrawn": "", "abstract": "Mathematics is as important as ever, but our math education systems have not kept pace with the world students are entering. Ubiquitous data, easily available computational tools, and now AI are changing what students need from mathematics and how they will use it. Outdated courses or methods of instruction act as barriers for many students and fail to fully prepare students for the mathematical work happening in modern science, industry, public life, and research.\n\nThis talk will discuss nascent efforts to update the mathematics we offer students, highlighting two examples:  (1) the Mathematical Sciences Education Board (MSEB) at the National Academies and its efforts to address math education at all levels, from Kindergarten through graduate schools, and (2) TPSE’s Modernizing Undergraduate Mathematics Summit which brought together higher education leaders to reimagine undergraduate experiences, from non-STEM majors through mathematics and statistics majors.", "id": "Paper/61487", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61487"}, {"title": " Order-Theoretic Constructions in Union-Closed Families of Sets \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/17847"], "source_sha256": "48a0d619ff4ff79586583aeff4ff00e74a2dd3cdd00179e95570ad425c726560", "withdrawn": "", "abstract": "The union-closed sets conjecture (sometimes referred to as the Frankl conjecture) asserts that every nontrivial, finite, union-closed family of sets has an element that appears in at least half of its members. Despite decades of research, attempts, and remarkable progress on the conjecture, it remains open. In this talk, we give a brief survey of the problem and some notable results and progress. We also explore some order-theoretic constructions that produce averaging-free arguments of classical results that work in arbitrary (perhaps infinite) union-closed settings.", "id": "Paper/61490", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61490"}, {"title": " From Tarski and Macintyre to o-minimality and Hensel minimality and point counting on definable sets \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18557"], "source_sha256": "3aa6aaae9c463f65e435a3b83d3b391d1749209e84c8de1fc819ac008a0554d2", "withdrawn": "", "abstract": "In this survey talk, I will sketch how celebrated results by Tarski and Macintyre about quantifier elimination have evolved into the general notions of o-minimality \nand Hensel minimality. Furthermore, I will sketch how one can count and bound the number of rational points lying on definable sets, in both the o-minimal and the \nHensel minimal settings. This partly concerns joint work with Floris Vermeulen and Immanuel Halupczok on the analogue of Pila-Wilkie's o-minimal counting results \nin the Hensel minimal setting. If time permits, I will discuss some variants and further questions. The model theory of real closed and non-real-closed (even non-archimedean)fields plays a key role as do the definable sets, in connection to geometry and number theory. I will try to convey some recent applications and relations to other fields of such counting results.", "id": "Paper/61513", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61513"}, {"title": " Commutative Algebra Versus Classification Theory \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18559"], "source_sha256": "c5f72d27775818be17d0685f1d768d1562e53bec91b4fc9077f06e385bd9503a", "withdrawn": "w", "abstract": "tbd", "id": "Paper/61515", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61515"}, {"title": " Reducibilities and Algorithms \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18560"], "source_sha256": "594bee77d7559505f8cb57aa6ceccd0b7235e37446bf23ff024c79f2cea6d67c", "withdrawn": "w", "abstract": "TBD", "id": "Paper/61516", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61516"}, {"title": " Amenability and hyperfiniteness \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18561"], "source_sha256": "32a0991c728cec2f3a7f6e211a44d87b3f50b0ba26b23a5769ca96a182db2528", "withdrawn": "w", "abstract": "tbd", "id": "Paper/61517", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61517"}, {"title": " Universal Projection Symmetry and Boundary Reduction in a Class of 2D Nonhomogeneous Recurrence Relations ", "webprogram_exclude": "0", "session_ids": ["Session/19369"], "source_sha256": "198ab10d5866cedf13e7fcb7eac5cdf6e02c0d7dd8fe8e506f335c1822b29c2b", "withdrawn": "", "abstract": "We present an explicit solution to a class of two-dimensional, second-order linear nonhomogeneous recurrence relations featuring parameter-dependent binomial nonhomogeneous parts. By pairing generating function techniques with the method of undetermined coefficients, we derive exact closed-form expressions for the constituent sequences. We establish a universal projection symmetry showing that the global 2D system can be decoupled horizontally or vertically into independent 1D trajectories governed by distinct characteristic operators parameterized by $b$ and $c$. Furthermore, we prove that these two directional projections are completely equivalent ($T_\\lambda(k,n) = T_\\phi(k,n)$) if and only if the boundary initial states satisfy a compact algebraic constraint: $(1+b-c)t_{1,0} - ct_{0,1} = t_{0,0}$. Finally, we provide a geometric and algebraic interpretation of this reduction, demonstrating how the boundary conditions compress a full four-dimensional solution space down to a diagonalized two-dimensional eigenspace via a unique coefficient absorption mechanism.", "id": "Paper/61518", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61518"}, {"title": " Optimal Monte Carlo integration on matrix manifolds ", "webprogram_exclude": "0", "session_ids": ["Session/17807"], "source_sha256": "3f0f32ae5cad497e8e73337c9b28fb70cd25cf6804c319acab80fa1aaaf7ea44", "withdrawn": "", "abstract": "Sampling on matrix manifolds arises throughout high-dimensional statistics and scientific computing, yet minimax-optimal quadrature rules for such spaces have been largely unavailable. This talk develops optimal-order (up to log factors) weighted quadrature rules for Monte Carlo integration in Sobolev RKHSs over matrix manifolds. We treat the Stiefel, Grassmann, flag, and Lagrangian Grassmann manifolds, each over the reals, complex numbers, or quaternions. The rules use i.i.d. uniform evaluation points on the manifold. Weights are chosen to minimize worst-case RKHS error subject to a sum-to-one constraint, which lets us bypass the generally intractable kernel mean embedding. We construct computable Matérn kernels of Frobenius distance between matrices that reproduce the target Sobolev spaces with equivalent norms, enabling practical implementation. Open-source numerical experiments validate the theory, including an application to simultaneous approximation of intrinsic volumes via the Cauchy–Kubota formula. We close with results beyond i.i.d. sampling, including transformations of quasi-Monte Carlo points from the unit cube onto the manifold, and schemes that jointly optimize both the points and the weights. These directions connect naturally to the session's broader themes in high-dimensional sampling.", "id": "Paper/61527", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61527"}, {"title": " Bang-Bang Switching and Chattering in a Speed-Dependent Circular Motion Model ", "webprogram_exclude": "0", "session_ids": ["Session/18160"], "source_sha256": "d02ca5278be389023fae8666fd3877b6b4d590c4143dc3296a74b982b21470f8", "withdrawn": "", "abstract": "\\begin{abstract}\nWe study a minimum-time control problem for a point mass moving in the plane under switching circular dynamics. The particle starts from rest, accelerates with constant tangential acceleration, and follows a path whose instantaneous turning radius is proportional to its speed. Hence the angular speed has constant magnitude, and the only control is the choice of clockwise or counterclockwise turning. The particle begins at a fixed initial position and heading and must reach the origin, with final heading and final speed left free.\n\nUsing Pontryagin's Maximum Principle, we derive the Hamiltonian system for the pure minimum-time problem. Since the control enters the Hamiltonian linearly and takes values in $\\{-1,1\\}$, candidate optimal controls have bang-bang structure: they switch between the two turning directions according to the sign of the costate associated with the heading variable. This gives a structural characterization of optimal candidates, but does not directly determine the switching times.\n\nWe compare free switching with a regularized problem that assigns a fixed cost to each switch. In the free-switching case, rapid alternation between clockwise and counterclockwise turning can make the accumulated angular change small, suggesting chattering behavior and approximate motion with small average angular velocity. In the switching-cost problem, the objective is $J=T+\\lambda N$, where $T$ is travel time, $N$ is the number of switches, and $\\lambda>0$ is the switch penalty. Finally, we numerically investigate the finite-switch problem by optimizing the durations between switches subject to the endpoint constraint. The results illustrate the tradeoff between shorter travel time and switching complexity.\n\\end{abstract}", "id": "Paper/61558", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61558"}, {"title": " Scott - DNS Testing \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18130"], "source_sha256": "a9d6fb67fd7c7fe40e1f9db84e6cb09a3efa8e5b482f5f4ebb78894ea3a994e4", "withdrawn": "w", "abstract": "", "id": "Paper/61585", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61585"}, {"title": " StateSight: Benchmarking Latent Spatial-State Reconstruction in Vision-Language Models ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "4ea3091d7989f57f77727f93e803a186f5a9e7c2a6ba7bcf1ad3829a92d593ff", "withdrawn": "", "abstract": "Vision-language models are increasingly used for multimodal question answering, yet their ability to reconstruct latent spatial structure from a single image remains difficult to isolate. Broad benchmarks often combine perception, optical character recognition, domain knowledge, linguistic priors, and reasoning in the same evaluation. We introduce StateSight, a procedurally generated benchmark for cube-net opposite-face reasoning, occluded cube-tower counting, and 4-neighbor connected-component counting. Each task family contains 300 single-image prompts with deterministic oracle labels and exact-match scoring. OpenAI GPT-5.5, using the API model identifier \\texttt{gpt-5.5}, achieved 59.3\\%, 33.3\\%, and 28.3\\% accuracy across the three tasks, while Claude Sonnet 5 achieved 53.3\\%, 18.7\\%, and 7.3\\%. All final direct runs had zero format errors. A 30-participant human baseline on 60 items exceeded both models on every task, with mean accuracies of 80.8\\%, 68.8\\%, and 64.3\\%. Visible-derivation analysis identified recurring errors in image-state reconstruction and reasoning procedure. We also introduce StateSight-Steps, a companion dataset of 900 interleaved image-text examples and 3,600 deterministic intermediate visual states. The results show that format-valid responses can mask failures to recover the spatial structure required for verifiable visual inference.", "id": "Paper/61631", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61631"}, {"title": " Emergent Inequality in Collaboration Networks: A Mechanistic Model of Nonlinear Preferential Attachment ", "webprogram_exclude": "0", "session_ids": ["Session/18386"], "source_sha256": "89fe6293f87225eacb9021b5cf80f3962b6c9f98a765f6968f8d9a77f1477fbb", "withdrawn": "", "abstract": "", "id": "Paper/61636", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61636"}, {"title": " Revisiting the generalized Segal–Bargmann transform for Poisson distribution ", "webprogram_exclude": "0", "session_ids": ["Session/17976"], "source_sha256": "3b72ae9a5756c6ebcd590c693b09fdbf7108eeab230b07454f02014c38c00f4f", "withdrawn": "w", "abstract": "Segal–Bargmann transform is the unitary operator $\\mathbb{S}$ between the complex $L^2$-space of the standard Gaussian distribution $\\mu$ on $\\mathbb{R}$, and the Bargmann space $\\mathbb{F} (\\mathbb{C})$of entire functions on $\\mathbb{C}$. For Gaussian process, this is well-known studies in (both) finite and infinite dimensional cases. However, we are interested in Meixner class of orthogonal polynomials (Hermite, Charlier, Laguerre, Meixner, Meixner--Pollaczak). In this work, we deal with the generalized Segal--Bargmann transform for Charlier polynomials related to Poisson distribution. Additionally, we observe normal ordering in Weyl algebra. At some point, it can be associated with operators (creation, annihilation) in Particle Systems.", "id": "Paper/61652", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61652"}, {"title": " Diffenential Geometry in Non-Commutative Algebra ", "webprogram_exclude": "0", "session_ids": ["Session/17954"], "source_sha256": "1f6697739809d14316e1729554fc32f05cea0a6994ee26d44206efbe78253269", "withdrawn": "", "abstract": "$\n\\require{color}\n\\newcommand\\gi[1]{\\textcolor{red}{#1}}\n\\newcommand\\aU[2]{#1^{\\gi{#2}}}\n$\nLet $B$ be Banach algebra\nand $M$ be topological space.\nIf there exists homeomorphism\n\\[\nf:M\\rightarrow N\n\\]\nof topological space $M$\ninto convex set $N$ of the space $\\aU Bn$,\nthen homeomorphism $f$ is called\nchart\nof the set $M$.\n\nThe set $M$ is called\nsimple $B$-manifold\nof class $C^k$\nif for any two charts\n\\[\nf_1:M\\rightarrow N_1\\subseteq\\aU Bn\n\\]\n\\[\nf_2:M\\rightarrow N_2\\subseteq\\aU Bn\n\\]\nthere exists diffeomorphism\n\\[\nf:\\aU Bn\\rightarrow\\aU Bn\n\\]\nof class $C^k$ such that\n\\[\nf_1\\circ f=f_2\n\\]\n\nTopological space $M$ is called\ndifferential $B$-manifold\nof class $C^k$\nif topological space $M$\nis a union of simple $B$-manifolds\n$M_i$, $i\\in I$,\nand intersection\n$M_i\\cap M_j$\nof simple $B$-manifolds\n$M_i$, $M_j$\nis also simple $B$-manifold.\n\nI considered definition of connection and curvature on\ndifferential $B$-manifold.\nStudying of torsion brings us to concept\nof non-commutative sum of vectors.", "id": "Paper/61657", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61657"}, {"title": " Kernel-Preserving Dynamics and Symmetry Classification for Synchronization Subspaces ", "webprogram_exclude": "0", "session_ids": ["Session/19339"], "source_sha256": "20eb055d8d17749586fa75637c0a6412b016617f116fb2621970eb1fd6217922", "withdrawn": "", "abstract": "\\documentclass{article}\n\\usepackage{amsfonts, amsmath, amssymb, amsthm}\n\\begin{document}\n\nWe present a framework for synchronization in bipartite quantum systems in the language of operator algebras and finite group representation theory. The central object is the synchronization subspace $\\mathcal{K} := \\ker(T_A \\otimes I - I \\otimes T_B) \\subseteq \\mathcal{H}_A \\otimes \\mathcal{H}_B$, defined as the kernel of a difference operator between two self-adjoint clock observables on finite-dimensional Hilbert spaces. We show that $\\mathcal{K}$ is preserved exactly by a commutative unital $*$-subalgebra of compatible Hamiltonians, giving an algebraic characterization of kernel-preserving dynamics.\n\nTwo main results extend this picture. First, a perturbative stability theorem: if $\\|[H,K]\\| \\leq \\varepsilon$ with $K = T_A \\otimes I - I \\otimes T_B$, then any normalized $|\\psi(0)\\rangle \\in \\mathcal{K}$ evolves so that $\\|K|\\psi(t)\\rangle\\| \\leq \\varepsilon |t|$. The proof uses Duhamel's formula and a Gr\\\"onwall estimate, and the bound is sharp, witnessed by a $\\sigma_z$ example on $\\mathbb{C}^2 \\otimes \\mathbb{C}^2$. A fidelity corollary under a spectral gap assumption gives $F(t) \\geq 1 - \\varepsilon^2 t^2$.\n\nSecond, a representation-theoretic classification under finite group symmetry. Given unitary representations $\\rho_A, \\rho_B$ of a finite group $G$ and equivariant self-adjoint observables $T_A \\in \\mathrm{End}_G(\\mathcal{H}_A)$, $T_B \\in \\mathrm{End}_G(\\mathcal{H}_B)$, the synchronized subspace is the diagonal isotypic component $\\mathcal{K}_G = \\bigoplus_{\\lambda \\in \\widehat{G}} V_\\lambda \\otimes V_\\lambda$. By Schur's lemma, when $T_A, T_B$ arise from central elements of $\\mathbb{Z}(\\mathbb{C}[G])$, the kernel condition is equivalent to spectral alignment of irreducible representation labels across subsystems. The maximal algebra of $G$-equivariant synchronization-preserving Hamiltonians is the commutant of the joint action intersected with the commutant of $K$.\n\nSynchronization emerges as a structural invariant connecting approximate commutation, kernel-preserving dynamics, and symmetry-protected subspaces, with quantum time transfer as a motivating application.\n\n\\end{document}", "id": "Paper/61718", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61718"}, {"title": " \"Proof by Contradiction:\" When Students Succeed but Still Want the Lecture ", "webprogram_exclude": "0", "session_ids": ["Session/18341"], "source_sha256": "599a84f4d21c31520b0f9cedaf36d8edf8d681d127fb7c14aa4ecf8a787b5ba5", "withdrawn": "", "abstract": "While active learning is widely accepted, inquiry-based methods push boundaries by eliminating lectures and forcing students to drive learning through collaborative questioning. In a supplementary Introduction to Proofs course, the concept of proof by contradiction was taught using pure inquiry; students received problem sets and worked together with zero instructor lecturing. Interestingly, students completed their proofs to the same standard as differently taught techniques. However, student feedback was definitive: they overwhelmingly requested a return to additional lecture time. This reveals a fascinating disconnect: students can successfully master meaningful concepts while feeling highly demotivated by the discomfort of a self-driven classroom. This research was done as a result of a Teaching as Research project.", "id": "Paper/61735", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61735"}, {"title": " Yosida Algebraic Splitting Method for an Efficient Eddy Viscosity Algorithm for Stochastic Navier-Stokes Problems ", "webprogram_exclude": "0", "session_ids": ["Session/18281"], "source_sha256": "86153cd1c7f93ce994397f1ec8b39db6ab2a506abfc184c93127581b441ac6db", "withdrawn": "", "abstract": "This work proposes, analyzes, and tests an efficient Yosida algebraic splitting method for stochastic Navier–Stokes equations within an Ensemble Eddy Viscosity (EEV) framework. The main idea is to apply a Yosida-type algebraic splitting at each time step to the saddle-point system arising from the coupled velocity–pressure formulation. This decouples the velocity and pressure computations and substantially reduces the cost of solving the fully coupled system. The linearized Implicit–Explicit (IMEX) ensemble formulation further allows all stochastic realizations to share a common coefficient matrix at each time step, with only the right-hand-side vectors varying across realizations, reducing both computational cost and memory requirements. We establish the stability of the proposed method and show that it is first-order accurate in both time and space, and the scheme converges to an equivalent coupled formulation. The method is tested on several challenging benchmark problems, including channel flow over a unit square step, channel flow past a circular cylinder, and a 3D regularized lid-driven cavity problem. In all cases, the Yosida scheme performs well and converges to the equivalent coupled scheme, supporting the theoretical convergence results. These experiments demonstrate that the proposed method provides an accurate and computationally efficient alternative for stochastic flow simulations, including convection-dominated problems at high expected Reynolds numbers.", "id": "Paper/61750", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61750"}, {"title": " Asynchronous Resource Development for Online Statistics Students with Emphasis on Accessibility ", "webprogram_exclude": "0", "session_ids": ["Session/19341"], "source_sha256": "30c564e80823066f04bb7c03c597dcfb1ef9e48888d395c945c8c4fda90af853", "withdrawn": "", "abstract": "Online statistics courses are particularly challenging when taught asynchronously and this is especially true for many students in non-math fields seeking a degree requiring a course in math. Until recently, most resources outside the classroom were limited due to the lack of ability to type math in an efficient way on various platforms. In early 2025, we were part of a small group beta testing a new Articulate feature that integrates LaTeX so that math symbols and equations can be used more seamlessly in instructional content without having to create the math separately and insert it as a picture. Here we explore the use of Articulate Rise and Storyline to make interactive modules in statistics while keeping accessibility in mind when entire courses are taught asynchronously. We will discuss how we are transforming resources from PDF to interactive modules and incorporating video in a way that is easier to update as new versions of statistics tools are released.", "id": "Paper/61757", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61757"}, {"title": " CANCELLED Truths and falsehoods about the life and work of Florence Nightingale \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18554"], "source_sha256": "4000456e7e1323acac2cf34bfe690367e413ddab1ec96763d66041d2c50523a2", "withdrawn": "", "abstract": "In our exploration of Florence Nightingale’s life (1820–1910) and work, we have been impressed by her story and accomplishments. We have also encountered a number of  falsehoods and inaccuracies in our research. We will highlight these in an attempt to set the record straight about this amazing and complicated woman whose influence is still felt today.", "id": "Paper/61762", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61762"}, {"title": " Volume of Hermitian Quadrics in Complex Projective Space ", "webprogram_exclude": "0", "session_ids": ["Session/19368"], "source_sha256": "e7a64bbe4756a51294fa7a9d438e09bae94b118c20823dd91dfce805119dcfae", "withdrawn": "", "abstract": "The calculation of volumes for domains in complex projective space is an interesting problem in Hermitian geometry. We derive a closed-form volume formula for a hyper-quadric defined by a Hermitian matrix. We show that this volume is a function of the eigenvalues of the defining matrix, and that this function is symmetric in the positive and negative eigenvalues. The resulting volume formula is a rational function of these eigenvalues.", "id": "Paper/61765", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61765"}, {"title": " Wasserstein Dispersion Regularization for Robust Ranking and Selection Under Regime Shift ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "1b61236552be84e50a72263166cacf727c504cc95f7b4cdacd432aab15698f4d", "withdrawn": "", "abstract": "Ranking and selection from noisy finite samples is sensitive to both sampling error and to shifts between evaluation and execution environments. In this paper, we study a two-regime model where each candidate has regime-dependent reward distributions, so that empirical performance under the observed mixture may differ with performance under a shifted mixture. A common failure mode for this setting is that empirical mean selection can focus on candidates that are strong in the training regime but fragile across regimes. We suggest Wasserstein dispersion regularization for fixed-sample selection. For each of the candidates, the score is its empirical mean minus a penalty proportional to its one-dimensional \\(W_1\\) dispersion, equal to the average absolute deviation of the empirical reward distribution from its mean. The term acts as a data-driven stability penalty for candidates whose observed rewards are spread across regimes. In this paper, we derive a finite-sample concentration bound giving an \\(O(\\sqrt{\\log K/N})\\) uncertainty scale for comparing  \\(K\\) candidates from \\(N\\) samples. Simulations on stable, fragile, and noisy candidate classes emphasize that the regularized selector decreases regret and regime-sensitivity relative to empirical mean selection under distribution shift.", "id": "Paper/61766", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61766"}, {"title": " Are Real Numbers Real? A Reply to Wildberger ", "webprogram_exclude": "0", "session_ids": ["Session/17853"], "source_sha256": "03b32a074db6d1244ef96cc76670d3dc732176ba79beaf9c18b806a79a5418d3", "withdrawn": "", "abstract": "Over the past several years, Professor Norman Wildberger (University of New South Wales) has created several YouTube videos in which he argues that the concept of a \"real number\" is not well-defined. He examines the traditional attempts to define what the real numbers are supposed to be  in terms of Dedekind cuts, equivalence classes of Cauchy sequences, Stevin's infinite decimals, etc. and shows that all such attempts are flawed.  Part of what makes them flawed is that in one way or another, they all presuppose that a human being can accomplish an infinite number of separate tasks.  But the ancient Greeks rejected this presupposition and Wildberger rejects it as well. Indeed, Zeno's paradoxes of motion (as they pertain to the assumption that space and time are continuous rather than discrete) are based on this idea. Wildberger's radical position is that we should abandon real numbers and only work with the rationals.  In this regard, his views fit in with the philosophy of Ultrafinitism, which holds, among other things, that infinite sets and extremely large finite numbers have no mathematical validity.\n\nIn this paper, I show that Wildberger's arguments all depend on a critical metaphysical assumption.  I then argue that Wildberger's metaphysical assumption is just as dubious as the concept of an infinite set or the idea that a human being can accomplish an infinite number of separate tasks.  My conclusion is that although Wildberger's critique of real numbers has merit and should be taken seriously, his arguments are ultimately unconvincing.  Thus, the fields of analysis, topology, and differential geometry do not need to abandon Cantor's paradise.  (At least, not yet.  Stay tuned, the Ultrafinitists are just getting started.)", "id": "Paper/61785", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61785"}, {"title": " Conjugator Length in Generated Groups ", "webprogram_exclude": "0", "session_ids": ["Session/18213"], "source_sha256": "38439d809b59d91a3d1ca13544d74624fb53b84920a9608c34df2f370b39edb7", "withdrawn": "", "abstract": "We describe all functions $\\mathbb{N}\\rightarrow \\mathbb{N}$ that can be realized, up to the standard equivalence, as conjugator length functions of finitely generated groups. Furthermore, we show that any two increasing functions $f,g\\colon \\mathbb{N}\\to \\mathbb{N}$ can be simultaneously realized as conjugator length functions of finitely generated, commensurable  (in particular, quasi-isometric) groups.", "id": "Paper/61809", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61809"}, {"title": " Root reconstruction for first passage percolation on random graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18312"], "source_sha256": "3c2e313ecce1c133adc4f37bd9c0dfe2d221a23f90bd92ec3ea445d1f46c53cd", "withdrawn": "", "abstract": "We consider root reconstruction for first passage percolation trees on uniform random graphs with given degree sequences. Given such a first passage percolation tree, we show that a bounded number of guesses suffices to identify the root with a desired accuracy. More precisely, for any $\\varepsilon > 0$, there exists $K=K(\\varepsilon)$ such that $K$ guesses are required to identify the root with probability at least $1-\\varepsilon$, when the root is uniformly chosen and the graph is taken large enough. We identify a simple algorithm for identifying the root with the desired accuracy. A key input to the proof is a corresponding root reconstruction result for first passage percolation on a unimodular Bienaym\\'e tree.", "id": "Paper/61816", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61816"}, {"title": " Joint Prediction Regions for Future Records Based on Observed Record Values ", "webprogram_exclude": "0", "session_ids": ["Session/18343"], "source_sha256": "841543963a0bf685b7be4c186ff4ccb88bd52adc1b931eceadbaa6a6da3de9c0", "withdrawn": "", "abstract": "This work studies the problem of predicting future record values and the mean of future records. These predictions are important for understanding extreme events such as rainfall, floods, temperatures, global warming, earthquakes, and other hydrological processes. They also help describe long-term behavior and support planning and risk assessment. The main objective of this work is to construct joint prediction regions for future records. Several methods are developed, including equitable prediction regions, Bonferroni-based regions, and minimum-area prediction regions. A simulation study is used to compare these methods. The results show that the minimum-area prediction region gives a smaller region with good coverage and performs better than the other methods. Two real data examples are used to illustrate the proposed methods and show their practical use.", "id": "Paper/61818", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61818"}, {"title": " Non-parametric Multivariate Modified Compartmentalization Method for the Meaningful Organization and Analysis of Ordinal Outcomes ", "webprogram_exclude": "0", "session_ids": ["Session/19364"], "source_sha256": "91aa6f42e75bd7d6dd4c73c5010e0bac42733ad2a087ab4e8cc61a460ba6e693", "withdrawn": "", "abstract": "The increasing integration of healthcare delivery systems provides an opportunity to manage entire episodes of care in a patient-focused manner and to assess the impact of care on patient outcomes, including patient-reported outcomes (PROs). PROs are often relevant in assessing diagnostic evaluations and can be used to capture a patient's everyday experience with a medical product, including experiences outside of the clinician's office and the effects of the treatment on daily activities and functionality. In some cases, PRO measures enable us to capture important health status information that cannot yet be detected by other measures, such as mood and sleep quality.\n\nHere, we present a novel approach to analyze univariate and multivariate ordinal PROs using the Modified Compartmentalization Method (MCM) as well as Multivariate Modified Compartmentalization Method (MMCM), respectively. This method helps preserve the complexity of the data while providing a clinically and statistically meaningful organization and analysis. It also provides the tools necessary for investigating large, complex datasets. By breaking down these complex variables, this analytical methodology generates accurate solutions while upholding the fundamental integrity of our system.", "id": "Paper/61826", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61826"}, {"title": " Inferring Climate-Sensitive Rodent Species Interactions with Uncertainty Quantification Using Classical and Data-Driven Ecological Models ", "webprogram_exclude": "0", "session_ids": ["Session/18009"], "source_sha256": "965c41c2069f8342e9383b1f4c7d59063122e58da5f30412fd44afa86a33cb3e", "withdrawn": "", "abstract": "Understanding how weather variability influences species interactions is essential for interpreting long-term community dynamics, especially in rodent systems that include disease reservoir species. We analyze a three-decade (1973-2003) Kansas grassland rodent dataset involving five coexisting species: \\textit{Sigmodon hispidus}, \\textit{Microtus} spp., \\textit{Peromyscus leucopus}, \\textit{Peromyscus maniculatus}, and \\textit{Reithrodontomys} spp. We pair rodent abundances with Kansas weather data from the same study period and select six weather variables to examine associations between extreme weather events, inferred interaction strengths, and interaction uncertainty. We first apply a classical five-species competitive Lotka--Volterra model with AICc-based yearly model selection to identify active competition networks across years. The selected models indicate that competition is generally sparse, with many years dominated by only a few active interactions and a recurring competitive triangle involving \\textit{Sigmodon}, \\textit{Microtus}, and \\textit{Reithrodontomys}. Pearson correlation and Dynamic Time Warping analyses further suggest that drought-related variables are among the strongest weather-associated drivers of inferred competition coefficients. To extend this mechanistic analysis, we use a data-driven ensemble model-averaging framework to quantify uncertainty in time-varying interaction strengths. Rather than relying on a single best estimate, this approach evaluates multiple plausible interaction structures and distinguishes consistently supported interactions from ambiguous ones. We further correlate interaction uncertainty to the six weather variables to identify when uncertainty increases, under which weather conditions, and for which species relationships. Because the community includes \\textit{P. maniculatus}, a known reservoir of hantaviruses, these findings provide ecological context for future studies of climate-sensitive reservoir-community dynamics. Overall, this work shows that uncertainty-aware data-driven inference can extend classical Lotka--Volterra model selection by providing a more reliable interpretation of weather-sensitive species interactions in long-term rodent communities.", "id": "Paper/61829", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61829"}, {"title": " Fast Solvers for the Convection-Diffusion Equation ", "webprogram_exclude": "0", "session_ids": ["Session/17987"], "source_sha256": "5cfa2896ea4dec422bae226a379883fae205faa7a9c4d743b2b85d33706dd20c", "withdrawn": "", "abstract": "Many problems in science and engineering are modeled using partial differential equations. After these equations are discretized on a computer, they produce large systems of linear equations that must be solved efficiently. For realistic simulations, standard direct methods such as Gaussian elimination can become too expensive, making iterative methods and preconditioning essential. \n\nThis project studies efficient iterative solvers for linear systems arising from elliptic and hyperbolic partial differential equations. We first review fundamental linear algebra techniques and iterative techniques such as stationary iterative methods and Krylov subspace methods, and examine how preconditioners can improve the convergence of an iterative solver. Particular attention is given to multigrid and domain decomposition methods, two widely used approaches for solving elliptic problems efficiently. \n\nThe project then investigates how methods that perform well for elliptic equations work for hyperbolic equations. Elliptic and hyperbolic operators have different mathematical and spectral properties, which can strongly influence solver behavior. Using these differences as a guide, we aim to develop, implement, and test preconditioners for linear systems arising from hyperbolic discretizations. The broader goal is to understand which ideas from elliptic solvers can be adapted successfully and which require new approaches.", "id": "Paper/61855", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61855"}, {"title": " Building a Projection for FEEC in NGSolve ", "webprogram_exclude": "0", "session_ids": ["Session/17987"], "source_sha256": "fa2a45c8fe103c18b8821540f4822c3fa00c6776758c072d997d3a6d56012967", "withdrawn": "", "abstract": "Our project is in applied mathematics, particularly in the area of numerical analysis for\npartial differential equations (PDEs). Bounded commuting projections are essential for the\nanalysis of finite element exterior calculus (FEEC) applied to various PDEs. The canonical\nprojections are unfortunately not bounded in the $L^2$ norm. Thus, researchers have worked on\nconstructing other projections that are both commuting and bounded. In this work, we present\ncode for FEEC software packages that implement such projections. Using tetrahedral meshes,\nwe work with the de Rham sequence and define projections onto the FEEC spaces (e.g., the\nLagrange, Nedelec, Raviart-Thomas, and DG spaces). The key idea is to build weight functions\nthat live on FEEC spaces themselves. To do this, we have to solve them in a two-step process.\nIn the second step, there is a small linear system we have to solve for each geometric object\n(e.g., vertices, edges, faces, tetrahedra of the mesh).", "id": "Paper/61857", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61857"}, {"title": " Structure-Preserving Numerical Methods for Flow and Transport in Porous Media ", "webprogram_exclude": "0", "session_ids": ["Session/18166"], "source_sha256": "5471c8a44db204f276d01e51023f8a4959542a6755a8ea87b88e1a5aa964ec2d", "withdrawn": "", "abstract": "Differential equations provide the mathematical foundation for modeling many complex processes in science and engineering. Computational models allow scientists and engineers to study phenomena that may be too expensive, dangerous, or impractical to reproduce experimentally. In porous media applications, these models are used to describe subsurface flow, contaminant transport, and multiphase displacement. Reliable predictions are essential for applications such as groundwater protection, energy production, and carbon sequestration. Porous media problems are especially challenging because their solutions may contain sharp fronts, strong material contrasts, and physically constrained quantities such as concentration or saturation. Standard numerical methods may produce oscillations or values outside the physically admissible range, even when the overall approximation appears accurate. Because computational predictions are only useful when they remain physically meaningful, preserving these properties is critical. This project builds on recent work by Fabien et al. (MIT, University of Wisconsin-Madison) from 2025 and 2026 involving a new bound-preserving finite volume–discontinuous Galerkin scheme. The method combines the robustness of finite volume discretizations with the high-order accuracy of discontinuous Galerkin methods. The novel contribution of this project is the first application of this bound-preserving framework to porous media models. We will implement the method for representative flow and transport problems and investigate its accuracy, stability, and ability to preserve physically admissible solutions. The goal is to develop a reliable computational tool that supports more trustworthy scientific and engineering predictions.", "id": "Paper/61858", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61858"}, {"title": " Pesto: Non-Conforming Mesh Refinement and De-refinement ", "webprogram_exclude": "0", "session_ids": ["Session/17987"], "source_sha256": "05d5366e848989932e0220f329006be2a6544b0ce8b7aef8ae1501129319cc85", "withdrawn": "", "abstract": "Meshes composed of simplicial elements are central to computer graphics, computational physics, engineering simulation, and scientific computing, where they provide a flexible representation of complex geometries and a foundation for numerical discretization. In large-scale simulations, adaptive mesh refinement is essential for resolving localized solution features while controlling computational and memory costs.\n\nMany existing mesh-adaptivity frameworks enforce a (1)-irregularity condition, restricting the number of hanging nodes permitted on an element edge. Although this assumption simplifies mesh management, it can cause refinement to propagate into neighboring regions, producing substantially more elements than are required by the underlying error indicator.\n\nWe present an open-source MATLAB framework for nonconforming adaptivity of two-dimensional simplicial meshes that permits arbitrarily many hanging nodes along element interfaces. The framework maintains hierarchical data structures for active elements and edges, refinement levels, and parent--child relationships between mesh entities. These structures support efficient connectivity updates, traversal of the refinement hierarchy, and consistent management of locally adapted meshes. Both refinement and de-refinement are supported, allowing resolution to be added or removed dynamically as solution features evolve.\n\nTo the best of our knowledge, this is the first open-source MATLAB framework to combine unrestricted hanging-node configurations with explicit active-edge and active-element hierarchies and reversible refinement and de-refinement. By eliminating the (1)-irregularity restriction, the framework enables highly localized adaptation without unnecessary refinement of surrounding elements, with the potential to reduce mesh size, memory consumption, and computational work in large-scale parallel simulations.", "id": "Paper/61862", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61862"}, {"title": " Connections Between the Elasticity Complex and Simplicial Topology ", "webprogram_exclude": "0", "session_ids": ["Session/18166"], "source_sha256": "1520a842e50c9e65cd972c569ed569c92131d2deff525addca1528d39d744675", "withdrawn": "", "abstract": "We first focused on deriving the elasticity complex from the de Rham sequence through the framework of Finite Element Exterior Calculus (FEEC). This complex has gained enormous attention in the last decade in numerical analysis, particularly in the FEEC community. The derivation highlights differential operators that enable us to define the complex and understand underlying structures. Expanding on this notion, the project explores the relationship between the elasticity complex and simplicial complexes. We study how a commuting diagram between the de Rham complex and generalized cochains provides informative insight into simplicial topology. In particular, we are interested in defining an analogous diagram using the elasticity complex rather than the de Rham complex, thereby establishing a relationship with discrete spaces. Guided by the work of Christiansen (2011) and his geometric topological framework, we have studied a meaningful relationship between the elasticity complex and abstract spaces. By comparing these continuous forms, the project aims to give further insight into how elasticity can be interpreted through linear mappings.", "id": "Paper/61863", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61863"}, {"title": " Strong Collapsibility and a Code for Verification of Strang’s Conjecture ", "webprogram_exclude": "0", "session_ids": ["Session/18166"], "source_sha256": "6ec1ffb3284afa795f4d9c17e739d29878dddf693b6845aa9ccd3a9bf14bb8f4", "withdrawn": "", "abstract": "Splines, which are piecewise polynomial functions with given smoothness, are used in numerous applications such as computer aided geometric design, algebraic geometry and for implementation of the finite element method. In many applications, it is important to know the dimension of the space of splines over a domain, but this continues to be an open problem. Strang's conjecture predicts the dimension of the space of $C^1$ continuous splines of degree at most $k$ over a polygonal domain with no holes. For the cases,  $k=4$ and $k \\geq 5$ the conjecture has been proven true. For the case $k=2$, Morgan-Scott provided a counterexample. In this project, we begin by relating the space of $C^1$ continuous splines of degree at most $k$ to various other function spaces. With the aid of some intrinsic operators on these spaces, we obtain a complex that yields an equivalence statement to Strang’s conjecture. The equivalent statement admits a computational approach to the conjecture and thus we present a NGSolve code to check Strang’s conjecture for a given mesh. In addition, we prove that if the simplicial complex associated to the triangulation of a region is strongly collapsing, Strang's conjecture holds for $k=2.$", "id": "Paper/61864", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61864"}, {"title": " Identities for Weighted Sums of Integer Partitions ", "webprogram_exclude": "0", "session_ids": ["Session/19321"], "source_sha256": "36489e8a43667f60f23d16cdfc051eca94cd7b6f796754102688141e0c18009f", "withdrawn": "", "abstract": "Integer partitions play a pivotal role in mathematics and its applications through their power to index diverse structures. In economics, they describe resource distributions; in chemistry, they classify certain organic compounds. In both fields, weighted sums of these indexing partitions reveal structural insights about the underlying systems. In this talk, we explore a family of identities involving weighted sums of integer partitions and demonstrate how they naturally extend the relationships between mathematical structures analogous to those seen in economics and chemistry. We will then discuss relationships with the dominance lattice, and provide generating functions and asymptotics for these sums.", "id": "Paper/61884", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61884"}, {"title": " An Ethical Framework for Mathematics Instructors’ Use of AI in Assessments of Student Learning ", "webprogram_exclude": "0", "session_ids": ["Session/18137"], "source_sha256": "60d052adb7497240b4e93ccf17e3f4327a643a264f657f1ae3d201552b58b66e", "withdrawn": "", "abstract": "Artificial intelligence tools can now detect features of student work, interpret what those features reveal about a student's reasoning, and deliver a grade, feedback, or routing decision based on that interpretation. Individual mathematics instructors deciding whether and how to use these tools are left with little organized guidance. Governance-level AI ethics frameworks address developers and policymakers, and much of the assessment literature predates AI's current interpretive capability.\n \nThis talk presents a framework for that instructor-level decision; namely, a 3x4 matrix crossing the detect-diagnose-act functions AI performs in assessment against four principles of professional ethics adapted from biomedical ethics. The resulting twelve cells pose instructor-actionable questions rather than prescribing answers. I ground the four principles directly in the instructor-student relationship and principles of professional ethics, and argue that the diagnose function carries the greatest ethical weight in mathematics specifically, where validity is determinate in a way that it is not in most interpretive grading.\n \nI'll close with the framework's sharpest practical finding, that the courses where AI adoption is most strongly motivated (large, high-stakes, low in per-student familiarity) are precisely the courses where these obligations are hardest to discharge through individual review, making oversight design an ethical requirement rather than an afterthought.", "id": "Paper/61923", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61923"}, {"title": " On the generalized (p, q)-Analogues of Elzaki transform and its application to (p, q)-difference equations ", "webprogram_exclude": "0", "session_ids": ["Session/19336"], "source_sha256": "dea8cf4880d6a75a1c8245bd9469778987c42865def639271b653883d5a46f72", "withdrawn": "", "abstract": "In this paper, we introduce and study the (p, q)-analogues of the Elzaki transform. We formulate and analyze the corresponding transforms of the first and second kinds, yielding results that extend the classical theory and establish their fundamental properties. Towards applications, the proposed framework is utilized to provide an effective method for solving (p, q)-difference equations and related analytical problems.", "id": "Paper/61932", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61932"}, {"title": " Optimal Transport on Lie Group Orbits ", "webprogram_exclude": "0", "session_ids": ["Session/19337"], "source_sha256": "81bed9932b039f4f53739a957fd30c2dfed0b9c60248f46f475593196f706682", "withdrawn": "", "abstract": "In its most general form, the optimal transport problem is an infinite-dimensional optimization problem, yet certain notable instances admit closed-form solutions. We identify the common source of this tractability as \\textit{symmetry} and formalize it using Lie group theory. Fixing a Lie group action on the outcome space and a reference distribution, we study optimal transport between measures lying on the same Lie group orbit of the reference distribution. In this setting, the Monge problem admits an explicit upper bound given by an optimization problem over the stabilizer subgroup of the reference distribution. The reduced problem's dimension scales with that of the stabilizing subgroup and, in the tractable cases we study, is either zero or finite. Under mild regularity conditions, a feasible point of this reduced problem whose induced transport map satisfies a c-convex first-order certificate makes the upper bound tight for both the Monge and Kantorovich formulations, with the optimal map realized by a group element. For the quadratic cost on a finite-dimensional Hilbert space and affine-induced actions, the c-convex certificate reduces to an algebraic condition: the candidate map must have self-adjoint positive semidefinite linear part. We give a structural criterion, based on Cartan theory, that guarantees this condition. When the linear image of the acting group admits a global Cartan decomposition and its fixed-point subgroup is contained in the linear image of the stabilizer of the reference law, the compact component can be absorbed by the stabilizer, yielding a transport map with a self-adjoint positive definite linear part. This orbit-based viewpoint unifies known closed-form solutions, such as elliptical distributions, and yields new closed-form solutions for Wishart, inverse-Wishart, and matrix beta type~II distributions under the squared Frobenius cost.", "id": "Paper/61961", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61961"}, {"title": " Learned Priors in Ill-Posed Image Restoration and Their Propagation into Morphological Measurement ", "webprogram_exclude": "0", "session_ids": ["Session/17972"], "source_sha256": "15ee1dfc2a0f7f69dc3d8154dea05e26aa4d31d344c946fc8d58672ff16d6e2c", "withdrawn": "", "abstract": "Quantitative morphology — counting objects and measuring their areas and thicknesses — underlies image analysis throughout biology. These pipelines increasingly open with a deep-learning restoration step applied before anything is measured. Because that recovery is ill-posed, the data cannot select an answer on its own; each model supplies a prior, learned from its training set rather than chosen. Writing its action as I' = I + ΔI, we ask a question that arises wherever images become numbers: does the choice of prior propagate into the measurement?\n\nWe compare a generative adversarial model (Real-ESRGAN), a shifted-window attention model (SwinIR), and a channel-attention model (Restormer) on Brewster-angle micrographs of phase-separating monolayers whose morphologies resemble domains in biological membranes. Raw and restored images pass through one pipeline: adaptive histogram equalization, k-means segmentation, connected-component labeling, and medial-axis thickness estimation via the exact Euclidean distance transform. More instructive is a case in which the total area is conserved, yet the restored images resolve into systematically thinner and more numerous domains.", "id": "Paper/61992", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/61992"}, {"title": " SoTL’s Impact on and Value to the Mathematics Community ", "webprogram_exclude": "0", "session_ids": ["Session/18341"], "source_sha256": "aaf0f12728b25e915c53b854075802e8b236b6f2d2e4711a052c4c5d24461995", "withdrawn": "", "abstract": "This talk will focus on the impact of SoTL as revealed through analysis of survey responses from self-identified practitioners of SoTL in the mathematics community. Preliminary results of the survey, reported at JMM 2023, focused on the demographics of the respondents and their beliefs and motivations about SoTL. Our new results on SoTL’s impact draw on an analysis of the types of questions the practitioners investigated, the populations they studied, and the dissemination they did, along with a further analysis of their beliefs and motivations. We will argue that encouraging more engagement with SoTL by valuing its practice and facilitating the dissemination and utilization of its results would contribute to improving collegiate mathematics.", "id": "Paper/62010", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62010"}, {"title": " Rising Adoption of AI Tools Among Math Students: A Three-Year Study (2024–2026) ", "webprogram_exclude": "0", "session_ids": ["Session/18346"], "source_sha256": "230557fb79e8778fe351ca242b3a69bb3c7812ce5851211402e5bc3f59d558f2", "withdrawn": "", "abstract": "This study examined awareness, use, frequency, and helpfulness of AI in mathematics learning across three summer semesters of Calculus III and Differential Equations, with 197 students total (64 in 2024, 73 in 2025, 60 in 2026). We used Claude Sonnet 5 to code open-ended student responses into our categories. \nWe discuss adapting the approach of Anthropic's \"What 81,000 People Want from AI\" on a classroom scale, so that individual instructors can extract similar qualitative insight from their own students' discussions and artifacts. The four most significant year-over-year changes were: a decline in negative sentiment, an increase in reported helpfulness, an increase in usage frequency, and an increase in using AI to prepare for exams. The results suggest students are using AI more, finding it more helpful, and feeling more positive about it over time. However, concern about the accuracy of AI-generated information remained the single largest reported concern throughout the study. The possibility of analyzing changes using ANOVA with 0.1 significance level is discussed.", "id": "Paper/62019", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62019"}, {"title": " Connection-oriented mathematical thinking ", "webprogram_exclude": "0", "session_ids": ["Session/18088"], "source_sha256": "e1711b48f1dc588f516c3db0e1f3dcd097e2fe1717662c4518ea348d4025e6b4", "withdrawn": "", "abstract": "Many students, including math majors, experience their courses–arithmetic, geometry, algebra, calculus, ...–as islands of knowledge with few bridges.  Yet cognitive psychology indicates that the utility and adaptability of knowledge depends more on how well that knowledge is mentally structured than on its amount.  And that structure takes the form of a network of deep connections.  For example, if you understand problem A, and if problem B is structurally similar to A, though perhaps in a different context, then your knowledge of A should transfer, and enable you to understand B.  Cognitive psychology indicates that “far” transfer is rare, and, when it occurs, it is domain specific and done by experts in that domain.  The main obstacle seems to be failure to see and use the structural connection between A and B.  In fact, even when one understands both A and B, one may not see their connection.  My response to this is that, if seeing and using non-obvious mathematical connections is not a common habit of mind and skill, then we should find ways to teach it.\nConnection-oriented mathematical thinking (COMT) is an explicit framing of this goal.  My talk, beyond explaining COMT, will illustrate some explicit designs of instructional activities intended to support the learning of COMT.  The mathematical problems involved are accessible to High School students, but the connection between them can be more subtle, and discerning them engages a novel, but important, kind of mathematical reasoning.", "id": "Paper/62026", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62026"}, {"title": " Dynamics of Fish Harvesting Models: The Impacts of Strong Allee Effect and Variable Storage ", "webprogram_exclude": "0", "session_ids": ["Session/18160"], "source_sha256": "7bedac3e121683e5b9ee3a32c6604ea61300bcecb9f055ebb65def4caa369541", "withdrawn": "", "abstract": "We present two mathematical bioeconomic models describing the dynamics of fish populations under harvesting activity and fish storage. In both models, the fish stock, harvesting effort, and stored stock vary with time. We assume that the fish population follows logistic growth and that the harvesting rate is given by the Holling type II (hyperbolic) functional response. Moreover, the price is assumed to be the same for fish sold from storage and fish sold immediately. The two models differ by the inclusion of a strong Allee effect, which describes the correlation between population size and individual fitness. For each model, we establish conditions for the existence of a unique positive equilibrium and analyze the local stability of all equilibria. We further provide conditions that ensure the occurrence of a transcritical bifurcation and Hopf bifurcation in each system. Our results highlight the significance of considering both storage and the strong Allee effect in developing sustainable fishing practices, especially when initial population size is sparse. Numerical simulations were conducted to support theoretical results.", "id": "Paper/62031", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62031"}, {"title": " A Bioeconomic Model of Fish Harvesting with Variable Market Price: Stability and Bifurcation Analysis ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "8a77dd14f4d20bb82cb32503be135c0c2e8a479e07ed55c596c9573a93c5a9c2", "withdrawn": "", "abstract": "We present a mathematical bioeconomic model describing fisheries with variable market price. In the model, we consider the time evolution of fish stock, harvesting effort, and market price of fish, where the fish population is assumed to follow logistic growth and the harvesting rate is given by the Holling type II (hyperbolic) functional response. Price is assumed to vary with respect to the difference between supply and demand, where supply is the instantaneous catch and demand is given by a monotone decreasing function in price. We establish conditions for the existence of positive equilibria and analyze the local stability of all equilibria. We further provide conditions that ensure the occurrence of a transcritical bifurcation, saddle node bifurcation, and Hopf bifurcation in the system. Our results indicate that the market forces of supply and demand are significant in determining the sustainability of fish populations under harvesting practices. Numerical simulations were conducted to support theoretical results.", "id": "Paper/62032", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62032"}, {"title": " Dynamics of Non-autonomous Logistic Equations with Holling Type II Functional Response and Bounded Coefficients ", "webprogram_exclude": "0", "session_ids": ["Session/18243"], "source_sha256": "1fa5c63a569838b0ae931c4426efcf77c17b85b7b13df5f873936eda704f3ae7", "withdrawn": "", "abstract": "We study the nonautonomous logistic equation with Holling type II (hyperbolic) functional response and positive bounded coefficients. In the context of ecology, this model governs the population growth of a self-limiting species under saturated harvesting activity. We establish conditions for which the equation has exactly two bounded solutions, one positive and one negative, that do not approach the zero-solution in the past and in the future. Furthermore, we prove that the positive bounded solution is a forward attractor for all positive solutions, and the negative bounded solution is a forward attractor for all negative solutions above a threshold determined by the half-saturation constant. Moreover, the zero-solution is a repeller for all solutions between the aforementioned bounded solutions, and thus, we obtain an attractor-repeller-attractor configuration. The dynamics of solutions above or below the attractors are also discussed.", "id": "Paper/62033", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62033"}, {"title": " Hyperbolicity-Preserving Stochastic Galerkin Methods for Conservation Laws Based on Associative Truncated Products on Polynomial Spaces ", "webprogram_exclude": "0", "session_ids": ["Session/17872"], "source_sha256": "9dd1c234a31817a68e2d9c50934d64a87ffd96995265f5a3ce5a615c7e27b09b", "withdrawn": "", "abstract": "Stochastic Galerkin discretizations of nonlinear hyperbolic conservation laws can lose hyperbolicity because the standard pseudospectral product is generally nonassociative. We introduce a framework for hyperbolicity-preserving stochastic Galerkin systems based on associative truncated products on polynomial spaces. In one stochastic dimension, we characterize these products via a single polynomial datum, identify examples with favorable symmetry and spectral properties, and prove convergence to the classical product as polynomial degree grows. For rational-flux systems, we derive conditions ensuring hyperbolicity. Applications to the Euler equations demonstrate accurate, robust performance.", "id": "Paper/62058", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62058"}, {"title": " The Bishop–Phelps–Bollobás property for extremally disconnected ranges ", "webprogram_exclude": "0", "session_ids": ["Session/18363"], "source_sha256": "a90860dc311f4d05eec3c4b0514a8bc6570867ba65bbf3ede47b5cd12c7bb19d", "withdrawn": "", "abstract": "A pair of Banach spaces $(X,Y)$ has the Bishop--Phelps--Bollob\\'as property (BPBp) if every norm-one operator that almost attains its norm at a point of the unit sphere can be simultaneously approximated by a norm-attaining operator together with a point at which the norm is attained. For ranges of the form $C(K)$, the BPBp is known when the domain is\nAsplund or when $K$ is scattered, and the BPBp for Asplund operators is known for arbitrary domains. For general extremally disconnected $K$, the problem had remained open. We prove that $(X, C(L))$ has the BPBp for every \\textit{separable} Banach space $X$ and every extremally disconnected compact Hausdorff space $L$, over both the real and complex scalars. The general non-separable case remains open. This is joint work with Tattwamasi Amrutam, Chunlin Liu, and Monika.", "id": "Paper/62059", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62059"}, {"title": " Geometrical Properties of the Generalized Berezin Range on the Hardy Space ", "webprogram_exclude": "0", "session_ids": ["Session/18277"], "source_sha256": "c96cfacfafdc650d7a0f6c78c9cb6c4bae49162b92f68ab603703e7097c5a74f", "withdrawn": "", "abstract": "The geometric structure of a generalized Berezin range, namely, the $q$-Berezin range of bounded linear operators on the Hardy space, is investigated, with particular emphasis on its convexity properties and its relation to the classical Berezin range. A central contribution of this work is to study the Berezin range in a constrained setting\n\\[\n\\langle \\hat{k}_{w_1}, \\hat{k}_{w_2} \\rangle = q, \\quad 0<q\\leq 1,\\ w_1,w_2\\in\\mathbb{D}\r\n\\] involving normalized reproducing kernels. It plays a fundamental role in the formulation and analysis of the $q$-Berezin range. Based on this framework, several structural properties are established, revealing its geometric behavior. The convexity property is investigated for a variety of important classes of operators. In particular, for diagonal operators, a necessary and sufficient condition for convexity is obtained. For Toeplitz operators, a $q$-Poisson kernel approach is employed to characterize the $q$-Berezin range associated with both analytic and harmonic symbols, illustrating the influence of the symbol on the geometry of the range. The behavior of the $q$-Berezin range is also studied for weighted shift and certain classes of composition operators. The results highlight the role of the parameter $q$ on the geometric structure of the Berezin range and provide a broader perspective on operator-theoretic geometry in reproducing kernel Hilbert spaces, offering a foundation for future investigations of $q$-analogues in operator theory.", "id": "Paper/62061", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62061"}, {"title": " Shifted Lower Bruhat Intervals are EL-Shellable ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "1460d875e70bb67c054ff3288cc15699e3e8e09027b9972f0fd6a48c81e3ded2", "withdrawn": "", "abstract": "Let $W$ be an arbitrary Coxeter group. The shifted Bruhat interval\n$[w_1,w_2]\\,x^{-1}$, the translate of the Bruhat interval $[w_1,w_2]$ by an element $x$, is partially ordered by the Bruhat order of $W$. These posets arise from affine pavings of Richardson varieties, and in general they are neither twisted intervals nor tilted Bruhat intervals. Our main result is that the shifted lower intervals $[e, w]x^{-1}$ are EL-shellable for every Coxeter group, via an explicit labeling of each cover by a reflection. Along the way we show that $[e, w]x^{-1}$ is a graded poset with a unique maximum given by the Demazure product and a unique minimum given by an opposite Demazure operator that we introduce.", "id": "Paper/62062", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62062"}, {"title": " Banach spaces with the (MB∗) and p-L-Limited∗ Properties ", "webprogram_exclude": "0", "session_ids": ["Session/19339"], "source_sha256": "59a9629f1a3dfd9d6cad10441e46110e8635b856fe682964ae458cbd42f039a7", "withdrawn": "", "abstract": "We study the topological connections between the localized geometric properties in Banach space theory. Specifically, we investigate the connection between the Property (MB∗) and the p-L-limited ∗ structures.\nA Banach space X has the Property (MB∗) if every V ∗-set in X is a\nDunford–Pettis set. Let X be a Banach space satisfying Property (MB∗). Suppose Y is a Banach space and T : Y → X is a bounded linear operator with an unconditionally converging adjoint T∗ : X∗ → Y ∗. Then we get some results on the T∗(K) if K ⊂ X∗ is a p-L-limited∗ subset of Y ∗. Also we investigate V ∗-sets and weakly-p-L-sets.", "id": "Paper/62063", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62063"}, {"title": " Using Parametrized Physics-Informed Neural Networks to Approximate Solutions to the Quantum Anharmonic Oscillator ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "af55cd63acd77fa0701629a88d550999c9a76587202cf21f40f2bc7b8ad78dde", "withdrawn": "", "abstract": "The 1D Quantum anharmonic oscillator with potential $V(x) = \\frac{1}{2}m\\omega x^2 + \\lambda x^4$ has no closed-form solutions. It is conventionally solved by diagonalizing a Hamiltonian matrix on a spatial grid, which must be repeated for every value of the anharmonicity term $\\lambda$. To avoid this, a Physics-Informed Neural Network (PINN) whose inputs are the spatial coordinates $x$ and the parameter $\\lambda \\in [0.005,20]$, and whose outputs are the $k$ lowest energy eigenvalues is trained. It is trained using a custom loss function based on the variational principle and Ky Fan's minimum principle which allows an ordered set of energy eigenvalues for some $\\lambda \\in [0.005,20]$ to be found. A single trained network acts as a surrogate across the entire range of $\\lambda s$, returning eigenvalues –thus, eigenstates– for any $\\lambda$ in one forward pass. The network produces the three lowest eigenvalues to within $0.2\\%$ of exact diagonalization over $\\lambda \\in [0.05,20]$, with accuracy decreasing as $\\lambda \\to 0$. Moreover, a fixed-$\\lambda$, non-parametrized network recovers the five lowest eigenstates within $0.13\\%$ in each case. We further explore an extension to the unstable regime $\\lambda <0$, where the potential is unbounded from below, with potential applications to $\\mathcal{PT}-$symmetric quantum mechanics.", "id": "Paper/62064", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62064"}, {"title": " Blowup phenomena for fluid equations ", "webprogram_exclude": "0", "session_ids": ["Session/17749"], "source_sha256": "0168e00a1723017aad804be40d7d7161b9815f2c031d9882c27ee66a4b5f10c8", "withdrawn": "", "abstract": "We will discuss some constructions to produce blowup phenomena for fluid equations and models.", "id": "Paper/62066", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62066"}, {"title": " Bystander effect emerges from individual psychological prospects ", "webprogram_exclude": "0", "session_ids": ["Session/18220"], "source_sha256": "171cb6451a4145e268b6dab118ebae1b419ae7ee2ae99743e3eda4095ca7fd32", "withdrawn": "", "abstract": "The bystander effect is a social psychological phenomenon in which individuals are less likely to help a person potentially in need if there are others present. Sociologists and psychologists have proposed multiple plausible reasons for the bystander effect, from situational ambiguity and social contagion to diffusion of responsibility and mutual denial. We build a new model of an individual’s decision to intervene in a bystander situation based on these social psychological hypotheses, along with ideas borrowed from prospect theory. The model yields an explicit bystander curve which demonstrates, for the first time, that the bystander effect emerges from social risk perception among non-coordinating individuals in ambiguous bystander situations. Expanding upon this static model, we explore the effect of social learning, where individuals update their perceived risk of intervening after experiencing or witnessing the social repercussions of previous interventions. A novel result of this piecewise-smooth dynamical system model, with threshold-driven switching behavior, is that social learning exacerbates the bystander effect. We validate both the static and dynamic models using a new database of 42 experimental and observational studies across a wide range of bystander situations, demonstrating the importance of both population heterogeneity and social learning rates on the emergence of observed bystander curves. This provides a straightforward and generalizable explanation for the observed phenomenon, which may suggest effective interventions tailored to specific bystander situations.", "id": "Paper/62067", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62067"}, {"title": " Finding the Distribution of the Length of the Longest Path of Acyclic Orientations on Complete Multipartite Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18160"], "source_sha256": "6934705f138a1c9e3986f961644cc9d3c3247306a9ed7b89e5b0ab66e9ad4d72", "withdrawn": "", "abstract": "Motivated by a question by Peter J. Cameron, we investigate the distribution of the length\nof the longest path in a randomly sampled acyclic orientation on a graph. Focusing on the\nsetting of complete multipartite graphs, we obtain a generating function by deriving and\nsolving a recursive system of equations. The multivariate generating function we obtain\ncan be viewed as a refinement of a generating function given by Donald E. Knuth for the\ntotal number of acyclic orientations on a multi-partite graph; namely, an additional variable\n$u$ marks the longest path length, and the generating function reduces to Knuth’s generating function when $u = 1$. Normalizing our enumerative generating function provides a probability generating function addressing the question of Cameron. We will conclude by discussing evidence toward the conjecture that the distribution of the longest path length is asymptotically Gaussian.", "id": "Paper/62078", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62078"}, {"title": " Reduced integable systems and binary Darboux transformations ", "webprogram_exclude": "0", "session_ids": ["Session/18283"], "source_sha256": "f6dbadcef405f1706cf94999d28566f33912cc60acc1eada39e39f64804ff976", "withdrawn": "", "abstract": "We will investigate new integrable systems obtained through group reductions. Lax pairs will be employed to derive the corresponding reduced integrable systems and their associated binary Darboux transformations. Soliton solutions will be constructed from the zero seed, with representative examples including both local and nonlocal reduced matrix nonlinear Schrödinger equations and modified Korteweg–de Vries equations.", "id": "Paper/62093", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62093"}, {"title": " From Folding Paper to Proofs ", "webprogram_exclude": "0", "session_ids": ["Session/18235"], "source_sha256": "a21bf11117a054fb2e46f4a9e82ddee02997c14b15d39c11a1447d4f4386693c", "withdrawn": "", "abstract": "One of our favorite ways to play with geometry is to fold paper (Patty Paper) to build shapes, from complex origami figures to classical curves like conic sections. A fun and engaging activity that our high school students enjoy is the process of building an ellipse from a circle and a point inside the circle. Last year, one student wondered: after creating an ellipse from a circle, what happens if we repeat the process starting from the generated ellipse? She wanted to determine the algebraic equation of the resulting curve, leading her to develop a deeper fluency in translating geometric properties into algebraic statements.\n\nEarlier this year, another student built on her work and decided to keep going. Using Python to explore the resulting curves, moving the original point around and iterating the process, he discovered a surprising phenomenon on the sixth iteration when the point is outside the circle! Formulating his observation precisely took substantial mathematical work, ultimately allowing him to prove that his numerical approximations uncovered a necessary consequence of the underlying geometry.\n\nIn this poster, we share the framework we use to engage curious and thoughtful students, inviting them into a mathematical space where their minds can wander and they can ask new questions of their own. This evolving exploration of conic sections serves as a case study in how a simple hands-on activity can lead students to play, question, discover, conjecture, and ultimately to prove.", "id": "Paper/62098", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62098"}, {"title": " Limit Functions in non-Autonomous Polynomial Iteration ", "webprogram_exclude": "0", "session_ids": ["Session/19357"], "source_sha256": "9467af2306e38578c61c05a2c6f9dd93e118196afb0f96517f2fba5a7f395594", "withdrawn": "", "abstract": "The possibilities for limit functions on a Fatou component for the iteration of a single polynomial or rational function are well understood and quite restricted. In non-autonomous iteration, where one considers compositions of arbitrary polynomials with suitably bounded degrees and coefficients, one should observe a far greater range of behaviour. We show this is indeed the case and we exhibit a bounded sequence of quadratic polynomials which has a bounded Fatou component on which one obtains as limit functions every member of the classical Schlicht family of normalized univalent functions on the unit disc. The proof is based on quasiconformal surgery and the use of high iterates of a quadratic polynomial with a Siegel disc which closely approximate the identity on compact subsets. Careful bookkeeping using the hyperbolic metric is required to control the errors in approximating the desired limit functions and ensure that these errors ultimately tend to zero.", "id": "Paper/62153", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62153"}, {"title": " Homeostasis Patterns and Infinitesimal Homeostasis in Reaction Networks ", "webprogram_exclude": "0", "session_ids": ["Session/18257"], "source_sha256": "a0ac8cc96e468461027e9bb65891dc4f9ec13a2ac0178bf3f5f6e75e58cdb94b", "withdrawn": "", "abstract": "Homeostasis is a regulatory mechanism that keeps a specific variable close to a prescribed value as other variables fluctuate. This notion can be formulated rigorously when a system is modeled as an input-output network with distinguished input and output nodes, where the dynamics determine the corresponding input-output function. In this setting, homeostasis can be defined infinitesimally, namely when the derivative of the input-output function vanishes at an isolated point. Combined with graph-theoretic ideas from combinatorial matrix theory, this provides a framework for computing homeostasis points and classifying homeostasis types.\n\nIn the first part of the talk, we introduce the notion of a homeostasis pattern, a set of nodes that are simultaneously infinitesimally homeostatic, and show that all such patterns can be described using a combinatorial structure associated with the network, called the homeostasis pattern network. In the second part, we study infinitesimal homeostasis in chemical reaction networks, where conservation laws complicate the standard analysis. We present criteria for the existence of infinitesimal homeostasis with and without conservation, and introduce the notion of infinitesimal concentration robustness, where the output remains nearly constant under perturbations of conserved quantities.", "id": "Paper/62157", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62157"}, {"title": " How do simple rotations affect the implicit bias of Adam? ", "webprogram_exclude": "0", "session_ids": ["Session/18330"], "source_sha256": "5069e908d39050586e762371cea20ca837d717b05287f199e3c4c1cbed78468f", "withdrawn": "", "abstract": "Adaptive gradient methods such as Adam and Adagrad are widely used in machine learning, yet their effect on the generalization of learned models – relative to methods like gradient descent – remains poorly understood. Prior work on binary classification suggests that Adam exhibits a “richness bias,” which can help it learn nonlinear decision boundaries closer to the Bayes-optimal decision boundary relative to gradient descent. However, the coordinate-wise preconditioning scheme employed by Adam renders the overall method sensitive to orthogonal transformations of feature space. We show that this sensitivity can manifest as a reversal of Adam’s competitive advantage: even small rotations of the underlying data distribution can make Adam forfeit its richness bias and converge to a linear decision boundary that is farther from the Bayes-optimal decision boundary than the one learned by gradient descent. To alleviate this issue, we show that a recently proposed reparameterization method – which applies an orthogonal transformation to the optimization objective – endows any first-order method with equivariance to data rotations, and we empirically demonstrate its ability to restore Adam’s bias towards rich decision boundaries.", "id": "Paper/62161", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62161"}, {"title": " An Existence Theorem for Monomorphisms from <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"6.419ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 2763.7 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">C[0,1]</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-43\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-5B\" d=\"M118 -250V750H255V710H158V-210H255V-250H118Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-5D\" d=\"M22 710V750H159V-250H22V-210H119V710H22Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-43\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-5B\" x=\"760\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-30\" x=\"1039\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2C\" x=\"1539\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-31\" x=\"1984\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-5D\" x=\"2485\" y=\"0\"></use>\n</g>\n</svg> into Pure C<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.054ex\" height=\"2.009ex\" style=\"vertical-align: -0.171ex;\" viewBox=\"0 -791.3 453.9 865.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">^*</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2217\" d=\"M229 286Q216 420 216 436Q216 454 240 464Q241 464 245 464T251 465Q263 464 273 456T283 436Q283 419 277 356T270 286L328 328Q384 369 389 372T399 375Q412 375 423 365T435 338Q435 325 425 315Q420 312 357 282T289 250L355 219L425 184Q434 175 434 161Q434 146 425 136T401 125Q393 125 383 131T328 171L270 213Q283 79 283 63Q283 53 276 44T250 35Q231 35 224 44T216 63Q216 80 222 143T229 213L171 171Q115 130 110 127Q106 124 100 124Q87 124 76 134T64 161Q64 166 64 169T67 175T72 181T81 188T94 195T113 204T138 215T170 230T210 250L74 315Q65 324 65 338Q65 353 74 363T98 374Q106 374 116 368T171 328L229 286Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-2217\" x=\"0\" y=\"513\"></use>\n</g>\n</svg>-algebras ", "webprogram_exclude": "0", "session_ids": ["Session/18382"], "source_sha256": "a30ee780705920a21ca04e7a34ffa94116ae70275ba1018ae9f3b3ccf30bbbeb", "withdrawn": "", "abstract": "We establish an Elliott-type existence theorem for embeddings of $C[0,1]$ into a simple unital separable and pure C$^*$-algebra $A$ with a quasitrace.  Combined with earlier results of Jacelon, Strung and Toms this gives a complete classification of these morphisms up to approximate unitary equivalence.  We proceed by considering the variety of spectral measures that can be induced by quasitraces on the spectrum of a self-adjoint operator in $A$.\nThis amounts to a naturally induced continuous affine map from the simplex of quasitraces of the C$^*$-algebra into regular faithful Borel probability measures on the spectrum of the operator under consideration.  \nIf the spectrum is the closed unit interval then we prove that any such map is realized by some positive contraction in $A$.", "id": "Paper/62163", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62163"}, {"title": " Zero-divisor Graphs of Quandle Rings ", "webprogram_exclude": "0", "session_ids": ["Session/18255"], "source_sha256": "c1eb123609ccb41c1a0aa5389847b3361549292f399c50e0e187fd100a9175f0", "withdrawn": "", "abstract": "A \\textit{quandle} is a set $Q$ with a binary operation $\\ast\\,:\\,Q\\times Q\\to Q$ satisfying the following axioms: \n\n(i) For all $x\\in Q, \\, x\\ast x=x$, \n\n(ii) For all $y\\in Q$, the map $\\beta_y\\,:\\,Q\\to Q$ defined by $\\beta_y(x)=x\\ast y$ is invertible, and \n\n(iii) For all $x,y,z\\in Q$, $(x\\ast y)\\ast z=(x\\ast z)\\ast (y\\ast z)$.\n\nThe three axioms of a quandle algebraically encode the three Reidemeister moves in knot theory.  Let $R$ be an associative ring with unity, and $R[Q]$ be the set of all formal finite $R$-linear combinations of elements of $Q$:\n$$R[Q]:=\\Big\\{\\displaystyle\\sum_i\\,\\alpha_ix_i\\,|\\,\\alpha_i\\in R,\\,x_i\\in Q\\Big\\}$$  \nThen, $R[Q]$ is a non-associative ring with coefficients in $R$. The ring $S:=R[Q]\\oplus Re,$ where $e(\\notin Q)$ is a symbol that satisfies $e(\\sum_{i}^{}\\alpha_ix_i)=\\sum_{i}^{}\\alpha_ix_i=(\\sum_{i}^{}\\alpha_ix_i)e$ is called the extended quandle ring of $Q$. We investigate zero-divisor graphs of extended quandle rings. \n\nThis is a joint work with Gregory Churchill (SUNY Oswego), Indu Rasika Churchill (SUNY Oswego), and Bhitali Kousik (Tezpur University).", "id": "Paper/62174", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62174"}, {"title": " Near-Trinions: Complete Classification of Unital Three-Dimensional Real Associative Algebras ", "webprogram_exclude": "0", "session_ids": ["Session/18336"], "source_sha256": "cbcb27969aab01703bb77d0232313d4f11cc33186ad2759a32a0c2e64f61db95", "withdrawn": "", "abstract": "Frobenius' theorem settles, definitively, the question of three-dimensional real division algebras: there are none. What it leaves open --- and what this paper addresses --- is the question of which three-dimensional real associative algebras actually exist. We call these \\emph{near-trinions} and classify them completely, up to $\\RR$-algebra isomorphism. The answer is exactly six isomorphism classes; we provide canonical representatives, explicit multiplication tables, and a collection of module-theoretic invariants sufficient to distinguish every pair. The classification proceeds by stratifying on the radical dimension $d$: Wedderburn--Artin resolves the semisimple stratum; in the $d=1$ stratum, the Peirce decomposition locates the radical generator in either a diagonal or off-diagonal corner, producing the commutative and non-commutative branches respectively and ruling out the residue field $\\CC$ by a characteristic sign obstruction; and the $d=2$ stratum splits on whether $\\Jac(A)^2$ vanishes. The argument not only recovers the six classes but explains why the radical dimension takes values in $\\{0,1,2\\}$, why the $d=1$ case splits on commutativity, and why no near-trinion with residue field $\\CC$ can exist. One direction for subsequent work is proposed.", "id": "Paper/62176", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62176"}, {"title": " Three Single-Variable Summer Calculus Reflections on Substitution, Leibniz Notation, and Taylor’s Theorem ", "webprogram_exclude": "0", "session_ids": ["Session/19349"], "source_sha256": "b036ab879e3b288f179d8e8868fe5be8d1192cd0a7c5f767244e523aeb29df5b", "withdrawn": "", "abstract": "In terms of the facet of calculus and STEM-literacy education I have constantly reflected upon in-semester calculus-related coursework audited in the last five years, aside with recently taking upper-level real analysis and most recently Calculus Two in the past summer semester. Inconclusive, this article is an collection of a few small topics that have the value in general situations, literacy of reading math and science writing and potentially critical inquiry, on how we get accurate changed range in the new variable after a $u$-substitution, a premature recap on Leibniz notation, and Taylor's theorem which normally concludes a semester while suffering from shortage of time and links with practical considerations. The perspective here is based on a decaded-long applying calculus skill porportionally in graduate school, self-examination and re-learning into American collegiate curriculum, and some educational considerations for which I amend from a learner's perspective for rigor.", "id": "Paper/62183", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62183"}, {"title": " Another Look at the Static PDE Approach to Multidimensional Extrapolation ", "webprogram_exclude": "0", "session_ids": ["Session/18281"], "source_sha256": "71fb5fc260dca485e291a0813c4205112e2245e5e4b13c264aa47202e3e05f10", "withdrawn": "", "abstract": "We present a modification of the static PDE based extrapolation method of Aslam (SIAM Journal on Scientific Computing, 2014) for extending smooth fields across interfaces implicitly defined as zero level sets. Our approach introduces relaxed upwind finite differences as a key component of the fast sweeping method. Unlike existing approaches, it requires function values and their normal derivatives only on the first grid layer inside the domain adjacent to the interface, thereby improving computational efficiency and flexibility. To further enhance accuracy, we introduce a simple boundary reconstruction technique that significantly reduces the numerical error in the extrapolated solution near the interface. Numerical experiments demonstrate improved performance across a wide range of domain geometries, including those with high curvature features.", "id": "Paper/62207", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62207"}, {"title": " The Minkowski Dimension of the image of an arboreal Galois representation ", "webprogram_exclude": "0", "session_ids": ["Session/17755"], "source_sha256": "0768bfc292ac1ecd796e604d44e6c5173a4f9b8eeba42cfab22a44541e1658a1", "withdrawn": "", "abstract": "We consider the Minkowski dimension of the arboreal Galois group $G_{f,\\alpha}$ associated to a rational map $f:\\mathbb{P}^{1}\\rightarrow\\mathbb{P}^{1}$ and also a base point $\\alpha\\in\\mathbb{P}^{1}(K).$ This group is naturally a subgroup of the automorphism group of the infinite $d$-ary rooted tree whose vertices are indexed by the backward orbit $f^{-\\infty}(\\alpha).$ We show that the Minkowski dimension exists for the profinite iterated monodromy groups $G_{f}^{\\arith}$ and $G_{f}^{\\geom},$ and that these two groups have the same dimension. We prove a dichotomy theorem stating that $G_{f}^{\\arith}$ and $G_{f}^{\\geom}$ are either the full tree automorphism group or else have non-maximal dimension. We identify several cases of interest in which non-maximality $\\overline{\\dim}(G_{f,\\alpha})<1,$ including the cases of postcritical base point, the case of periodic base point, the case in which $f$ is a nontrivial iterate, and also the postcritically finite case. We identify several cases of interest in which minimality $\\dim(G_{f,\\alpha})=0,$ including the power, Chebyshev, Latt\\`es, and abelian cases. We formulate a conjecture on dimension minimality for quadratic polynomials, which if true would imply the $d=2$ case of a conjecture of Andrews-Petsche on abelian arboreal Galois groups. It is joint work with my advisor Clayton Petsche.", "id": "Paper/62210", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62210"}, {"title": " A Two-Pathogen Invasion Model of White-Nose Syndrome ", "webprogram_exclude": "0", "session_ids": ["Session/19359"], "source_sha256": "5651a8a7c3208354e68133175904be2fbe0e0b877ed3bd71916c5a793942a45e", "withdrawn": "", "abstract": "White-nose syndrome (WNS) is a fungal disease caused by Pseudogymnoascus destructans (Pd) that affects hibernating bats. It has caused widespread mortality and a near-extinction status among several bat species in the United States. With the discovery of a distinct species of WNS-causing fungus, currently denoted Pd-2, a second wave of disease could have disastrous consequences. We constructed a compartmental model consisting of a system of differential equations modeling two strains circulating in a population. Our mathematical models can be used to better understand disease dynamics and the potential outcomes of disease mitigation strategies before a second wave of WNS strikes North America.", "id": "Paper/62211", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62211"}, {"title": " On LLM-based assistants’ performance in rigorous proving ", "webprogram_exclude": "0", "session_ids": ["Session/18272"], "source_sha256": "4632e76e4e091ec4cbbd2d8b2e07672bfd54f39bf5827aee9eac446a1821700e", "withdrawn": "", "abstract": "Recent results in solving and AI assistance in solving the open problems of high and medium complexity in mathematics may create the impression that there are no obstacles in pursuing any mathematical problem using $LLM$s. \n\nHowever, one can notice that (at least, in the context of the Jacobian conjecture, Erdős problems, and the Navier-Stokes Millennium Problem, leaving its relevant solution aside), $LLM$ assistance proved most useful in providing counterexamples which mathematicians (admittedly) considered unlikely in the first place. \n\nMoreover, assuming an $\\bf{autonomous}$ execution of a reasoning $LLM$, we prove a result that establishes a performance ceiling for $LLM/GPT$, Meta-Hyper Ceiling, and a wide range of self-improving agentic models and beyond.\n\nIt generates a few practical questions:\n\n1) How high is this ceiling?\n\n2) What complexity of proof does the ceiling correspond to (and what is a suitable complexity for the context (besides a measure based on the length of the proof))?\n\n3) What about the usage of $LLM$-based assistants in obtaining the proofs? What is the necessary level of intervention in the autonomous execution of a model to ensure a high propensity for success?\n\nIn this talk, we answer these questions by examining an instructive case of autonomous, self-improving recursive models and concluding with a discussion of Energy-Based Models ($EBM$) as alternatives and their own limitations.", "id": "Paper/62219", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62219"}, {"title": " Isogenies and Hecke Operators on Elliptic Cohomology ", "webprogram_exclude": "0", "session_ids": ["Session/18287"], "source_sha256": "483c9a75db8159d193c75ecae6cdc9a8b085dffc5112914b2965acc9cc1247cd", "withdrawn": "", "abstract": "Operations on tempered cohomology theories (and complex-periodic cohomology theories more generally) are known to be intimately related to the isogenies of their associated algebraic groups. The Adams operations on K-theory, for example, are associated with the $k$th power map on $\\mathbb{G}_m$. Their analogues at height $2$, Hecke operators on elliptic cohomology, are not as well-understood. In this talk, I will describe a spectral algebreo-geometric approach to studying these operators. This begins with the spectral moduli stack of isogenies of oriented elliptic curves, which I show to be a (nonconnective) spectral Deligne-Mumford stack using a connected-étale decomposition and a generalization of Lurie's theorem on the representability of derived Hilbert spaces. We will then apply this to construct stacky Hecke operators in a manner similar to their classical moduli-theoretic construction—with the notable caveat that in the spectral case, Grothendieck duality introduces a nontrivial twist.", "id": "Paper/62222", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62222"}, {"title": " Hadamard Deep Autoencoders for Manifold Learning Enabled Text Decoding ", "webprogram_exclude": "0", "session_ids": ["Session/19345"], "source_sha256": "8342cc73d2857eacfc7b9fdcaf4d8f8e3356e1af8cedec056c727755c37bc597", "withdrawn": "", "abstract": "End-to-end encryption (E2EE) is a security method that ensures communication between two parties, preventing unauthorized access to the data. However, such E2EE platforms can be used by criminals to protect their communications, hindering law enforcement efforts to investigate crimes. Thus, while E2EE provides a layer of security for legitimate users, it creates challenges for law enforcement by allowing criminals to evade detection. Here, we investigate the use of machine learning—specifically, long short-term memory (LSTM) and deep autoencoders—for the task of decrypting text-based messages without prior knowledge of the encryption scheme. The study is motivated by whether neural sequence models can learn to reverse a deterministic character-level encryption through exposure to input-output examples alone. We generate data, i.e., sentences, encrypted via a fixed and unknown substitution cipher. The models are trained to map encrypted character sequences back to their original form with cross-entropy loss. Since the sentences vary in length, the masking process is implemented using the Hadamard approach in which the loss function is computed pointwise. The trained models achieve near-perfect performance on held-out validation and test sets. The best performance of the LSTM and autoencoder models is attained by incorporating them with Bayesian hyperparameter optimization. A key observation is that the LSTM and the autoencoder learn both the decryption mapping and linguistics, and generalize to new sentences that they have never seen.", "id": "Paper/62228", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62228"}, {"title": " From Tidal Prediction to Zeta Zeros ", "webprogram_exclude": "0", "session_ids": ["Session/18554"], "source_sha256": "d13e5dc6d90543f94ffafa5574c46dcfda1b3b131009600dda098e55d24345b2", "withdrawn": "", "abstract": "The presentation has two overlapping themes. The first starts with the competing tidal theories of Descartes (vortex) and Newton (gravitational). In 1738 the French Académie Royale des Sciences held a competition for the best explanation of the cause of tides. The winners were Bernoulli, Cavalleri, Euler, and McClarin. All but Cavalleri presented refinements of Newton’s gravitational theory. In 1799 Laplace provided equations that related the tides to the moon and the sun and set the stage for the next work.\n\nKelvin, using the Laplace equations, developed three essential instruments for tidal prediction: a tide gauge, a harmonic analyzer, and a tide predicting machine, TPM. The TPM summed cosines, taking account of amplitude and phase, of the harmonic components of lunar and solar motion. The tide predicting machine at Liverpool, driven by a hand crank, included 14 tidal components.\n\nThe second theme starts with a Titchmarsh project to count the zeros of the Riemann zeta function. Using the Riemann-Siegel formula, he expressed the zeta function on the critical line as sums of cosine terms. He employed tables of logarithms and of cosines to sum the terms “by hand” at closely spaced points and observed the sign pattern to count zeros. Turing decided to extend the calculations, had seen the Liverpool TPM, and recognized the mechanical method could compute the sums and help count zeros. Turing initially considered using the pully system of Kelvin’s TPM but instead designed an electric motor driven gear-based machine (1939).\n\nWhen England entered WWII in September 1939, Turing was called to Bletchley Park to help break the German Enigma machine. Turing didn’t complete his zeta function electro-mechanical computer but was instrumental in the development of an electro-mechanical computer, the Bombe, to help decrypt Enigma.", "id": "Paper/62240", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62240"}, {"title": " Minimal Homotopies in Three Dimensions: A Cable System Approach ", "webprogram_exclude": "0", "session_ids": ["Session/19358"], "source_sha256": "7be7ca9c5a03007be63ea7a97d998b71c8810b4d26a1b47127c145d2bb0a8a3d", "withdrawn": "", "abstract": "We study null homotopies of immersed spheres in R^3 and the volume swept out during contraction. For C^1 immersions whose self-intersection set is finite and contains no two-dimensional components, we introduce cable systems, a combinatorial structure that connects each bounded complementary region to the exterior. From this construction we define the cable index and prove that it coincides with the Brouwer degree on every complementary region. This correspondence yields a computable degree-weighted lower bound for the swept volume of any Lipschitz null homotopy. We further show that this bound is attained for a class of orientation-consistent homotopies whose indices evolve monotonically. In the special case where the immersion bounds an immersed ball, we construct an explicit volume-minimizing homotopy realizing the lower bound. Finally, we present a linear-time algorithm for computing all cable indices from a finite cable system, providing an efficient method for evaluating the lower bound.", "id": "Paper/62241", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62241"}, {"title": " Non-uniqueness of advection-diffusion equations via instantaneous blow-up ", "webprogram_exclude": "0", "session_ids": ["Session/17952"], "source_sha256": "3d64d59c1a637b546cdc24c934c097b9cb8f4a7ea2f5612f09c77ef76c900652", "withdrawn": "", "abstract": "We provide two results on the sharp non-uniqueness of the advection-diffusion equation. For the first part, we construct infinite energy jump through instantaneous blow-up, while the finite energy jump is by mixing. The methods are different from the earlier work by Moerschell and Sorella. We also prove a dichotomy theorem for the passive scalar.", "id": "Paper/62242", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62242"}, {"title": " Existence of Minimal Homotopies for Immersed Planar Curves ", "webprogram_exclude": "0", "session_ids": ["Session/18266"], "source_sha256": "70ad0b955b929ab30d4737e0759712aae01db43ab9beec38a144b33858ad8988", "withdrawn": "w", "abstract": "We study the existence of area-minimizing homotopies between homotopic curves in the\nplane. While the classical Plateau problem establishes the existence of least-area surfaces\nspanning a single Jordan curve, the corresponding existence theory for homotopies between\ncurves is more subtle and is not directly covered by the same framework. Existing results\nin the plane are mainly based on combinatorial and algebraic methods, such as decomposing\ncurves into self-overlapping subcurves. These methods are highly effective in the planar setting,\nbut they are often tied to special classes of curves and rely strongly on the local structure of\nthe self-intersections, frequently assuming transverse crossings. In contrast, our approach is\ngeometric and variational, and does not depend on the local structure of the self-intersections.\nOur approach adapts classical minimal surface methods by lifting an immersed planar curve with self-intersections into higher co-dimension, where it becomes embedded. For such a lifted curve, we apply Douglas’s solution of the Plateau problem to obtain an area-minimizing disk. For closed curves of class ", "id": "Paper/62243", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62243"}, {"title": " On the Numerical Solution of a Boundary Value Problem for a Nonlinear Ordinary Differential Equation ", "webprogram_exclude": "0", "session_ids": ["Session/17872"], "source_sha256": "b84ae0d13aa985925c19cb6d36a3a1ff9a575e7bdf85817888a8c094ac189f97", "withdrawn": "", "abstract": "\\begin{abstract}\nThis work is devoted to the construction and analysis of a finite difference scheme for a boundary value problem for the nonlinear ordinary differential equation\n\\[\nU_{xx}+p(x)(U_x)^2+q(x)U_x+f(x,U)=0.\n\\]\nThe nonlinear term containing the square of the first derivative creates additional difficulties in the analysis of numerical approximations. A finite difference scheme is proposed for the considered problem, and the properties of the discrete solution are investigated. In particular, a comparison theorem for the discrete problem is established. Furthermore, the existence of a solution to the finite difference problem is proved, and the convergence of the discrete solution to the solution of the continuous boundary value problem is established.\n\\end{abstract}", "id": "Paper/62252", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62252"}, {"title": " To be announced \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18641"], "source_sha256": "a3c0c915114ad980146fba82b6cb5657ba2abb726b5f3e391acfb59aeb3302f1", "withdrawn": "w", "abstract": "To be announced", "id": "Paper/62264", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62264"}, {"title": " From Life Tables to Simulation: Exploring Mortality Data in the Classroom ", "webprogram_exclude": "0", "session_ids": ["Session/19341"], "source_sha256": "79c64eada0d15927ee0dac5de595002c47cf809b9200e79b63b247aeeeaeb71e", "withdrawn": "", "abstract": "Life contingencies is often one of the first actuarial science courses in which students encounter mortality data, yet classroom activities frequently emphasize deterministic calculations rather than data exploration and simulation. This presentation describes a classroom project that integrates real-world mortality data from the Human Mortality Database with Monte Carlo simulation to help students connect life tables with simulation-based approaches to survival analysis. Using Excel, students investigate historical mortality trends, compare populations, estimate survival probabilities through Monte Carlo simulation, and interpret the results in the context of actuarial science. Designed for undergraduate actuarial science courses, the project requires no programming experience and can be readily adapted for a wide range of classrooms. The presentation will discuss the project's design, classroom implementation, instructional insights, and practical suggestions for instructors interested in incorporating real-world data and simulation into undergraduate actuarial science courses. This presentation is based on a recently accepted peer-reviewed article for publication in Scatterplot: The MAA Journal of Data Science.", "id": "Paper/62272", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62272"}, {"title": " Optimal Self-Assembly of Nanostructures Using a Flexible DNA Tile Model ", "webprogram_exclude": "0", "session_ids": ["Session/17953"], "source_sha256": "3f1f692ef89b7cfa7eda36d957c73441324c1432f586003b499c47a84f27cb5d", "withdrawn": "", "abstract": "The flexible tile model introduced for DNA self-assembly provides a graph-theoretic framework for studying the construction of nanostructures from branched junction molecules. Within this model, the efficient realization of a target graph depends upon minimizing the number of tile and bond-edge types while guaranteeing assembly. In this work, we investigate these parameters for several graph families like the sun, sunlet, and kayak paddle graphs. These families exhibit a wide range of structural characteristics, from highly symmetric configurations to more variable constructions, providing a rich setting for studying self-assembly optimization. We establish structural properties that influence tile and bond-edge assignments and derive new bounds on the minimum numbers of required tile and bond-edge types. In addition, we will also present an algorithmic framework for bounding bond-edge requirements under the most restrictive assembly conditions. This approach exploits the relationship between bond-edge assignments and graph isomorphism through the analysis of 2-switch operations, allowing the identification of edge pairs that must be assigned distinct bond-edge types to prevent the formation of smaller or nonisomorphic competing assemblies. Our results expand the collection of graph families for which self-assembly parameters are known and contribute to the broader study of graph-based DNA nanostructure design.", "id": "Paper/62279", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62279"}, {"title": " Intentional Innovation: Reimagining Math Teaching and Learning with AI ", "webprogram_exclude": "0", "session_ids": ["Session/18137"], "source_sha256": "47902d0d7da14af6757ef980aaff6402920fda4a5d0c021ddc1ad25f7d7d764f", "withdrawn": "", "abstract": "With the rapid rise of generative AI tools like ChatGPT, we are entering a new era of possibilities in mathematics education. AI offers powerful opportunities to design tools that enhance math learning and teaching—when used intentionally and grounded in research. Yet many existing AI applications overlook the complexity of mathematics teaching and learning, risking the reinforcement of existing inequities or low-impact strategies. In this presentation, Copur-Gencturk showcases innovative applications from her research to demonstrate how AI can be purposefully leveraged to empower educators and improve math learning.", "id": "Paper/62303", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62303"}, {"title": " Fractional calculus within two Banach spaces and Amplified Neural Network Approximation ", "webprogram_exclude": "0", "session_ids": ["Session/19362"], "source_sha256": "698efc2fcfa191c967c9b066ca60e984b73d4a76e570899a14f9a7b39f900b91", "withdrawn": "", "abstract": "Here we deal with the univariate and abstract multi-composite specific\nsigmoid activated quantitative approximation of Banach space valued con-\ntinuous functions on a compact interval or on a Banach space. These hap-\npen by quasi-interpolation Banach space valued specific multi-composite\nsigmoid activated neural network operators. We perform also the re-\nlated Banach space valued and Banach space originating specific multi-\ncomposite sigmoid activated fractional and abstract approximations. These\nmulti-composite sigmoid activated infinitely many approximations are de-\nrived by establishing Jackson type inequalities involving the modulus of\ncontinuity of the engaged function or its Banach space valued high order\nderivative or fractional derivaties. Our operators are defined by using a\nmulti-composite density function induced by seven known and basic sig-\nmoid functions. The approximations are pointwise and with respect to\nthe uniform norm. The related Banach space valued and Banach space\noriginating feed-forward neural networks are with one hidden layer.", "id": "Paper/62312", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62312"}, {"title": " Computational Discrete Global Geometric Structures ", "webprogram_exclude": "0", "session_ids": ["Session/19345"], "source_sha256": "e75276a4c57d83a1b0ecf72e0785be7d62a28392b84cfe8216c77967ce2bdba1", "withdrawn": "", "abstract": "This talk covers our recent paper, a Feature Article to be published in the October 2026 issue of the Notices of the AMS.\n\nMany abstract mathematical concepts expressible by equations or functions in a \\emph{single} coordinate system already have mature \\emph{computational} frameworks for obtaining concrete numerical values and have been widely applied to technical problems across disciplines. In contrast, the \\textit{global} geometric structures (sections of fiber bundles satisfying certain conditions) cannot be described by equations in a single local coordinate frame; they are only well-defined via multiple equations on a collection of overlapping coordinate charts, together with their transition functions. Thus, the conventional  \\emph{computational} paradigm based on a single coordinate system no longer applies to such global structures.\nWe introduce and define the emerging research area of \\emph {Computational Discrete Global Geometric Structures} (CDGGS) and provide a  perspective on it, which includes three major components:\n\n1.Moving beyond the traditional \\emph{computational} mindset toward an \\emph{algorithmic} one, focusing the design of  algorithms and implementing  codes that  capture the global structures and properties of diverse global geometric structures.\n\n2. Employing computer graphics techniques to achieve the visualization  of diverse global geometric structures, as illustrated by the figures in this paper.\n\n3. Applying the aforementioned algorithms and code to  some technological research fields,   thereby establishing a bridge between  abstract global geometric concepts and their potential practical engineering applications.\n \nThe motivation from applications of CDGGS is long-term and hard to achieve in the short term. As a complement, visual illustrations offer immediate and strong intuitive motivation.As the illustration of global geometric structures brings about compelling visual appeal, it naturally attracts broader interdisciplinary audiences and fosters diverse public engagement initiatives, which have gradually evolved into an organic component of the CDGGS research field.", "id": "Paper/62339", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62339"}, {"title": " Exact Refinement Equivalence for Integer-Weighted Union-Find Decoding ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "78af87d1b254a1b8b40e961f6e7e00a3fc2891c8163a926345505b627dcbe253", "withdrawn": "", "abstract": "Integer-weighted union-find (UF) decoding suits nonuniform detector noise, but treating a weight-$q$ edge as a length-$q$ path does not itself establish equivalence or preserve logical output. We give a certification framework: a weighted state and its seven deterministic phases are exactly conjugate to ordinary UF on the unit-edge subdivision. A clock-parity invariant bars overshoot, while Kruskal-stub forest-choice analysis handles refined spanning trees. Explicit relative chain maps $(P_2,P_1,P_0)$ and chain homotopy preserve syndrome boundaries and logical classes. For fixed $K<\\infty$, nonuniform aperiodic weights in $\\{1,\\ldots,K\\}$ retain the inputs of the ordinary-UF threshold proof; block-correlated noise is controlled by $(\\xi p)^{1/K}$, yielding a uniform threshold, not a numerical-threshold improvement. Software certificates, a 9,654-mechanism audit at 1,682 locations, and a frozen IQM-Garnet campaign (88 circuits, 98 jobs, 76,400 shots) validate record plumbing and finite responses, not decoder performance. Finally, a homology-gated escalation decoder (SVHG--CMP--UF), with sparse-validity implementation and RTL kernels, has finite CPU and preverification evidence; it is not a complete FPGA implementation.", "id": "Paper/62340", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62340"}, {"title": " A Global Touring of Art Exhibition of Computational Discrete Global Geometric Structures ", "webprogram_exclude": "0", "session_ids": ["Session/18232"], "source_sha256": "e4ea45221a70c7e523359cac5c8315e303809f80b966c3cf07c2b1f2d90211a8", "withdrawn": "", "abstract": "In “On Proof and Progress in Mathematics” Thurston posed the question:\n“How do mathematicians advance human understanding of mathematics?”\nHe addressed this question through a variety of activities, including  a fashion show.\nWe also address this question with public engagement by organizing a  global traveling exhibition of  ``computational discrete global geometric structures'', which commenced in 2024, and also introduced in   our forthcoming Feature Article appearing in the October 2026 issue of Notices of the AMS,\n\nThese artworks are visualizations of concepts in differential geometry and topology generated via computer graphics techniques using our original code. Featured subjects include harmonic foliations, holomorphic quadratic differentials, meromorphic quadratic differentials, translation surfaces, differential 1-forms, and the Calabi flow.\n\nCurrently, 33 universities, science and technology museums, general museums,   libraries, conference centers, and science popularization bases  are participating in this touring exhibition.   On‑site photos are available on the \\href{https://mp.weixin.qq.com/s/yQhA9uQIB2KhbWA9JmbU8g}{project website}. \nThe audience of the exhibition has expanded beyond scholars and university students to include children of many ages. Through this touring exhibition, we have surprisingly found that global geometric structures empowered by visualization have  gradually connected scholars from diverse disciplines more closely and promoted active academic interaction among them.We plan for the exhibition to run for 10 years, with 100 universities participating in the  tour.\n\nMotivated by the Umbilic sculpture at Stony Brook University and the Boy Surface sculpture at Oberwolfach, we plan to install six sculptures illustrating harmonic foliations at six universities. These sculptures share the same geometric shape, while the foliations on their surfaces belong to distinct Whitehead equivalence classes. We expect these homologous sculptures distributed across six campuses to create a kind of “choral resonance,” inspiring more scholars to pursue further numerical constructions of other global geometric structures through algorithms and code.", "id": "Paper/62342", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62342"}, {"title": " Numerical Identification of Stationary States and Their Stability in a Model of Quantum Droplets ", "webprogram_exclude": "0", "session_ids": ["Session/18109"], "source_sha256": "724755871ea76fd0d991c703ed69fbcf236f0999a8a43939330e7984b89624e6", "withdrawn": "", "abstract": "In this work, we are motivated by a recent variant of the nonlinear Schrödinger (NLS) equation describing cold, dilute atomic condensates with quantum fluctuation effects. Our goal is to develop robust numerical methods capable of uncovering diverse stationary solutions in such NLS models. Specifically, and in line with recent theoretical and experimental interest, we focus on ultracold quantum droplets in Bose mixtures influenced by the Lee–Huang–Yang quantum fluctuation correction and study these systems in one- and two-dimensional settings. To this end, we deploy several numerical techniques. The homotopy grid method allows systematic refinement from coarse to fine spatial discretizations in one dimension, while the dimension-by-dimension homotopy approach extends one-dimensional solutions to two-dimensional domains. These methods effectively detect broad families of stationary states, many of which have not been previously reported, to the best of our knowledge. Furthermore, they enable the monitoring of solution continuation and bifurcation phenomena. During our investigation, we encounter unusual bifurcation events, including nonstandard pitchforks and saddle-center bifurcations, which exhibit novel stability transitions. For example, we identify continuous pathways connecting vortex and dark soliton stripe branches, absent in the standard cubic defocusing model. Overall, the presence of competing mean-field and quantum fluctuation interactions leads to a richer bifurcation structure than in traditional cubic NLS systems. These findings suggest that similar complex bifurcation and stability phenomena may appear in other settings, including higher-dimensional systems or models with competing nonlinearities such as cubic-quintic interactions, highlighting the importance of further theoretical and numerical exploration.", "id": "Paper/62343", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62343"}, {"title": " The Everywhere Failure of Square \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18646"], "source_sha256": "aa899e2cffc4ff5ddbaaff548a9be404b9aead9381f1177cbc7e6f73dfa93b64", "withdrawn": "w", "abstract": "To be announced", "id": "Paper/62347", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62347"}, {"title": " Role of feedback and feedforward loops in non-monotonic response ", "webprogram_exclude": "0", "session_ids": ["Session/17383"], "source_sha256": "cb55a82c6446c186fd0411e720de49944bda2a9ec3259402e2d7043a2c25ef5c", "withdrawn": "", "abstract": "A response curve measures the output of a system at steady state against an input parameter, which could be the strength of a stimulus, or the value of a parameter. Its derivative defines the local sensitivity. Non-monotonic response curves, also by the name of biphasic response and hormesis, had been observed in biological systems. While incoherent feedforward loops are widely  believed to be a necessary mechanism for biphasic response, we show how feedback loops can provide an alternative mechanism.", "id": "Paper/62351", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62351"}, {"title": " Optimization of free-time controlled constrained sweeping processes and applications ", "webprogram_exclude": "0", "session_ids": ["Session/18245"], "source_sha256": "76bee76c48e5b2392ccde5d9dbb91f65a2274c91ddb67036da3fb64c0d743574", "withdrawn": "", "abstract": "This talk is devoted to advanced optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type, in which the duration of the dynamic process is optimized. To address these problems, we employ the method of discrete approximations together with advanced tools from variational analysis to derive necessary optimality conditions for the original continuous-time problem. These results are applied to several practical models, including nanoparticle dynamics and robotic systems. Key contributions also include the development of numerical algorithms to solve these optimization problems, using the Python Dynamic Optimization library GEKKO to simulate solutions to the posed robotics problems for an arbitrary fixed number of robots.", "id": "Paper/62363", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62363"}, {"title": " Mathematical Analysis of Nuclear Position Problems in Fly Cells ", "webprogram_exclude": "0", "session_ids": ["Session/18357"], "source_sha256": "038456fa8ad23e7aadf73996253e3f2340b305c81efc5a11d641b67630787b23", "withdrawn": "", "abstract": "Nuclear placement and shape are tightly linked to intracellular transport, yet quantitative principles connecting geometry to transport efficiency remain incomplete. We develop and analyze two diffusion-based models for fly muscle cells in which nuclei are modeled as small elliptical inclusions. In an absorption setting, uniformly produced signal is removed at nuclear boundaries, leading to an MFPT Poisson problem with Neumann conditions on the cell membrane and Dirichlet conditions on nuclei. A matched-asymptotic expansion for \\varepsilon \\rightarrow 0 yields a two-term approximation for the MFPT and nuclear uptake fluxes; the correction term reveals how ellipse orientation and aspect ratio enter through dipole and quadrupole moments coupled to the Neumann Green’s function. In a production setting, nuclei act as localized sources for a screened diffusion equation. We validate the theory using finite element computations on a disk with elliptical exclusions and on realistic cell geometries extracted from imaging data, aided by high-order boundary-integral evaluation of Green’s functions using chunKIE. We then pose constrained optimization problems to identify nuclear configurations that minimize MFPT or improve distribution, and we compare optimized arrangements with experimental nuclear data to assess which geometric features are most predictive of transport performance.", "id": "Paper/62368", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62368"}, {"title": " A Partial Group <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.732ex\" height=\"2.343ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -863.1 1176.4 1008.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathrm {C}^{*}</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-43\" d=\"M56 342Q56 428 89 500T174 615T283 681T391 705Q394 705 400 705T408 704Q499 704 569 636L582 624L612 663Q639 700 643 704Q644 704 647 704T653 705H657Q660 705 666 699V419L660 413H626Q620 419 619 430Q610 512 571 572T476 651Q457 658 426 658Q322 658 252 588Q173 509 173 342Q173 221 211 151Q232 111 263 84T328 45T384 29T428 24Q517 24 571 93T626 244Q626 251 632 257H660L666 251V236Q661 133 590 56T403 -21Q262 -21 159 83T56 342Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2217\" d=\"M229 286Q216 420 216 436Q216 454 240 464Q241 464 245 464T251 465Q263 464 273 456T283 436Q283 419 277 356T270 286L328 328Q384 369 389 372T399 375Q412 375 423 365T435 338Q435 325 425 315Q420 312 357 282T289 250L355 219L425 184Q434 175 434 161Q434 146 425 136T401 125Q393 125 383 131T328 171L270 213Q283 79 283 63Q283 53 276 44T250 35Q231 35 224 44T216 63Q216 80 222 143T229 213L171 171Q115 130 110 127Q106 124 100 124Q87 124 76 134T64 161Q64 166 64 169T67 175T72 181T81 188T94 195T113 204T138 215T170 230T210 250L74 315Q65 324 65 338Q65 353 74 363T98 374Q106 374 116 368T171 328L229 286Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-43\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-2217\" x=\"1021\" y=\"612\"></use>\n</g>\n</svg>-Algebra for Discrete Quantum Groups ", "webprogram_exclude": "0", "session_ids": ["Session/17834"], "source_sha256": "305b3cb2572e4108829c25602603add67dd093177b5fa40d5358e0392120c32b", "withdrawn": "", "abstract": "In the late 90’s, Exel defined a universal $\\mathrm{C}^{*}$-algebra $\\mathrm{C}^{*}_p(\\Gamma)$ for a discrete group $\\Gamma$.  This $\\mathrm{C}^{*}$-algebra encodes the partial representation theory of $\\Gamma$.  In this talk, I discuss a newly developed theory of partial representations of a discrete quantum group $\\mathbb{G}$, and how to construct an analogous universal $\\mathrm{C}^{*}$-algebra $\\mathrm{C}^{*}_p(\\mathbb{G})$ that encodes the partial representation theory of $\\mathbb{G}$.  Moreover when a suitable amenability hypothesis is satisfied, I will show how to realize this universal $\\mathrm{C}^{*}$-algebra as a Mortia equivalent corner of a special crossed product.  As a corollary, all partial representations of such a discrete quantum group $\\mathbb{G}$ dilate to a unitary representation in a canonical way.  This is a joint work with Alcides Buss and Lucas Hall.", "id": "Paper/62378", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62378"}, {"title": " Non-Orientable 4 Genus of Pretzel Knots ", "webprogram_exclude": "0", "session_ids": ["Session/18193"], "source_sha256": "a3252f4010404de9fbd441e9673dc2f452bed2672c9179fb99e6b56b772e5d58", "withdrawn": "", "abstract": "Given a knot $K$, the non orientable 4-genus $\\gamma_4(K)$ is an invariant given by the minimum first Betti number over all non-orientable surfaces in four dimensions with boundary $K$. We investigate $\\gamma_4(K)$ for pretzel knots, specifically asking when does a pretzel knot bound a Mobius strip (i.e. when $\\gamma_4=1$). By combining obstruction techniques such as linking form (Gilmer and Livingston) and diagonalization (Jabuka and Kelly) with explicit constructions of Möbius strips coming from band moves, we determine $\\gamma_4(K)$ for many pretzel knots.", "id": "Paper/62380", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62380"}, {"title": " Recent progress toward the Eisenbud–Huneke–Ulrich conjecture ", "webprogram_exclude": "0", "session_ids": ["Session/17373"], "source_sha256": "5a4d62a7a62b3d37c485c8b474b0744d7cc1ef87c2ddf8074f18d18143acc206", "withdrawn": "", "abstract": "We study $\\mathfrak{m}$-primary ideals in a polynomial ring with partially linear (virtual) resolution. We establish an effective bound beyond which the powers of such an ideal coincide with powers of the maximal ideal. In particular, we prove the Eisenbud--Huneke--Ulrich conjecture in the case of linearly presented ideals. We obtain an upper bound on their Castelnuovo--Mumford regularity, extending Macaulay’s bound and a theorem of Eisenbud--Huneke--Ulrich. We also conjecture a lower bound for the number of minimal generators of such ideals in terms of the number of linear steps. We prove that this bound holds when the ideal is generated by quadrics or is (virtually) linearly presented.", "id": "Paper/62384", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62384"}, {"title": " On the Geometry of the Algebraic Davis–Wielandt Shell and Norm-Parallelism in <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.852ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 1228 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">C^*</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-43\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2217\" d=\"M229 286Q216 420 216 436Q216 454 240 464Q241 464 245 464T251 465Q263 464 273 456T283 436Q283 419 277 356T270 286L328 328Q384 369 389 372T399 375Q412 375 423 365T435 338Q435 325 425 315Q420 312 357 282T289 250L355 219L425 184Q434 175 434 161Q434 146 425 136T401 125Q393 125 383 131T328 171L270 213Q283 79 283 63Q283 53 276 44T250 35Q231 35 224 44T216 63Q216 80 222 143T229 213L171 171Q115 130 110 127Q106 124 100 124Q87 124 76 134T64 161Q64 166 64 169T67 175T72 181T81 188T94 195T113 204T138 215T170 230T210 250L74 315Q65 324 65 338Q65 353 74 363T98 374Q106 374 116 368T171 328L229 286Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-43\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-2217\" x=\"1094\" y=\"513\"></use>\n</g>\n</svg>-Algebra ", "webprogram_exclude": "0", "session_ids": ["Session/18382"], "source_sha256": "c086d2e2bceed0376053bf1654d382fe0a37f4fb1a11f23ffd53d036afdbabb5", "withdrawn": "", "abstract": "The Davis--Wielandt shell and the Davis--Wielandt radius are fundamental tools in the geometric analysis of operators. Their algebraic counterparts for elements of unital $C^*$-algebras are investigated using a state-space approach. Several geometric properties of the algebraic Davis--Wielandt shell are established, including a characterization of shell inclusion and a detailed analysis of the associated height function, whose non-negativity, concavity, and upper semicontinuity are proved. Some estimations for the algebraic Davis--Wielandt radius are derived. Structural relationships between norm-parallelism and the algebraic Davis--Wielandt radius are also explored, leading to new characterizations and criteria. These results provide a unified geometric framework for the algebraic Davis--Wielandt shell and radius, enriching the study of numerical-range-type invariants in unital $C^*$-algebras.", "id": "Paper/62391", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62391"}, {"title": " Bisecting Mass Assignments in <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.897ex\" height=\"2.343ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -863.1 1247.1 1008.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbb {R}^n</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJAMS-52\" d=\"M17 665Q17 672 28 683H221Q415 681 439 677Q461 673 481 667T516 654T544 639T566 623T584 607T597 592T607 578T614 565T618 554L621 548Q626 530 626 497Q626 447 613 419Q578 348 473 326L455 321Q462 310 473 292T517 226T578 141T637 72T686 35Q705 30 705 16Q705 7 693 -1H510Q503 6 404 159L306 310H268V183Q270 67 271 59Q274 42 291 38Q295 37 319 35Q344 35 353 28Q362 17 353 3L346 -1H28Q16 5 16 16Q16 35 55 35Q96 38 101 52Q106 60 106 341T101 632Q95 645 55 648Q17 648 17 665ZM241 35Q238 42 237 45T235 78T233 163T233 337V621L237 635L244 648H133Q136 641 137 638T139 603T141 517T141 341Q141 131 140 89T134 37Q133 36 133 35H241ZM457 496Q457 540 449 570T425 615T400 634T377 643Q374 643 339 648Q300 648 281 635Q271 628 270 610T268 481V346H284Q327 346 375 352Q421 364 439 392T457 496ZM492 537T492 496T488 427T478 389T469 371T464 361Q464 360 465 360Q469 360 497 370Q593 400 593 495Q593 592 477 630L457 637L461 626Q474 611 488 561Q492 537 492 496ZM464 243Q411 317 410 317Q404 317 401 315Q384 315 370 312H346L526 35H619L606 50Q553 109 464 243Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJAMS-52\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-6E\" x=\"1021\" y=\"581\"></use>\n</g>\n</svg> with Hypercubes ", "webprogram_exclude": "0", "session_ids": ["Session/18240"], "source_sha256": "d5a52bebc9ec8fdf4dc2073a34e512f2eb9bd3131773ac223f215cb5fef2f54d", "withdrawn": "", "abstract": "We generalize mass bisection theorems to mass assignments. A $k$-dimensional mass assignment continuously gives a smooth measure on every $k$-dimensional affine subspace of $\\mathbb{R}^d$. In particular, it was recently shown that in $\\mathbb{R}^d$, $d+1$ mass distributions can be bisected at once with a $d$-dimensional hypercube. We generalize this and show that $d+1$ mass assignments to $k$-dimensional affine subspaces of $\\mathbb{R}^d$ can be bisected with a single $k$-dimensional hypercube in a $k$-dimensional linear subspace that contains any specified $k-1$ vectors. Our proof is topological, and uses a recent Borsuk-Ulam type result on Stiefel manifolds.", "id": "Paper/62431", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62431"}, {"title": " Spectrum of trees of diameter 4 for the distance Laplacian matrix ", "webprogram_exclude": "0", "session_ids": ["Session/18146"], "source_sha256": "14d18323307157b5ad8d13491dbd6769e0d7315d6768f14b3ab00c5045131cf5", "withdrawn": "", "abstract": "Graphs can be encoded into a matrix according to some rule. The eigenvalues of the matrix are used to understand the structural properties of graphs. If two graphs share a set of eigenvalues, they are called cospectral. A tree is a graph with no cycles, and for most matrix representations, almost all trees have a cospectral mate. The distance Laplacian matrix is found by subtracting the distance matrix from the diagonal transmission matrix. There is an open conjecture that trees, for their distance Laplacian matrices, do not have a cospectral mate and are therefore spectrally determined. We explicitly find the spectrum of a family of trees of diameter 4 and how it is uniquely defined by its parameters.", "id": "Paper/62443", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62443"}, {"title": " On gcd-graphs over matrix rings ", "webprogram_exclude": "0", "session_ids": ["Session/18227"], "source_sha256": "6d106fc18e0e32dbf071c66eef8d28d0331a1e11d3d9ee15282c392f4a21d722", "withdrawn": "", "abstract": "Graphs defined over finite rings are well studied in the literature. The study of these graphs benefits from rich connections between several areas of mathematics, including number theory, algebra, combinatorics, and graph theory, and these connections often lead to interesting interactions between algebraic and combinatorial structures. In this article, we investigate gcd-graphs defined over matrix rings with coefficients in finite fields.  We show that these graphs exhibit several interesting graph-theoretic properties. Along the way, we also prove some results on the structure of matrix rings, which may be of independent interest.", "id": "Paper/62445", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62445"}, {"title": " Biochemically Informed Neural Ordinary Differential Equations ", "webprogram_exclude": "0", "session_ids": ["Session/17811"], "source_sha256": "5c5bcfbf97162598051e6fbddd7f36fac7d7be03b0c709ed1f73bc99b2f1d7df", "withdrawn": "", "abstract": "Ordinary differential equation models of biochemical reactions are often formulated as stoichiometric systems in which the dynamics arise from a collection of interacting processes. A central challenge is that the functional form of each process is rarely known a priori and may be difficult to infer from data. We propose biochemically informed neural ordinary differential equations (BINODEs), a neural-ODE framework that retains the stoichiometric structure of mechanistic models while representing individual processes by neural networks. In BINODEs, the outputs of neural network processes (NNPs) are mapped to state derivatives through a linear layer analogous to a stoichiometric matrix. This architecture allows biological side information, such as process-specific inputs, sign constraints, and monotonicity assumptions, to be built directly into the model. We characterize the approximation properties of NNPs for several standard biochemical rate laws and show that the proposed framework recovers both trajectories and process-level structure in Monod, Lotka–Volterra, pharmacokinetic, and ultradian endocrine models. These results suggest that BINODEs offer a useful compromise between mechanistic interpretability and data-driven flexibility for modeling partially known biochemical or biological dynamical systems.", "id": "Paper/62462", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62462"}, {"title": " The Lean Number of a Hypergraph ", "webprogram_exclude": "0", "session_ids": ["Session/18338"], "source_sha256": "3097d73ff62348920061930868174fa65d062137a830dbe443685e452e5d383e", "withdrawn": "", "abstract": "Inspired by the notion of tricolorability of knots, we introduce the concept of \\textit{lean coloring} for hypergraphs and the associated \\textit{lean number} of a hypergraph. \nLean coloring often involves very few colors, yet still requires the methods of usual graph coloring, forcing the overall complexity to be NP-Hard. We provide two alternative formulations of the lean coloring problem that involve a type of coloring on abstract simplicial complexes and a partial coloring on bipartite graphs. \nWe then provide bounds for the lean numbers of hypergraphs that are $k$-uniform, $k$-partite, wide-path connected, or $r$-complete.\nWe conclude with some directions for future work and present the lean numbers of $130$ knots and links.", "id": "Paper/62469", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62469"}, {"title": " XIMERA and Open Educational Resources versus Traditional Textbooks in Linear Algebra: Implications for Passing Rates and Course Design ", "webprogram_exclude": "0", "session_ids": ["Session/19341"], "source_sha256": "b3322e5cb05423c6f0a87daf6ddb050e75593d0eece23125d83aeaadd454ae97", "withdrawn": "", "abstract": "Linear algebra is a foundational gateway course for students pursuing degrees in science, technology, engineering, mathematics, data science, and other quantitatively intensive fields. Yet it is also widely recognized as a conceptual threshold where many students struggle to transition from procedural computation to structural reasoning with vector spaces, linear transformations, eigenvalues, and proofs. This transition is difficult because it requires students to coordinate multiple representations (symbolic, geometric, and structural), reason for systems and subspaces, and interpreting algorithmic procedures (e.g., elimination) as mathematical objects. When students cannot make this shift, the consequences are high: introductory linear algebra becomes a bottleneck that contributes to delayed degree progress, course repetition, and attrition from STEM pathways. \n\nOpen Educational Resources (OER) have expanded rapidly as institutions respond to affordability concerns and pursue equity in access. OER improves “day-one” availability of course materials, allows instructors to customize scope and sequence, and reduces hidden barriers that may disproportionately affect first-generation students and students from economically disadvantaged backgrounds. However, much of the empirical OER evidence in undergraduate mathematics is concentrated in calculus, college algebra, and high-enrollment general education courses. There is comparatively limited research on interactive OER platforms in linear algebra, even though the course’s abstraction and high cognitive demands suggest that immediate feedback and scaffolded practice may be particularly important. \n\nThis project advances the current state of knowledge substantively by extending interactive OER research into introductory linear algebra and by focusing on outcomes central to persistence and equity: exam-score trajectories across the semester and end-of-course success (earning a grade of C or higher). Instead of framing success only as a final grade, the study conceptualizes learning as a trajectory. Exam trajectories capture whether students improve, stagnate, or decline at different points in the semester, providing actionable information about when students need support.", "id": "Paper/62470", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62470"}, {"title": " A Protocol for Comparing the Causal Impact of Prenatal and Perinatal Factors on Autism ", "webprogram_exclude": "0", "session_ids": ["Session/19353"], "source_sha256": "2aac1d3755acf4d8204d4dbfb20678005f2f7816cb61a0c76275c68fd60be97e", "withdrawn": "i", "abstract": "Over the past several decades, autism has moved to the forefront of the medical zeitgeist, in part because its prevalence has risen in ways that are not yet fully understood. This has sharpened interest in identifying early-life factors that may contribute. Yet such factors are difficult to study and interpret using observational data. We present a protocol that analyzes case–control data from a multi-site autism study and places prenatal and perinatal factors on a common footing. Using Bayesian Additive Regression Trees (BART), we estimate how the probability of autism would change under different factor values, and express this change both as a relative risk and as an attributable fraction. We then show how these conditional quantities combine to yield population-level effects, describing how prevalence would change under a population-wide shift in these factors. We state the assumptions required to identify these effects from case-control data and show how they can\nbe used to quantify the contribution of each factor. The protocol provides a transparent and rigorous framework for evaluating early-life factors in autism and interpreting their potential impact.", "id": "Paper/62472", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62472"}, {"title": " Discrete Superconvergence Analysis for Quantum Magnus Algorithms of Unbounded Hamiltonian Simulation ", "webprogram_exclude": "0", "session_ids": ["Session/17702"], "source_sha256": "48c3f4a52e47dd0ab2b3947384885453fac4d1245f7ac824ff33546d2922cbbb", "withdrawn": "", "abstract": "Motivated by various applications, unbounded Hamiltonian simulation has\nrecently garnered great attention. Quantum Magnus algorithms, designed to achieve\ncommutator scaling for time-dependent Hamiltonian simulation, have been found to\nbe particularly efficient for such applications. When applied to unbounded Hamiltonian simulation in the interaction picture, they exhibit an unexpected superconvergence\nphenomenon. However, existing proofs are limited to the spatially continuous setting\nand do not extend to discrete spatial discretizations. In this work, we provide the first\nsuperconvergence estimate in the fully discrete setting with a finite number of spatial\ndiscretization points $N$, and show that it holds with an error constant uniform in N. The\nproof is based on the two-parameter symbol class, which, to our knowledge, is applied\nfor the first time in algorithm analysis. The key idea is to establish a semiclassical framework by identifying two parameters through the discretization number and the time step\nsize rescaled by the operator norm, such that the semiclassical uniformity guarantees the\nuniformity of both. This approach may have broader applications in numerical analysis\nbeyond the specific context of this work.", "id": "Paper/62491", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62491"}, {"title": " On differential-algebraic elimination of the spinor field from the Maxwell–Dirac electrodynamics ", "webprogram_exclude": "0", "session_ids": ["Session/17978"], "source_sha256": "5a8e684499d1c5560e59153153dc14be50ecdec1acdf8149a287f2fce9c14a67", "withdrawn": "", "abstract": "We investigate whether the spinor field can be differential-algebraically eliminated from the Maxwell--Dirac equations in a particular gauge. To this end, we construct a generic truncated power-series solution and linearize the prolonged system of the Maxwell--Dirac equations about this solution. We then analyze the ranks of the coefficient matrices associated with the linearized system. Our results indicate that, generically, the spinor components are uniquely determined by the electromagnetic field and its derivatives. Furthermore, the fourth-order time derivatives of the components of the electromagnetic four-potential are uniquely determined by derivatives of the lower order with respect to time. These findings strongly suggest that the spinor field can be differential-algebraically eliminated, and the resulting equations describe independent evolution of the electromagnetic field, i.e., a Cauchy problem can be formulated in terms of the electromagnetic variables alone.\n\nThis result can be applied to derive equations of motion for the model of wave functions as plasma-like collections of a large number of particles and antiparticles. This enables the simulation of quantum phase-space distribution functions, such as the Wigner distribution function, which are not necessarily non-negative.", "id": "Paper/62497", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62497"}, {"title": " Matrices and quadratic matrix polynomials with corresponding spectra ", "webprogram_exclude": "0", "session_ids": ["Session/17942"], "source_sha256": "430c1b63b64faf6c9ef13ab2f5ddcf7d3a508fc25fbc11a993047eff17df661f", "withdrawn": "", "abstract": "It is shown that the eigenvalues of a large class of matrices \ncan be computed as those of a quadratic matrix polynomial whose \ncoefficients are of much smaller size than that of the matrices\nwhen those matrices are sparse.\n \nSuch a matrix polynomial can be used, other than for the actual computation \nof the eigenvalues, to provide more detailed spectral information \nthan would be possible by using just the original matrix. \nThis leads, in particular, to new lower and upper bounds on the \nmagnitudes of the nonzero eigenvalues, including bounds of a directional \nnature. The upper bounds are often significantly more accurate than \nexisting ones, while also being computationally less demanding. \nThe lower bounds are especially noteworthy as effective lower bounds are \noften not available when the matrix is singular.", "id": "Paper/62513", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62513"}, {"title": " On the Twisted Group Ring Isomorphism Problem ", "webprogram_exclude": "0", "session_ids": ["Session/19342"], "source_sha256": "c3f61bbc7bbaa9b84c334ff6fb4c482f9160cf9f85dce0d32e875a2ceda395fe", "withdrawn": "", "abstract": "We investigate the problem of determining isomorphisms between twisted complex group algebras of finite $p$-groups, a question closely related to the classical group algebra isomorphism problem. Our study centers on an invariant called the generalized corank, which plays a significant role in the analysis of twisted complex group algebra isomorphisms. We establish a solution for non-abelian $p$-groups whose generalized corank is at most three.", "id": "Paper/62521", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62521"}, {"title": " A Modular Filter for Prime Constellations ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "60465833df9f28d9397db6c1cc9bc361c9af25e9fc8e29faf9a36feeacaa5810", "withdrawn": "", "abstract": "We study obstructions to single-digit mutations that transform one prime constellation into another. For a constellation with locking modulus $L$, a mutation at position $i$ in base $b$, changing digit $d$ to $d'$, requires $L\\mid(d'-d)b^i$. This yields an exact modular rejection rule for pruning impossible mutations before primality testing.\n\nWe derive a modular reachability criterion: a permissible digit difference exists precisely when $L/\\gcd(L,b^i)\\le b-1$. For twin primes, this proves that no positive-position mutation can produce another twin-prime anchor in bases $2$ or $5$.\n\nWe also prove the Position-$0$ Trap: in base $L+1$, the only possible position-$0$ differences are $\\pm L$, forcing one resulting integer to be divisible by $L+1$ and hence prime only if it equals $L+1$. Thus position $0$ is impossible unless $L+1$ itself anchors the constellation. The same obstruction applies to the twin-prime and prime-quadruplet examples studied here. Computational tests support the modular criteria and falsify previously conjectured parity-based position rules.", "id": "Paper/62525", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62525"}, {"title": " On the existence and regularity of weakly nonlinear stationary Boltzmann equations: a Fredholm alternative approach ", "webprogram_exclude": "0", "session_ids": ["Session/18441"], "source_sha256": "2547c7c3cf78d5130a2213a7250d8f9e19d1af96cc3cdc00ae873eda29d0ff07", "withdrawn": "", "abstract": "The celebrated Fredholm alternative theorem works for the setting\nof identity compact operators. This idea has been widely used to solve linear\npartial differential equations. In this talk, we demonstrate a generalized\nFredholm theory in the setting of identity power compact operators, which\nwas suggested in Cercignani and Palczewski to solve the existence of the\nstationary Boltzmann equation in a slab domain. We carry out the detailed\nanalysis based on this generalized Fredholm theory to prove the existence\ntheory of the stationary Boltzmann equation in bounded three-dimensional\nconvex domains. To prove that the integral form of the linearized Boltzmann\nequation satisfies the identity power compact setting requires the regularizing\neffect of the solution operators. Once the existence and regularity theories for\nthe linear case are established, with suitable bilinear estimates, the nonlinear\nexistence theory is accomplished", "id": "Paper/62541", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62541"}, {"title": " Operator learning meets inverse problems ", "webprogram_exclude": "0", "session_ids": ["Session/18447"], "source_sha256": "13c97446d64661f6ca571c301435eaf408f0d4f9a8aba25af0bf7a5de46c004e", "withdrawn": "", "abstract": "Operator learning offers a robust framework for approximating mappings between infinite-dimensional function spaces. It has also become a powerful tool for solving inverse problems in the computational sciences. This talk focuses on methodological and theoretical developments at the intersection of operator learning and inverse problems. We pay special attention to emerging measure-centric formulations that treat observed data or unknown parameters as probability distributions.", "id": "Paper/62542", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62542"}, {"title": " Groups Having a Character of Maximal Degree ", "webprogram_exclude": "0", "session_ids": ["Session/17832"], "source_sha256": "109b6b9a7aad2c8e59697343b5af5c9f48e343fac972d7ab7a346c86b982f65c", "withdrawn": "", "abstract": "This is joint work with Sara Jensen.\n\nLet $G$ be a group, let $d$ be a character degree, and let $e$ be the integer so that $|G| = d(d+e)$.  It has been shown when $e > 1$ that $|G| \\le e^4 - e^3$.  In this paper, we consider the groups where $|G| = e^4 - e^3$.  It is known that $e$ must be a power of a prime.  We classify the groups where $e$ is a prime and where $e$ is $4$, $9$, and $25$.  In so doing, we find a new nonsolvable Camina pair.", "id": "Paper/62550", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62550"}, {"title": " Statistical learning under mean independence ", "webprogram_exclude": "0", "session_ids": ["Session/18036"], "source_sha256": "1574fa79717ddca2403eefa96fddaa369913c924b6c02a884f97c3191881fec3", "withdrawn": "", "abstract": "Many statistical models rely on the assumption that noise variables are independent, which often leads to useful identifiability properties. However, full independence is a strong assumption that may not hold in many real-world settings. In this talk, I will consider two classical models: Independent Component Analysis (ICA) and Linear Non-Gaussian Acyclic Models (LiNGAM). We show that the independence assumption can be relaxed by assuming only mean-independence conditions without losing identifiability of the models. Our main identifiability result is based on a generalization of the spectral theorem from matrices to higher-order tensors: a generic symmetric tensor with an orthonormal basis of eigenvectors has a unique such basis. Moreover, our results come with new algorithms to recover the parameters under these weaker assumptions.", "id": "Paper/62566", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62566"}, {"title": " How Crowding Shapes Diffusion on Networks ", "webprogram_exclude": "0", "session_ids": ["Session/19351"], "source_sha256": "da1561b50761e162a47fe19879de9501fafa783f25cb099459731390718d47a3", "withdrawn": "", "abstract": "Network structure is often treated as fixed, while functional organization is inferred from the\ndynamics unfolding on it. Here, we bridge this gap by defining edges through pairwise interac-\ntion dynamics, where both node dynamics and local features are intrinsically encoded, yielding a\nfunctional network in which structure emerges from the underlying processes. We investigate this\nframework in nonlinear random walks—mean-field models of diffusion with volume exclusion that\nare nonlinear on heterogeneous networks and linear otherwise. For connected undirected graphs, we\nanalyze the rate of convergence to equilibrium for n interacting walkers and introduce a localization-\nbased reduction exploiting the spontaneous concentration of Laplacian eigenvectors on specific nodes\nin large random graphs. We show analytically, and validate numerically, that in scale-free networks\nthe Jacobian spectrum of the nonlinear random walk undergoes a characteristic spectral deformation: eigenvalues associated with peripheral, low-degree nodes are compressed toward the origin,\nwhile those linked to hubs are systematically displaced outward. This nonlinear spectral reorganization reveals how heterogeneity and crowding jointly redefine the effective dynamical structure of\nthe network, offering a principled mechanism for dynamical organization in complex systems.", "id": "Paper/62575", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62575"}, {"title": " Unifying singular value decompositions of tensors via aligned orthogonality ", "webprogram_exclude": "0", "session_ids": ["Session/18355"], "source_sha256": "286c0b8dd332b90f7436b727538a9126e5c729e9bcfbf048df2886d0544572d3", "withdrawn": "", "abstract": "We study basis-aligned two-orthogonal (bato) tensors, which can be written as a sum of critical rank-one approximations whose factors are singular vectors of their flattenings. As such, bato tensors admit a Tucker decomposition and a canonical polyadic decomposition that are related to each other. We prove that generic bato decompositions are identifiable and that their truncations are critical low-bato-rank approximations. We also compute the dimension of the set of bato tensors, and identify the irreducible components of its Zariski closure with isotopy classes of maximal partial Latin hyperrectangles. Many important tensors are bato, such as determinants, matrix multiplication tensors, and other structure tensors of algebras.", "id": "Paper/62577", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62577"}, {"title": " Pointwise error estimates for the optimal recovery of solutions to Laplace’s equation ", "webprogram_exclude": "0", "session_ids": ["Session/18258"], "source_sha256": "5ded00cb79dbed5f556fa4159cf6e3afe708fd53db8de287ff4c714db1610b8f", "withdrawn": "", "abstract": "We consider an optimal recovery problem for the Poisson problem when the boundary data is unknown but belongs to a model class. A finite number of measurements of the solution to recover are provided to alleviate the lack of information. This presentation focuses on the case where measurements consist of point evaluations on the interior of the computational domain. A key ingredient in the algorithm for numerically computing an optimal recovery is the finite element approximation of the Riesz representers associated with the point evaluation at the measurement locations. Our main result is a pointwise error estimate for the Riesz representers, and we apply this result to obtain sharper estimates measuring the performance of the recovery algorithm in $H^1$, $L^\\infty$, and for quantities of interest. Numerical results confirm the theoretical error rates in the mesh parameter and motivate future work in this area.", "id": "Paper/62579", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62579"}, {"title": " Heavenly Elliptic Curves over Cubic Fields ", "webprogram_exclude": "0", "session_ids": ["Session/18076"], "source_sha256": "d3d3584d049ccbd963aa4c5c75686be5acfa9882ff15973ec70c2e12ba81bfaa", "withdrawn": "", "abstract": "We call an elliptic curve $E/K$ heavenly at $\\ell$ when the field extension $K(E[\\ell^\\infty])/K(\\mu_\\ell^\\infty)$ is pro-$\\ell$ and unramified away from $\\ell$. These extra arithmetic constraints on $E$ guarantees an upper-triangular representation of $G_K$ on the $\\ell$-torsion of the curve. Work of Rasmussen and Tamagawa has shown that for a fixed number field $K$ of degree at most three, there are only finitely many $K$-isomorphism classes of heavenly elliptic curves when we let $\\ell$ vary through all primes. Recently, McLeman and Rasmussen explored a “bi-directional” finiteness result where both the prime of interest and the quadratic field of definition are allowed to vary. In this talk we will discuss analogues of their results for heavenly elliptic curves defined over cubic number fields. We will also discuss under what conditions the trace of a heavenly elliptic curve behaves like the trace of a curve with complex multiplication.", "id": "Paper/62580", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62580"}, {"title": " The Local Topological Quantum Order property for some two-dimensional AKLT models ", "webprogram_exclude": "0", "session_ids": ["Session/17925"], "source_sha256": "38eca1ec65b8527b6ba08008fb4c7581732f8e801f0961bba30808ba3f0296e3", "withdrawn": "", "abstract": "A characteristic feature of topological insulators is the spectral gap above their ground state in the bulk. The robustness of topological phases of quantum many-body systems requires a spectral gap above the ground states that is stable under gentle perturbations of the Hamiltonian. This stability property is closely related to the so-called Local Topological Quantum Order (LTQO) property. We report on a recent proof of the LTQO property for some two-dimensional AKLT models and explain the connection with spectral gap stability.", "id": "Paper/62590", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62590"}, {"title": " Sketching the Global Landscape of Nonconvex Optimization via Weakly Convex Relaxations ", "webprogram_exclude": "0", "session_ids": ["Session/18245"], "source_sha256": "3c8cf8e70895740c356e834a48bae3cb1a8b06841d90b1ed441cf83159aa8e99", "withdrawn": "", "abstract": "Convexification is a classical technique in global optimization, but standard convex relaxations are typically one-shot: they provide a single convex surrogate that cannot be systematically tightened. As a result, convexification has played a limited role in nonlinear programming, where progressively improving approximations are often essential. In this paper, we introduce a parametric relaxation framework for a broad class of nonconvex optimization problems. The relaxation is governed by a parameter $\\gamma$ that explicitly trades off between the convexity of the surrogate model and its tightness to the original objective. A key feature of this framework is its pointwise hierarchical certificate property: $\\gamma=0$ certifies global minimizers, while larger values certify increasingly weaker global quadratic supports. We establish the variational properties of this framework and justify $\\gamma$-proximal stationarity as a certificate for quantifying the tightness of stationary points relative to global optimality.  Our framework naturally recovers several known relaxations and provides a new way to systematically strengthen the weak relaxation. Numerical experiments demonstrate the effectiveness of the proposed method in navigating nonconvex landscapes.", "id": "Paper/62595", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62595"}, {"title": " Machine computations of the <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.769ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 1192.4 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">E_2</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-45\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-32\" x=\"1044\" y=\"-213\"></use>\n</g>\n</svg> page of the <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.678ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 722.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbb {R}</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJAMS-52\" d=\"M17 665Q17 672 28 683H221Q415 681 439 677Q461 673 481 667T516 654T544 639T566 623T584 607T597 592T607 578T614 565T618 554L621 548Q626 530 626 497Q626 447 613 419Q578 348 473 326L455 321Q462 310 473 292T517 226T578 141T637 72T686 35Q705 30 705 16Q705 7 693 -1H510Q503 6 404 159L306 310H268V183Q270 67 271 59Q274 42 291 38Q295 37 319 35Q344 35 353 28Q362 17 353 3L346 -1H28Q16 5 16 16Q16 35 55 35Q96 38 101 52Q106 60 106 341T101 632Q95 645 55 648Q17 648 17 665ZM241 35Q238 42 237 45T235 78T233 163T233 337V621L237 635L244 648H133Q136 641 137 638T139 603T141 517T141 341Q141 131 140 89T134 37Q133 36 133 35H241ZM457 496Q457 540 449 570T425 615T400 634T377 643Q374 643 339 648Q300 648 281 635Q271 628 270 610T268 481V346H284Q327 346 375 352Q421 364 439 392T457 496ZM492 537T492 496T488 427T478 389T469 371T464 361Q464 360 465 360Q469 360 497 370Q593 400 593 495Q593 592 477 630L457 637L461 626Q474 611 488 561Q492 537 492 496ZM464 243Q411 317 410 317Q404 317 401 315Q384 315 370 312H346L526 35H619L606 50Q553 109 464 243Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJAMS-52\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-motivic Adams spectral sequence ", "webprogram_exclude": "0", "session_ids": ["Session/17701"], "source_sha256": "1021cfc4d039c751c5cfa3dce8fd6455268734cb51fe2eeccf5005a4c8321fd8", "withdrawn": "", "abstract": "Computing the homotopy groups of spheres is one of the central and most enduring problems in algebraic topology. While these groups are easy to define, their structure is remarkably difficult to uncover. A motivic analogue of this problem leads to the bigraded $\\mathbb{R}$-motivic stable stems, fundamental invariants of the $\\mathbb{R}$-motivic stable homotopy category. A leading approach to compute the $\\mathbb{R}$-motivic stable stems is via the $\\mathbb{R}$-motivic Adams spectral sequence. In this talk, I plan to compute the $E_2$ page of the $\\mathbb{R}$-motivic Adams spectral sequence in a range via the $\\rho$-Bockstein spectral sequence. A key challenge is then to determine the differentials in the $\\rho$-Bockstein spectral sequence. I will discuss our use of a SAT solver as a tool for computating this Bockstein spectral sequence. This approach systematizes the hand calculations of Belmont–Isaksen and extends them to a significantly larger range.", "id": "Paper/62641", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62641"}, {"title": " The Unique Limit of the Glimm-Lax Construction for Sobolev Data and Rigidity Thresholds for Conservation Laws ", "webprogram_exclude": "0", "session_ids": ["Session/17822"], "source_sha256": "5b00953d4c70af4d3d8c1334968c01665bb60b6007e59dc4e9b0dc9df1357d01", "withdrawn": "", "abstract": "We consider 1-d systems of hyperbolic conservation laws with two unknowns. A famous construction of Glimm & Lax shows that global-in-time \"Glimm-Lax\" weak entropy solutions exist in this setting for any initial data with small $L^\\infty$ norm [Mem. Amer. Math. Soc. (1970), no. 101]. In this talk, I will report on results showing that solutions with initial data in any fractional Sobolev space are unique in the full class of Glimm--Lax solutions. As a secondary result, we further prove an upper bound on the rigidity threshold separating uniqueness and non-uniqueness for $C^\\alpha$ solutions at $\\alpha=\\frac{1}{2}$. This is based on joint work with Cooper Faile and Sam Krupa.", "id": "Paper/62689", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62689"}, {"title": " Fostering Rate Reasoning as a Foundation for Precalculus Learning ", "webprogram_exclude": "0", "session_ids": ["Session/18068"], "source_sha256": "db9702a34af66a6c0ea43f81e3659c0c7f3b83d9cb82fa3408fdd999e02334d1", "withdrawn": "", "abstract": "This preliminary design-based research study is part of a larger project investigating how instruction can foster students’ covariational reasoning about rate in precalculus. Conventional instruction often treats slope and rate as formulas or computed ratios, whereas covariational reasoning emphasizes coordinated change between quantities. The present study focuses on Unit 1, the linear-functions unit of the larger project. Drawing on covariational reasoning and APOS theory, Unit 1 aims to support students in coordinating generalized-ratio reasoning, in which rate is understood as an invariant ratio across equivalent pairs of changes, and unit-rate reasoning, in which a per-one relationship can be used iteratively or multiplicatively to generate corresponding changes. These forms of reasoning are intended to support students' development toward an interiorized conception of rate as a multiplicative operator relating arbitrary changes through Δy=rΔx, and ultimately toward an encapsulated conception of rate as a mathematical object that can itself be acted upon. \n\nInteractive graphing applets and paper-and-pencil tasks coordinate graphical, algebraic, tabular, and contextual representations. Applet features and task prompts are deliberately designed to make selected relationships visible while withholding others, requiring students to construct and explain covariational and multiplicative relationships rather than simply read values or apply routine procedures.\n\nData include pre- and post-assessments, student written work, classroom observations, and follow-up interviews. Assessment and interview responses are coded using rubrics aligned with the developmental framework to examine students’ generalized-ratio, unit-rate, multiplicative-operator, and object reasoning. Written and interview data are also analyzed to investigate the reasoning pathways through which students coordinate and generalize these conceptions. The presentation will report preliminary results from the first full implementation of Unit 1 and discuss implications for refining both the instructional trajectory and the proposed developmental framework for rate reasoning.", "id": "Paper/62716", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62716"}, {"title": " The transversal achievement game on a square grid ", "webprogram_exclude": "0", "session_ids": ["Session/18243"], "source_sha256": "a4a1a3cb67d36990a64e31b88a74aad826bceb1b20a5f8a7b7b930a21094bf17", "withdrawn": "", "abstract": "In the transversal achievement game on the $n\\times n$ board, two players alternately claim cells, and the first to own a transversal---a set of $n$ cells of which no two share a row or column---wins. Ranđelović showed that the first player wins for every $n\\ge4$, while the game is a draw for $n=2,3$. We give an independent proof that the first player wins for $n\\ge4$ that additionally establishes a bound on the length of the win: the given strategy forces a win by ply $2n+3$, i.e.\\ on the first player's $(n+2)$-nd move, for every $n\\ge4$. The proof yields a strategy that is fully determined by a fixed rule on the current position and can thus be implemented directly. We isolate the use of the hypothesis $n\\ge4$ to two steps in the analysis, explaining why the argument fails at $n=3$. An exhaustive computational search implementing the strategy verifies it against every legal defense for $n=4,5,6$, confirming both the strategy's validity and that the $2n+3$ bound is attained in these cases.", "id": "Paper/62719", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62719"}, {"title": " The Grothendieck Hypothesis and Weak Orientals ", "webprogram_exclude": "0", "session_ids": ["Session/18287"], "source_sha256": "ec7d88f70101fb8df34aea1c5accb7ababf5777aacac3afb66ed3587966903b2", "withdrawn": "", "abstract": "The Grothendieck Hypothesis asserts that Grothendieck infinity groupoids provide a model for homotopy types, identifying higher groupoids with spaces up to homotopy. In this talk, I will discuss an approach to the hypothesis that I have recently been working on using the construction of weak orientals, which are intended to encode the higher-dimensional and coherent composition of embedded simplices in an infinity groupoid. I will explain how these simplicial structures lead to a nerve functor from infinity groupoids to simplicial sets and how contractibility properties of the resulting orientals forces certain results: the key one being that if the canonical semi-model structure on Grothendieck infinity groupoids exist, then it is a model structure.", "id": "Paper/62727", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62727"}, {"title": " Two Galois-Theoretic Measures of Algebraic Complexity ", "webprogram_exclude": "0", "session_ids": ["Session/18356"], "source_sha256": "7dfdf5023eea06e9c53576cb51eaa871f0658430531fd475d6f9cb2b0d11e71c", "withdrawn": "", "abstract": "Applied algebraic geometers often crudely measure the difficulty of solving polynomial systems with the notion of algebraic degree, which counts the number of complex-valued solutions to such a system. One can refine this notion through consideration of such systems' Galois groups. I will begin by recalling one such refinement dubbed \"Galois width\", an intrinsic measure of complexity for the Galois group that measures the exact complexity of solving in a simplified computational model. Although Galois width is a useful notion, it is only the beginning of a bigger story. I will discuss ongoing work on a different refinement which, although not intrinsic to the Galois group, is better-suited to the analysis of parametric numerical continuation methods. The talk will include discussion of applications from computer vision, enumerative geometry, and optimization that motivate and illustrate the theory.", "id": "Paper/62740", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62740"}, {"title": " Reconfiguration and Failed Zero Forcing Sets ", "webprogram_exclude": "0", "session_ids": ["Session/17921"], "source_sha256": "2c50d146870f8721349ce008857aabb668a4278893073f116628250e8ce4939e", "withdrawn": "", "abstract": "Zero forcing is a graph coloring process with connections to linear algebra, combinatorics, and graph reconfiguration. In this talk, we consider the token addition/removal (TAR) graphs associated with failed zero forcing sets of a graph, and ask how much information about the original graph is captured by this structure. We show that, for connected graphs, isomorphic failed zero forcing TAR reconfiguration graphs determine the collection of failed zero forcing sets up to relabeling. We also discuss connections to forts and related graph structures.", "id": "Paper/62742", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62742"}, {"title": " New isometric preduals of the trace class <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.279ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 981.4 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathcal {C}_1</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJCAL-43\" d=\"M201 -25Q167 -25 136 -14T75 23T29 94T12 202Q12 290 50 394T161 574Q227 642 303 673T433 704Q435 705 457 705Q533 701 533 640Q533 606 507 548T464 474Q431 444 396 444Q381 444 381 453Q381 459 388 473T407 513T428 563Q433 580 433 594Q433 636 381 636Q314 636 260 594T175 489T128 363T112 247Q112 157 153 101T273 44Q347 44 398 121Q413 144 437 157T481 171Q496 171 496 160Q496 150 476 123Q426 56 350 16T201 -25Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJCAL-43\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-31\" x=\"745\" y=\"-213\"></use>\n</g>\n</svg> and possible applications to Fixed Point Theory ", "webprogram_exclude": "0", "session_ids": ["Session/18363"], "source_sha256": "e7ca861c379df7364b82f0fc85a55be3dafb2878d2dba16bd633a84a8619416b", "withdrawn": "", "abstract": "We provide new examples of isometric preduals $X$ of the trace class $\\mathcal{C}_1 = \\mathcal{C}_1(\\mathcal{H})$ (i.e., $X^* \\cong \\mathcal{C}_1$), such that each $X$ is a non-commutative analogue of the space of convergent sequences $c$ in various ways. In particular, $X^* \\cong \\mathcal{C}_1$, $c$ is an isometric predual of the sequence space $\\ell^1$,\n   and $\\mathcal{C}_1$ is a non-commutative analogue of $\\ell^1$.\n\nAll of our isometric preduals $X$ of $\\mathcal{C}_1$ are such that $X^*\\cong \\mathcal{C}_1$ using the standard duality of $(\\mathcal{B}(\\mathcal{H}))^* \\cong \\mathcal{C}_1 \\bigoplus_1 (\\mathcal{K}(\\mathcal{H}))^{\\perp}$ restricted to $X$.\nAlso, we prove that our first example of a new trace class predual $X$ is not isometrically isomorphic to the space of compact operators $\\mathcal{K}(\\mathcal{H})$, the standard isometric predual of the trace class.\n\nMotivated by recent work of M. Japón, M. Malec, and Ł. Piasecki, we will explore possible  applications of these results to fixed point theory.", "id": "Paper/62754", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62754"}, {"title": " Biodiversity: Topological Data Analysis for Context-Enhanced Point Data ", "webprogram_exclude": "0", "session_ids": ["Session/18327"], "source_sha256": "e4329accd03fb94b1bbcc179a759ce6734c15d59527c59d5a4cd4df75ccfd84d", "withdrawn": "", "abstract": "We develop a framework to apply topological data analysis to point data which has been enhanced by contextual information; something has been observed somewhere.  We use biodiversity as a case study for doing this.\n\nOur method is to add information to a persistence barcode.  This allows us to consider a collection of modified barcodes, and in fact compare them.  We apply a collection of statistical tools to a collection of such barcodes representing biodiversity in 20 midsized cities in the United States, using data from the Global Biodiversity Information Facility.  The results are consistent with a number of expectations.", "id": "Paper/62759", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62759"}, {"title": " On Latency and Volatility ", "webprogram_exclude": "0", "session_ids": ["Session/18058"], "source_sha256": "d75508a2b15c01d0094ed317ab5fce719fba910971c50923d3068c3bf7aead68", "withdrawn": "", "abstract": "We present a simple model of the effects of latency on the properties of observed asset prices. In our model, latency is a delay between the observed asset price and its true, but latent fundamental price. Because of latency, the observed asset price shadows the true but latent asset price at some deformed time away. Deformation in a clock gives rise to fluctuations in volatility. We provide an asymptotic result that links latency to the volatility of volatility.", "id": "Paper/62765", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62765"}, {"title": " Subset Sums and Cyclic V Shaped Permutations ", "webprogram_exclude": "0", "session_ids": ["Session/18386"], "source_sha256": "e340119d3227f0d942674bca71a54339a1e1061c9ce3b0273f402730997e63f4", "withdrawn": "", "abstract": "A permutation of $[n]={1,\\dots,n}$ is cyclic V-shaped if it consists of a single cycle and its one-line notation decreases to $1$ and then increases. Let $CVP(n,k)$ denote the set of such permutations with $1$ in position $k$. Dougherty-Bliss and Elizalde proved that $|CVP(n,k)|$ equals the number of $(k-1)$-element subsets of ${1,\\ldots,n-1}$ whose elements sum to $1$ modulo $n$. We seek an explicit bijective explanation of this equality.\n\n\nWe construct bijections for $k=2,3,4$ using the cyclic distances between consecutive elements preceding $1$ in the cycle decomposition. We also reformulate the problem in terms of the left sets of cyclic V-shaped permutations, namely the elements appearing to the left of $1$. For $k=4,5$ we prove necessary and sufficient modular conditions on the left sets.\n\n\nFor larger $k$, recording these distances as a set can lose information about their multiplicities and order. We classify how unordered distance sets fail to uniquely determine the permutation. To retain the ordering, we show that an ordered cyclic-distance tuple uniquely determines the permutation for every fixed $n$ and $k$, providing a framework for extending the bijection.", "id": "Paper/62774", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62774"}, {"title": " Computations and applications of real monodromy action ", "webprogram_exclude": "0", "session_ids": ["Session/18042"], "source_sha256": "92af8bd1eb6bde9bc2a48a1a8e84f066ca48509b82772427d4f652219573c428", "withdrawn": "", "abstract": "The Galois/monodromy group describes how solutions of parameterized polynomial equations can interchange over the complex numbers.  The corresponding structure over the real numbers is the real monodromy structure which describes tiered behavior of how individual collections of real solutions can interchange.  This talk will describe a new algorithm for computing real monodromy structures and demonstrate the approach on several examples.  This is joint work with Maggie Regan, Emma Schmidt, and Charles Wampler.", "id": "Paper/62792", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62792"}, {"title": " Trimodal contrastive learning for joint conditional probability estimation in fluid dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/18239"], "source_sha256": "06d4bb07bc2b7061955608283fb3ceafc40157a9d8f8aac369725b5844422a0e", "withdrawn": "", "abstract": "Multimodal observations of physical systems can provide complementary information about a shared latent state, but it is not always clear whether adding modalities improves inference. We study this question in Lagrangian data assimilation, using contrastive learning to align Eulerian velocity fields with Lagrangian trajectories for recovery of the underlying flow. However, extensions to more than two modalities are often constructed as sums of pairwise losses, which model conditionals such as $p(u\\mid v)$ but need not capture higher-order conditionals such as $p(u\\mid v,z)$. This gap is especially significant in physical systems where individual modalities can carry marginal predictive power but offer strong information jointly. \n\nTo resolve this, we present a trimodal contrastive framework that directly quantifies joint alignment among three latent representations. We first validate our framework on Gaussian benchmarks with analytically tractable conditional distributions and mutual information, enabling direct comparison with exact higher-order distributions. We then apply the method to fluid dynamics and test whether passive tracer observations provide additional information about the Eulerian flow. Our results show that incorporating tracer data improves recovery relative to pairwise baselines, suggesting that higher-order multimodal objectives can exploit complementary physical observations not fully captured by pairwise alignment.", "id": "Paper/62805", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62805"}, {"title": " Multilayer Network Analysis Illuminates MicroRNA Determinants of Cancer ", "webprogram_exclude": "0", "session_ids": ["Session/17953"], "source_sha256": "b4d9eb43a9538c65d2faeaa262174e4e9104f8dbb4296f36770f5298f3bef525", "withdrawn": "", "abstract": "MicroRNA (miRNA) are key regulators of the transcriptome, driving many vital biological processes. Because of their significant role in cellular regulation, their dysregulation has been strongly linked to oncogenesis of cancer. As a result, miRNA-based cancer therapeutics have been of recent interest, but miRNA’s functional mechanisms and emergent properties are not understood well enough to develop safe, effective therapeutic options. Here, we present a graph theoretic approach to illuminate miRNA cooperation and function in cancer by creating various miRNA networks using sequence and expression data from 30 cancer datasets obtained from the Cancer Genome Atlas (TCGA). To determine the impetus behind miRNA cooperation, we compare graphs constructed using sequence similarity metrics to graphs constructed from expression and target data. These comparisons revealed that seed similarity has high edge overlap with the miRNA projections of bipartite miRNA-mRNA target networks (median edge overlap = 0.68) but does not guarantee simultaneous expression (median edge overlap = 0.20 with miRNA co-expression networks). Thus, we show that miRNA cooperate to provide biological robustness for cellular regulation. Using this result along with the TCGA expression data we construct 30 multilayer miRNA functional cancer networks. Using network clustering and pathway enrichment methods on our resulting networks, we identify cooperative miRNA functions. Comparisons of miRNA functions across our networks revealed widespread context-dependency, with miRNA functional associations never achieving a Jaccard distance less than 0.89 despite high similarity between expressed miRNA (maximum Jaccard distance of 0.52). Despite this context dependency, we observe that whenever collagen or PDGF signaling pathways were expressed they were associated with the miR-29-3p family. These functions link the miR-29-3p family to the epithelial-to-mesenchymal transition, making it a potentially robust, context-independent cancer therapeutic. Overall, we have developed a pipeline that reveals emergent miRNA biology, helping us better understand their complexity. We can use this pipeline to efficiently screens cooperative miRNA combinations to identify oncogenic drivers, potentially leading to novel therapeutics.", "id": "Paper/62812", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62812"}, {"title": " One Setup for Five Rules: The Fill-the-Cell Grid, and the Register It Runs On ", "webprogram_exclude": "0", "session_ids": ["Session/19341"], "source_sha256": "07984cd76f93fdc9ec6f60d4e261edb7280470e0949cabfca0d776478d5dcbac", "withdrawn": "", "abstract": "Students often stall before the mathematics starts — not on the concept, but on where to write the first piece down. I describe one visual routine, filled cell by cell, that gives five rules the same first move: the product, quotient and chain rules, single-application integration by parts, and u-substitution. Pieces into cells, one operation per cell, recombine the same way. An error shows up as an empty or wrong cell rather than a tangle in one line. The trigonometric integral shown is solved by u-substitution.\n\nFour devices in it are specific, not general.  The first is the routine itself: a student meets one habit, not five procedures. In the chain rule, an empty box keeps the operation apart from its content. In the quotient rule, a start cell fixes the order of subtraction. In substitution, a circle is drawn tightly around the coefficient, so the only thing marked is the thing that travels. The reciprocal is written every time, even when it cancels. A student who skips it has decided that it cancels, and that decision is the thing they cannot yet make reliably. \n\nThe mathematics is standard, and the visual is not mine. The tabular lineage for integration by parts runs Folley (1947), Murty (1980), Horowitz (1990) and Rock (2016); the cross for the derivative rules is common practice with no single source. Putting them under one setup is the part I am claiming.\n\nWhat I want to ask this session is what a setup like this needs before it will work in someone else's room. Mine ran in a bilingual classroom: ishtiqaq and takamul for derivative and integral, dharb when we multiply across the cross, al-bast and al-maqam in the quotient grid. I did not bring these in. My students had them and I did not, so I asked, in the first week. The asking is what another instructor can copy; the words are not. So how much of a tool like this is method, and how much is register?\n\nNo outcome data is reported. Materials are open, CC-BY.", "id": "Paper/62847", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62847"}, {"title": " Why Does Modern AI Work and Where Does It Fail? A Mathematical Perspective ", "webprogram_exclude": "0", "session_ids": ["Session/18473"], "source_sha256": "9c5656e2f42bfc7ca327ba96f7b87173f5e07a9b39c6fb7c4c625f4fe1661406", "withdrawn": "", "abstract": "Artificial intelligence has achieved remarkable success across science and society, yet our mathematical understanding of why modern AI systems work—and when they fail—remains surprisingly incomplete. \n\nIn this lecture, we survey recent advances toward a mathematical understanding of deep learning, addressing performance guarantees and reliability. We then turn to fundamental limitations, particularly concerning computability, and discuss their surprising connections to alternative computing paradigms such as neuromorphic computing.", "id": "Paper/62867", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62867"}, {"title": " Multiplicity of Solutions for a Nonlinear Diffusion Model ", "webprogram_exclude": "0", "session_ids": ["Session/18378"], "source_sha256": "51bfc2a36cdb8888be72715afdb910799b8dae891205951e01334f9950f1beb0", "withdrawn": "", "abstract": "We consider a nonlinear equation $-\\mathcal{L} u(x) = f(x, u(x))$ with a super-quadratic nonlinearity, $f$, and a nonlocal operator, $\\mathcal{L}$, generated by a special class of radially symmetric $L^1$ convolution kernels with finite second moments, that includes sign-changing kernels. We prove the existence of nontrivial solutions using the classical Mountain Pass Theorem, a central result in minimax theory that equates solutions of our equation to critical points of a corresponding energy functional. This existence result holds with both homogeneous nonlocal Dirichlet and nonlocal Neumann boundary conditions. We supplement these theoretical results with numerical simulations for various nonlinearities with odd maximal degree in the unknown $u$. The numerical scheme exploits the resulting energy landscape which allows one to adapt a gradient descent algorithm.", "id": "Paper/62875", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62875"}, {"title": " The Cop Number of Token Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "907406e636c1ab9582e70be871f19639fd8dd99c739f684ddcda8a002804ce91", "withdrawn": "", "abstract": "Cops and Robbers is a two player vertex-pursuit game played on graphs. In the game, several cops attempt to capture a single robber. The \\textit{cop number} of a graph $G$ is defined to be the minimum number of cops needed to guarantee capture of the robber playing on $G$. Given a graph $G$ and positive integer $k$, we can construct the \\textit{$k$-token graph of $G$}. The vertices of the token graph are all the size-$k$ subsets of $V(G)$, and two vertices are adjacent if their symmetric difference is an edge of $G$. We investigate the cop number of token graphs of various simple graphs, including caterpillar graphs and complete bipartite graphs.", "id": "Paper/62878", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62878"}, {"title": " Upper chromatic number of generalized quadrangles ", "webprogram_exclude": "0", "session_ids": ["Session/18193"], "source_sha256": "84bc83aef0b60ae2eb869758e02d01566e30ed3adc7c7526b1cf1a3116b7351a", "withdrawn": "", "abstract": "In geometry, a generalized quadrangle is an incidence structure whose main feature is the lack of any triangles yet containing many quadrangles.  Such a generalized quadrangle can be regarded as a hypergraph in which points and lines are identified with vertices and hyperedges, respectively.  A vertex coloring is said to be rainbow on a hyperedge if all vertices contained in that hyperedge are assigned distinct colors;  if no edge is rainbow the coloring is called rainbow-free.  For a given hypergraph $H$, the maximum integer $k$ for which there exists a rainbow-free $k$-coloring is called the upper chromatic number of $H$, denoted $\\overline{\\chi}(H)$.  In this work we establish upper and lower bounds for the upper chromatic number of certain generalized quadrangles.  Moreover, we show that $\\overline{\\chi}(\\mathcal{Q}(4,2))=6$ and $\\overline{\\chi}(\\mathcal{Q}(4,3))=21$ .", "id": "Paper/62886", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62886"}, {"title": " Embedding into duo rings ", "webprogram_exclude": "0", "session_ids": ["Session/17949"], "source_sha256": "27a648599221dbba830f54008b0bb19238316cbacf9d68c89681474aa559e332", "withdrawn": "", "abstract": "We construct a domain that does not embed in a duo ring. (A ring is duo when\nits left and right ideals are all two-sided.) On the other hand, we show that a large class\nof rings can be embedded in duo rings. This leads to the construction of a duo ring whose\npolynomial ring is not semicommutative (definition recalled in the talk).", "id": "Paper/62888", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62888"}, {"title": " A Stochastic Reaction-Advection Model for Axonal Prion Propagation ", "webprogram_exclude": "0", "session_ids": ["Session/18239"], "source_sha256": "fd607a34d12d5412b5680f95c6f76fdbddd638477193772c1f4aa31fa3650a69", "withdrawn": "", "abstract": "Prion diseases are characterized by the misfolding of healthy proteins into toxic forms, which spread throughout the brain and cause other healthy proteins to misfold. Similar processes are also common to several neurodegenerative diseases, such as Alzheimer's Disease and Parkinson's Disease. The interaction between axonal transport, local biochemical dynamics, and network connectivity is not fully understood. \n\nAs a proof-of-concept, we formulate a stochastic network reaction--advection toy model in which each neural region is represented by a one-dimensional axonal domain, \\(x\\in[0,L]\\). Over each region $i=1,\\ldots,N$, the toy model quantifies the concentration of toxic protein $u_i$ being advected anterogradely with velocity $v>0$ and extracellular toxic protein concentration $w_i$, where $u_i$ grows logistically and $w_i$ and $u_i$ continuously exchange across the cell membrane. To represent system noise, we include a multiplicative stochasticity component using a Wiener sheet. Inter-regional propagation is modeled through a directed weight matrix, where the toxic protein leaving region $i$ is partitioned and advected into other regions $j \\neq i$. The resulting system of stochastic partial differential equations is solved using a finite volume method with upwinding and Strang splitting. Simulations are performed on directed networks with $N=2$ and $N=3$ regions.\n\nThe resulting graphs show a wave-like diffusion of the toxic protein concentration from one brain region/neuron through the axon to other brain regions/neurons.\n\nOur simulations suggest that as a prion disease takes effect in the brain, the buildup of toxic proteins may take place over several cycles of anterograde transport through the connectome.", "id": "Paper/62889", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62889"}, {"title": " The Domination Number of the <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.211ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 521.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">k</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6B\" d=\"M121 647Q121 657 125 670T137 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291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-4B\" x=\"0\" y=\"0\"></use>\n<g transform=\"translate(849,-150)\">\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-6E\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-2C\" x=\"600\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-6D\" x=\"879\" y=\"0\"></use>\n</g>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "f745c8b0cc861a05f625127aebff2993e66ac276be4cafaf37ec892cda4ada20", "withdrawn": "", "abstract": "Given a graph $G$ and positive integer $k$, we can construct the \\textit{$k$-token graph of $G$, $F_k(G)}. The vertices of the token graph are all the size-$k$ subsets of $V(G)$. Two token graph vertices are adjacent if their symmetric difference is an edge of $G$. We present results fully classifying the domination number of $2$-token graphs of complete bipartite graphs, $F_2(K_{n,m})$. We bound the domination number of general $k$-token graphs of complete bipartite graphs by using maximal degree and independence number.", "id": "Paper/62893", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62893"}, {"title": " Machine Learning for Mathematical Graph Search and Discovery ", "webprogram_exclude": "0", "session_ids": ["Session/17911"], "source_sha256": "d348398e5dd0d6b8a82b9b693a5ffe7ed755928dde4889d5d437f0ff175404ef", "withdrawn": "", "abstract": "Computing certain graph invariants across large collections of graphs can be prohibitively expensive, limiting mathematical discovery and exploration of graph spaces. We use machine learning methods to investigate whether readily computed graph properties can predict more expensive properties and ultimately support tools for mathematical graph search. Specifically, for a graph $G$, we predict whether the zero forcing number $Z(G)$ differs from the more computationally expensive enhanced zero forcing number $\\widehat{Z}(G)$.\n\nAs a preliminary study, we first investigate using graphs of order 10 and find that relatively inexpensive graph invariants and structural properties can effectively distinguish graphs for which $Z(G) \\neq \\widehat{Z}(G)$. We also investigate which graph properties are most informative for this prediction. These results are a step toward an information retrieval system in which mathematicians could search large graph collections for candidate graphs based on desired properties or a graph supplied as an example, narrowing the space in which more expensive exact computations are needed.", "id": "Paper/62906", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62906"}, {"title": " Quasi-minimization: The Golden Key for Convergence of Solutions to Parameterized Optimal Control Problems ", "webprogram_exclude": "0", "session_ids": ["Session/18443"], "source_sha256": "4720cdd3aa9756ca221cf0ef772995ef3ebbc1323dc4ac641b14e15f876e7c84", "withdrawn": "", "abstract": "Quasi-minimization is an effective mechanism for studying non-convex energy functionals arising in nonlinear elasticity theory and materials science, including when the energy itself does not have a global minimizer. In this talk we will discuss optimal control problems where the constraint is the quasi-minimization of an energy functional depending on a nonlocal gradient arising from peridynamics, a contemporary integral equation-based model for crack propagation and fracture. The main challenges in the analysis arise from the lack of uniqueness of minimizers for the constraining energy. With this obstacle in mind, we discuss existence of solutions to the optimal control problem, and convergence results for solutions to those of a corresponding “local” optimal control problem with a constraining energy depending on the classical gradient.", "id": "Paper/62907", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62907"}, {"title": " Skeletal Homology- Singular Homology at Scale ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "87efa8a81ee87b4db17aef2026c705611ff9647f2c54a8f081f1a53dd7e8478a", "withdrawn": "", "abstract": "Skeletal homology is the homology of the chain complex of skeletal simplices, which are functions from the 0-skeleton of the standard simplex whose image diameter is less than a given scale. We show that, for arbitrary metric spaces, skeletal homology is naturally isomorphic to the simplicial homology of the VR complex at the same scale. We introduce the ultradiamond metric on skeletal chains, for which the boundary operator is 1-Lipschitz. This allows us to establish a basic stability principle showing that sufficiently close cycles represent the same homology class after a controlled change of scale. From this result, we obtain several stability theorems for skeletal homology. Finally, by adapting methods from classical singular homology, we prove strong generalizations of Hausmann’s theorem and Latschev’s theorem. These results extend topological recovery beyond the traditional Riemannian-manifold setting and provide new conditions under which homology at scale recovers the topology of the underlying metric space.", "id": "Paper/62920", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62920"}, {"title": " Skeletal Homology: Singular Homology at Scale ", "webprogram_exclude": "0", "session_ids": ["Session/18114"], "source_sha256": "97820b378100b9c7255a51e5bef5e049c8461d17aec73fc779339db16296c342", "withdrawn": "", "abstract": "Skeletal homology provides a direct way to study the topology of a metric space at a chosen scale by using simplices whose images have diameter smaller than that scale. We show that, for arbitrary metric spaces, skeletal homology is naturally isomorphic to the simplicial homology of the corresponding Vietoris–Rips complex. We introduce the ultradiamond metric on skeletal chains, for which the boundary operator is one-Lipschitz. This allows us to establish a basic stability principle showing that sufficiently close cycles represent the same homology class after a controlled change of scale. From this result, we obtain several stability theorems for skeletal and Vietoris–Rips homology. Finally, by adapting methods from classical singular homology, we prove strong generalizations of Hausmann’s theorem and Latschev’s theorem. These results extend topological recovery beyond the traditional Riemannian-manifold setting and provide new conditions under which homology at scale recovers the topology of the underlying metric space.", "id": "Paper/62922", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62922"}, {"title": " Strategic Loss Reporting under Bonus–Malus Systems ", "webprogram_exclude": "0", "session_ids": ["Session/18124"], "source_sha256": "40e6e4e3192f1e21c4164f65a92abacab46b11b53c214868198dfa8e47ee9ff4", "withdrawn": "", "abstract": "Bonus–malus systems (BMS) are widely used in insurance to adjust premiums based on individual claim history. While such systems are intended to incentivize safer behavior, they also create incentives for policyholders to underreport small losses in order to avoid future premium increases. We study a game-theoretic insurance model in which a monopoly insurer designs a BMS anticipating the reporting and coverage choices of a heterogeneous population of policyholders. \n\nGiven a finite horizon, an arbitrary number of rate classes, and a deductible contract, we characterize each policyholder's optimal loss-reporting barrier under exponential utility. The optimal barrier decomposes into three components: the deductible, the difference in future premiums capturing class transitions, and a risk adjustment term given by the difference in certainty-equivalent costs. We establish the existence of an optimal deductible for each initial rate class. Anticipating these responses, the insurer chooses BMS loadings to maximize expected profit, yielding an equilibrium between the insurer and the population of policyholders. The analysis provides a tractable framework for understanding strategic behavior and equilibrium pricing under experience rating mechanisms.", "id": "Paper/62924", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62924"}, {"title": " Diophantine avoidance, primitive elements, and normal basis theorem ", "webprogram_exclude": "0", "session_ids": ["Session/17913"], "source_sha256": "e0afaf8dd8bba9486e2320a8dd0692e6431500e84f8faa9c3fd0a81c65788fbe", "withdrawn": "", "abstract": "Diophantine avoidance has been studied by several authors in recent years. This refers to effective results on existence of points of bounded size in a given algebraic set avoiding some specified subsets. The famous primitive element theorem states that every number field $K$ is of the form $\\mathbb{Q}(\\alpha)$ for some element $\\alpha$ in $K$. From the proof of this theorem, it is clear that not only there are infinitely many such primitive elements in $K$, but in fact most elements in $K$ are primitive. One natural question to ask is about finding a primitive element of small “size”, where we use a height function to measure size. We discuss the conjecture of Ruppert and known results in this direction, as well as our recent work on this problem. In addition, we provide the standard and effective version of normal basis theorem, obtaining an explicit bound in terms of the degree and discriminant of $K$, where $K/\\mathbb{Q}$ is a Galois extension. At the end, we discuss a particularly good bound in the case of prime degree. This is joint work with Lenny Fukshansky at Claremont McKenna College.", "id": "Paper/62929", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62929"}, {"title": " Automated Quantification of Stereotypical Motor Movements in Autism using Persistent Homology ", "webprogram_exclude": "0", "session_ids": ["Session/18007"], "source_sha256": "b67428b85bf8006484ec86b6d2e0ff5fe11c0e71204434fe2569a8c143d0321f", "withdrawn": "", "abstract": "Stereotypical motor movements (SMM) are a core diagnostic feature of autism and remain difficult to quantify across individuals and developmental stages in an efficient and valid way. The current paper presents a novel pipeline that leverages Topological Data Analysis to quantify and characterize recurrent movement patterns. Specifically, we use persistent homology to construct low-dimensional, interpretable feature vectors that capture geometric properties associated with SMM in autistic people by extracting periodic structure from time series derived from pose estimation landmarks in video data and accelerometer signals from wearable sensors. We demonstrate that these features, combined with simple classifiers, enable accurate automated quantification of SMM in autistic people. Visualization of the learned feature space reveals that extracted features generalize across individuals and are not dominated by person-specific SMM. Our results highlight the potential of using mathematically principled features to support more scalable, interpretable, and person-agnostic characterization of SMM in autistic people in naturalistic settings.", "id": "Paper/62931", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62931"}, {"title": " CaMPers: Chiral Multiparameter Persistence for Embryonic Flow Fields ", "webprogram_exclude": "0", "session_ids": ["Session/19358"], "source_sha256": "6bb43236ba5c4c36cf62a7014dbe26abf2da3ab2fba8c151f2d5362f089c356b", "withdrawn": "", "abstract": "Chirality in vector fields is commonly characterized by local differential quantities such as vorticity, while persistent homology describes multiscale topology through metric relationships. Neither perspective determines how same-handed vector interactions organize across spatial scales. We introduce \\emph{Chiral Multiparameter Persistence} (CaMPers), a framework for vector fields sampled on Riemannian manifolds. For each parameter tuple $\\mathbf{p}=(d,\\tau,\\phi,r)$, CaMPers constructs positive and negative directed flag complexes whose edges encode spatial proximity, forward alignment, angular consistency, and signed rotation. The resulting multiparameter persistence modules track how clockwise and counterclockwise interaction networks assemble into higher-order topological structures as interaction distance increases. Integrating their Euler characteristics over the non-distance parameters produces handed Euler characteristic curves and a normalized chiral Euler dominance curve. Unlike vorticity, CaMPers measures the organization of rotational interactions rather than only their local magnitude or net bias.\n\nWe apply CaMPers to two embryonic systems that express chirality through different physical observables. In time-resolved cortical actomyosin flow fields from \\textit{C.~elegans} embryos, the chiral Euler curves recover the expected ordering of wild-type, achiral, and reversed-handedness conditions. Moreover, time points with nearly identical mean curl can exhibit visibly different flow organizations and strongly separated CaMPers curves. As a complementary proof of principle, we analyze depth-resolved nematic nuclear-director fields surrounding Hensen's node in quail tissue. The representative post-twist field exhibits a stronger depth-dependent chiral organization that persists across a broad range of interaction scales, whereas the corresponding pre-twist organization weakens at larger scales. Together, these applications show that net rotation and multiscale chiral organization are complementary observables across dynamic polar flows and static nematic tissues.", "id": "Paper/62932", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62932"}, {"title": " Scaling laws in the site-frequency spectrum of far-from-equilibrium populations ", "webprogram_exclude": "0", "session_ids": ["Session/18350"], "source_sha256": "ce9b1d391faf9cd6acfdc30bdef117e8a9eefce2e7545644de790da627c43724", "withdrawn": "", "abstract": "The site-frequency spectrum (SFS), consisting of the counts of mutant alleles in a sample of genomes, is one of the principal summaries used to reconstruct population history from genomic data. While many computational approaches exist to approximate the SFS under general demographic histories, the interplay between large samples, recent growth, and population size has been poorly understood theoretically. With Yuval Simons, we develop tractable and quantitative approximations for the SFS across a wide range of demographic histories. Under large sample sizes, we describe how the abundance of rare variants, mutant alleles shared by a small fraction of the population, are governed principally by the present-day rate of population growth and shape of recent growth. We utilize this framework to study the inverse problem for demographic inference: how much demographic information can be recoevered from noisy SFS data collected across many genomic regions? This provides a route from asymptotic coalescent theory to quantitative questions of identifiability, statistical resolution, and experimental design. Together, these results clarify which features of population history are visible in the SFS, at which frequency scales they appear, and how reliably they can be inferred from genomic data.", "id": "Paper/62934", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62934"}, {"title": " Classification of rational triple points in positive characteristic, index <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.162ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 500.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">1</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-31\" x=\"0\" y=\"0\"></use>\n</g>\n</svg> covers, III ", "webprogram_exclude": "0", "session_ids": ["Session/19356"], "source_sha256": "c83a69de2de8d093f625300cde0838b973d0b1e2821790561f76a42e7204160e", "withdrawn": "", "abstract": "I am working on classifying rational triple points of dimension two in positive characteristic. \nIn characteristic $0$, any rational triple point $\\mathrm{Spec}R$ is known to be taut, i.e., its weighted dual graph uniquely determines the isomorphism class of $\\mathrm{Spec}R$. So the classification given by Tjurina in $\\mathbf C$ is clearly marked by such dual graphs \nwhose classification goes back to Artin in 1966.  \nI have recently settled the classification of taut rational triple points in $p>0$,  so I would like to report the current state of the next: classifying non-taut rational triple points, which can only exist in $p=5, 3, 2$. \nAmong such non-taut rational triple points, the three classes which do not belong to the type A, B, C, D, F, H in Tjurina's notation exhibit very peculiar properties in $p=2$.   \nFor example, the tangent map $H^1(X, S_X)\\to \\mathrm{D}_R(k[\\epsilon]/(\\epsilon^2))$ can fail to be injective, where $\\pi:X\\to \\mathrm{Spec}R$ is the minimal resolution of such a rational triple point, $S_X$ is a subsheaf of $\\Theta_X$ generated by logarithmic derivations, $\\mathrm{D}_R$ is the deformation functor of $\\mathrm{Spec}R$. By cohomological arguments, it is also suspected that there are infinitely many isomorphism classes of such rational triple points in $p=2$ for a fixed weighted dual graph.  \nI would like to settle this last question, and give conceptual explanations for these phenomena.", "id": "Paper/62970", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62970"}, {"title": " Rigidity and convex geometry of exponential mixtures ", "webprogram_exclude": "0", "session_ids": ["Session/19338"], "source_sha256": "339323a68bb60a51632262496a9c8d558ebd8a7447fd190951754ea7f454a64b", "withdrawn": "", "abstract": "The laws of k-tuples that extend to infinite exchangeable sequences form a convex set, whose points admit barycentric representations through de Finetti directing measures. We study the convex subsets obtained by exponential mixtures. Under natural rigidity and regularity assumptions, such mixtures form faces of the convex set for every k >= 3, and every point of the face has a unique directing law. Moreover, such a face is exposed (i.e. the exact infimum set of a non-negative affine functional) only when k>= 4. These are sharp results that connect de Finetti theory and non-parametrix mixture identifiability with the convex geometry of infinite-dimensional spaces.", "id": "Paper/62979", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62979"}, {"title": " Metastable wells in exponential random graph models ", "webprogram_exclude": "0", "session_ids": ["Session/18312"], "source_sha256": "b03a547e17be4cefcf5cad2ade18d22a4f34340a8c868c961f10d6d0473576e7", "withdrawn": "", "abstract": "Exponential random graph models (ERGMs) are exponential tilts of Erdos-Renyi models where higher-order interactions promote the presence of small subgraphs like triangles. These models exhibit metastable behavior at low temperatures (strong interaction), and decompose as mixtures of phase measures or metastable wells. We present a variety of novel results for these metastable wells, including quantitative CLTs and sharp bounds on the Wasserstein distance between an ERGM in a metastable well and a corresponding Erdos-Renyi model. A common thread in these results is the careful analysis of relevant quantities under a natural Markov chain sampling algorithm.", "id": "Paper/62998", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/62998"}, {"title": " Modeling the Impact of Dynamic Insecticide Resistance on Malaria Transmission and Control ", "webprogram_exclude": "0", "session_ids": ["Session/18327"], "source_sha256": "6b44583557e7e411fc1584237067ea2f7d7fcb22822f573e23a9b569f85e5bd0", "withdrawn": "", "abstract": "Malaria remains a major public health challenge, with the effectiveness of vector-control interventions increasingly threatened by the emergence and spread of insecticide resistance in mosquito populations. In this study, we formulate and analyze a mathematical model of malaria transmission that incorporates insecticide-treated nets (ITNs), indoor residual spraying (IRS), vaccination, and dynamic evolution of insecticide resistance, whose evolution is driven by intervention-induced selection pressure and the fitness cost associated with resistance. We establish the positivity and boundedness of solutions and derive the resistance-adjusted reproduction number. The local stability of the disease-free equilibrium is investigated and conditions for the existence of  endemic equilibria are established. To identify intervention strategies that  reduce malaria burden and limit the emergence of insecticide resistance, we formulate and analyze an optimal control problem incorporating ITN use, IRS application, treatment, and vaccination. Numerical simulations  demonstrate that intensive insecticide-based interventions can substantially reduce malaria transmission while simultaneously generating selection pressure that favors resistant mosquitoes, potentially compromising long-term control. Our results highlight the importance of explicitly accounting for resistance evolution when designing integrated malaria-control strategies.", "id": "Paper/63006", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63006"}, {"title": " Variational Implicit Solvation model with Size-Modified Poisson Boltzmann and Diffuse interface ", "webprogram_exclude": "0", "session_ids": ["Session/19344"], "source_sha256": "0e71cf55e427e79db7b29a937f4f7390c0a2ba95f44c19044c42f9fd56f325dc", "withdrawn": "", "abstract": "Diffuse-interface variational implicit solvation models (VISMs) have recently been developed for the efficient computation of Ensemble Average Solvation Energy (EASE), eliminating the need to average over thousands of molecular snapshots generated by molecular dynamics simulations. However, the resulting coupled nonlinear PDE system is computationally challenging to solve for realistic biomolecular systems. Moreover, the classical Poisson--Boltzmann (PB) model neglects finite ion-size effects and may predict unphysically high ion concentrations near molecular surfaces. In this work, we develop and implement a novel size-modified VISM incorporating the steric ionic effects through the size-modified PB equation (SMPB). To the best of our knowledge, this is the first study to numerically couple the fully nonlinear SMPB equation with the $p$-Laplacian for the computation of EASE. The resulting coupled nonlinear system is solved with an Alternating Direction Implicit (ADI) method accelerated by a relaxation strategy that stabilizes the coupling between the electrostatic potential and the evolving interface. The proposed model and numerical algorithms are validated through convergence studies together with benchmark calculations of solvation free energies and electrostatic binding affinities for a variety of molecular systems. Finally, we show that finite ion-size effects and the short-range repulsive branch of the Lennard--Jones potential are both required for a Stern layer to emerge within the VISM framework; a nonzero steric parameter is necessary.", "id": "Paper/63017", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63017"}, {"title": " Evaluating the Impact of Network Sparsification on Graph-Theoretic Analysis of Weighted Brain Networks ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "ce4df1c60536dd55668330602684bebe709e333e1c6e446c76c8112f49756996", "withdrawn": "", "abstract": "Graph-theoretic methods are widely used to characterize weighted networks, but the resulting network measures depend on how the weighted connections are sparsified before analysis. Different sparsification strategies can change network topology and influence the interpretation of graph-theoretic measures, making it difficult to assess the robustness and reproducibility of results. This work investigates how the choice of sparsification method affects the results of graph-theoretic analysis of weighted connectivity networks from functional magnetic resonance imaging (fMRI). \nWeighted brain networks are constructed from Pearson correlation matrices, which are computed from resting-state fMRI data from individuals with Alzheimer’s disease and cognitively normal controls. Three sparsification methods are used: single absolute thresholding, multi-absolute thresholding, and proportional thresholding. Global and regional graph measures, including clustering coefficient, participation coefficient, betweeness centrality, local and global efficiency, modularity, and small-worldness, are compared across sparsification methods. \nResults show that many graph-theoretic measures are sensitive to the choice of sparsification method. Absolute thresholding introduces variability due to changes in network density, with observed group differences varying across thresholds, which highlights the importance of evaluating network measures over a range of thresholds. Proportional thresholding produces a more consistent comparison with fixed densities.\nThis work demonstrates that sparsification is an important component of graph construction and should be considered when interpreting graph-theoretic analyses of weighted networks. Ongoing work investigates topological data analysis as a threshold-independent approach for identifying network structures that persist across multiple connectivity scales.", "id": "Paper/63027", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63027"}, {"title": " J Ernest Wilkins Jr.: From Chicago to New Mathematical Frontiers ", "webprogram_exclude": "0", "session_ids": ["Session/18164"], "source_sha256": "fd57b28af4dc0d672b67d66aa3762507d1ed6c90143eab6d9083e8d0deaa8c47", "withdrawn": "", "abstract": "What does it look like when mathematical curiosity meets a changing world? This lecture explores the journey of J. Ernest Wilkins Jr., a young mathematician from Chicago whose work helped address major scientific and engineering challenges of the twentieth century. Through examples from Wilkins’ contributions to nuclear science, engineering, and applied mathematics, this talk highlights how mathematical ideas can cross disciplines, shape scientific discovery, and drive innovation. The lecture will also connect Wilkins’ work to today’s grand challenges in areas such as AI, energy, and emerging technologies, illustrating the continuing role of mathematics in shaping the future.", "id": "Paper/63036", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63036"}, {"title": " Creativity in Problem-Solving: The Case of Mathematical Agency ", "webprogram_exclude": "0", "session_ids": ["Session/18088"], "source_sha256": "14a447a161bb51b924de1820ca132852423d7cd6607537d3ce0ee21f1ed9cedc", "withdrawn": "", "abstract": "This study seeks to develop our understanding of the relationships between mathematical agency and mathematical resilience in problem-solving contexts, as well as to examine their significance in affecting retention in STEM majors. Student success in undergraduate level mathematics courses is heavily influenced by a number of psychological factors, including resilience to challenge and feelings of ownership of problem-solving strategies. Performance evaluation is typically conducted via problem-solving tasks, on which success has been shown to relate to strategy fluency, strategy flexibility, content knowledge, and the ability to justify one’s solutions to a given problem. Previous research has explored mathematical agency and its relationship with metacognition and persistence across mathematics courses, but no research to date has explored the relationship between agency, flexibility in problem solving, and resilience in problem-solving within a single mathematics course.", "id": "Paper/63046", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63046"}, {"title": "  A Double-Inertial Algorithm for Variational Inequalities and Fixed Point Problems with Applications to Image Restoration  ", "webprogram_exclude": "0", "session_ids": ["Session/18364"], "source_sha256": "fc5f941a84a2e2800d905ce2fc28b34e7527a32bee4f7cb6bc25562069471e25", "withdrawn": "", "abstract": "This work introduces a double‑inertial algorithm with adaptive step sizes to approximate a common solution of split variational inequality problems and fixed‑point problems under a quasi‑monotonicity framework in real Hilbert spaces. We establish strong convergence of the proposed method under mild and standard assumptions. Numerical experiments demonstrate that our algorithm outperforms several existing methods in the literature, including additional comparisons on image restoration tasks, highlighting its efficiency and practical applicability.", "id": "Paper/63052", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63052"}, {"title": " Persistent Homology of Some Function Spaces ", "webprogram_exclude": "0", "session_ids": ["Session/18330"], "source_sha256": "4c77d06d8aaacc61394f5c08443b46210a1133ab56d74fe00c408625b81b91f5", "withdrawn": "", "abstract": "Persistent homology is a standard tool in topological data analysis, but it can be used to measure the costs of some resource during deformations.  For instance, long finite bars of potential energy are a sign of rugged geometry and can indicate stable structures that in the presence of appropriate catalysts can be converted into one another.  In recent years, we have learnt a lot about the persistent homology of function spaces, with the filtering function being log(L), the logarithm of the Lipschitz constant.    I will say a few words about possible motivations for such problems, but will mainly focus on the mathematical ideas - some trivial and maybe useful observations, and some recent results that were considerably more elusive.  (The math will be based on joint work with Jonathan Block and Fedor Manin.)", "id": "Paper/63063", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63063"}, {"title": " Goodness-of-fit test for the Dirichlet distribution ", "webprogram_exclude": "0", "session_ids": ["Session/19364"], "source_sha256": "9791c09970f1164f6e3967003282a2af3713365fee46c80fd1c1b045b3494263", "withdrawn": "", "abstract": "The Dirichlet distribution is a widely used multivariate model for compositional data, such as microbiome relative abundance profiles. However, a rigorous goodness-of-fit (GoF) framework for assessing whether observed data follow a Dirichlet distribution remains limited. Existing GoF methods can be computationally intensive, and their performance for dimensions greater than two ($d>2$) has not been adequately studied. In particular, although Empirical Distribution Function (EDF)-based tests, including the Kolmogorov-Smirnov (KS), Anderson-Darling (AD), and Cramér-von Mises (CvM) tests, have been extended to multivariate settings, their performance for Dirichlet data remains undocumented. Three major challenges arise when applying EDF-based tests to the Dirichlet distribution: the lack of a closed-form distribution function for $d\\geq3$, the absence of a natural ordering for multivariate observations, and the computational difficulty of evaluating differences and integrals between theoretical and empirical distribution functions in higher dimensions. To address the first challenge, we propose a two-step transformation based on Beta decomposition and the Rosenblatt transformation, which maps $(d-1)$-dimensional simplex data to the $(d-1)$-dimensional unit hypercube. Although this transformation enables multivariate EDF-based testing, computing the resulting KS, AD, and CvM statistics can become computationally demanding as dimensionality increases. While an analytical solution exists for the continuous multivariate CvM integral, we propose a Parametric Bootstrap Chi-square (PB-CS) test as a computationally efficient alternative. The frequency-based approach avoids the multivariate ranking problem and provides a straightforward implementation. We extend Doane’s rule to determine the number of bins and employ a quasirandom binning strategy based on Sobol sequences and Voronoi partitioning. Through extensive simulation studies, we evaluate Average Size (AvS) and Average Power (AvP) for the multivariate CvM and PB-CS tests. Results show that CvM performs well in lower dimensions, whereas PB-CS provides superior or comparable performance as dimensionality increases ($d>3$).", "id": "Paper/63068", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63068"}, {"title": " Examining Reflective Practices Among Mathematics Graduate Student Instructors Through Journaling and Community Discussions ", "webprogram_exclude": "0", "session_ids": ["Session/18236"], "source_sha256": "a31a3c282a9dc4a67742d84182f2830c34a8f73950f61ff472a1902c856308c1", "withdrawn": "", "abstract": "Mathematics graduate student (MGs) instructors play a vital role in undergraduate instruction, yet limited pedagogical preparation often leads them to default to traditional, survival-driven teaching methods. This talk presents a reflection-centered professional development model designed for MGS instructors teaching undergraduate courses. Grounded in Schön’s reflective practice and Mason’s Discipline of Noticing, the PD integrates weekly \"brief-but-vivid\" journaling with peer-faculty community discussions. We highlight how this low-stakes structure heightens classroom noticing, disrupts routine habits, and enables instructors to translate critical reflections into student-centered instructional changes.", "id": "Paper/63106", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63106"}, {"title": " Equivalence Classes of Generalized Fibonacci Sequences Modulo <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.259ex\" height=\"2.009ex\" style=\"vertical-align: -0.671ex; margin-left: -0.089ex;\" viewBox=\"-38.5 -576.1 542 865.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">p</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-70\" d=\"M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-70\" x=\"0\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18239"], "source_sha256": "193889dd67f16e1ebe6ec76557ae3f9827522880113c3e3ac2eaf7dc7470ef8c", "withdrawn": "", "abstract": "There are unknown properties relating to the periodicity of the Fibonacci sequence modulo a prime $p$. Generalized Fibonacci sequences satisfy the Fibonacci recurrence relation and begin with any two integers. This project aims to understand the Fibonacci sequence modulo $p$ by investigating generalized Fibonacci sequences modulo $p$. \n\nWe introduce an equivalence relation on generalized Fibonacci sequences modulo $p$ based on shifts and scalar multiplication. For $p \\equiv \\pm 2 \\pmod 5$, we use number-theoretic and group-theoretic techniques to prove that the cardinalities of all non-trivial equivalence classes of generalized Fibonacci sequences modulo $p$ are the same. We also determine a formula relating the number of equivalence classes of generalized Fibonacci sequences modulo $p$ to the period of the Fibonacci sequence modulo $p$. These results may give us further conditions on the period of the Fibonacci sequence modulo $p$.\n\n\\textit{This project was conducted under the mentorship of Professor Ira Gessel of Brandeis University and the supervision of Eden Sylvester of UC Santa Barbara.}", "id": "Paper/63111", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63111"}, {"title": " Self-similar solutions of 2D incompressible Euler equations ", "webprogram_exclude": "0", "session_ids": ["Session/17822"], "source_sha256": "6f1a1aad27d50c70dfc5cc9e79b78dca88eedb4c52a16f8ef5a6310a6e1af45d", "withdrawn": "", "abstract": "Uniqueness of weak solutions to the two-dimensional incompressible Euler equations (2D Euler) beyond the bounded-vorticity regime remains a fundamental problem. Self-similar solutions provide a framework for studying singular behavior and possible nonuniqueness. This talk presents several recent constructions of self-similar solutions of 2D Euler. First, we construct self-similar spiral solutions arising as perturbations of a radial homogeneous vortex. Next, homogeneous steady states are discussed, including solutions whose pseudo-velocity fields have multiple stagnation points. Finally, I show that, for every 1<a<2, a self-similar solution exists for any (-a)-homogeneous initial vorticity, without any smallness or sign assumption. The solution is obtained through an inviscid limit of hypodissipative self-similar profiles.\r\n\r\nThe result on homogeneous steady states is joint work with Matei Coiculescu. Time permitting, I will also discuss potential connections between these constructions and nonuniqueness for weak solutions with unbounded vorticity.", "id": "Paper/63114", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63114"}, {"title": " Injectivity of symmetric polynomial maps on partitions ", "webprogram_exclude": "0", "session_ids": ["Session/19321"], "source_sha256": "07e56ffdf94fcbabe22181635955a9330f878c6603f3e98da99819521b15d582", "withdrawn": "", "abstract": "Introduced by Ballantine, Beck, and Merca, the elementary symmetric partition function $\\mathrm{pre}_k$, defined on the set of partitions with at least $k$ parts, has been a topic of recent interest. We prove that $\\mathrm{pre}_k$ is injective on the set of $m$-ary partitions for positive integers $m \\ge k$, generalizing a $k = 2$ result of Ballantine, Beck, Merca and Sagan, and complementing a result of Hadelyn, Niergarth, Li and Li showing that, for each $k \\ge 3$, $\\mathrm{pre}_k$ is not injective on partitions of $n$ with length $2k$ for infinitely many $n$. We introduce the skew Schur partition function $\\mathrm{prs}_{\\lambda'/\\mu'}$, prove injectivity results for particular choices of $\\lambda',\\mu'$, and describe an application to representation theory.", "id": "Paper/63123", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63123"}, {"title": " Poetic Architectures of Mathematics: Structure, Metaphor, and Creative Pathways to Conceptual Understanding ", "webprogram_exclude": "0", "session_ids": ["Session/17091"], "source_sha256": "60f020f1dfcf93ac0c37cf379b5e7bb99182ecc9a99c0811e59a6f5ed913fda4", "withdrawn": "", "abstract": "Can the architecture of a poem reveal the architecture of a mathematical idea? What new dimensions of mathematics become visible through poetry? Poetry illuminates and strengthens mathematical concepts, creating an architecture for mathematical thought. Our poetic architecture is structural and metaphorical: patterns organize poems; metaphor makes abstraction tangible.\n\nThrough workshop exercises in writing and discussion, Dobson and Lutken (2026) explore mathematics as poetic subject, structure, and metaphor—from numbers, symmetry, and primes to category theory and arithmetic geometry. E. R. Lutken’s “Carpenter’s Song” and “π” illuminate the properties and personalities of numbers; “Reflection” mirrors language across an axis; and “Infinity in Hand” intricately builds a poem through the sieve of Eratosthenes.\n\nThe poetic architecture opens into a shimmering, lyrical register. S. Dobson’s “Decembris” gives the Fibonacci sequence a wintry, Keatsian lyricism, while her confessional-categorical poem “Diamond” draws category theory and arithmetic geometry into a prismatic poetic register. In Dobson’s “’Twas the Functorial Night,” a luminous crescendo of mathematical, literary, and sensory allusion affectionately reimagines a beloved Christmas poem as a radiant mathematical Christmas.", "id": "Paper/63125", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63125"}, {"title": " Social influences within a crowd evacuating under stress: towards a realistic model of emergency evacuation ", "webprogram_exclude": "0", "session_ids": ["Session/18260"], "source_sha256": "73ed426fbf91278bce6f9480399866e7c7702038fb252f9d8cd8523a81a48224", "withdrawn": "", "abstract": "Stress is a key factor in emergency evacuations. However, most laboratory experiments on evacuations are performed in low-stress environments limiting their ability to inform realistic models of pedestrian evacuation. To overcome this challenge, we recently conducted a first-of-its-kind study to uncover the role of stress and personality in emergency evacuations. We induced physiological stress in a subset of evacuating group of participants using a cold pressor task before they exit a maze under low-light conditions while fire alarms blared. We recorded a rich high-dimensional behavioral, physiological, and psychological profile of each participant consisting of head position and orientation, shoulder position, electrocardiography, and detailed self-reports. Our results show that stress and personality mediate evacuation times, average speeds, and head movement. \n\nIn this talk, I will dig deeper into the mechanisms behind the collective decisions taken by the evacuating groups that may have led to behavioral differences. In particular, I will use information-theoretic measures of transfer entropy and mutual information, calculated on behavioral and physiological time series, to build a directional network of social influence. This in turn will help answer questions such as who influenced whom, how far the influence was carried, and along what modality (e.g. speed, turning behavior, head movement, etc.). Results from these analyses are expected to inform the next generation of realistic models of emergency evacuations where agents have personalities, interact within a perceptual range, and stress can spread through actions.", "id": "Paper/63130", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63130"}, {"title": " Approximation in Contrastive Representation Learning and LLM alignment ", "webprogram_exclude": "0", "session_ids": ["Session/17945"], "source_sha256": "02b5bda4795ad2faedba6a23028e985bf255156eae2b5b2c1640d624a107965e", "withdrawn": "", "abstract": "We study approximation problems arising in two modern AI paradigms: contrastive representation learning and LLM alignment. For both, we investigate how learning objectives based on comparisons or preferences approximate their underlying population targets, and characterize the resulting approximation and estimation errors. Our results reveal a common theoretical perspective underlying these different learning problems.", "id": "Paper/63139", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63139"}, {"title": " A Mathematical Model of Oncolytic Virotherapy under Immune Suppression ", "webprogram_exclude": "0", "session_ids": ["Session/18275"], "source_sha256": "31a745fdc82a40984503d4315ade4642c6718c3869f97fef4c8f8f0a97a7c084", "withdrawn": "", "abstract": "Oncolytic viruses must replicate sufficiently within a tumor to be effective, yet the immune system can both support antitumor activity and eliminate the virus before it spreads. To investigate how this dual role of the immune response shapes virotherapy outcomes, we formulate a five-compartment ordinary differential equation model that tracks uninfected and infected tumor cells, immune cells, dead cellular material, and free virus under time-dependent immune suppression. After establishing a positively invariant bounded region, we analyze the equilibria and their local stability under constant immune suppression. A next-generation calculation produces a viral reproduction number that determines whether the infection-free tumor state remains stable or can be invaded by the oncolytic virus. Virus-persistent and interior coexistence equilibria describe additional possible long-term outcomes. We also derive an effective lesion-radius relation that incorporates viable tumor cells, immune-cell infiltration, and retained dead material. Sensitivity analysis and numerical simulations show that the infected-cell lysis rate has broad influence across the system, while changes in viral abundance do not necessarily produce proportional changes in tumor burden or lesion size. Under the selected baseline conditions, periodic immune suppression produces tumor-control trajectories comparable to constant suppression with approximately fyfty percent lower cumulative modeled exposure. These results illustrate how a mechanistic ODE model can provide valuable insight into viral persistence, treatment timing, and the interpretation of macroscopic measures of treatment response.", "id": "Paper/63143", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63143"}, {"title": " A Deterministic Homotopy Framework for Constrained Multi-Objective Optimization with Application to Optimal Power Flow Problem. ", "webprogram_exclude": "0", "session_ids": ["Session/19322"], "source_sha256": "a62f8584ae27f41cff79f12f86bf0fe5fbae2386ad213e28af224a3dcc59b3ce", "withdrawn": "", "abstract": "This presentation focuses on solving multi-objective optimization (MOO) problems by transforming them into a parameterized single-objective formulation using a weighted-sum approach. We develop a homotopy-based framework to compute Karush–Kuhn–Tucker (KKT) points for MOO problems. The proposed homotopy map continuously deforms an easily solvable system into the KKT conditions, yielding a deterministic and structure-preserving continuation path.\n\nUnder mild regularity assumptions, we establish global convergence of the homotopy trajectory to a Pareto-stationary solution for any initial point chosen in the interior of the feasible region. Numerical experiments demonstrate robust convergence even when initialized from infeasible points, indicating stability beyond the theoretical guarantees.\n\nEfficient predictor–corrector continuation strategies are employed to trace the homotopy path, along with adaptive step-size control and parallelization to enhance computational performance. Numerical results on benchmark problems compare the proposed approach with classical scalarization methods, such as the weighted sum method, ϵ-constraint method, global criterion method, and lexicographic method, as well as the evolutionary algorithm NSGA-II, demonstrating competitive computational efficiency and consistent solution quality. In addition, we apply the proposed method to a convex three-objective direct-current (DC) multi-objective optimal power flow (MOPF) problem on the IEEE 5-bus transmission network. These results highlight the effectiveness of the homotopy framework for constrained multi-objective optimization and motivate extensions to more general problem settings and robust solution strategies.", "id": "Paper/63150", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63150"}, {"title": " A class of II<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.054ex\" height=\"1.676ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -432.6 453.9 721.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">_1</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-31\" x=\"0\" y=\"-213\"></use>\n</g>\n</svg> factors without non-trivial crossed product decompositions ", "webprogram_exclude": "0", "session_ids": ["Session/18383"], "source_sha256": "627fe289789a84ebe73aaf0681de75c4b1ea59628232d5e50d7f3f37e58c5ec8", "withdrawn": "", "abstract": "In this talk, I will present the first examples of separable II$_1$ factors $M$ that admit no non-trivial crossed product decompositions: $M\\not\\cong B\\rtimes_\\sigma G$, for any trace preserving action of an infinite countable group $G$ on a tracial von Neumann algebra $(B,\\tau)$. Our approach relies on constructing separable II$_1$ factors $M$ with the strong rigidity property that every embedding of $M$ into its tensor product square $M\\overline{\\otimes}M$ arises from the canonical embeddings $x\\mapsto x\\otimes 1$ and $x\\mapsto 1\\otimes x$. This is joint work with Adrian Ioana and Hui Tan.", "id": "Paper/63153", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63153"}, {"title": " Computations with Mackey Functors ", "webprogram_exclude": "0", "session_ids": ["Session/17701"], "source_sha256": "ce3798b8f7c35b55b4a7f2ddf13677757be396c544b615f479c9effeb922a82b", "withdrawn": "", "abstract": "In equivariant stable homotopy theory, Mackey functors play the role that would classically be filled by Abelian groups. Consequently, many theorems are proved by (e.g.) analyzing spectral sequences of Mackey functors. Such computations tend to be tedious, since Mackey functors are more complex (i.e. consist of more data) than Abelian groups. In this talk, I will showcase a general-purpose software library for computations with Mackey functors, and highlight some applications. The software was developed in group work at the June 2026 ICERM workshop \"Machine Computation in Homotopy Theory\".", "id": "Paper/63171", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63171"}, {"title": " Is it Real?: Optimal Control of an SIR model of Misinformation through Educational Campaigns ", "webprogram_exclude": "0", "session_ids": ["Session/18239"], "source_sha256": "cab4e883edc229e7a2e1e5e31860864d95a2d0f155122d9c1041d8ab7a9aabb4", "withdrawn": "", "abstract": "While misinformation has long been a societal challenge, the modern accessibility of the internet has accelerated its spread, slowing consensus on critical global issues and driving societal polarization. To quantitatively evaluate and mitigate the viral spread of false narratives, this study introduces an epidemiologically inspired Susceptible-Critically Literate-Misinformed (SCM) compartmental model. The system utilizes a set of ordinary differential equations that incorporate targeted educational campaigns as an active intervention variable. To accurately reflect digital behavior, the model also introduces a distinct natural exit rate from the misinformed compartment, isolating individuals who leave the system due to platform churn or extreme polarization. Mathematical analysis guarantees the system's validity through proofs of positivity and boundedness. Additionally, the Misinformation-Free Equilibrium is derived using the Next Generation Matrix method to compute the basic reproduction number (R0). To ground the theoretical framework in real-world dynamics, Physics-Informed Neural Networks (PINNs) were applied to the PHEME dataset–comprising over 105,000 tweets across multiple crisis events–to extract empirical transmission rates. Subsequent sensitivity analysis revealed that the viral transmission rate is the overwhelmingly dominant factor driving the system. To combat this spread efficiently, the study employs optimal control theory, utilizing Pontryagin’s Maximum Principle and a quadratic cost function to determine the most effective educational intervention strategy. The results demonstrate that implementing an optimal quadratic educational control, which never exceeds an effort intensity of 64%, successfully reduces the peak misinformed population by 99.1% and decreases the total spread of misinformation across the population by 98.0%.", "id": "Paper/63179", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63179"}, {"title": " Global solvability of the one-phase Muskat problem ", "webprogram_exclude": "0", "session_ids": ["Session/19363"], "source_sha256": "886832fb8abddbb9a1c15d9670ab0e644c31271fc2315628557173dcf2158a78", "withdrawn": "", "abstract": "The Muskat problem describes the evolution of the interface between two immiscible fluids or dry region and wet region in a porous media. I will present the recent progress on the global solvability of the one-phase Muskat problem in various scenarios (i) including the effect of surface tension (ii) finite bottom.", "id": "Paper/63183", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63183"}, {"title": " Dynamical Systems Analysis of Diffusively Coupled FitzHugh–Nagumo Neural Networks: Synchronization, Stability, and Bifurcation on Weighted Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/19351"], "source_sha256": "a2b847327b6245f02ce89af92c320ad0f3dc05d372bb05bb2c5cca13d6feafc6", "withdrawn": "", "abstract": "Understanding how individual neuron dynamics translate into collective network behavior remains a fundamental challenge in computational neuroscience. Analytical understanding of network dynamics is therefore often limited by assumptions regarding behavior or network topology, with many studies relying largely on numerical simulation. Abnormal neuron synchronization patterns are characteristic of several neurological disorders, such as epileptic seizures. Unlike existing analyses that typically rely on specific network architectures, we develop a topology-independent analytical framework for studying diffusively coupled FitzHugh–Nagumo networks on general weighted undirected graphs. Using dynamical systems theory, we derive conditions for bifurcations—which characterize transitions between qualitatively distinct neuronal behaviors—of individual neurons with respect to model parameters and external current. We then study synchronous equilibria of the coupled n-neuron system, analytically deriving the parameter regions in which these equilibria are stable. We classify local single-parameter bifurcations of these equilibria in terms of eigenvalues of the graph Laplacian matrix, establishing a relationship between network structure and synchronous behavior. Using these Laplacian eigenvalue conditions, we derive upper bounds on maximum weighted degree for equilibrium stability and bifurcation regimes. Finally, we develop a generalized framework for extending stability and bifurcation analysis beyond fully synchronized states to more complex collective behaviors, including partial synchronization and non-synchronized states. These results provide a mathematically rigorous framework for understanding how connectivity patterns shape collective neural behavior and may inform future studies of abnormal synchronization associated with neurological disorders. This work aligns with the United Nations Sustainable Development Goal #3: Good Health and Well-Being.", "id": "Paper/63185", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63185"}, {"title": " Linear and algebraic structures in nonlinear subsets in Banach function spaces ", "webprogram_exclude": "0", "session_ids": ["Session/17782"], "source_sha256": "7e17607e7d53dc722d824065b04008764bd4710c6c743517693f43af20449c38", "withdrawn": "", "abstract": "The lineability problem concerns the search for linear structures in collections of mathematical objects where such structures are not immediately apparent. This problem has been considered in various contexts, such as real and complex analysis, operator theory, and dynamical systems. In this talk, we discuss the existence of linear structures in certain nonlinear subsets of Banach function spaces. In particular, we identify certain nonlinear subsets of Orlicz-Lorentz spaces, a natural generalization of both Orlicz and Lorentz spaces, that are spaceable; in other words, each of these subsets together with zero contains an infinite-dimensional closed vector subspace.\n\nThis talk is based on joint work with Luis Bernal-Gonz\\'alez, Daniel L. Rodr\\'iguez-Vidanes, and Juan B. Seoane-Sep\\'ulveda.", "id": "Paper/63192", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63192"}, {"title": " Daugavet property and geometry of Banach spaces ", "webprogram_exclude": "0", "session_ids": ["Session/19339"], "source_sha256": "6e5e501a3065656c0dd3dba45254847ce5443ed1bbf2b5bbe427473cca0445c9", "withdrawn": "", "abstract": "A Banach space $X$ has the Daugavet property if every rank-one operator $T: X \\rightarrow X$ satisfies $\\|I + T\\| = 1 + \\|T\\|$. While the Daugavet property was originally described as an operator-theoretic phenomenon, a geometric interpretation of this property in terms of slices of the unit ball has played an important role in the subsequent study and classification of Banach spaces with the Daugavet property and related properties. Recently, localized notions of this property were introduced to describe points of the unit sphere with analogous Daugavet-type behavior. In this talk, we discuss the Daugavet property in Banach function spaces and characterize Orlicz-Lorentz spaces having the Daugavet property. In the process, we also identify a geometric obstruction to this property.\n\nThis talk is based on several joint works with Anna Kami\\'nska, Han Ju Lee, and \\'Oscar R\\'oldan.", "id": "Paper/63194", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63194"}, {"title": " Prime divisors in dynamical sequences and the inverse Galois problem for iterated Galois groups ", "webprogram_exclude": "0", "session_ids": ["Session/18259"], "source_sha256": "399266170ed871b6df6bb527f956c9320c7535547b30cb6c962c13af69bd9312", "withdrawn": "", "abstract": "Take your favorite rational function, choose a starting point, and consider its orbit under iteration. If we regard the set of all primes dividing at least one term in this sequence, what is the Dirichlet density of this set? \n\nThis question, together with many others in number theory, is studied using the same machinery: iterated Galois groups. \\\\\n\nIn this talk, we introduce a new structural property, called virtually mixing, and prove that every iterated Galois group satisfies it. This new concept quantifies the level of self-replication of the group. When complete self-replication fails, the obstruction is captured by a finite quotient. The quotient and its associated normal subgroup can be computed explicitly using the ramification portrait. \\\\\n\nIt turns out that the quotient also encodes dynamical and geometric data of the rational function, reflects ergodic properties of the iterated Galois group, provides a new necessary condition for the inverse Galois problem of this family of groups, and has direct consequences for arithmetic questions such as prime divisibility in dynamical sequences.", "id": "Paper/63258", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63258"}, {"title": " What Highly Coordinated Courses Become Capable of Accomplishing: Human and Organizational Capabilities in Undergraduate Mathematics Teaching ", "webprogram_exclude": "0", "session_ids": ["Session/18250"], "source_sha256": "38c96651a109db1cadb7ef4679275ea1570f1369d673a5a8bf9e47162c47cf4b", "withdrawn": "", "abstract": "Course coordination is widely implemented in undergraduate mathematics departments to promote instructional consistency across multi-section courses. However, research and practice often view coordination narrowly through administrative mechanisms or isolated pedagogical reforms. Building upon literature in mathematics education, faculty development, and organizational change, this presentation formalizes the definition of a Highly Coordinated Course (HCC) as an integrated instructional system in which coordination is embedded in the routine operation of the course through intentionally designed Course Coordination Mechanisms (CCMs). Drawing on years of implementation in multi-section core mathematics courses at the United States Air Force Academy, we present a dual-capability framework distinguishing between Human Capabilities (teacher preparation and onboarding, continuous faculty development, and leader and leadership development) and Organizational Capabilities (knowledge management, course continuity, organizational resilience, collective responsibility, sustainable pedagogical implementation, continuous improvement, and assessment alignment). We articulate the operational mechanisms that cultivate these capabilities and examine key structural trade-offs, including balancing instructor autonomy with course alignment, as well as tradition with innovation. By shifting attention from administrative tasks to the human and organizational capabilities that coordinated courses develop, this talk offers department leaders and course coordinators a structural lens and actionable strategies for transforming multi-section course coordination into a sustainable driver of faculty growth and departmental resilience.", "id": "Paper/63332", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63332"}, {"title": " Math Connections Theater: Investigating Theatrical Embodied Approaches and Humor in Communicating and Experiencing Undergraduate Mathematics ", "webprogram_exclude": "0", "session_ids": ["Session/18068"], "source_sha256": "b63aeec26c16b072d427a001c73e6fa22837e46fee3f4e01de5a4b956267666f", "withdrawn": "", "abstract": "Math Connections Theater (MCT) is a collaborative initiative involving students of diverse majors and backgrounds who create comedy skits on various mathematical topics, including GEMDAS, combinatorics, limits of partial sums, L’Hôpital’s rule, the Monty Hall problem, topology, and proofs. Although prior initiatives have successfully integrated mathematics and the performing arts (e.g., Hudak, 2023; Kazzazi, 2020), MCT is, to our knowledge, the first to deliberately fuse mathematics and humor on the stage. This study explored the phenomenon of MCT by investigating how actors experienced and communicated abstract mathematical ideas through performance. We developed and applied the Theatrical Embodiment Framework (adapted from Nemirovsky & Ferrara, 2009) to analyze recordings of seven MCT skits, attending to verbal and nonverbal humor as well as body motions, gestures, facial expressions, eye gaze, tone of voice, dialogue, and interactions with props. Our analysis revealed that the actors employed embodied theatrical techniques, such as breaking the fourth wall, between-actor dialogue, and using props to communicate mathematical ideas from the stage, while simultaneously engaging with mathematics. For each skit, we created diagrams tracing how mathematical ideas evolved and were embodied by the actors. The thematic analysis of these diagrams showed that these theatrical strategies allowed the actors to ground abstract mathematical ideas into concrete experiences for the audience without sacrificing mathematical rigor. Our findings contribute to the discussion of the intertwinement of teaching and acting and suggest that theatrical techniques can serve as resources for undergraduate mathematics instruction. We therefore invite educators to consider incorporating theatrical techniques into their instruction, including lesson planning and assessment, to enhance student engagement and broaden access to mathematics education.", "id": "Paper/63439", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63439"}, {"title": " Infinite Belligerent Jump Inversion and Computable Scott Analysis ", "webprogram_exclude": "0", "session_ids": ["Session/17922"], "source_sha256": "a821a8f8319c774d48c5f05dbc9ddad4052c5ecce7a22b6be66582b6fec7f673", "withdrawn": "", "abstract": "In this talk, we will discuss the infinite belligerent jump inversion, extending Harrison-Trainor's finite unfriendly jump inversion to the transfinite levels. Using this tool, we determine the optimal interaction between syntactic complexity and oracle complexity for computable Scott sentences and formulas distinguishing computable structures. For example, in computable Scott analysis, it is well known that a computable structure with a $\\Pi_\\alpha$ Scott sentence has a computable $\\Pi_{2\\alpha}$ Scott sentence. We apply the infinite belligerent jump inversion to show the sharpness of the statement, thereby also identifying the sources of the discrepancy between boldface and lightface complexities.", "id": "Paper/63446", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63446"}, {"title": " Asymptotic moments of the reciprocal sum of distinct parts in <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"0.84ex\" height=\"2.009ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -719.6 361.5 865.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">t</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-74\" d=\"M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-74\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-regular partitions ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "ca60b49ad23550efd8d239e278fbf3ff91c42950bd99770d6f3b3371a8d1f024", "withdrawn": "", "abstract": "The asymptotic study of sums of reciprocals of parts in integer partitions was initiated by Kim and Kim and has attracted considerable attention in recent years. Extending one of their results, we investigate the reciprocal sum of \\emph{distinct parts} in $t$-regular partitions for all $t\\geq 2$. We employ Wright's circle method and related tools to derive asymptotic formulas for the first two raw moments, from which we obtain asymptotic expressions for the mean and variance with explicit dependence on $t.$", "id": "Paper/63449", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63449"}, {"title": " Two-Spectrum Inverse Reconstruction for Weighted Four-Cycles ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "ae73fd5a05fa8d1fdf753c247dd8e8402110b444efa7bcc38bec2ced3b2ad608", "withdrawn": "", "abstract": "We study an inverse spectral problem for positive edge weights on the four-cycle. A single weighted-Laplacian spectrum is generically insufficient to determine the weights: on an open dense subset of weight space, the local isospectral fiber is one-dimensional. We show that adding the spectrum obtained after entrywise squaring of the edge weights yields global reconstruction up to the dihedral symmetries of the cycle, without assuming distinct weights. In fact, five scalar spectral coefficients suffice. Four recover the elementary symmetric polynomials and hence the unordered weight multiset, while a fifth order-sensitive coefficient determines the opposite-edge pairing. We also prove local Lipschitz stability on compact sets with uniformly separated weights. As a geometric application, we study cyclic quadrilaterals and show how the same framework distinguishes local identifiability from global nonuniqueness and gives global recovery for Gaussian edge weights at two coupled scales.", "id": "Paper/63461", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63461"}, {"title": " When do trajectories matter? Identifiability analysis for stochastic transport phenomena ", "webprogram_exclude": "0", "session_ids": ["Session/18127"], "source_sha256": "e32fae2836f0d9d79c1f56bbdaeaed28f0b2e13c8addfa9f9092b2516ed68845", "withdrawn": "", "abstract": "Stochastic models of diffusion are routinely used to study dispersal of populations, including populations of animals, plants, seeds and cells. Advances in imaging and field measurement technologies mean that data are often collected across a range of scales, including count data collected across a series of fixed sampling regions to characterize population-level dispersal, as well as individual trajectory data to examine at the motion of individuals within a diffusive population. In this work we consider a lattice-based random walk model and examine the extent to which model parameters can be determined by collecting count data and/or trajectory data. Our analysis combines agent-based stochastic simulations, mean-field partial differential equation approximations, likelihood-based estimation, identifiability analysis, and model-based prediction. These combined tools reveal that working with count data alone can sometimes lead to challenges involving structural non-identifiability that can be alleviated by collecting trajectory data. Furthermore, these tools allow us to explore how different experimental designs impact inferential precision by comparing how different trajectory data collection protocols affects practical identifiability.", "id": "Paper/63479", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63479"}, {"title": " Effective Hecke Eigenvalue Equidistribution over the Atkin-Lehner Subspaces ", "webprogram_exclude": "0", "session_ids": ["Session/19367"], "source_sha256": "d198a1172f5fdccee3f780af75992c06c81b67573386079dcd24e615bfaff353", "withdrawn": "", "abstract": "For a fixed prime $p$, let $\\mu_p$ denote the $p$-adic Plancherel measure. Then the first main goal of this presentation is to show effective (and moreover explicit) $\\mu_p$-equidistribution of the $p$-th Hecke eigenvalues over the Atkin-Lehner subspaces $S_k^\\sigma(N) \\subseteq S_k(N)$ and $S_k^{\\operatorname{new}, \\sigma}(N) \\subseteq S_k^{\\operatorname{new}}(N)$. We then highlight five applications of this explicit equidistribution result. For the first application, we generalize a vertical analog of the Atkin-Serre conjecture due to Kim to the Atkin-Lehner setting. For the second application, we obtain explicit bounds on the number of newforms $f \\in S_k^{\\operatorname{new}, \\sigma}(N)$ for which a fixed prime $p$ is extremal over $S_k^{\\operatorname{new}, \\sigma}(N)$. For the third application, we prove explicit asymptotics for the number of $\\mathbb{F}_{p^r}$-points on the modular Jacobian $J_0(N),$ as well as on its factors $J_0^{\\operatorname{new}}(N),$ $J_0^\\sigma(N),$ and $J_0^{\\operatorname{new}, \\sigma}(N)$. We also make explicit an asymptotic result of Serre concerning point counts of the modular curves $X_0(N)$. For the fourth application, we generalize lower bounds due to Murty and Sinha on the sizes of large $\\mathbb{Q}$-simple factors of $J_0(N)$ to analogous bounds for $J_0^\\sigma(N)$. Finally, for the fifth application (which will be discussed by our coauthors in a separate JMM talk), one can use our explicit equidistribution result to prove that only finitely many modular Jacobians are supersingular modulo $p$.", "id": "Paper/63480", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63480"}, {"title": " A splitting mixed finite element method for a stochastic Keller-Segel system with gradient-type multiplicative noise ", "webprogram_exclude": "0", "session_ids": ["Session/17850"], "source_sha256": "2307dad99921861e491d9e73ddd21852a0652bcd9791ed7eae18ab329b88084b", "withdrawn": "", "abstract": "In this talk, I present a fully discrete finite element method for a stochastic Keller--Segel system driven by multiplicative Stratonovich transport noise, which models chemotactic dynamics under randomly fluctuating environments. The numerical scheme combines a Crank--Nicolson discretization in time with a splitting mixed finite element approximation in space. Compared with the deterministic counterpart, the analysis is significantly more challenging due to the interaction between the nonlinear chemotactic coupling and the stochastic transport term. To overcome these difficulties, we establish several stability estimates for both the continuous and fully discrete systems by employing nonlinear Gronwall-type inequalities together with delicate stochastic energy arguments. Under suitable regularity assumptions and a mild mesh constraint relating the temporal and spatial discretization parameters, we derive the optimal strong convergence estimate of order $\\mathcal{O}(k^{1/2}+h),$ where $k$ and $h$ denote the temporal and spatial mesh sizes, respectively. Numerical experiments are presented to confirm the theoretical convergence rates and to illustrate the effectiveness of the proposed method. The simulations further indicate that the approximate density remains nonnegative and exhibits finite-time blow-up behavior for sufficiently large initial data.", "id": "Paper/63503", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63503"}, {"title": " Extensions on Reproducing Kernel Hilbert Spaces ", "webprogram_exclude": "0", "session_ids": ["Session/17749"], "source_sha256": "0457fa2fbf3c465394578d869b70b988b903a45d05dc3a74999e1f75351a7d78", "withdrawn": "", "abstract": "Starting with the definition of Reproducing Kernel Hilbert Spaces (RKHS), we briefly recall some previous results and then present a recent result on RKHS.", "id": "Paper/63515", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63515"}, {"title": " Connectivity of Friends and Strangers Graphs Using Minimum Degree ", "webprogram_exclude": "0", "session_ids": ["Session/19360"], "source_sha256": "7f65deb61749f10f946035d88d87a024cd13fd2618c5e0e952dcb365fe9377e2", "withdrawn": "", "abstract": "Given graphs $X$ and $Y$ on $n$ vertices, Defant and Kravitz defined the Friends and Strangers graph $\\mathrm{FS}(X,Y)$ whose vertices are bijections $\\si:V(X)\\to V(Y)$. We examine the  connectivity and diameter of $\\mathrm{FS}(X,Y)$ based on the minimum degrees of $X$ and $Y$, denoted $\\delta(X)$ and $\\delta(Y)$. We resolve a conjecture of Bangachev that if $X$ and $Y$ are connected graphs and $2\\min\\{\\delta(X),\\delta(Y)\\}+3\\max\\{\\delta(X),\\delta(Y)\\}\\ge 3n$, then $\\mathrm{FS}(X,Y)$ is connected. Furthermore, we show that the condition $2\\min\\{\\delta(X),\\delta(Y)\\}+3\\max\\{\\delta(X),\\delta(Y)\\}\\ge 3n$ proposed by Bangachev is the optimal linear hypothesis that ensures $\\mathrm{FS}(X,Y)$ is connected. We prove there exists an absolute constant $C$ such that for any adjacent vertices $a,b\\in V(X)$ and any vertex $\\si\\in V(\\mathrm{FS}(X,Y))$, $a$ and $b$ can swap positions in at most $C$ moves. Furthermore, we prove that if $X$ and $Y$ are connected graphs and $2\\min\\{\\delta(X),\\delta(Y)\\}+3\\max\\{\\delta(X),\\delta(Y)\\}\\ge 3n$, then the diameter of $\\mathrm{FS}(X,Y)$ is $O(n^2/\\min\\{\\delta(X),\\delta(Y)\\})$, and that this bound is sharp. Moreover, we show that even for possibly disconnected graphs $X$ and $Y$, the condition $2\\min\\{\\delta(X),\\delta(Y)\\}+3\\max\\{\\delta(X),\\delta(Y)\\}\\ge 3n$ implies that the diameter of any connected component of $\\mathrm{FS}(X,Y)$ is $O(n^2)$. This work improves the diameter results of Akella and Li, and resolves many of their questions.", "id": "Paper/63540", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63540"}, {"title": " On Plank Coverings of Cube Annuli ", "webprogram_exclude": "0", "session_ids": ["Session/18193"], "source_sha256": "09837fcc7b0efc151e0cd1f1be1e9d76ee60c98a8322fbd4b3342af55dc4a579", "withdrawn": "", "abstract": "We study plank coverings of cube annuli $Q\\setminus \\delta Q\\subset \\mathbb{R}^d$, where $Q$ is the $d$-dimensional unit hypercube and $\\delta Q$ is a homothetic copy of $Q$ that lies in its interior. In 2003, Bezdek proved that if $\\delta\\le 1-1/\\sqrt 2$ and $d=2$, then total plank width at least 1 is required to cover $Q\\setminus \\delta Q$. Moreover, this result is independent of the position of the hole $\\delta Q$. In 2010, Smurov, Bogataya, and Bogatyi extended this result to $\\mathbb{R}^d$ when $\\delta\\le 1-1/\\sqrt d$ for all positive integers $d\\ge 2$. We improve these results in dimensions $2$ and $3$ by showing that there exist small values $\\varepsilon_2$ and $\\varepsilon_3$ such that if $\\delta\\le 1-1/\\sqrt{d}+\\varepsilon_d$, then total plank width at least 1 is still required to cover $Q\\setminus \\delta Q$ in dimensions $2$ and $3$ respectively. This result provides evidence in favor of a conjecture attributed to Bezdek, Smurov, Bogataya, and Bogatyi that $\\delta\\le 1-1/d$ implies total plank width $1$ is required to cover $Q\\setminus \\delta Q\\subset \\mathbb{R}^d$ for all positive integers $d$.", "id": "Paper/63542", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63542"}, {"title": " Balanced Root Systems and a Schellekens-Type List for Holomorphic Vertex Operator Algebras of Central Charge 32 ", "webprogram_exclude": "0", "session_ids": ["Session/18270"], "source_sha256": "058dbfb861ef66e287ba79dbc98a2028a2412f1cd96c8dbce3e0b712411206f2", "withdrawn": "", "abstract": "We study a special class of holomorphic vertex operator algebras (VOAs) that we call \"balanced\". For a balanced, holomorphic VOA $V=\\mathbb{C}\\mathbf{1}\\oplus V_1\\oplus ...$ with $c=32$ or $40$ we show that the Virasoro vectors of $V$ and the subVOA generated by $V_1$ coincide and use this result to provide a Schellekens-type list of possible root systems that may occur.", "id": "Paper/63553", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63553"}, {"title": " Minimal enclosing balls via geodesics ", "webprogram_exclude": "0", "session_ids": ["Session/18069"], "source_sha256": "1e6a6484db6aa45933bcfb23cb800fa64afe0616877243cc0695a1ede28cbdfa", "withdrawn": "", "abstract": "The minimum enclosing ball problem dates back nearly two centuries, to work of Sylvester.  Solution algorithms are often geometric in nature. To highlight the metric ingredients underlying their efficiency, we focus on a simple geodesic-based method. A recent subgradient-based study analyzed this method in nonpositively curved settings, including Euclidean and Hilbert spaces, Hadamard manifolds, and phylogenetic tree space.  We present a simpler, intuitive and self-contained complexity analysis, with an improved convergence rate. We then extend the analysis to geodesic spaces with curvature bounded above.", "id": "Paper/63557", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63557"}, {"title": " Enumerating Symplectic Skew-Adjoint Nilpotent Matrices over Finite Fields ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "b93869c75eefef024ee97aa3c55f1d584345e60edb26348e68f342c0fa9bd85c", "withdrawn": "", "abstract": "Nilpotent matrices are square matrices $N$ satisfying $N^k=0$ for some positive integer $k$, where the smallest such $k$ is called the index of nilpotence. We work with nilpotents over a finite field $\\BF_q$, since this keeps enumeration finite. Fine and Herstein counted all nilpotent $n \\times n$ matrices over $\\BF_q$, and Lusztig counted nilpotents of a fixed rank. Kung and Stong developed a cycle-index framework for counting general linear transformations over $\\mathbb{F}_q$ which can be specialized to count fixed index nilpotents by summing over Jordan partitions. Fulman and Guralnick proved similar Jordan type counts for nilpotents in symplectic Lie algebras over fields of odd characteristic. These results can be used to find fixed index counts, but they are not expressed directly in terms of matrix size, rank, and index. In this paper, we give explicit formulas for the number of rank $r$, index 2 and index 3 nilpotent matrices in the symplectic Lie algebra $\\mathfrak{sp}(V,\\omega)$ over $\\mathbb{F}_q$. Instead of summing over Jordan types, we derive these formulas through direct combinatorial arguments and verify them against the Jordan type counts of Fulman and Guralnick for odd $q$.\n\nThis research was conducted under the direction of Professor Eric Grinberg in the Department of Mathematics at the University of Massachusetts Boston.", "id": "Paper/63565", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63565"}, {"title": " GEN AI IN PROOF-BASED MATH COURSES: A PILOT STUDY ", "webprogram_exclude": "0", "session_ids": ["Session/19355"], "source_sha256": "4b719d0746b1d617cba38c71975463aa298ff67e0f4f8ef8e2cfd359c899894c", "withdrawn": "", "abstract": "With the rapid rise of generative AI in higher education, understanding how students use AI is increasingly important. This exploratory study examines student use and\nperceptions of generative AI across three proof-based undergraduate mathematics courses:\na first-semester abstract algebra course, a topology course, and a second-semester abstract\nalgebra course. In each case, course policy permitted some use of generative AI. Drawing on\nsurvey responses and student interviews, we analyze how students engaged with AI tools as well as\ntheir perceptions of generative AI’s usefulness, accuracy and limitations.", "id": "Paper/63581", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63581"}, {"title": " A Kalman Filter Based Approach to NV Diamond Data Fusion For Improved Temperature Sensing ", "webprogram_exclude": "0", "session_ids": ["Session/19364"], "source_sha256": "4e9f76825b36bfc4cceda2e23921d81e97144171851f8471b30c6ed5f723f8d5", "withdrawn": "", "abstract": "Nitrogen‑vacancy (NV) centers in diamond have been demonstrated to enable high sensitivity temperature measurements using multiple modalities. Standalone optically detected magnetic resonance (ODMR) offers robust temperature estimates albeit with high latency, whereas all-optical based measurements provide millisecond resolution but suffer from poorer long-term accuracy. In this work we demonstrate a hot-start Kalman filtering approach that fuses the two modalities, leading to a 57\\% improvement in accuracy. The fused estimate  achieves higher long-term accuracy with lower latency, demonstrating a viable route to implementation of self‑correcting, high‑precision NV‑diamond temperature sensing schemes", "id": "Paper/63588", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63588"}, {"title": " A Complete Adaptive SVD Algorithm for Dual Reduced Biquaternion Matrices ", "webprogram_exclude": "0", "session_ids": ["Session/17954"], "source_sha256": "ef0681a5b8f0fc1fab2fd05b7c001ad827df16859a9be175d72f9682af6d8f8d", "withdrawn": "", "abstract": "We present an adaptive singular value decomposition (SVD) algorithm for dual reduced biquaternion (DRB) matrices. Using the idempotent decomposition, a DRB matrix is\nrepresented by two independent dual complex component matrices. Each component first undergoes a dual complex Householder bidiagonalization, after which an a posteriori\nquality indicator is applied to the resulting factors. If the factors pass the test, the dual number bidiagonal matrix is diagonalized by a complete SVD construction. Otherwise, only the affected component is recomputed by a direct\ncomplete dual complex SVD.\n\nThe algorithm covers general, rank-deficient, purely infinitesimal, zero, and wide matrices, as well as repeated and nearly repeated standard singular values. Numerical experiments produce residuals near double-precision roundoff for general dense inputs and representative special and limiting cases, and show that the safeguard detects unreliable bidiagonalization factors in tests with repeated spectra or severe separation between\nthe standard and infinitesimal parts. A non-blind color image watermarking experiment illustrates the integration of the proposed DRB-SVD into a multichannel image processing workflow.", "id": "Paper/63611", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63611"}, {"title": " Rational points and zero-cycles on torsors: a question of Totaro ", "webprogram_exclude": "0", "session_ids": ["Session/18076"], "source_sha256": "2424972a8d7e95b17bf692b06ffc6026a3a0de3a7a0a9cfb940c161f248f2e12", "withdrawn": "", "abstract": "For a linear algebraic group $G,$ several of its fundamental problems can be unified into a problem\nof characterizing $G$-torsors over an arbitrary field $k.$  In 1994, Serre asked the question : \n    For a smooth connected linear algebraic group $G$ over a field $k,$ if a $G$-torsor $X$ admits a zero cycle of degree 1, does it have a $k$-rational point? \n    \n    Since a $G$-torsor $X$ has a $k$-rational point if and only if its corresponding cohomology class in $H^1(k,G)$ is trivial, the cohomological version of this question is of great interest. Pioneering results by Springer, Bayer-Fluckiger and Lenstra, Black, Bhaskar have shown several affirmative answers to this question.  \n\n    \nIn 2004, Totaro generalized Serre's question for zero cycles of degree $d\\geq1.$ In its generality, Totaro's question  has counterexamples due to Parimala, Gordan-Sarney and Suresh, Florence among others. However, Black and Parimala's work shows affirmative results to Totaro's question for semi-simple simply connected groups in low rank. \n\nIn this talk, I plan to give a survey of the works done related to these questions along with my work of this problem for absolutely simple adjoint classical linear algebraic groups in low rank as well as for over function fields of $p$-adic curves. \nI will focus on detailing some of the techniques from the theory of quadratic and hermitian forms and invariance theory that helped us to get these affirmative answers. We will also discuss some of the cases for which this question is still open and some broader connection to arithmetic of algebraic groups.", "id": "Paper/63632", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63632"}, {"title": " Time-Adaptive Sample Average Approximations for Stochastic Control ", "webprogram_exclude": "0", "session_ids": ["Session/18245"], "source_sha256": "a7aeb62148e48c6206cb9ad007d9f200e619ca551b41bbd9a3d5cbc95174c799", "withdrawn": "", "abstract": "Stochastic control problems governed by stochastic differential equations are posed over two continuous domains: time and probability.\nStandard numerical approaches typically discretize time before sampling.\nWe reverse this order, first fixing a finite collection of driving paths to obtain a bona fide sample average approximation while retaining continuous-time dynamics for each realization.\nThe sampled equations can then be treated pathwise, allowing each realization to carry its own adaptively refined temporal mesh.\n\nWe establish stability estimates for sample objective values and adjoint gradients under approximation of the driving paths.\nFor general multidimensional noise, rough-path analysis controls these errors in a rough-path metric.\nUnder scalar noise, or more generally commuting diffusion fields, a Doss–Sussmann representation yields stability in the uniform norm of the driver and sharper rates.\n\nThe resulting estimates involve problem- and path-dependent constants that are generally unavailable in computation.\nThey nevertheless fit naturally within adaptive inexact trust-region methods, whose accuracy mechanisms require only that function and gradient errors be bounded by an unknown constant times a solver-controlled tolerance.\nOptimization progress can therefore prescribe the required accuracy and drive samplewise temporal refinement without estimating the stability constant.\nThis framework couples sample average approximation, pathwise error control, and globally convergent optimization for continuous-time stochastic control.", "id": "Paper/63675", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63675"}, {"title": " On compact embeddings into Lp and fractional spaces ", "webprogram_exclude": "0", "session_ids": ["Session/18441"], "source_sha256": "d7100beb7d5ea1c8b20a4cdea121f7511fd0a131b7edce28912d314fde0fd528", "withdrawn": "", "abstract": "\\begin{center}\n{\\sf Dedicated to  Prof. Carlos Tomei on occasion of his 70th birthday. } \\end{center}\n\n\n\\noindent{\\bf Abstract}\n\n\nThe study of the fractional Laplacian operator $(-\\Delta)^s$ in $\\mathbb{R}^N$ with Dirichlet boundary conditions gained enormous momentum through its identification with a Neumann operator in $\\mathbb{R}^N\\times (0, \\infty)=\\mathbb{R}^{N+1}_+$, a method mainly introduced by Caffarelli and Silvestre. Since then, several other operators have been studied using this method. In general, a crucial question is attached to this method: is the  embedding (in the trace sense) on the ground space $L^q(\\mathbb{R}^{N})$ compact? This question is very important  when dealing with problems of existence of solutions. This paper aims to answer this question for some operators.\n\nPassing to an abstract setting, let $X,Y$ be Hilbert spaces and $\\mathcal{A}\\colon X\\to X'$ a continuous and symmetric operator. We suppose that $X$ is dense in $Y$ and that the embedding $X\\subset Y$ is compact. In this paper we show some consequences of this setting for the study of the fractional operator attached to $\\mathcal{A}$ in the extension setting $\\Omega\\times(0,\\infty)$ or $\\mathbb{R}^{N+1}_+$. Being more specific, we will give some examples where the embedding of the extension domain into  $L^2(\\Omega)$ is compact, even in the case $\\Omega=\\mathbb{R}^N$.", "id": "Paper/63680", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63680"}, {"title": " Shannon Capacity and Related Graph Invariants for Lexicographic Products ", "webprogram_exclude": "0", "session_ids": ["Session/18020"], "source_sha256": "5bc3c6d88fdaadec452fa1c9ba2340e147d6be5a00624a32df97956f3ed9dc81", "withdrawn": "", "abstract": "Zero-error communication is studied through the Shannon capacity of lexicographic products of graphs. The lexicographic product models communication in which one graph describes confusability between classes, while the other describes confusability within each class. We study lexicographic products of finite, simple, undirected graphs, together with the Lov\\'{a}sz theta function and the fractional Haemers number. The Shannon capacity is proved to be supermultiplicative under lexicographic products in either order, and these products are compared with the strong product. We explicitly construct three countably infinite families of lexicographic powers based on the Schl\\\"{a}fli graph, the McLaughlin graph, and its second subconstituent; in each family, pairing each member with its complement yields strict supermultiplicativity and arbitrarily large multiplicative gaps. Bounds and exact-capacity criteria for lexicographic products are derived, and the resulting upper bounds are shown to be incomparable. The Shannon capacities of lexicographic products involving Kneser graphs, their complements, and $q$-analogues of Kneser graphs are determined. It is also shown that a lexicographic product with a complete outer factor preserves the Shannon capacity of an arbitrary  \ninner factor. The capacities of iterated lexicographic powers are determined, including those of self-complementary graphs that are vertex-transitive or strongly regular. Elementary, self-contained proofs are also given for three known results: the multiplicativity of the Lov\\'{a}sz theta function and the fractional Haemers number under lexicographic products, and the equality of the fractional and ordinary Lov\\'{a}sz theta functions. Finally, an open problem concerning the Shannon capacities of lexicographic and strong products is posed. The full version of this work is available at \\texttt{arXiv:2608.06573}.", "id": "Paper/63684", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63684"}, {"title": " Secret Sharing for Secure Storage with PUFs ", "webprogram_exclude": "0", "session_ids": ["Session/18389"], "source_sha256": "56f46a3b0c412a60d725ed3aaebdede9db05544d035a3d8fd4b6756d6515b28a", "withdrawn": "", "abstract": "In this talk, we present a new proposed secret sharing scheme for secure storage using physically unclonable functions (PUFs). In our construction, capacitive PUF measurements are first quantized into symbols over a finite field and then used to mask the shares of a ramp secret sharing scheme. This scheme protects a cryptographic key, which is used to encrypt the message; the resulting ciphertext is then stored in non-volatile memory. Our construction achieves deterministic, perfect secrecy for the key, without relying on probabilistic noise assumptions. The message is therefore computationally secure under the underlying encryption scheme. We also characterize how many bits of quantization are needed for the scheme to work, as a function of the key size, the reconstruction error budget, and the adversarial erasure budget. Finally, we show that when physical damage is localized, grouping neighboring measurements can reduce the required quantization level.", "id": "Paper/63687", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63687"}, {"title": " Posets and the nilradicals of seaweed algebras ", "webprogram_exclude": "0", "session_ids": ["Session/18334"], "source_sha256": "f411d74b45166305e2d713f0b9989a2eb381d56734af649b1377cb5c6b4aaa2d", "withdrawn": "", "abstract": "Seaweed algebras form a class of Lie algebras for which a number of algebraic invariants can be computed combinatorially.  One such invariant is the index, which is notorious for being difficult to compute.  Defining seaweed algebras originally as subalgebras of $\\mathfrak{gl}(n)$, Dergachev and Kirillov found that their index could be computed by counting paths and cycles in a corresponding planar graph called a meander. Here, we discuss the nilradicals of seaweed algebras. As it turns out, these subalgebras belong to a family of nilpotent Lie algebras defined by posets, aptly called nilpotent Lie poset algebras. Our main results show that the underlying posets as well as the index of nilradicals of seaweed algebras can be determined using modified versions of Dergachev and Kirillov's meander.", "id": "Paper/63690", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63690"}, {"title": " From Answers to Evidence: Teaching Mathematics with MATLAB Copilot, MATLAB Grader, and Agentic AI ", "webprogram_exclude": "0", "session_ids": ["Session/18137"], "source_sha256": "22ef6be5a5f68ff75690bbc4396341ae84ac6d3fc9f6867b274318a9d92cf61d", "withdrawn": "", "abstract": "Students increasingly encounter artificial intelligence as an answer generator, coding partner, and tutor, creating a central challenge for mathematics educators: how can AI support exploration without replacing the reasoning that instruction is intended to develop? This presentation demonstrates a classroom workflow that connects MATLAB Copilot, MATLAB Grader, and agentic AI to make students’ mathematical thinking visible and reviewable. Through examples drawn from vector operations, function behavior, numerical approximation, and model interpretation, students use MATLAB Copilot to ask questions, generate or explain code, and refine an approach. They then test claims against computations, visualizations, and instructor-designed MATLAB Grader assessments that provide deterministic checks and immediate feedback.\n\nThe presentation also shows how agentic teaching workflows can help instructors turn learning objectives into draft activities, assessment items, reference solutions, and tests, while preserving instructor review and accountability. Rather than treating AI use as simply permitted or prohibited, the proposed approach separates exploratory assistance from independent demonstration of learning. It asks students to document prompts, inspect output, explain revisions, and justify conclusions using mathematical evidence. Attendees will leave with a practical framework for discussing students’ perceptions of AI, designing mathematics activities that encourage productive AI collaboration, and using validated assessment evidence to distinguish fluency with an AI tool from understanding of the underlying mathematics.", "id": "Paper/63700", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63700"}, {"title": " Standards-Based Grading Across the Calculus Sequence ", "webprogram_exclude": "0", "session_ids": ["Session/17812"], "source_sha256": "168cbc7de59ea482de6ce004d55c348e19fe54aa13bbc1edd84fd3fe911ea802", "withdrawn": "", "abstract": "With the rise of AI “helping” students with their homework, in-class assessments are becoming increasingly crucial for gauging student proficiency. However, student performance on traditional assessments does not always reflect their current level of understanding, and a low test grade early in the course has the potential to derail the entire semester. In contrast, standards-based grading allows students to master course material and fulfill course outcomes at their own pace. This talk will examine the evolution and implementation of a standards-based grading system across the Calculus sequence and provide attendees with tips and considerations for implementing standards-based grading in their own classrooms.", "id": "Paper/63701", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63701"}, {"title": " Gradient Sampling Algorithm for Noisy Nonconvex Nonsmooth Optimization ", "webprogram_exclude": "0", "session_ids": ["Session/18069"], "source_sha256": "d9e75e4b47d1089b3aba38d71114c5d1f7d4ce229cffe765098d013587ae690e", "withdrawn": "", "abstract": "An algorithm is presented for minimizing locally Lipschitz objective functions that may be nonconvex and/or nonsmooth.  The algorithm, which is built upon the gradient-sampling methodology, is designed specifically for cases when objective and generalized gradient values might be subject to bounded, uncontrollable errors.  A novel assumption pertaining to such errors in nonsmooth settings is introduced that decouples the noise that may be present due to typical errors in derivative estimates with noise that may be due to misidentification of segments of differentiability of the objective.  Similarly to state-of-the-art guarantees for noisy smooth optimization, it is proved for the algorithm that, with probability one, either the sequence of objective values will decrease without bound or the algorithm will generate an iterate at which a measure of stationarity is below a threshold that depends proportionally on the error bounds for the objective function and generalized gradient values. The results of numerical experiments are presented, which show that the algorithm can indeed perform approximate optimization robustly despite errors in objective and generalized gradient values.", "id": "Paper/63702", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63702"}, {"title": " Topological Symmetry Groups ", "webprogram_exclude": "0", "session_ids": ["Session/18867"], "source_sha256": "9b15c277be756bd160ef799b431dfece7b6128e45800c39aa03e5b101513f807", "withdrawn": "", "abstract": "Chemists have defined the {\\it point\ngroup} of a molecule as the group of rigid symmetries of its molecular graph in\n$\\mathbb{R}^3$.  While this group is useful for analyzing the symmetries of rigid molecules, it does not include all of the symmetries of  molecules which are flexible or can rotate around one or more bonds.  To study the symmetries of such molecules, we define the {\\it topological symmetry group\\/} of a \ngraph embedded  in $\\mathbb{R}^{3}$ to be the subgroup of the\nautomorphism group of the abstract graph that is \ninduced by homeomorphisms of $\\mathbb{R}^{3}$. In this talk, I will  present a survey of results about the topological symmetry group including the REUF project that I led on this topic.", "id": "Paper/63703", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63703"}, {"title": " Using the Topological Analogue of Unique Ergodicity as Minimality to transform N partition functions of N Unique Universes into a Unique partition Function of a New Universe \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18321"], "source_sha256": "1edb383bff89f14fa8482316cd43e10fd21e69f5f3fe5ac286e230d1318ab40a", "withdrawn": "", "abstract": "Using the results of page 86 of \"Ergodic Theory\" by Blumenthal, A, and Young L.S. We use the idea of Unique Ergodicity to reduce the sum of N partition functions of Universes into a new partition function of a universe. This new partition function via quantum field theory will be a rigorous wave function of a universe which naturally has a non-zero energy, thereby replacing the ADM wavefunction of the Universe methodology with a new formalism that includes a time component in the universe's wavefunction and allows us to introduce Ergodic mixing of prior universes in its evolution equation.", "id": "Paper/63713", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63713"}, {"title": " CANCELLED Chromatic symmetric functions and change of basis \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/19321"], "source_sha256": "f479e704e5121bb6c4eed0ad12ac6190e456499cc231d1f1e8d09419d21fc2c5", "withdrawn": "", "abstract": "For a graph $G$, let $X(G)$ be Stanley's chromatic symmetric function.   We show that if $e_\\lambda$ appears with nonzero coefficient in the elementary symmetric function expansion for $X(G)$, then the shape of $\\lambda$ gives bounds on the independence number and clique number of $G$, a result which we call the Alpha-Omega Lemma.  This is done by first considering the expansion of $X(G)$ in terms of monomial symmetric functions and then doing a basis change.  The Alpha-Omega Lemma can be used to prove results about divisibility properties of the coefficents and about acyclic orientations of $G$ with a given number of sinks.  This is joint work with Foster Tom.", "id": "Paper/63719", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63719"}, {"title": " 3-dots, Densities, and Truchet Tiles ", "webprogram_exclude": "0", "session_ids": ["Session/18365"], "source_sha256": "61c930d6d3294056c0e2d49a85cc043e2a4db6a6ba27b7a5f8357d7d74d29b0f", "withdrawn": "", "abstract": "We discuss some results related to a beautiful example of Ledrappier, the 3-dot shift system, a $\\mathbb Z^2$-shift which is 2-mixing but not mixing of all orders. We describe the example, the connection to formal Laurent series over finite fields, and some recent work-in-progress on providing a simple numerical certificate for the existence of many distinct invariant measures (as shown by Einsiedler). This is joint work in progress with Abrams, Costa, Harriss, Kassabov, and Whitney, and grew out of drawing pictures of dots on graph paper. More recently, we have been exploring questions about related Truchet tilings, inspired by work of Hooper and earlier work of Pete.", "id": "Paper/63722", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63722"}, {"title": " Extended Kalman Filtering for Low-Cost, Aircraft Localization On and Near the Ground ", "webprogram_exclude": "0", "session_ids": ["Session/18239"], "source_sha256": "62579c5888ddfce72c8c71977ed6b6830d4c3b7ce59217073904354f6e406d35", "withdrawn": "", "abstract": "The GPS, radar and other specialized sensors that airports use to locate aircraft have accuracy limitations due to signal obstructions near the ground and are prohibitively expensive for smaller airports. We introduce cameras as alternative or supplementary sensors and formulate localization as a nonlinear filtering problem, and estimate the state with the Extended Kalman Filter.\n\nWe fit smoothing cubic splines to historical aircraft position data to generate realistic flight trajectories, and derive simulated GPS, radar and camera measurements from these trajectories. For a given aircraft, we feed these measurements into the Extended Kalman Filter and report state estimates with 95\\% confidence regions based on the filter’s output.\n\nWe show that fusing camera measurements with idealized models of existing airport radar and GPS measurements yields comparable estimation accuracy. Relative to GPS and GPS-and-radar configurations, camera inclusion reduces root mean squared error by about 60\\% and 25\\% respectively, for a nominal increase in projected cost.\n\nFinally, we expand our solution by simulating trajectories for several aircraft and use the Multiple Hypothesis Tracking algorithm to assign data to each aircraft. The resulting combinatorial assignment explosion is suppressed by weighing the different possibilities and only maintaining the high-probability assignments.", "id": "Paper/63723", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63723"}, {"title": " test - dyl \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18554"], "source_sha256": "672e8661730e53ba4d4f157d0cf4d0b3d471570db43d1cc2583f43d815c5452f", "withdrawn": "w", "abstract": "test", "id": "Paper/63768", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63768"}, {"title": " The Bethe-Hessian down to the percolation threshold ", "webprogram_exclude": "0", "session_ids": ["Session/18146"], "source_sha256": "cee2cdc9da60b22c2d726332b0526c58c0c64109c271ff2a62a806751cbad9e8", "withdrawn": "", "abstract": "The Bethe-Hessian is a symmetric matrix for which the negative spectrum has been observed to\nencode the informative structure of sparse stochastic block models. We prove that, in the stochastic\nblock model where all vertices have expected degree d > 1, the number of negative eigenvalues of the\nBethe-Hessian is exactly the number predicted by the eigenvalues of the planted model lying outside\nthe bulk spectrum. The condition d > 1 is optimal, and matches a regime in which existing spectral\napproaches based on larger non-Hermitian matrices apply. Our result extends a theorem of Stephan and\nZhu, who established the same conclusion under the assumption d ≥ 2.\n\nOur improvement relies on two main ideas. First, we construct test vectors on the 2-core, where\ndegree fluctuations are substantially smaller, and then extend them to the entire graph while controlling the\nquadratic form. Second, we construct the test vectors using an isotropic basis of the underlying Markov\nrandom field, with coefficients adapted to each relevant planted eigenvalue. This allows us to control the\nfluctuations of the test vectors throughout the sparse regime.", "id": "Paper/63772", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63772"}, {"title": " Sequential chaotic oscillations in excitatory–inhibitory threshold–linear networks ", "webprogram_exclude": "0", "session_ids": ["Session/18320"], "source_sha256": "721571ee5bc24d4369a0b8d3a84871111e6b272d59b7979bb3b14254a53471c9", "withdrawn": "", "abstract": "Metastable states, a phenomenon observed in brain dynamics and many other systems, have been proposed as a key feature of healthy brain function, reflecting a balance between integration and segregation. However, it remains unclear how to capture this behavior within a dynamical-systems framework. In this paper, we propose sequential chaotic oscillations (SCOs), arising in excitatory-inhibitory threshold-linear networks (E-I TLNs), as a candidate dynamical mechanism for sequential metastability. As a simple form of chaotic itinerancy, SCOs occur under constant input and consist of a sequence of metastable states whose transition order can be predicted by the underlying graph. To identify the parameter regime for SCOs, we develop new graph rules for E-I TLNs and use them to characterize the fixed point structure of E-I TLNs on paths and cycles. Our results show that the emergence of SCOs requires unstable singleton fixed points and sufficiently strong inhibition. \nIn addition to SCOs, we find that E-I oscillations need not be synchronized. Motivated by this, we introduce a decomposition into the $z$-mode and the mean mode, which capture excitatory differences and overall network activity, respectively. These modes are then used to distinguish attractors associated with the full-support fixed point of E-I TLNs on cycles.", "id": "Paper/63789", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63789"}, {"title": " Coloring sparse random Cayley graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18312"], "source_sha256": "71e9b9a95e1e4eeec2f2496e5da1c36022b262409533eb28e925d6536d83f48c", "withdrawn": "", "abstract": "It is shown that there exists $c > 0$ so that the Cayley graph over any finite abelian group $Z$ generated by $c \\log |Z|$ random elements is properly 3-colorable with high probability (as $|Z| \\to \\infty$). This is asymptotically tight and improves the best-known bound due to Alon of $\\frac{1}{4}\\log \\log |Z|$ elements. It also settles the abelian case of Alon's suggestion that a bound of $c \\log |G|$ may hold for any finite solvable group $G$.", "id": "Paper/63790", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63790"}, {"title": " The Two Circle Problem For Harmonic Functions on Homogeneous Trees ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "3fecff7f338ad378c94fe354178e60c533efc47c0a08cfaefdbd236f65724953", "withdrawn": "", "abstract": "A complex-valued function $f$ on the vertices of a homogeneous tree $\\mathfrak{X}$ of degree $q+1$ is defined to be \\textit{harmonic} if $\\mu_1f=f$, where $\\mu_1$ is the spherical mean-value operator of radius 1. We proved an analogue of Delsarte's Theorem from Euclidean space for homogeneous trees. Writing the radius-$k$ mean value operator as a polynomial in $\\mu_1$, we use properties of resultants and Eisenstein's Criterion to show that if $\\mu_{k}f=\\mu_{\\ell}f=f$, then for almost all $q$, a sufficient condition for $f$ harmonic is at least one of $k$ and $\\ell$ odd. Additionally, we prove that for $k$ and $\\ell$ relatively prime, our result holds for all values of $q$.", "id": "Paper/63792", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63792"}, {"title": " Linear equations and chromatic thresholds in <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.943ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 1267.1 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">B_h</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-42\" d=\"M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-42\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-68\" x=\"1074\" y=\"-213\"></use>\n</g>\n</svg> sets ", "webprogram_exclude": "0", "session_ids": ["Session/19346"], "source_sha256": "0cee7256197416ac683b9155dbe4632c809805679da1489c3ac7af83f20d3de4", "withdrawn": "", "abstract": "We derive sparse analogs of several Roth-type results, showing that they hold in $B_h$ sets of near-maximum size. It is known that if $S \\subset \\mathbb{Z}_N$ is $B_h$ then $|S| \\le C_hN^{1/h}$. We show that if $S$ is furthermore free of solutions to a linear equation $E$ with more than $2h$ variables then $|S| \\le D_h N^{1/h}$, where $D_h < C_h$. As a key input, it is established that $B_h$ sets of size $\\Theta(N^{1/h})$ are Fourier pseudorandom. If $E$ has a certain subdivision structure, we prove that $|S| = o(N^{1/h})$. The case of Sidon sets ($h=2$) was previously studied by Conlon, Fox, Sudakov, and Zhao as well as Prendiville.\n\nFocusing on the case $h=2$, we further show that if $E$ has a zero-sum subcollection of at least five coefficients and $S$ is Sidon with no solutions to $E$, then either $|S| = o(N^{1/2})$ or $S$ generates a Cayley graph over $\\mathbb{Z}_N$ with bounded chromatic number. On the other hand, we construct Sidon $S$ with $|S| = \\Omega(N^{1/2})$ and $\\chi(\\mathbb{Z}_N,S) = \\omega(1)$ such that $S$ is also free of multiple equations with zero-sum subcollections of four coefficients. This can be viewed as a sparse analog of a result of Liu, Wu, Yang, and Zhang characterizing linear equations with vanishing chromatic threshold.", "id": "Paper/63793", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63793"}, {"title": " Randomly piercing algebraic sets ", "webprogram_exclude": "0", "session_ids": ["Session/18139"], "source_sha256": "2767e3ec2e456fcfefc8e4bb50678cf1a050512ec30e16720a0c2b6667e4e102", "withdrawn": "w", "abstract": "How large of a random subset $D \\subset \\mathbb{F}_p^n$ does one need to almost surely intersect zero sets cut out by at most $s$ polynomials each of degree at most $k$? We determine the sharp threshold for this problem for all fixed $s$ and $k$. A corollary is that there exists a dense subset $A \\subset \\mathbb{F}_p^n$ free of $k$-term arithmetic progressions with common difference in a sufficiently small $D$, improving the lower bound for what is known as Szemer\\'edi's theorem with random differences. Our bound is the first to capture dependence of $|D|$ on $|A|$ in the finite field setting. Based on joint work with Daniel Altman.", "id": "Paper/63795", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63795"}, {"title": " Temporal Response Function Estimation Using Banded Ridge Regression to Study Neurophysiological Encoding of Narrative Speech ", "webprogram_exclude": "0", "session_ids": ["Session/18239"], "source_sha256": "8aef9c7f05e63e38a6208627de912e83fb1fcd0be977ce7cb7510e1555a1230c", "withdrawn": "", "abstract": "Many data analysis problems involve estimating relationships from high-dimensional datasets with correlated predictors. In these settings, ordinary least-squares regression often produces unstable estimates, motivating the use of regularization methods such as ridge regression. Classical ridge regression applies a single regularization parameter across all predictors, even when different groups of variables have different statistical properties.\nThis project investigates banded ridge regression as an extension of ridge regression for temporal response function (TRF) estimation, a linear modeling framework used to study the relationship between continuous speech and electroencephalography (EEG) recordings. Speech is represented using several feature spaces, including multiband acoustic envelopes, phonetic onset events, and word onset events, each converted into time-lagged predictors. Because these feature spaces differ in size and structure, banded ridge regression assigns a separate regularization parameter to each group instead of using a single penalty for the entire model. This allows the model to better account for the unique characteristics of each type of speech feature.\nThis project demonstrates how concepts from linear algebra, regression, and statistical learning can be applied to problems in computational neuroscience. By combining structured regularization with linear encoding models, this work explores mathematical methods for improving the analysis of complex biological data and lays the groundwork for incorporating additional speech features into future models.", "id": "Paper/63813", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63813"}, {"title": " Scalable Inference for Complex Survey Data Using the Survey-Adjusted Weighted Likelihood Bootstrap ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "dfd5df200323cbe720146e39de013bba43a7d13ed342026f98d81a6c0ace52e5", "withdrawn": "", "abstract": "Survey data are widely used across public health and social science research, but their sampling designs create challenges for statistical inference. Unequal selection probabilities can violate assumptions underlying standard regression methods and lead to biased estimates or underestimated uncertainty. This study applies the Survey-adjusted Weighted Likelihood Bootstrap (S-WLB) to data from the Youth Risk Behavior Surveillance System (YRBSS) to examine the relationship between demographic characteristics and reported marijuana use among adolescents.\nBecause the available YRBSS data are reported at a subgroup level rather than as individual-level observations, individual respondents’ data are reconstructed from reported sample sizes and outcome proportions. Logistic regression models are then fit using both unweighted and frequency-weighted approaches, with sample size serving as a proxy for the unavailable survey weights. The S-WLB procedure extends this framework by repeatedly perturbing the likelihood weights and refitting the model, producing a distribution of coefficient estimates that captures additional sampling variability. This approach is compared with conventional unweighted and weighted regression methods in terms of both point estimates and uncertainty intervals.\nResults show that demographic predictors exhibit generally consistent directional effects across modeling approaches. The S-WLB coefficient estimates remain closely aligned with weighted regression estimates while producing substantially wider uncertainty intervals. \nThese findings demonstrate that incorporating survey structure can affect statistical inference, and S-WLB provides a more realistic assessment of variability without requiring computationally costly Bayesian methods. Despite limitations arising from reconstructed data and the use of sample size as a proxy for official survey weights, the results suggest that S-WLB is a promising approach for inference in survey settings.", "id": "Paper/63814", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63814"}, {"title": " Classes of signed graphs admitting only main eigenvalues ", "webprogram_exclude": "0", "session_ids": ["Session/18146"], "source_sha256": "2308c7aa310df25d2303a8adfa0e91e7e87a9331edb9cfcd5e82349629da2649", "withdrawn": "", "abstract": "We study the existence of switching equivalent realizations whose eigenvalues are all main for several families of signed threshold graphs. In particular, we prove this property for connected signed antiregular graphs, complete split graphs, and threshold graphs generated by sequences of the form $(0^{t_1}1^{s_1})(0^{t_2}1^{s_2}).$ For these graph classes we confirm the conjecture of Akbari, Fran\\c{c}a, Ghasemian, Javarsineh, and de Lima [Linear Algebra Appl.\\ 614 (2020), 270--280] on the existence of a switching in which every eigenvalue is main. We also discuss several more general classes of threshold graphs, as well as some possible extensions.", "id": "Paper/63815", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63815"}, {"title": " From Feynman Diagrams to Formulas for Mathematical Constants ", "webprogram_exclude": "0", "session_ids": ["Session/19361"], "source_sha256": "c77761f2e43df1a80568bee01baaa0fce17345207b0c579932bd2b92674d64d6", "withdrawn": "", "abstract": "Feynman integrals arise in quantum field theory as mathematical expressions encoding particle interactions. \nIn the process of their evaluation, many mathematical constants arise, from $\\pi$ to Riemann zeta values and elliptic periods, making Feynman integrals a potential source of formulas for mathematical constants. \n\nRecently, interest in this direction has been growing: \nfamilies of Feynman integrals evaluate to multiple zeta values (Brown, 2009);\nseries for $\\pi$ and $\\zeta(2)$ arise from string amplitudes (Saha and Sinha, 2024).\nYet these formulas have been found sporadically, through individual insight and creativity, and there is no systematic method for generating them.\n\nWe present a method that turns Feynman diagrams into geometric spaces of formulas for mathematical constants: the integral of each diagram yields a Conservative Matrix Field (CMF; Elimelech et al., 2024), in which each direction corresponds to a different sequence of rational approximations to the constants carried by the integral. \n\nA single known Feynman integral therefore generates a whole family of formulas, which can be drawn as directions in a lattice whose axes are the edges of the diagram.\n\nWe show that multiple types of Feynman diagrams---e.g., bubble, sunrise, banana, triangle, conformal-box and kite diagrams---can be used to generate CMFs that produce new formulas for $\\pi$, logarithms of integers, zeta values, Clausen values and gamma-function periods.\n\nAs an example, consider the massless two-loop kite diagram.\n\\[\nI(p;\\boldsymbol{\\nu};x,y;D)\n=\n\\int\n\\frac{\n    d^D k_1\\,d^D k_2\\,\n    \\delta\\!\\left(x-\\ell\\cdot k_1\\right)\n    \\delta\\!\\left(y-\\ell\\cdot k_2\\right)\n}{\n    \\bigl[(k_1-p)^2\\bigr]^{\\nu_1}\n    \\bigl[(k_2-p)^2\\bigr]^{\\nu_2}\n    \\bigl[k_1^2\\bigr]^{\\nu_3}\n    \\bigl[k_2^2\\bigr]^{\\nu_4}\n    \\bigl[(k_1-k_2)^2\\bigr]^{\\nu_5}\n},\n\\qquad\n\\ell^2=0,\n\\quad\n\\ell\\cdot p=1.\n\\]\nWe construct a six-dimensional CMF from this integral in which \nevery trajectory yields rational approximations to $\\pi$ and $\\log 2$.", "id": "Paper/63883", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63883"}, {"title": " Data-Driven Dynamical Modeling of Seasonal Fish Migration ", "webprogram_exclude": "0", "session_ids": ["Session/19365"], "source_sha256": "848592569041ca7b262aec1afbef7a7807da3c669a40aab047ba3da3939264d1", "withdrawn": "", "abstract": "American shad (Alosa sapidissima) is an anadromous fish native to the Connecticut River whose upstream migration has been monitored for decades through daily fish-passage counts at Holyoke Dam in Massachusetts. We combine this long-term passage record with water temperature and river-discharge data to investigate whether the seasonal progression of migration can be represented by a low-dimensional dynamical system. Sparse Identification of Nonlinear Dynamics (SINDy) is applied to cumulative annual passage trajectories to identify a governing differential equation directly from the data. For each migration year $y$, we define $F_y(t)$ as the fraction of the annual run completed by time $t$. Numerical differentiation is not required because normalized daily passage counts provide direct observations of the migration rate $\\frac{dF_y}{dt}$.\nUsing passage records from 1976–2025, SINDy recovered a model closely approximating logistic dynamics, with the migration-rate parameter modulated by environmental forcing. The identified model relates migration progression to river-discharge anomalies and lagged water temperature, with temperature approximately seven days earlier providing the strongest predictive skill.\nThe environmentally forced model is evaluated using leave-one-year-out cross-validation and predicts major cumulative passage dates with mean errors of approximately 1–2 days. Years with interrupted or multi-pulse passage show larger departures from logistic dynamics, suggesting additional biological, environmental, or operational mechanisms. The results suggest that a simple environmentally forced dynamical law captures the dominant migration pattern, while departures from this law provide a means of identifying atypical migration years.", "id": "Paper/63894", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63894"}, {"title": " Effects of negative-density dependent emigration on landscape models with Strong-Allee growth terms ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "10f4c8dae238007cdccac017727566ce164f27115efe162f1f3c031dfc0bc5c6", "withdrawn": "", "abstract": "We study positive solutions to a steady-state one-dimensional landscape ecological model with a strong-Allee growth reaction term, namely when the reaction starts with a negative per-capita growth rate, increases to a positive maximum, then decreases back to zero at the carrying capacity. We assume negative density-dependent emigration (-DDE) at one of the edges between the habitat and the exterior, with hostile (Dirichlet) boundary conditions satisfied at the other edge. We obtain bifurcation diagrams for positive solutions (in terms of a parameter proportional to the habitat size). In the case of strong -DDE, for large habitat sizes, we prove there exist at least four positive steady states. This contrasts sharply with previously studied models having hostile boundaries at both edges, for which only two steady states are known.", "id": "Paper/63905", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63905"}, {"title": " <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.083ex\" height=\"1.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -576.1 466.5 721.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">e</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-65\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-positive partitions for chromatic symmetric functions ", "webprogram_exclude": "0", "session_ids": ["Session/19321"], "source_sha256": "35cdd669c12a18944abb4f77494bd96c0537e3844a31506dbe0fa4069139ff04", "withdrawn": "", "abstract": "We show that the partitions that always appear with nonnegative $e$-coefficients in chromatic symmetric functions of finite graphs are precisely the hook partitions.", "id": "Paper/63912", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63912"}, {"title": " Complex dynamics of excitable McKean-Vlasov dynamics and applications to Parkinson’s disease ", "webprogram_exclude": "0", "session_ids": ["Session/18320"], "source_sha256": "3a9875b9f12037a5dbe9815e9d758a9228cff13f2bff52c21c2e9c540a72aa88", "withdrawn": "", "abstract": "In brain, large-scale networks of neurons, each subject to random fluctuations, self-organize into collective behaviors underlying both physiological responses to stimuli and pathological brain states. Furthermore, biological neurons exhibit complex dynamics, often referred to as excitable units: each possesses a globally stable resting state, but perturbations exceeding a threshold trigger large transient excursions before returning to rest: these are the spikes, or action potentials, through which neurons communicate with each other. This talk presents new results on the collective dynamics of large networks of such excitable, noisy units.\n\nI will describe the mean-field limit of these systems as network size diverges (a McKean-Vlasov process) and characterize how the resulting dynamics depend on noise intensity. In particular, I will show that noise and excitability interact to generate stochastically periodic behaviors associated with collective oscillations, a phenomenon that vanishes at both weak and strong coupling. Considering small and large coupling limits, I will show that synchrony can only emerge in an intermediate coupling regime, a signature absent in strongly or weakly coupled systems or in the noiseless system.\n\nI will then explain recent efforts to use this better understanding of stochastic dynamics in the context of Parkinson's disease (PD), a neurodegenerative disorder marked by altered excitability and abnormal collective synchrony. In PD, neurons become more excitable, and collective synchronization emerge, similar to excitable McKean-Vlasov systems. I will thus use our model to explore the mechanisms of action of Deep Brain Stimulation (DBS), a chronic stimulation therapy for Parkinson's disease that abolishes synchrony and reduces symptoms. A distinguishing feature of our model is the impact of DBS on information processing: in the regime where oscillations vanish, information is maximized. I will conclude by presenting a new dataset collected from Parkinsonian patients implanted with DBS electrodes, designed to test the hypothesis that DBS acts by restoring information-processing capability in the affected circuit.", "id": "Paper/63916", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63916"}, {"title": " A generalization of Frenkel’s formula ", "webprogram_exclude": "0", "session_ids": ["Session/17942"], "source_sha256": "54406e9dafb2c7a88786c55f3e16702f7dd20ae3de47e2b9b21bbf231d944e4c", "withdrawn": "", "abstract": "We define a divergence operator for two positive definite Hermitian matrices. The trace of this operator reduces to the quantum relative entropy.  We give an integral representation of the divergence operator, which generalizes the new integral fomula by Frenkel. We extend our integral representation\nto bounded self-adjoint operators and $p$-Schatten  class of compact positive operators.   We give conditions for  convergence of integral formulas  for two operators appearing in the divergence operator,  and pose an open problem.\n\\bibitem{Fre23} P. E.  Frenkel, Integral formula for quantum relative entropy implies data processing inequality,Quantum 7, 1102 (2023).\n\\bibitem{Fri25} S. Friedland,  A generalization of Frenkel's formula,  arXiv:2602.10962, 2026.", "id": "Paper/63925", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63925"}, {"title": " Low Discrepancy Sequences that Are Good for Arbitrary Sample Sizes ", "webprogram_exclude": "0", "session_ids": ["Session/17807"], "source_sha256": "910a54def1550a2edb9bdc712d79d8a17329780fdc76e5cb583d6c75a40fde96", "withdrawn": "w", "abstract": "Low discrepancy sequences used for quasi-Monte Carlo computations are often opti-\nmized for a sequence of sample sizes, such as powers of a prime base. This is particularly\ntrue for lattices and digital sequences. While the preferred sample sizes are best, the\nuser might not be able to fully control the node set because of budget constraints or\nmissing data. We explore how well one can do for arbitrary sample sizes, in particular\nfor lattices and Kronecker sequences. We provide both theoretical and empirical results.", "id": "Paper/63926", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63926"}, {"title": " Topological decoding of grid cell activity via path lifting to covering spaces ", "webprogram_exclude": "0", "session_ids": ["Session/18320"], "source_sha256": "7d5c9fab289ac4773294ced217cd4402fefc1797c11728788be4640e4432d6c6", "withdrawn": "", "abstract": "High-dimensional neural activity often reside in a low-dimensional subspace, referred to as neural manifolds. Grid cells in the medial entorhinal cortex provide a periodic spatial code that are organized near a toroidal manifold, independent of the spatial environment. Due to the periodic nature of its code, it is unclear how the brain utilizes the toroidal manifold to understand its state in a spatial environment. We introduce a novel framework that decodes spatial information from grid cell activity using topology. Our approach uses topological data analysis to extract toroidal coordinates from grid cell population activity and employs path-lifting to reconstruct trajectories in physical space. The reconstructed paths differ from the original by an affine transformation. We validated the method on both continuous attractor network simulations and experimental recordings of grid cells, demonstrating that local trajectories can be reliably reconstructed from a single grid cell module without external position information or training data. These results suggest that co-modular grid cells contain sufficient information for path integration and suggest a potential computational mechanism for spatial navigation.", "id": "Paper/63934", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63934"}, {"title": " Singularity formations in kinetic equations ", "webprogram_exclude": "0", "session_ids": ["Session/18050"], "source_sha256": "c6f717793100565b4a60b01c24857e0cbaa93743e724ed4c1ecefbca48a860fd", "withdrawn": "", "abstract": "The Landau equation, introduced by Lev Landau in 1936, is a modification of the Boltzmann equation to specific applications in plasma physics and describes the interactions and collisions among charged particles in a plasma. The mathematical investigation of the Landau equation has been active for several decades, with researchers exploring various aspects of its behavior and properties. While the homogeneous version of this equation has been fully understood, the inhomogeneous equation remains a very difficult problem.  In this talk we show that solutions to the Landau equation presents implosion singularities. Some singularities are \"lifted\" from the Euler equations, and some arise purely from kinetic effects.", "id": "Paper/63948", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63948"}, {"title": " A <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"7.49ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 3224.9 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">10 \\times 42</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-31\"></use>\n <use xlink:href=\"#E1-MJMAIN-30\" x=\"500\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-D7\" x=\"1223\" y=\"0\"></use>\n<g transform=\"translate(2223,0)\">\n <use xlink:href=\"#E1-MJMAIN-34\"></use>\n <use xlink:href=\"#E1-MJMAIN-32\" x=\"500\" y=\"0\"></use>\n</g>\n</g>\n</svg> Chomp bar with three winning opening moves, and a staircase theorem for winning bites ", "webprogram_exclude": "0", "session_ids": ["Session/19366"], "source_sha256": "57251fb5a296c7f353780b0139e681719964447225a2abe35a0aa7fd5e578fac", "withdrawn": "", "abstract": "Chomp is played on an $a \\times b$ grid; a move removes a chosen cell together with everything below and to the right of it, and the player forced to take the poisoned corner loses. Gale's strategy-stealing argument shows that the first player wins every bar other than $1 \\times 1$, but it exhibits no winning move, and Gale asked in 1974 whether that move is always unique. It is not: Thompson found that $8 \\times 10$ has two. Ekhad and Zeilberger, having tabulated all bars up to $14 \\times 14$, asked for a bar with at least three.\n\nWe exhibit one: the $10 \\times 42$ bar has exactly three winning opening bites, at $(5,36)$, $(7,30)$ and $(8,26)$. The computation solves the ideal lattice of a $10 \\times 45$ box, some $2.9 \\times 10^{10}$ positions, by retrograde dynamic programming with one bit per position; the result was re-derived in a different lattice and counter-signed by an independently written engine.\n\nWe also prove that the winning bites of any bar form a strict antichain, with at most one in each row and each column, and that every square bar has an odd number of winning moves. A census over the searched region yields eighteen bars with exactly two winning moves and one with three.", "id": "Paper/63950", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63950"}, {"title": " KSA Theorem Polynomial Functions Of all Real Coefficients ", "webprogram_exclude": "0", "session_ids": ["Session/19368"], "source_sha256": "a80fd1b32a9088346b8d23ec0b6bd0d4c099b350d974b20d3386beff2120de76", "withdrawn": "", "abstract": "KSA Theorem: Polynomial function of all real coefficients\n\n\\[\n{f}({x}) = {a_{n}x_{n}} + {a_{n−1}x_{n−1}} + {a_{n−2}x_{n−2}} +\n{a_{n−3}x_{n−3}} + \\cdots + {a_{2}x_{2}} + {a_{1}x} + {a_{0}}\n\\]\n\ncan not have all real zeros (roots), even though all coefficients are\nreal if (1) none of the zeros (roots) is 0 (zero) and (2) ${a_{1}}_{2}\n< 2{a_{0}} {a_{2}}$.", "id": "Paper/63952", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63952"}, {"title": " RKT Theorem: The Sum of The Rth Power of The Roots in The Equation ", "webprogram_exclude": "0", "session_ids": ["Session/19368"], "source_sha256": "81e305f5e7fc2a8f3f090f95aa2e714b7181996e8cc3c1dfe24fa14e6d95d70c", "withdrawn": "", "abstract": "RKT Theorem: The sum of the $r^{th.}$ power of the roots of the\nequation\n\n\\[x^{n} +\np_{1}x^{n - 1} + p_{2}x^{n - 2} + p_{3}x^{n - 3} + \\ldots\\cdots +\np_{n - 2}x^{2} + p_{n - 1}x + p_{n} = 0\\]\n\nis defined by $s_{r}$ and\n$S_{m} = s_{1} + s_{2} + s_{3} + \\ldots + s_{m - 1} + s_{m}$,\nif $S_{m}$ have finite limit when $m \\rightarrow \\infty$, then\nthat finite limit is\n\n\\[\\lim_{n \\rightarrow \\infty}S_{n} = \\frac{- \\left( p_{1} + {2p}_{2} +\n{3p}_{3} + \\ldots + {np}_{n} \\right)}{\\left( 1 + p_{1} + p_{2} + p_{3}\n+ \\ldots + p_{n - 1} \\right)}\\]", "id": "Paper/63953", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63953"}, {"title": " Lines and Curves in Art ", "webprogram_exclude": "0", "session_ids": ["Session/17986"], "source_sha256": "a4959ca8301e0d0c6ec2d8805221cbffc2908dede6963782d2f4d0cbd1da6d0b", "withdrawn": "", "abstract": "The difference between lines and curves is striking in art. For example, \\textit{The Milkmaid} by Johannes Vermeer, mainly composed using curves, shows a warm and comforting figure. On the other hand, the figure in \\textit{Woman with a Water Pitcher}, also by Vermeer, is cool and aristocratic, mainly composed with lines and angles.  In these two pictures, we see that the properties of lines and curves---slope, length, and curvature---make a significant contribution to the emotional impact of the work. In this talk, we will see different ways that artists such as Franz Marc, Charles Sheeler,  William H.~Johnson, and Alma Thomas have used lines and curves in their work.", "id": "Paper/63969", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63969"}, {"title": " Phase Transitions in Turnpike Theory for Mean-Field Games ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "20d15e08e862fec3c6e7be618a5c09dd9b19bbad28022ce574c9275b870f23fa", "withdrawn": "", "abstract": "We study a translation-invariant mean-field game on the flat torus with interaction $F(x,m)=\\gamma (K*m)(x)$, where $K$ is smooth, even, and mean-zero. The interaction is of potential type, arising as the first variation of a quadratic energy, though the stationary system is not treated variationally.\n\nLinearizing around the uniform equilibrium yields mode-wise $2\\times 2$ systems with dispersion $\\sigma_\\xi(\\gamma)=\\nu^2(2\\pi|\\xi|)^4+\\gamma(2\\pi|\\xi|)^2\\hat K(\\xi)$. If $\\hat K$ is negative for some mode, a finite threshold\n\\[\n\\gamma_c=\\min_{\\hat K(\\xi)<0}\\frac{\\nu^2(2\\pi|\\xi|)^2}{|\\hat K(\\xi)|}\n\\]\nmarks loss of stability; otherwise $\\gamma_c=+\\infty$. Near criticality, the spectral gap scales as $\\rho(\\gamma)\\sim C_*\\sqrt{\\gamma_c-\\gamma}$.\n\nFor $\\gamma<\\gamma_c$, the uniform state is exponentially stable in the turnpike sense for finite-horizon problems, with rate $\\rho(\\gamma)$. At $\\gamma=\\gamma_c$, the gap closes and, after phase fixing and center-manifold reduction, one obtains algebraic midpoint decay of order $T^{-1/2}$. For $\\gamma>\\gamma_c$, a branch of nonuniform stationary solutions bifurcates via a pitchfork-type amplitude equation, with translations generating the full family.\n\nFinally, under standard asymptotic-consistency assumptions on symmetric $N$-player equilibria in the subcritical regime, we obtain qualitative propagation of chaos, without quantitative rates.", "id": "Paper/63976", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63976"}, {"title": " Local Matroids and Local Arrays of Tropical Linear Series ", "webprogram_exclude": "0", "session_ids": ["Session/19342"], "source_sha256": "faeda65ceaf20ffc0c8030c6a210b4aeb18b8fee25c772ab6d7e9904e4d85659", "withdrawn": "", "abstract": "Competing definitions of linear series on tropical curves have been proposed in the literature, including tropical linear series and combinatorial limit linear series. These seemingly distinct approaches give rise to two related combinatorial objects: the local matroid, which records the local structure of a linear series near an associated divisor, and the local array, which records the bending behavior of the linear series near a point of the tropical curve. In this talk, I will discuss my result that locally weakly recursive tropical linear series are combinatorial limit linear series. I will also present preliminary results on the relationship between local matroids and local arrays.", "id": "Paper/63998", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/63998"}, {"title": " Recursive Formula for the Equations of Hessenberg Varieties ", "webprogram_exclude": "0", "session_ids": ["Session/17996"], "source_sha256": "a97df262ca7df2c4490bfaee39de887ba711516cc1ca780d5624f597a6de3d6c", "withdrawn": "", "abstract": "Hessenberg varieties are subvarieties of the flag variety, defined by containment conditions on flags with respect to a linear operator. The study of these varieties lies in the intersection of algebraic geometry, combinatorics, and representation theory. In this talk, we explore a geometric framework for determining the closed subvariety structure of a general Hessenberg variety $\\mathcal{H}(X,h)$ for any linear operator $X$ and Hessenberg function $h$. By introducing a natural partial order on Hessenberg functions, we show how relations among functions illuminate the geometry of their corresponding varieties. In particular, we derive a concrete, recursive formula that explicitly computes the defining equations of $\\mathcal{H}(X,h)$ within each Schubert cell.  As an application, we provide an alternative geometric proof of Tymoczko's results on the existence of affine pavings of a given Hessenberg variety and on the dimension count of its cells.", "id": "Paper/64002", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64002"}, {"title": " Maximum loop nullity and loop zero forcing number ", "webprogram_exclude": "0", "session_ids": ["Session/18227"], "source_sha256": "8ebef14922b4fa08ccbfe20ffb82945973e49587677218f116e284ca0526f1d4", "withdrawn": "", "abstract": "The loop zero forcing number $\\operatorname{Z}_\\ell(G)$ was introduced in 2013 by Barioli et al.~in [Parameters related to tree-width, zero forcing, and maximum nullity of a graph, \\emph{J.~Graph Theory}, 72:146--177, 2013], but there has been only limited study of that parameter there and since. The associated nullity parameter, $\\operatorname{M}_\\ell(G)$ = the maximum loop nullity among real symmetric matrices described by of a graph $G$ and having all diagonal entries nonzero,  has not been previously  studied. Results about $\\operatorname{Z}_\\ell$ and $\\operatorname{M}_\\ell$ will be presented.", "id": "Paper/64005", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64005"}, {"title": " Tensors, entanglement, separability, and complexity ", "webprogram_exclude": "0", "session_ids": ["Session/18294"], "source_sha256": "487e6a906819148c9d1c95e0cc3b0e82f55ca5a9af337a3264d77589dd94ffc3", "withdrawn": "", "abstract": "The aim of this talk is to show how to characterize the entanglement and separability of d-partite states,  using some known and new norms on tensors.\nThe geometric measure of entanglement of a pure state is one of most natural ways to quantify the entanglement, which is simply related to the spectral norm of a tensor state.   On the other hand, the logarithm of the nuclear norm of the state and density tensors can be considered as its ``energy''.  We introduce the notion of Hermitian and density tensors,  and the subspaces of bi-symmetric and bi-skew-symmetric Hermitian tensors, which correspond to Bosons and Fermions respectively.  We show that separable density tensors,  and strongly separable bi-symmetric density tensors are characterized by the value (equal to one) of their corresponding nuclear norms.   In general,  these characterizations are NP-hard to verify.  The above quantities are computed in polynomial time when we restrict our attention to Bosons:  symmetric $d$-qubits, or more generally to symmetric $d$-qunits in $C^n$,  and the corresponding bi-symmetric Hermtian density tensors, for a fixed value of $n$.\n\\bibitem{Fri25} S. Friedland, Tensors, entanglement, separability, and their complexity, arXiv:2509.21639, 2025.", "id": "Paper/64006", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64006"}, {"title": " Platelet plug microstructure and flow modulate fibrin gelation dynamics: Insights from computational simulations ", "webprogram_exclude": "0", "session_ids": ["Session/17988"], "source_sha256": "da6963ac013ac57df8c4dfeffc6adfcb67f0595453f3b6f96ff831938b1fdf95", "withdrawn": "", "abstract": "During blood clot formation, the architecture of the growing platelet aggregate is heterogeneous, with areas of densely and loosely packed platelets. The surface of activated platelets facilitates biochemical coagulation reactions, ultimately resulting in the formation of a fibrin network which stabilizes the thrombus. How platelet-plug microstructure and flow jointly govern the onset and development of fibrin is not completely understood. Here, we present a 2D discrete-continuum computational framework that integrates a pre-adhered, discrete platelet aggregate, a reduced coagulation model on discrete platelet surfaces, and a fibrin polymerization model under physiologically relevant shear conditions. By treating platelets as discrete surfaces rather than a continuum, we can investigate how the free fluid volume to platelet surface area ratio in the clot affects substrate uptake and binding/unbinding to platelet surfaces. Our results suggest that early fibrin gelation dynamics are influenced by both flow and intraplug architecture and that chemical accumulation and transport within the aggregate determines the location of the initial fibrin gel. This framework can provide a basis for future microfluidic studies of platelet–coagulation interactions under flow.", "id": "Paper/64009", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64009"}, {"title": " Computability of Julia Sets and Hyperbolicity for Complex Hénon Maps ", "webprogram_exclude": "0", "session_ids": ["Session/19357"], "source_sha256": "baa76924e4f432cf29407824756293b1b01d2961ec61d5fa928ffadf2311c0d8", "withdrawn": "", "abstract": "Complex Hénon maps are among the most important examples of polynomial dynamical systems in several complex variables, exhibiting rich behavior that extends many phenomena from one-dimensional complex dynamics. In recent joint work with Christian Wolf, we investigate computability questions for complex Hénon maps and, more generally, polynomial diffeomorphisms of two complex variables.  \n\nI will discuss our results on the computability of Julia sets and on the algorithmic structure of parameter space. For hyperbolic maps, we establish computability of the Julia set, semi-decidability of hyperbolicity, and lower computability of the hyperbolicity locus. I will also describe newer work extending computability of Julia sets beyond the hyperbolic setting to classes of non-hyperbolic maps whose Fatou components are attracting basins. In contrast, I will illustrate how the presence of neutral dynamics can lead to non-computable Julia sets, paralleling phenomena known from one-dimensional complex dynamics. \n\nThe talk will emphasize the interplay between computable analysis, hyperbolic dynamics, and several complex variables, and will provide an overview of recent progress and open questions.", "id": "Paper/64022", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64022"}, {"title": " On information controls ", "webprogram_exclude": "0", "session_ids": ["Session/18328"], "source_sha256": "ffe7fcd4957e3f26f0aa88c775c0b73f575808b6e3e61868e9e8f8ad6eb280a1", "withdrawn": "", "abstract": "In this talk, we investigate an optimization problem where the information serves as the control variable. More precisely, the control takes the form of a sub-$\\sigma$-algebra of a given $\\sigma$-algebra, or a sub-filtration of a given filtration. We discuss an insider trading problem as a motivating example, and present preliminary results in a continuous-time dynamic framework. We develop an It\\^o’s formula for smooth functions defined on $\\mathcal{P}_2(\\mathcal{P}_2(\\mathbb{R}^d))$, the space of laws of random probability measures on $\\mathbb{R}^d$. This It\\^o's formula gives rise to a Hamilton–Jacobi–Bellman (HJB) equation on $\\mathcal{P}_2(\\mathcal{P}_2(\\mathbb{R}^d))$, which characterizes the dynamic value function of the information control problem. The talk is based on joint work with Jianfeng Zhang (USC).", "id": "Paper/64024", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64024"}, {"title": " Higer Dimensional Maps That Are Weakly Post-Critically Finite ", "webprogram_exclude": "0", "session_ids": ["Session/18259"], "source_sha256": "21c6b2d049540b664bcbb65022c77b741765335adb2324006200118c2b9c2130", "withdrawn": "", "abstract": "The critical locus of a morphism $f:\\mathbb{P}^N\\to\\mathbb{P}^N$ has codimension $1$. When $N\\ge2$,\nIngram--Ramadas--Silverman (MR4577329) and Gauthier--Taflin--Vigny (MR5082538) have shown that\nthe post-critically finite (PCF) maps are not Zariski dense in the moduli space of such maps, in contrast to\nthe situation when $N=1$. In this talk we explore some weaker notions of PCF in higher dimensions. This\nis very much work in progress.", "id": "Paper/64025", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64025"}, {"title": " A Multi-Stage Mathematics Placement Framework for Students First Year as Undergraduates In Modeling and Calculus ", "webprogram_exclude": "0", "session_ids": ["Session/18091"], "source_sha256": "55cd86ea232359ecb428359d3cf4bef80d4b788a01a29103b185fcd26c41fcc9", "withdrawn": "", "abstract": "The United States Military Academy has developed a comprehensive mathematics placement framework that integrates multiple measures of student preparation to support evidence-based placement decisions for more than 1,200 incoming cadets annually. Prior to arrival, cadets are placed into MA103 (Data-Driven Modeling) or MA153 (Advanced Data-Driven Modeling) using an online placement survey, high school performance, and institutionally developed placement criteria. During the fall semester, cadets complete one of three differentiated calculus placement assessments based on their mathematical background to determine placement into the appropriate spring mathematics course—MA104 (Single Variable Calculus), MA204 (Single Variable Calculus Review + Multivariable Calculus), or MA255 (Multivariable Calculus). Placement decisions are further informed by instructor observations and early course performance. This presentation describes the design and implementation of the two-stage placement framework and the analytical methods used to evaluate placement accuracy, student outcomes, and the effectiveness of multiple measures in informing placement decisions. Results will inform ongoing refinement of placement criteria to improve student success in foundational mathematics courses.", "id": "Paper/64044", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64044"}, {"title": " Tree-presented groups and their computable cores ", "webprogram_exclude": "0", "session_ids": ["Session/17922"], "source_sha256": "cfecd31d646d5818f9956cde389fdfe6d1701e4c2d6773039c8d2d5f6b91110f", "withdrawn": "", "abstract": "Ideas from computability theory have long been applied to countable groups.\nThe undecidability of the word problem for finitely presented groups,\nestablished independently by Boone and by Novikov in the 1950’s,\nwas an early success in this area.  More recently, countable groups in general\nhave been the subject of study by computability theorists, who have\ndeveloped standard notions of a \\emph{computable group} and a\n\\emph{c.e.-presented group}.  (The latter is more general, encompassing\nall finitely presented groups and more.  ``C.e.’’ stands for ``computably enumerable.’’)\n\nMore recently, computability has been applied to compact topological groups\nand other structures of the cardinality of the continuum, in a way closely\nconnected to descriptive set theory.  Here the elements of a group\nmay be viewed as paths through a tree, compatible with the topology\nof the group, and the group multiplication is required to be a ``type-2 computable’’\nfunction on these paths.\n\nWe will give a gentle introduction to these concepts, and to some connections\nbetween them, by using the notion of the \\emph{computable core} of a\ntree-presented structure, which is the subject of current work by Jason Block\nand the speaker.  We will describe the Turing degree spectrum of a countable\ngroup, and will also discuss computable categoricity for countable groups.\nThese are both standard notions in countable computable structure theory,\nand applying them to the computable cores of profinite groups will yield\ncertain insights into the complexity of the profinite groups themselves.\nExamples will include the additive group of the $p$-adic integers, the absolute\nGalois group of the rational numbers, and a new group cooked up\nby Block and Miller in order to investigate the maximal complexity\npossible in the computable core of a profinite group.", "id": "Paper/64061", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64061"}, {"title": " Monogenic Fields of Cryptographic Size ", "webprogram_exclude": "0", "session_ids": ["Session/19355"], "source_sha256": "decc48cce8e10d4421f4fe58f8e5b5715ebfb218379a3a264a0a970149438e81", "withdrawn": "", "abstract": "For a monic irreducible $f\\in\\mathbb{Z}[x]$ of degree $n$ and an integer $c$, we study the palindromic transform $F(x)=x^n f(x+x^{-1}+c),$ which produces a polynomial of degree $2n$. We give a discriminant formula $\\disc(F)=f(c+2)f(c-2)\\disc(f)^2,$ sufficient conditions for the irreducibility of $F$, and a criterion showing that $F$ is monogenic when $f$ is monogenic and $f(c+2)f(c-2)$ is squarefree, together with a matching non-monogenicity criterion. Iterating the transform yields monogenic number fields of degree $2^k n$ from a fixed base; as an explicit example, we construct a monogenic field of degree $512$ from $x^4+x+1$.", "id": "Paper/64065", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64065"}, {"title": " From Subsonic to Supersonic: Recent Progress on Multidimensional Euler–Poisson Flows ", "webprogram_exclude": "0", "session_ids": ["Session/18342"], "source_sha256": "e4ecfb7bcfe8eb2772b9af8cef2745d04bb08e269d6b071372ee254e7bd91cf5", "withdrawn": "", "abstract": "Over the past decade, significant progress has been made on the existence and local stability of multidimensional subsonic, supersonic, and smooth transonic solutions to the compressible Euler--Poisson system. \n\nIn the first part of this talk, I will survey these developments and discuss how they can be used to study classical problems in compressible fluid dynamics. In particular, I will explain their connection to the de Laval nozzle problem and recent progress toward understanding multidimensional transonic flows through nozzles.\n\nIn the second part, I will present recent results on the global uniqueness of subsonic solutions to the Euler--Poisson system. In contrast to perturbative uniqueness results, the uniqueness is established without assuming that the solutions are small perturbations of a fixed background state.", "id": "Paper/64069", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64069"}, {"title": " Swirling Dance: Circular Arm and Leg Dance Movements ", "webprogram_exclude": "0", "session_ids": ["Session/18233"], "source_sha256": "810377f614ea786bf9640312ca77995f72504a1d30066467f75674b1e9a18fc6", "withdrawn": "", "abstract": "Circular arm and leg movements are often used by dancers to create a swirling aesthetic. We have catalogued ways dancers typically execute these movements and show examples, attending to topological and other mathematical elements. The catalogue includes circular movements of two arms or of arms and legs, distinguishes circular direction, axes of rotation, and whether two circular movements are in or out of phase. We have created short videos and collected video links showing examples from dance and other movement disciplines. This study helps provide an overview and a new perspective for choreographers, dancers, and movement artists using such movements.", "id": "Paper/64076", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64076"}, {"title": " Average orders of automorphism groups and average-case complexity of Tensor Isomorphism problems ", "webprogram_exclude": "0", "session_ids": ["Session/16950"], "source_sha256": "e99f698d3aaf079cdf2cd8bc087223b66125c280d4b7314af4f0ab0e49b13b25", "withdrawn": "", "abstract": "The Tensor Isomorphism problem asks whether two tensors lie in the same orbit under the natural action of general linear groups. In quantum information theory, this corresponds to determining whether two multipartite pure states are SLOCC-equivalent. In the setting of finite fields, many fundamental isomorphism problems—including those of graphs, groups, algebras, and polynomials—reduce to testing isomorphism between structural tensors. \nIn this talk, I will first survey recent progress on tensor isomorphism from a complexity-theoretic perspective. I will then present a proof that the average order of automorphism groups of 3-tensors is constant. This result yields nearly tight upper bounds on the number of p-groups of Frattini class 2 and resolves several open questions posed by Blackburn, Neumann, and Venkataraman. I will also describe average-case polynomial-time algorithms for structural tensor isomorphism problems, which in turn suggest potential attacks on certain post-quantum digital signature schemes based on isomorphism assumptions. The main mathematical tools involved include fixed-point analysis and random matrix theory over finite fields.", "id": "Paper/64091", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64091"}, {"title": " Presence Is Not Placement: Auditing What Vibrato Metrics Measure ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "de5ccf11488316c32b1fa9eac3c0e9cac9243009a4cb42ee3a0f92b6dfa8596c", "withdrawn": "", "abstract": "Not all vibrato is created equal. Singers decide which notes receive more of it, and this decision contributes to phrasing. In VocalSet (Wilkins et al. 2018), notes held twice as long as their neighbors have about 16\\% deeper vibrato, and phrase-final notes have about 17\\% deeper vibrato. We ask whether a learned vibrato evaluator can detect this placement. To test this, we build WaveMaster, a MERT-based vibrato-presence classifier that follows the evaluation used in recent singing-synthesis work. We then edit recordings note by note. Our main modification keeps the same set of vibrato depths but assigns those depths to different notes. This removes most of the measured placement while holding overall depth fixed. The classifier’s mean vibrato probability changes by only +0.001 (95\\% CI [−0.003, +0.005]). Giving every note the same vibrato depth also earns perfect Style Accuracy. The result replicates on eight external singers and four training variants. Intermediate MERT representations retain note-depth information, but the time-averaged classifier uses it poorly. This is not a failure of binary classification but a mismatch between the metric and the goal of expressive control. A presence-only objective could therefore discard phrasing without penalty. Vibrato controls should be evaluated not only by whether vibrato is present, but also by where it occurs.", "id": "Paper/64108", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64108"}, {"title": " Multivariate max-min sampling operators: Theory and applications in image processing ", "webprogram_exclude": "0", "session_ids": ["Session/19339"], "source_sha256": "badd8e63345782c8d0ab4c337c6dbecdac60f89a53679871e4229c962e4b101e", "withdrawn": "", "abstract": "The approximation of functions using sampling-based operators has emerged as a prominent research area within approximation theory, with potential applications in signal analysis and image processing. We introduce and present a comprehensive study on the family of multivariate sampling operators based on max-min structure, and their utility in image processing tasks. Theoretically, the approximation properties have been established for functions in space of all continuous functions and the Orlicz spaces. The Orlicz spaces are extension of the Lebesgue spaces and consist of several interesting spaces, for instance,  the Exponential space and the Logarithmic space. Further, the utility of our proposed operators have been demonstrated through successful applications in image processing, in particular, image reconstruction, image upscaling and image inpainting, and the performance has been evaluated using  PSNR, SSIM and EPI.", "id": "Paper/64114", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64114"}, {"title": " Gromov’s conjecture on macroscopic dimension for Kähler manifolds ", "webprogram_exclude": "0", "session_ids": ["Session/17803"], "source_sha256": "7da3059d1b84b53b3c47e09c8d4b08bbba43e8aa8a4df5f86faacdab889b8dad", "withdrawn": "", "abstract": "The macroscopic dimension of a manifold is an isometry invariant that is at most $k$ if the large-scale geometry of the manifold can be modeled by a $k$-dimensional simplicial complex. Gromov’s conjecture predicts that if a closed $n$-dimensional manifold admits a metric of positive scalar curvature, then the macroscopic dimension of its universal cover is at most $n-2$. In this talk, we prove a weaker version of Gromov’s conjecture for K\\\"ahler metrics on smooth projective varieties: the macroscopic dimension is indeed at most $n-1$. We also discuss cases where the upper bound $n-1$ can be improved to the conjectured bound $n-2$.", "id": "Paper/64127", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64127"}, {"title": " Zig-zag ", "webprogram_exclude": "0", "session_ids": ["Session/17986"], "source_sha256": "7b41467392b03c46d2f5d446abe334f88b04522b7b8947c02a740da8d3d3f7b4", "withdrawn": "", "abstract": "This presentation will examine the symmetrical properties of zig-zag patterns, and demonstrate how they can be used to make art. Featuring glide reflection symmetry, the line of a basic zig-zag drawing can be thickened to create a zig-zag strip. These strips offer many design opportunities. One such example is rickrack, originally referred to as waved crochet braid. Invented in the mid- nineteenth century, rickrack is used as reinforcing edging and as decorative flourishes on clothing. In my own work, I have developed a paper zig-zag strip composed of a series of identical Isosceles triangles, inspired by rickrack textile decorative trim. I have incorporated my own hand-drawn lace surface patterns that preserve the glide reflection symmetry. Once I had the 2-D drawings complete, I wanted to take these pieces a step further and build 3-D sculptures. I used an accordion folding technique that separates the triangles from each other and then bifurcates each isosceles triangle by creating a fold from the vertex to the center of the base. Splitting the triangles in half in this manner creates a series of right triangles that are the building blocks for the sculptures. This technique, alternating the folds, creates a 3-D type of zig-zag with both convex and concave spikes. Bringing the two ends of the strip together to form a torus-like shape creates something resembling a crown. I have titled this form “Crown of Pythagoras”, because it was the perpendicular folds that formed the right triangles that made the transformation from a 2-D drawing to a 3-D sculpture possible. Another historical textile example that incorporates zigzags is Bargello needlework fabrics. This includes the popular flame patterns. These patterns use layers of zig-zags to create complex, undulating patterns. I continued my exploration into these designs. I have started to draw multiple zig-zags in a single drawing. This presents a new set of possibilities and well as new challenges. I did not expect my initial interest into a very simple geometric line drawing to lead to a year of new work.", "id": "Paper/64129", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64129"}, {"title": " Target dimensions for sphere maps ", "webprogram_exclude": "0", "session_ids": ["Session/18295"], "source_sha256": "a67117c028da79705382901f0cbea40df480d52fbe6c3858ae8588f437a38c2f", "withdrawn": "", "abstract": "Finding all monomial sphere maps of degree d in source dimension n amounts to solving an underdetermined  system of linear equations. The number N of non-zero monomials in a solution is of considerable interest in both CR Geometry and linear programming. We discuss the possible values of N in terms of n and d, obtaining in the process a number $G(n)$ such that, for each N bigger than $G(n)$, there is a solution with precisely N terms. The new part of the result is that this formula is asymptotic to\n$c n^{3/2}$.  Earlier results were quadratic in n. The formula is obtained via combinatoriaI reasoning, and I conjecture that the formula is sharp.", "id": "Paper/64155", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64155"}, {"title": " From Chalkboard to Chatbot....Who is Designing the Lesson? ", "webprogram_exclude": "0", "session_ids": ["Session/19349"], "source_sha256": "e3894344ab0568bf33580770d9d9a046bd3b3a308bd8f68c3120e520d143680f", "withdrawn": "", "abstract": "Generative Artificial Intelligence (AI) is all around us, and students are using it. While AI offers many possibilities in the field of education, it also has drawbacks and limitations. In this session we will share a lesson planning assignment used in a secondary mathematics methods course that helps students explore and better understand the abilities of AI for teaching and some ways it still has room to grow. We will share students’ thoughts and lessons learned.", "id": "Paper/64156", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64156"}, {"title": " Two invariants of type-preserving representations and applications ", "webprogram_exclude": "0", "session_ids": ["Session/18362"], "source_sha256": "131de92bff1507acdb939a298c6bbca0a86cca119190b5f49c7bddad1825761f", "withdrawn": "", "abstract": "We investigate the spaces of representations of surface groups into $\\mathrm{PSL}(2, \\mathbb{R})$. For closed surfaces, by the classic result of Goldman, the Euler class provides a complete classification of the connected components of the $\\mathrm{PSL}(2, \\mathbb{R})$-character variety. However, describing these components becomes more subtle when considering the relative character variety for punctured surfaces, which consists of type-preserving representations. In this talk, I will introduce two invariants of type-preserving representations, namely the relative Euler class and the sign, that characterize the connected components. As an application, I will show the existence of \\textit{totally hyperbolic} representations, giving a negative answer to a question of Bowditch. I will also discuss the relation between the existence of such representations and the mapping class group action on the relative character variety.", "id": "Paper/64177", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64177"}, {"title": " Ratios of Bounds on Arborescences ", "webprogram_exclude": "0", "session_ids": ["Session/19360"], "source_sha256": "38e6292b593b84957eb48bba8074f1aaa0c9c31d4bd67497e1f98f55ae83b712", "withdrawn": "", "abstract": "An arborescence rooted at $v_0$ is a subgraph $T$ of a directed graph $G$ such that $T$ is a spanning tree and every edge of $T$ is directed toward $v_0$. Given an Eulerian undirected graph $H$, we wish to bound the number of arborescences that Eulerian orientations of $H$ can have, and determine if these bounds are tight.\n\nSpecifically, for $H = K_{n,m}$, we prove an upper bound and show that upon picking a uniformly random Eulerian orientation this bound is achieved, up to a $1+o(1)$ factor, with high probability. We also prove upper and lower bounds that are tight up to a $1+o(1)$ factor for $H=K_n \\square K_m$.\n\nFinally, we use Fourier analysis to compute the number of arborescences for Eulerian orientations of Cayley graphs on finite cyclic groups, providing an exponential (in the number of vertices) ratio between the minimal and maximal number of arborescences of Eulerian orientations.", "id": "Paper/64188", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64188"}, {"title": " Conformally invariant equations with negative critical exponents on the three dimensional hyperbolic space ", "webprogram_exclude": "0", "session_ids": ["Session/17749"], "source_sha256": "508e23d8c39007c1270015ebfeae3a01cc338539f56653f0ca320cde27a0ce44", "withdrawn": "", "abstract": "We establish a symmetry result for positive entire solutions with a prescribed growth rate to the following fourth order equation on the 3-dimensional hyperbolic space $\\mathbb{H}^3$:\n$$P_2 u = -u^{-7},$$\nwhere $P_2$ denotes the fourth-order Paneitz operator. We prove that any positive solution on $\\mathbb{H}^3$ exhibiting exponential growth at infinity must, up to hyperbolic isometries, be radial and strictly increasing with respect to some point in $\\mathbb{H}^3$. Our proof relies on precise Green's function estimates based on Lu-Yang's formulae, and moving plane method on hyperbolic spaces.", "id": "Paper/64208", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64208"}, {"title": " Integrating ChatGPT into secondary mathematics education coursework ", "webprogram_exclude": "0", "session_ids": ["Session/18137"], "source_sha256": "14b930a5ede57df04dee91159406b686853aad2637b2a122476ff8a50c67dada", "withdrawn": "", "abstract": "The broad goal of this presentation is to introduce the notion of using AI chatbots, specifically Open AI’s ChatGPT, as an assistant for students in secondary mathematics education courses. It is essential that educators have information on ways that AI can be used in educational contexts, and how students react and respond to its use. The specific purpose of this presentation is twofold. First, I will informally share in-class student activities where students used ChatGPT to plan secondary math lessons. Second, I will share the results of two research studies. The first, “Using ChatGPT as a lesson planning assistant with preservice secondary mathematics teachers” found that while students were generally accurate in their assessment of ChatGPT’s pedagogical output, they were less accurate in their assessment of mathematical output. The second, “Using a Human-Computer Information Retrieval framework to examine preservice secondary mathematics teachers’ reactions to using ChatGPT as a lesson-planning assistant” found that students generally trusted ChatGPT as a brainstorming partner, yet this trust was not supported by their levels of satisfaction with actual lesson output. Specific mathematical output related to non-routine secondary-level mathematics problems will be shared, along with descriptive statistics and selected qualitative coding of students’ reactions to output. Suggestions will be made for use of generative AI chatbots in graduate and undergraduate educational contexts.", "id": "Paper/64221", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64221"}, {"title": " Combinatorics of Seaweed Meanders ", "webprogram_exclude": "0", "session_ids": ["Session/19346"], "source_sha256": "f83e9e0f5e3d72f0847c2926897fc632a8827de225f3911cb8478d454441f3b8", "withdrawn": "", "abstract": "Seaweed meanders were introduced by Dergachev and Kirillov in connection with \\textit{seaweed subalgebras} of $\\mathfrak{gl}_n$. We show that the index of a uniformly random seaweed meander satisfies a central limit theorem. We also extend work by Archer, Geary, and Laudone on the enumeration of seaweed meanders whose compositions have restricted parts. Finally, we give a connection to billiards in triangular shapes, which is related to a result of Eu, Fu, and Hsu.", "id": "Paper/64244", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64244"}, {"title": " Incorporating Ethical Reasoning in Calculus II ", "webprogram_exclude": "0", "session_ids": ["Session/18144"], "source_sha256": "35ee398267d277ae4e32b62cdd8449cf306a55b6f11476dd0c86f8d38763cf3f", "withdrawn": "", "abstract": "As a foundational part of STEM education, the calculus sequence is an ideal place to introduce students to the ethical practice of mathematics. However, with abstract topics like integration techniques and infinite series, this can be more difficult in Calculus II than in Calculus I. In this talk, I will present some Calculus II-based ethical reasoning questions that I developed in collaboration with Cathy Erbes (Hiram College). In addition, I will discuss my successes and challenges in implementing these problems in my own Calculus II course.", "id": "Paper/64248", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64248"}, {"title": " The Positive Mass Theorem in Arbitrary Dimensions ", "webprogram_exclude": "0", "session_ids": ["Session/18284"], "source_sha256": "e1956c26e74f98b03a8c016f440a4ebff8bbca059b5b77abc3e4194367a47588", "withdrawn": "", "abstract": "We present an inductive scheme for proving the positive mass theorem in arbitrary dimensions, extending the Schoen–Yau argument from dimensions at most 7 to the general case. This is a joint work with Simon Brendle.", "id": "Paper/64249", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64249"}, {"title": " How well is crumpling understood, and why bother? ", "webprogram_exclude": "0", "session_ids": ["Session/17370"], "source_sha256": "c1b8a973fd5814a68ee41c21e777bba6988d3d87d87bd12331cf1f06d0d5724b", "withdrawn": "", "abstract": "When a thin sheet is confined to dimensions much smaller than its length and width, the sheet typically becomes trapped in a complex state of sharp points and bends known as crumpled matter.  This state has fascinated researchers for many years, and many studies have been published.  But how well do we really understand crumpled matter?  In this talk I will focus specifically on predictions of a crumple’s response to an applied load and show how various current models approach the subject.  I will then show data we have gathered experimentally probing hundreds of crumpled sheets and show what seems predictable and what does not, in an attempt to highlight some shortcomings.  Finally, I will give a couple of examples of where this unique state of matter might find practical uses.", "id": "Paper/64254", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64254"}, {"title": " Frontier GPT Models for Research Mathematics: Reproducing Proofs and Tackling Open Problems ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "0c90d9697eb3d68777ad32e286f4a9dcb9ee0a4f69ab63423a9ebbf100acccff", "withdrawn": "", "abstract": "Large language models (LLMs) are improving at mathematical reasoning, but their reliability on research-level proofs and open problems remains uncertain. To assess this, we developed a multi-agent system that prepares problems from arXiv papers, generates candidate proofs, and evaluates them through mathematical and source checks, including searches for counterexamples and hidden assumptions. Using GPT-5.5 at extended reasoning effort, we evaluated 31 theorems from 27 papers published after GPT-5.5's knowledge cutoff of December 1, 2025. When each theorem statement was supplemented with relevant definitions and supporting lemmas from its source paper, 23 of 31 theorems (74\\%) were classified as reproduced: 21 by the automated final checker and 2 by separate Codex-agent reviews. With the theorem statements alone, 15 of 31 (48\\%) were classified as reproduced. Here, reproduced means that LLM-based verification stages agreed that a proof was complete and mathematically valid; it does not imply human verification. On two MathArena benchmarks, we compared one GPT-5.5 solver agent with a team of GPT-5.5 solver agents in our pipeline. The team achieved relative gains of about 9\\% on ArXivMath and 31\\% on BrokenArXiv, which tests whether LLMs reject plausible but false mathematical statements. We then used the pipeline on open problems with GPT-5.6 Sol models. This work produced a candidate counterexample to a conjecture in dynamical sampling; an explicit construction for Tunnell's map; a computer-assisted candidate proof of the Hasebe--Ueda conjecture on free additive convolution; and an expert-reviewed, symbolically checked analysis of linear scattering rules for a fixed configuration of five hard spheres. Several results remain provisional and require further review. Overall, these experiments identify a practical role for agentic AI: helping mathematicians test conjectures, find errors, check difficult computations, and eliminate unsuccessful proof strategies. Independent expert review or formal proof checking remains necessary before any new result is regarded as established.", "id": "Paper/64256", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64256"}, {"title": " The Polymath Jr Program: The First Seven Years ", "webprogram_exclude": "0", "session_ids": ["Session/17106"], "source_sha256": "09c561eebfba1543eb09c274520bacc77078349ced2dbb35bb627a922cdfc1a5", "withdrawn": "", "abstract": "During the pandemic response in 2020 many summer research programs were cancelled; several REU directors and their colleagues created the online Polymath Jr program, providing opportunities to hundreds of students that summer and all subsequent summers. Each year there are on the order of 10 - 15 research groups, each run by a professor or two, assisted by a postdoc / graduate student / advanced undergraduate, supervising between 4 and 25 students on a research project. In addition to producing original results, the program is a force multiplier for mentoring, as the research assistants learn how to design and run such programs. We report on the success and challenges, and discuss how people can participate in 2027 at all levels.", "id": "Paper/64258", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64258"}, {"title": " Linear combinations of cuspidal projections of products of Eisenstein series ", "webprogram_exclude": "0", "session_ids": ["Session/18239"], "source_sha256": "23d8aee871fa93f69804aa556ea854d44b3d1aeebbdcf113142a7fbbf231712c", "withdrawn": "", "abstract": "For an even integer $k\\geq4$, let $E_k$ be the Eisenstein series of weight $k$ for the full modular group $\\mathrm{SL}_2(\\mathbb{Z})$, and $S_k$ be the space of cusp forms of weight $k$ for $\\mathrm{SL}_2(\\mathbb{Z})$. It is known that the cuspidal projections of products of two Eisenstein series $\\left\\{E_{\\ell}E_{k-\\ell}-E_k: 4\\leq \\ell \\leq k-4\\right\\}$ form a spanning set for the space $S_k$. We consider when a linear combination of such cuspidal projections is a Hecke eigenform, and show that for fixed choices of $\\ell$'s and sufficiently large $k$, such a linear combination can never be a Hecke eigenform. Further, we prove that a linear combination of two cuspidal projections can never be a Hecke eigenform when $\\dim S_k > 2$. Lastly, we improve our result for small $k$ as a consequence of Maeda's conjecture.", "id": "Paper/64263", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64263"}, {"title": " Stochastic Gradient Descent on the Space of Probability Distributions ", "webprogram_exclude": "0", "session_ids": ["Session/18446"], "source_sha256": "27e1966adf4c3f5c4703600ac355c2d367f8e5712b44787c688468ea8de311e8", "withdrawn": "", "abstract": "Stochastic gradient descent (SGD) admits diffusion approximations that replace the complicated randomness of stochastic gradients by Gaussian noise, providing a powerful tool for understanding its dynamics and long-time behavior. We investigate whether an analogous approximation principle holds for optimization over probability measures, where the objective is a functional defined on the Wasserstein space $\\mathcal P_2$. The nonlinear geometry and infinite-dimensional nature of $\\mathcal P_2$ prevent a direct extension of the classical Euclidean theory. Using Lions differentiability, we lift the problem to a linear Hilbert space, where higher-order differential calculus becomes available. We then construct a Gaussian random-field approximation whose velocity field matches the mean and covariance of the original stochastic gradient. By exploiting this moment matching through higher-order Taylor expansions, we show that the Gaussian approximation captures the SGD dynamics with second-order weak accuracy. Our result provides a rigorous foundation for replacing sample-driven randomness by analytically tractable Gaussian fluctuations in stochastic optimization over probability measures.", "id": "Paper/64279", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64279"}, {"title": " Optimal pure quantum <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"4.941ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 2127.2 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">(r,\\delta )</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-3B4\" d=\"M195 609Q195 656 227 686T302 717Q319 716 351 709T407 697T433 690Q451 682 451 662Q451 644 438 628T403 612Q382 612 348 641T288 671T249 657T235 628Q235 584 334 463Q401 379 401 292Q401 169 340 80T205 -10H198Q127 -10 83 36T36 153Q36 286 151 382Q191 413 252 434Q252 435 245 449T230 481T214 521T201 566T195 609ZM112 130Q112 83 136 55T204 27Q233 27 256 51T291 111T309 178T316 232Q316 267 309 298T295 344T269 400L259 396Q215 381 183 342T137 256T118 179T112 130Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-72\" x=\"389\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2C\" x=\"841\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-3B4\" x=\"1286\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"1737\" y=\"0\"></use>\n</g>\n</svg>-locally recoverable codes from matrix-product construction ", "webprogram_exclude": "0", "session_ids": ["Session/18387"], "source_sha256": "22c9a1edba2c938842891f4a1d8c4ceb81bb62e9fc320a40741e8e4d52d60eca", "withdrawn": "", "abstract": "Locally recoverable codes (LRCs) are classical error-correcting codes widely used in large-scale distributed and cloud storage systems. Quantum locally recoverable codes of locality $(r,\\delta)$ (quantum $(r,\\delta)$-LRCs) are the quantum counterpart of classical $(r,\\delta)$-LRCs. They allow us to correct erasures at several positions using a trace-preserving quantum operation acting on qudits of a larger set of positions. Quantum  $(r,\\delta)$-LRCs, $\\mathcal{Q}(\\mathcal{C})$, can be constructed from classical Euclidean (or Hermitian) dual-containing codes $\\mathcal{C}$, and their recovery abilities are upper bounded by the minimum distance of the Euclidean (or Hermitian) dual of those codes. Parameters and localities of pure quantum $(r,\\delta)$-LRCs satisfy a Singleton-like bound;  codes attaining equality are referred to as optimal.\n\nWe consider matrix-product codes (MPCs)  $\\mathcal{C}$ and give constituent (or defining) matrices and conditions on the constituent codes such that the codes  $\\mathcal{C}$ satisfy the conditions to provide quantum $(r,\\delta)$-LRCs. As a consequence, we are able to determine their locality and parameters. Furthermore, we determine families of  optimal pure quantum $(r,\\delta)$-LRCs derived from them.\n\nThis is a joint work with C. Galindo, F. Hernando, and C. Munuera.", "id": "Paper/64283", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64283"}, {"title": " Nonlinear maps preserving <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.09ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 469.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\theta</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-3B8\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-biskew Lie triple product on factor von Neumann algebras ", "webprogram_exclude": "0", "session_ids": ["Session/19350"], "source_sha256": "7c6fd434e99343384f492354510f89cdceaa3f1f65c2b818a13f62eb1e62db87", "withdrawn": "", "abstract": "Let $\\mathcal{A}$ and $\\mathcal{B}$ be two factor von Neumann algebras of dimensions greater than $1$. For $S, T\\in\\mathcal{A},$ define the  $\\theta$-biskew Lie product by  $[S, T]_{\\theta}=ST^\\ast-\\theta TS^\\ast,$ where $\\theta\\in\\mathbb{C}\\setminus \\{0, \\pm 1\\}.$  In this talk, we show that any bijective unital mapping $\\boldsymbol{\\delta}:\\mathcal{A}\\to\\mathcal{B}$ satisfying $\\boldsymbol{\\delta}([[S, T]_{\\theta}, U]_\\theta)=[[\\boldsymbol{\\delta}(S), \\boldsymbol{\\delta}(T)]_{\\theta}, \\boldsymbol{\\delta}(U)]_\\theta$ for all $S, T, U\\in\\mathcal{A},$ is either a  linear $\\ast$-isomorphism or the conjugate of a linear $\\ast$-isomorphism.", "id": "Paper/64293", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64293"}, {"title": " Comparing Classes of Structures: The Art of Embedding ", "webprogram_exclude": "0", "session_ids": ["Session/18558"], "source_sha256": "91ff211e212d619eb8a86abc5321fd84958418f6e4ae8d9be82927c7a8508cd7", "withdrawn": "", "abstract": "Transforming mathematical objects into alternate structures, whether computing fundamental groups in algebraic topology, constructing group rings in algebra, or passing to the spectrum of a ring in algebraic geometry, is a foundational theme throughout modern mathematics.\nA central goal in mathematical logic, computability theory, and descriptive set theory is to systematically classify these transformations: when can one class of structures be encoded into another, and what prevents such encodings from existing?\nWe examine this framework across a spectrum of naturalness constraints, varying the requirements on the underlying embeddings from completely unrestricted maps to Borel measurable, Turing-computable, or faithful transformations.\nWe discuss both explicit embeddings that translate complex structures into unexpected contexts like the Farey graph and establish strict impossibility results when such encodings cannot exist.\nCentral to these negative results is Scott analysis, an apparatus originally developed within infinitary logic to analyze structural complexity via quantifier ranks.\nRemarkably, Scott analysis allows us to understand the setting of model counting and Vaught's conjecture, where we assume nothing about the embeddings, all the way to the most structured setting of faithful Borel embeddings.\nWe will particularly highlight some recent results using Scott analysis to uncover the structure of a counterexample to Vaught's conjecture and to prove the impossibility of a faithful embedding into the class of linear orderings.", "id": "Paper/64300", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64300"}, {"title": " Zero Forcing on Iterated Graph Models ", "webprogram_exclude": "0", "session_ids": ["Session/18106"], "source_sha256": "b981b30af0de4e7f209bdc59a1736a09f238e9c09d54b1ef766a085dd09b15c9", "withdrawn": "", "abstract": "Deterministic complex networks that use iterative generation algorithms have been found to more closely mirror properties found in real world networks than the standard uniform random graph models. In this talk we will further explore two such models, the Iterative Local Transitive (ILT) model and the Iterative Local Anti-Transitive (ILAT) model, both introduced by Bonato et. al. in 2009 and 2017, respectively. These models use ideas from Structural Balance Theory to generate edges through a notion of cloning where ``the friend of my friend is my friend'' and anticloning where ``the enemy of my enemy is my friend.'' As these models were inspired by social networks it is natural to consider information diffusion on these graphs. Here we will explore one such notion, zero forcing, which was first introduced by Barioli et. al. in 2008. We will discuss recent results on zero forcing and failed zero forcing for both ILT and ILAT graphs.", "id": "Paper/64335", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64335"}, {"title": " A robust subclass of the nontotal continuous degrees ", "webprogram_exclude": "0", "session_ids": ["Session/18589"], "source_sha256": "10a7f267a63ea912a53e56ef3a9dd23f076a7109ec1220d44bd499668a854619", "withdrawn": "", "abstract": "In 2004, Miller introduced the continuous degrees, which measure the computability-theoretic content of elements of computable metric spaces, and showed that they properly extend the Turing degrees. To show the existence of nontotal (i.e., non-Turing) continuous degrees, Miller constructed a \\textit{diagonally not computably diagonalizable (DNCD)} sequence: a sequence \\(\\alpha \\in [0,1]^\\omega\\) such that if \\({\\varphi_e^\\alpha \\downarrow} \\in [0,1]\\), then \\(\\alpha(e) = \\varphi_e^\\alpha\\). That is, \\(\\alpha\\) lists the \\(\\alpha\\)-computable reals from \\([0,1]\\) \\textit{in order}. \n\nIn 2013, Day and Miller showed that Levin's \\textit{neutral measures} also give examples of nontotal continuous degrees. These are measures on Cantor space for which every infinite binary sequence is random, even though tests have access to the measure itself.\n\nIt remains open whether every nontotal continuous degree contains a DNCD sequence or a neutral measure. In this talk, I will discuss ongoing work with Joseph S.\\ Miller in which we show that the degrees of DNCD sequences coincide with those of (weakly) neutral measures. These are exactly the continuous degrees \\(\\mathbf{a}\\) such that every Turing degree above \\(\\mathbf{a}\\) is $\\mathsf{PA}$ relative to \\(\\mathbf{a}\\). They form a robust class, whether or not it is a \\textit{proper} subclass of the nontotal continuous degrees.", "id": "Paper/64340", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64340"}, {"title": " Integrating Physics-Constrained Neural Networks with Invariance-Based Safety Certificates for Secure Cyber-Physical Systems ", "webprogram_exclude": "0", "session_ids": ["Session/19337"], "source_sha256": "f4788c539bfe1214dec27de1fdf37c60beb516e2b348d0b8bdaf77bfb114d44e", "withdrawn": "", "abstract": "Cyber‑Physical Systems (CPS) are increasingly exposed to adversarial sensor spoofing and actuator manipulation, motivating anomaly‑detection frameworks with mathematically provable safety guarantees. We present a digital-twin framework that integrates physics‑informed neural networks with Control Barrier Functions (CBFs) to enforce forward invariance of safe operating sets under adversarial disturbances. The framework embeds the system’s differential-algebraic power‑flow constraints and constructs a CBF‑based safety certificate that remains valid even when measurement channels are corrupted. We show that the resulting closed‑loop dynamics satisfy a provable boundary‑preservation condition and derive sufficient conditions under which the CBF‑augmented predictor maintains invariance despite false data injection. Simulation results on networked CPS models illustrate how the mathematical safety constraints reduce false alarms while guaranteeing state feasibility. This work connects machine‑learning with formal methods in control theory, offering a mathematically grounded approach to secure CPS operation.", "id": "Paper/64343", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64343"}, {"title": " Proofreading with limited energy ", "webprogram_exclude": "0", "session_ids": ["Session/18222"], "source_sha256": "23dd63126b21c59d4d0b5c39fe9083a1e1e6f5b313f1f2b962c2578d7504b135", "withdrawn": "", "abstract": "Biological systems ranging from DNA replication to antigen identification in the immune system all rely on the same algorithm to correct errors: kinetic proofreading. Canonical models of kinetic proofreading require infinite energy. While these models perform well in the limit where energy is abundant, many biological systems are constrained by limited resources. In this talk, I will introduce the design rules for kinetic proofreading with limited energy. We find a set of surprisingly simple laws, which together show that finite energy constraints fundamentally change the optimal architecture of a proofreading network. Finally, I will show how these design rules can be implemented in DNA nanotechnology, where they present an opportunity to significantly enhance single nucleotide mismatch discrimination.", "id": "Paper/64346", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64346"}, {"title": " From Logistic Growth to Spatial Invasion: A PDE Teaching Module in Mathematical Oncology ", "webprogram_exclude": "0", "session_ids": ["Session/17765"], "source_sha256": "6915edc97df1e9e895fe69548c3bb0eb26bb80e1129d06ccd97950a2402e9ea7", "withdrawn": "", "abstract": "Many students first encounter mathematical biology through ordinary differential equation models, yet spatial mechanisms are essential for understanding biological processes such as tumor invasion. This presentation introduces a student-centered teaching module in which students develop a partial differential equation model of tumor growth from familiar mathematical ideas. Students begin with the classical logistic ODE and examine why a model of total tumor burden cannot describe the spatial distribution or migration of tumor cells. By introducing a spatially dependent cell density, a local conservation law, and Fick’s law, they construct the Fisher – Kolmogorov – Petrovsky –  Piskunov (Fisher--KPP) reaction–diffusion equation. Students interpret the reaction and diffusion terms, identify the underlying biological assumptions, and formulate appropriate initial and boundary conditions. Finite-difference simulations allow them to visualize tumor-density profiles and advancing invasion fronts, explore the effects of proliferation and migration, and compare computed front speeds with the theoretical minimum wave speed. Further investigations consider tumor-detection thresholds, surgical resection, and recurrence. The module is suitable for courses in differential equations, partial differential equations, numerical methods, or mathematical modeling and demonstrates how a familiar ordinary differential equation can provide an accessible pathway into spatial modeling and mathematical oncology.", "id": "Paper/64364", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64364"}, {"title": " Learning fixed points of recurrent neural networks by reparameterizing the network model ", "webprogram_exclude": "0", "session_ids": ["Session/18007"], "source_sha256": "e8e405102ab4b4ad811477e65d7e75b7bece673034af656e531cbfde329408e5", "withdrawn": "", "abstract": "In computational neuroscience, recurrent neural networks are widely used to model neural activity and learning. In many studies, fixed points of recurrent neural networks are used to model neural responses to static or slowly changing stimuli, such as visual cortical responses to static visual stimuli. These applications raise the question of how to train the weights in a recurrent neural network to minimize a loss function evaluated on fixed points. In parallel, training fixed points is a central topic in the study of deep equilibrium models in machine learning. A natural approach is to use gradient descent on the Euclidean space of weights. We show that this approach can lead to poor learning performance due in part to singularities that arise in the loss surface. We use a re-parameterization of the recurrent network model to derive two alternative learning rules that produce more robust learning dynamics. We demonstrate that these learning rules avoid singularities and learn more effectively than standard gradient descent. The new learning rules can be interpreted as steepest descent and gradient descent, respectively, under a non-Euclidean metric on the space of recurrent weights. Our results question the common, implicit assumption that learning in the brain should be expected to follow the negative Euclidean gradient of synaptic weights.", "id": "Paper/64369", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64369"}, {"title": " A simultaneous mixing model in one dimension ", "webprogram_exclude": "0", "session_ids": ["Session/18378"], "source_sha256": "3b4002d3cff8e59636c85dfb0836773d22653532156f215097ab6d466997e977", "withdrawn": "", "abstract": "We propose a nonlocal-local coupling model with sharp interface that features the classical Dirichlet or Neumann boundary conditions. We discuss the well-posedness of the models and employ a spectral-based numerical method for validation. Through numerical experiments, the convergence of the coupling models to the classical interface counterparts as the nonlocal horizon vanishes are confirmed.", "id": "Paper/64376", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64376"}, {"title": " A Fitness Landscape Approach to Modeling Tick Diapause ", "webprogram_exclude": "0", "session_ids": ["Session/17860"], "source_sha256": "b8643aef69435db1b0b24d767105c791c515e01bc7119083aeb963d4068949f5", "withdrawn": "", "abstract": "Seasonal changes in temperature and day length strongly influence when ticks develop, become active, and search for hosts. In this talk, I will present a stage-structured compartmental model to investigate how diapause affects the long-term fitness of two tick species, {\\it Ixodes scapularis} and {\\it Ixodes pacificus.} Two threshold parameters that determine when nymphs and adults enter or leave diapause are varied over a two-dimensional parameter space. For each parameter pair, numerical simulations are used to compute long-term annual egg production, producing a fitness landscape from which optimal diapause strategies can be identified. I will then examine how these fitness landscapes change under different environmental conditions by interpolating between temperature and day-length profiles from two distinct climates. This allows us to study how environmental variation changes both reproductive fitness and the location of optimal diapause strategies. More broadly, the work illustrates how mechanistic population models and numerical fitness-landscape analysis can be used to investigate questions of adaptation in vector ecology. This work is in collaboration with Dr. Dorothy Wallace at Dartmouth College.", "id": "Paper/64392", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64392"}, {"title": " Intrinsic Divergence-Free RBF-FD Methods for Tangential Vector Fields on Embedded Surfaces ", "webprogram_exclude": "0", "session_ids": ["Session/18281"], "source_sha256": "1168bf4fa576a874aeaea09881ac184ff60ac1d14ef72a0538d16ac5c8dfaf9a", "withdrawn": "", "abstract": "A localized, structure-preserving radial basis function-generated\nfinite difference (RBF-FD) framework is presented for approximating\nthe surface Laplace-Beltrami operator applied to divergence-free\ntangential vector fields on smooth embedded surfaces. Building on\nmatrix-valued surface divergence-free kernels, the formulation\nrepresents the local approximation intrinsically in two-dimensional\ntangent coordinates and incorporates a compatible divergence-free\npolynomial space. A thin singular value decomposition is employed to\nobtain a numerically stable representation of the local polynomial\nconstraints while preserving the underlying approximation space.\nThe resulting local differentiation weights are assembled into sparse\nglobal operators, providing an efficient discretization that maintains\nthe tangential and divergence-free structure of the vector field.\nThe framework is examined on the unit sphere, ellipsoidal surfaces,\nand a geometrically challenging Dziuk-type surface. Numerical\nexperiments demonstrate high-order convergence across these geometries\nand highlight the influence of nonuniform surface geometry on local\nstencil accuracy. For the Dziuk surface, a geometry-informed\nnode-enrichment strategy is employed to increase local resolution in\nthe constricted end regions without modifying the underlying intrinsic\nRBF-FD formulation. The results demonstrate that the combined use of intrinsic\ntangent-coordinate representation, compatible divergence-free\npolynomial augmentation, localized stencil construction, and\ngeometry-informed node distribution provides an effective\nstructure-preserving framework for high-order approximation of the\nsurface Laplace--Beltrami operator applied to divergence-free\ntangential vector fields on general embedded surfaces.", "id": "Paper/64394", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64394"}, {"title": " Orbit closures of holonomy covers of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"5.345ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 2301.5 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">(1/k)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-31\" x=\"389\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2F\" x=\"890\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-6B\" x=\"1390\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"1912\" y=\"0\"></use>\n</g>\n</svg>-translation surfaces ", "webprogram_exclude": "0", "session_ids": ["Session/18269"], "source_sha256": "4254f6c3c7a5ff0abddc7ca285341df9d09952b0ff753c2b9374e9fbb3c1efd1", "withdrawn": "", "abstract": "A $(1/k)$-translation surface is a collection of polygons in the complex plane with sides identified pairwise by translations and rotations by $2\\pi/k$. Equivalently, it is a Riemann surface equipped with a $k$-differential. When $k=1$, these surfaces are called translation surfaces. Every $(1/k)$-translation surface unfolds into a translation surface called its holonomy cover. The space of translation surfaces has a nice $GL_2(\\mathbb{R})$-action which act as linear transformations on the polygonal representations. In this talk, we compute the $GL_2(\\mathbb{R})$-orbit closure of holonomy covers and discuss applications to counting problems on $(1/k)$-translation surfaces. This is joint work with Paul Apisa.", "id": "Paper/64406", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64406"}, {"title": " Accessible LaTeX PDF Presentations ", "webprogram_exclude": "0", "session_ids": ["Session/18092"], "source_sha256": "c2d8ead95422cc3a0df056bceb96f90d7ae57b0f25ba628dccf8957638ad19e1", "withdrawn": "", "abstract": "We will discuss how to use the latest LaTeX to create accessible PDFs, with a particular focus on accessible presentations.", "id": "Paper/64422", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64422"}, {"title": " The Structure of Oriented Graphs with DDM Labelings ", "webprogram_exclude": "0", "session_ids": ["Session/18867"], "source_sha256": "6ef193cfb91d62238af16e0aa9abb82b49d1bbcd6eee9a90b6b642dcedfa492f", "withdrawn": "w", "abstract": "We present constructive methods that create difference distance magic oriented graphs. Each method uncovers properties of oriented graphs that allow difference distance (DDM) labeling.", "id": "Paper/64433", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64433"}, {"title": " A duality of four-pointed, pure-cycle Hurwitz spaces ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "a598dbcb01cd702dd2aa4dff77b5d6ddcd1f3e07217af4f1fc2dabab360ae4a4", "withdrawn": "", "abstract": "We consider maps between spheres given some ramification data, where the number of these maps is described by its Hurwitz number. Liu and Osserman observed a mysterious symmetry of Hurwitz numbers under a specific involution of the ramification data, which we explain by constructing an isomorphism between the algebraic varieties that parameterize these maps. We provide two constructions: one group theoretic and the other linear algebraic.", "id": "Paper/64450", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64450"}, {"title": " Deep Signature Approach for McKean-Vlasov FBSDEs in a Random Environment ", "webprogram_exclude": "0", "session_ids": ["Session/18293"], "source_sha256": "7108783ae35b59f12f2acb1640dc538ac97bf41be260961c7a27439d547912cc", "withdrawn": "", "abstract": "Mean-field games with common noise model large populations subject to shared randomness. Their probabilistic formulation leads to McKean--Vlasov forward--backward stochastic differential equations (MV-FBSDEs) in a random environment, whose coefficients depend on conditional laws given the common noise. Existing numerical methods for such problems mostly treat interactions through expectations, low-order moments, or low-dimensional common factors, and do not directly address nonlinear dependence on conditional distributions.\n\nWe introduce a signature-based deep learning algorithm for MV-FBSDEs with common noise and nonlinear conditional-law dependence. The method uses an iterative scheme: empirical conditional laws generated from simulated common-noise paths are used to train signature-based maps approximating the distribution-dependent coefficients, and these learned maps are then reused in the Deep BSDE step. This avoids nested Monte Carlo evaluation of conditional laws during optimization. The main contribution is algorithmic. We also provide a population-level convergence result for an idealized version of the iteration, showing that the error is controlled by the supervised-learning residuals. Numerical experiments, including a Cucker--Smale flocking model with common noise, illustrate the performance of the method beyond conditional-moment interactions.", "id": "Paper/64454", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64454"}, {"title": " Endomorphisms for Poisson Torus ", "webprogram_exclude": "0", "session_ids": ["Session/18205"], "source_sha256": "02792bfb875a69b569a5ec9e4b6ac0b4d58cd7110a55a13128cf947038d7e744", "withdrawn": "", "abstract": "Let $\\Lambda=(\\lambda_{ij})$ be a skew-symmetric $n\\times n$ matrix with entries from a base field $\\Bbbk$ of characteristic zero. One can define a Poisson bracket on the Laurent polynomial algebra $P\\colon=\\Bbbk[x_{1}^{\\pm 1}, \\cdots, x_{n}^{\\pm 1}]$ via $\\{x_{i}, x_{j}\\}=\\lambda_{ij}x_{i}x_{j}$ for $1\\leq i, j\\leq n$. With such a Poisson bracket, $P$ is called a Poisson torus and denoted by $P_{\\Lambda}$. In this talk, we will present several results concerning the Poisson endomorphisms of $P_{\\Lambda}$. In particular, we prove that each Poisson endomorphism of $P_{\\Lambda}$ is an automorphism when $P_{\\Lambda}$ is Poisson-simple and establish a criterion for a Poisson endomorphism of $P_{\\Lambda}$ to be bijective. If time allows, we will also address the isomorphism and embedding problems for Poisson torus.", "id": "Paper/64487", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64487"}, {"title": " Understanding Who Stays and Who Leaves: A Detailed Statistical Analysis of Student Retention at a Small Liberal Arts College ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "2bd42c7db90637d2fb7c4397460c036f9afe0069a332d0a4fe231d104e282c0f", "withdrawn": "", "abstract": "Pre-enrollment psychosocial surveys are widely used at small liberal arts colleges, yet their value as retention predictors remains under explored. Using a standard pre-enrollment assessment administered to 359 first-year students at a liberal arts college, we evaluated the predictive capacity of early-semester psychosocial and demographic data. We analyzed responses using statistical tests and machine learning, achieving 66.4% accuracy. \n\nRetention proved multi-dimensional: social belonging, math confidence, and gender were strong positive predictors, while mental health concerns were associated with lower retention rates. While regression analyses identified several significant predictors, including social belonging, math confidence, and gender, no single factor dominated, and clustering analysis revealed no distinct at-risk profiles, indicating that institutions should prioritize holistic well-being rather than targeting any single risk group. \n\nOur main recommendation is a two-stage retention strategy: using pre-enrollment surveys for early psychosocial outreach, then layering in-semester behavioral data to improve accuracy and better support students.", "id": "Paper/64489", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64489"}, {"title": " Poisson derivations and cohomology groups for <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"11.87ex\" height=\"3.009ex\" style=\"vertical-align: -1.005ex;\" viewBox=\"0 -863.1 5110.9 1295.7\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title 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xlink:href=\"#E1-MJMATHI-3C3\" x=\"2907\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2C\" x=\"3479\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-3B4\" x=\"3924\" y=\"0\"></use>\n<g transform=\"translate(4376,0)\">\n <use xlink:href=\"#E1-MJMAIN-5D\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-70\" x=\"393\" y=\"-213\"></use>\n</g>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18278"], "source_sha256": "800583ebfc706a86d07911a712eb76ea5a20248eb81b8397be23dd1b8c1fe715", "withdrawn": "", "abstract": "In this talk, we present several results on the Poisson derivations and cohomology groups for the Poisson-Ore extension $\\Bbbk[x][y;\\sigma, \\delta]_{p}$.", "id": "Paper/64495", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64495"}, {"title": " A fruitfly and a butterfly help each other: from classification to regression and back ", "webprogram_exclude": "0", "session_ids": ["Session/18324"], "source_sha256": "e04c5350558c7621eecb354d7c997ee8e4d9f40255adf854c352f6664db6a763", "withdrawn": "", "abstract": "Classification and regression are the two main tasks for supervised machine learning. In this talk, we will present two novel approaches that explore the interface between classification and regression. First, we discuss an approach to regression tasks using classification which is motivated by the mechanism used by fruitflies to sense their environment. Specifically, we formulate a general framework for learning nonlinear input-output relationships by replacing complex global surrogate models with a finite library of representative local patterns. Second, we discuss an approach which exploits regression, in particular chaos, to enhance classification accuracy. Specifically, the available data that need to be classified are treated as vectors that are first lifted into a higher-dimensional space and then used as initial conditions for the evolution of a chaotic dynamical system for a prescribed temporal interval. The evolved state of the dynamical system is then fed to a trainable softmax classifier which outputs the probabilities of the various classes. We provide proof-of-concept examples for the advantages of the proposed approaches and discuss their potential for edge applications and the study of emergent phenomena.", "id": "Paper/64510", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64510"}, {"title": " Visual Aspects of Gaussian Periods ", "webprogram_exclude": "0", "session_ids": ["Session/18100"], "source_sha256": "80d5d93b3a224c62cca7f6170071c8b9c3b5d73fce9107e98e5d2b54ea4e1d9f", "withdrawn": "", "abstract": "Gaussian periods are certain sums of roots of unity that Gauss introduced in his work on straight edge and compass constructions of regular polygons.  Since then, Gaussian periods have played important roles in number theory and beyond.  It turns out that Gaussian periods also have striking visual properties!  This talk will explore the following question: What happens when you plot really large families of Gaussian periods in the complex plane?  About a decade ago, an undergraduate named Bob Lutz asked this question and opened the door to a surprisingly rich collection of illustrations.  This talk will be accessible to anyone with an undergraduate background in abstract algebra.  If you like nice pictures and surprising, new views on old subjects, this talk is for you.  If you can’t wait and want to start exploring before the talk (or alongside it), check out this app for Apple computers: https://apps.apple.com/us/app/gaussianperiods/id1622050577", "id": "Paper/64537", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64537"}, {"title": " Scaling Success in Introductory Mathematics at a Technological University: Course Coordination and the Coordinated Courses Committee ", "webprogram_exclude": "0", "session_ids": ["Session/18250"], "source_sha256": "0aed4cbb24ee6ed28206297472bedc5b1298d21578e40b0e7787e93a19e129b8", "withdrawn": "", "abstract": "Coordination across multi-section introductory mathematics sequences requires balancing departmental consistency with instructor autonomy. Over the past several years, our technological university has transformed the coordination of Precalculus, Calculus 1, and Calculus 2 to better support our predominantly engineering student body. This session highlights the development of shared instructor resources, including common problem sets and exams, and structured support for graduate student instructors, including weekly instructor meetings. We will also detail the role of our Coordinated Courses Committee—a collaborative body of coordinators and faculty that drives program consistency, identifies strengths of our approach, and troubleshoots challenges. Attendees will gain insights into how this model successfully lowered DFW rates and empowered instructional-track faculty, while exploring strategies to navigate the natural tension between high-level coordination and pedagogical innovation.", "id": "Paper/64575", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64575"}, {"title": " On Robin-Based Partitioned Schemes for Fluid-Poroelastic Structure Interaction: Part 2 ", "webprogram_exclude": "0", "session_ids": ["Session/17962"], "source_sha256": "003beb19de5369afe6802cdb4dab12bf6eaf9c57cb5e56ed033bcbe0df2c7854", "withdrawn": "", "abstract": "We present a partitioned numerical method for the fluid-poroelastic structure interaction problem based on Cauchy's `$\\theta$-like' scheme combined with Robin-Robin coupling conditions. This method consists of an iterative Backward Euler step followed by a Forward Euler step, which is equivalent to a linear extrapolation. The iterative procedure is proved to be convergent, assuming certain conditions on the time step and material parameters, under which the converged solution has also been shown to be stable. We also show an alternative numerical method based on a recursive correction approach, which has a similar structure but requires only two subiterations per time step. The performance of both methods will be shown in numerical examples.", "id": "Paper/64585", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64585"}, {"title": " Flexible-Tile DNA Self-Assembly of Select <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.211ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 521.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">k</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-6B\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-regular graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17953"], "source_sha256": "007f421850a355b7fedfaabb5e99153842cf3b7d9a0b502ce13adaf78a3e4bfd", "withdrawn": "", "abstract": "Several mathematical models have been developed to study DNA self-assembly, including DNA origami and models based on rigid or flexible tiles. We work within the flexible-tile model, in which branched-junction molecules are represented by vertices of a graph and their incident DNA arms by half-edges. A central problem in this setting is to determine the design parameters required to assemble a prescribed target structure. Previous research has addressed this problem through both general construction methods and the analysis of particular graph families. In this talk, we investigate the construction of 3-regular structures modeled by the Croissant graph and, more generally, $k$-regular structures modeled by hypercube graphs. Our results illustrate how the combinatorial properties of these graphs inform the design of DNA complexes in the flexible-tile model.", "id": "Paper/64591", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64591"}, {"title": " On Robin-Based Partitioned Schemes for Fluid-Poroelastic Structure Interaction: Part 1 ", "webprogram_exclude": "0", "session_ids": ["Session/17962"], "source_sha256": "574954fda5622db79d555b08487c8a0b4c3fb14c55952fd32f30ce66ad4bb113", "withdrawn": "", "abstract": "In this talk, we present some of the challenges associated with the development of partitioned numerical methods for the interaction between an incompressible, viscous fluid and a poroelastic structure. We propose a numerical method based on the Robin coupling conditions which overcomes some of these challenges, and present its stability and convergence analysis. While the method is conditionally stable, it is only sub-optimally convergent in time. To improve the rate of convergence, we introduce a second numerical method based on a Cauchy's `θ-like' scheme combined with Robin-Robin coupling conditions, which will be further detailed in Connor Parrow's talk.", "id": "Paper/64592", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64592"}, {"title": " Uniqueness and non-degeneracy of blowup solutions for Liouville systems ", "webprogram_exclude": "0", "session_ids": ["Session/18050"], "source_sha256": "b78d0e1d3afc8e36abba95b037a11af272f3c1cdf6e5642365fd5cf7c25784d9", "withdrawn": "", "abstract": "For a general class of Liouville system defined on a compact Riemann surface  we establish\nthe uniqueness of of blowup solutions under nondegeneracy assumptions. The nature of Liouville systems brings significant barriers for blowup analysis, \n we develop certain tools and extend them into a more general framework applicable to similar situations. Notably, to address the considerable challenge of a continuum of standard bubbles, we refine the techniques from Huang-Zhang  to achieve extremely precise pointwise estimates. Additionally, to address the limited information provided by the Pohozaev identity, we develop a useful Fredholm theory to discern the exact role that the Pohozaev identity plays for systems. The considerable difference between systems and a single equation is also reflected in the location of blowup points, where the uncertainty of the energy type of the blowup point makes it difficult to determine the sufficiency of pointwise estimates. In this regard, we extend our highly precise pointwise estimates to any finite order. This aspect is drastically distinct from analyses of single equations. This talk is based on a joint work with Zetao Cheng and Haoyu Li.", "id": "Paper/64596", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64596"}, {"title": " Algorithms and Differential Game Representations for Exploring Nonconvex Pareto Fronts in High Dimensions ", "webprogram_exclude": "0", "session_ids": ["Session/18024"], "source_sha256": "bd24e79b86f1ef937546f6acfa4ea4420666b8ee090218a01ec3ebf9981af65d", "withdrawn": "", "abstract": "We develop a new Hamilton-Jacobi (HJ) and differential games approach for exploring the Pareto front of (constrained) multi-objective optimization (MOO) problems. Given a preference function, we embed the scalarized MOO problem into the value function of a parameterized zero-sum game, whose upper value solves a first-order HJ equation that admits a Hopf-Lax representation formula. For each parameter value, this representation yields an inner minimizer that can be interpreted as an approximate solution to a shifted scalarization of the original MOO problem. Under mild assumptions, the resulting family of solutions maps to a dense subset of the weak Pareto front. Finally, we propose a primal-dual algorithm based on this approach for solving the corresponding optimality system. Numerical experiments show that our algorithm mitigates the curse of dimensionality (scaling polynomially with the dimensions of the decision and objective spaces) and is able to expose continuous curves along nonconvex Pareto fronts in 100D in just ~100 seconds. Distribution Statement A. Approved for Public Release; Distribution is Unlimited. PR 26-0024.", "id": "Paper/64598", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64598"}, {"title": " What Students Say vs. What Students Do: Supporting Classroom Dialogue on AI Tools and Online Homework Practices ", "webprogram_exclude": "0", "session_ids": ["Session/18137"], "source_sha256": "70a2badbbebdc804ac4d63fc0928a3ac0397d2921e9b8fd1075fa5c8f5662425", "withdrawn": "", "abstract": "As artificial intelligence (AI) tools become increasingly available to undergraduate students, mathematics instructors are faced with important questions about how students perceive these technologies and how those perceptions interact with broader learning practices. In this talk, I draw on two ongoing research projects. The first concerns my joint work with E. Ceyhan and S. Bowers and introduces a framework for both eliciting undergraduate students' perspectives on AI tools in mathematics courses and supporting productive classroom conversations about AI use. The second study, conducted with D. Hensley and H. Gilroy, investigates associations between Calculus I students' self-reported mindsets and patterns of behavior within an online homework system.  \n\nStudents describe a wide range of views about AI, characterizing it as everything from a valuable learning support to a potential obstacle to their learning. At the same time, our analyses of online homework behavior illustrate that students' stated beliefs and reflections do not always align with observable patterns of engagement. Our findings highlight the complexity of interpreting students' learning decisions and suggest caution when drawing conclusions about students' motivations, effort, or their use of technology based on a single source of evidence. I discuss implications for mathematics instructors, emphasizing how classroom dialogue can create opportunities for students to reflect on the role of AI technologies and their own approaches to learning.", "id": "Paper/64607", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64607"}, {"title": " Quantum Perturbation Optimization for Qubit-Qumode Computation ", "webprogram_exclude": "0", "session_ids": ["Session/18113"], "source_sha256": "433f138e8ee5955d3ee12cf874a1ce85ed798c9ac0573c4db6c8b9e23dd4f397", "withdrawn": "", "abstract": "Most of the existing quantum optimization algorithms focus on solving problems with discrete variables on qubit-based quantum computers. Qubit-based information encoding faces the scalability challenge when solving optimization problems with continuous variables. Recent research progress on qubit-qumode architecture has created a new opportunity to perform continuous-variable quantum computation. In this work, we propose a new quantum perturbation optimization (QPO) framework that allows us to efficiently encode and solve continuous and mixed-integer optimization problems. Based on time-dependent quantum perturbation theory, we design effective perturbation operators and demonstrate them with problems such as mixed-integer linear programming and mixed-integer bilinear optimization.", "id": "Paper/64614", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64614"}, {"title": " Covering Math Research News on Social Media ", "webprogram_exclude": "0", "session_ids": ["Session/18322"], "source_sha256": "cb17fa71656cce9ae0f12def63572c57b63d2ee7db86fe8ef12f6a6463e5607d", "withdrawn": "", "abstract": "Covering news in mathematical research to a general audience on social media is both an opportunity and a challenge. New results comes with an intrinsic interest that makes math feel alive and helps people feel connected to the community of mathematicians. However, math research can often be highly technical and hard to describe to a general audience. In this talk we'll discuss how to select math research that make good stories to showcase and how to choose angles within the larger stories that work well on social media.", "id": "Paper/64615", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64615"}, {"title": " Distance Optimization Inside the Grassmannian ", "webprogram_exclude": "0", "session_ids": ["Session/18302"], "source_sha256": "320cebad3610e94c94d90f78eae622450c991206975685116bef170df1e8fd6d", "withdrawn": "", "abstract": "The Grassmannian $\\mathrm{Gr}(k,n)$ may be realized as the set of symmetric $n \\times n$ projection matrices of rank $k$.\nWe study Euclidean distance optimization inside the Grassmannian: given a subvariety of $\\mathrm{Gr}(k,n)$ and a data point also in $\\mathrm{Gr}(k,n)$, find point on the subvariety that is closest to the data point. \nWe approach this problem from the perspective of applied algebraic geometry.\nWe introduce the Grassmann distance (GD) degree as the algebraic degree of this problem. We report on the GD degrees of geometrically meaningful subvarieties, including Schubert and positroid varieites. This talk is based on joint work with Andrea Rosana, Serkan Hoşten, and Bernd Sturmfels.", "id": "Paper/64619", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64619"}, {"title": " Competition outcomes in systems of differential equations with nonlinear diffusion ", "webprogram_exclude": "0", "session_ids": ["Session/18256"], "source_sha256": "3f2fdc6cc3bd90a9f4528e8d27949cd3ff5521b24bc703b7957cdc9150942ca0", "withdrawn": "", "abstract": "We examine systems of differential equations that model species competition in environments with spatially heterogeneous resources, highlighting results from projects completed with undergraduate students. Understanding competition outcomes can be helpful in understanding directions of evolution, the importance of adaptability, and give insight into invasive species management strategies. Classically, in systems where species employ linear diffusion, the slow diffuser has an advantage and outcompetes the fast diffuser. We discuss cases where a species is subject to nonlinear diffusion, namely $p$-Laplacian diffusion, and competing with a species employing classical, linear diffusion. This change in movement strategy can change the outcomes of species competition. We compare competition outcomes in the nonlinear case to the classical, linear case from both an ODE and a PDE perspective, as well as from a theoretical and numerical perspective.", "id": "Paper/64620", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64620"}, {"title": " NSF Programs for Mathematics Teaching and Learning ", "webprogram_exclude": "0", "session_ids": ["Session/19341"], "source_sha256": "58a5ae8012ab2a46defb9f760480427f3256b77e3cb752db9fc6832a46027b09", "withdrawn": "", "abstract": "The Scholarship of Teaching and Learning (SoTL) and programs in the NSF Directorate for STEM Education (EDU) are often complementary. In this session, we will discuss several NSF EDU programs that welcome SoTL as a mechanism to generate new knowledge for the education community, develop capacity for new approaches, adapt innovations in teaching and learning, discuss some common strengths across competitive proposals, and answer questions about NSF programs and procedures.", "id": "Paper/64632", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64632"}, {"title": " Persistence of species subject to nonlinear diffusion and heterogeneous environmental conditions ", "webprogram_exclude": "0", "session_ids": ["Session/17860"], "source_sha256": "1a1b82de51471c54677aad1dc1d4e3cebcb05ea1ec82a3afcc493256809a33e9", "withdrawn": "", "abstract": "We examine the ability of species employing various movement strategies to persist in an environment with drift – including environments with spatially heterogeneous resources and, in some cases, spatially heterogeneous drift. We explore this through the lens of partial differential equations and their connection to experimental results. Understanding when a species persists can be helpful in understanding directions of evolution, the importance of adaptability, and give insight into invasive species management strategies. In environments with drift, these models can have implications for species persistence in disturbed or flooded environments. In one case, we study a system of PDEs modeling a species employing nonlinear diffusion, specifically $p$-Laplacian diffusion, competing with a species employing classical, linear diffusion in an environment with drift. We compare competition outcomes, both from a numerical and theoretical perspective, to outcomes from a system where both species employ linear diffusion. We also consider data from experimental results on strains of \\textit{C. elegans} that employ different movement speeds. Abundance is measured in response to various drift and resource conditions. We compare these results to a PDE model of the experimental setup to gain further insight to the drivers behind the relationship between abundance and movement.", "id": "Paper/64645", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64645"}, {"title": " DeGroot Dynamics on Multiplex Networks with Directed and Acyclic Interlayer Connectivities ", "webprogram_exclude": "0", "session_ids": ["Session/18260"], "source_sha256": "7314637297e25591b6305cea735f49e8163e292ccac1c037487e739f984da8b9", "withdrawn": "", "abstract": "In models of opinion dynamics, researchers typically examine how an individual’s opinion on one topic is influenced by the opinions of their neighbors in a network. However, people’s opinions on\na topic are also influenced by their opinions and their neighbors’ opinions on related topics. In an election, for example, the opinions of a voter on a variety of issues inform their opinions of electoral\ncandidates. In this talk I will present a multiplex extension of the traditional DeGroot consensus model that we study to consider the influence between people’s opinions on multiple distinct topics. In our multiplex DeGroot model, different network layers represent distinct topics and directed interlayer edges (which are not allowed to form cycles) encode relationships between distinct topics. In our model, an individual’s opinion on one topic is influenced both by the opinions of their neighbors on that topic and by their own opinions on related topics. I will present an outline of our proof that our multiplex DeGroot model converges to a limit state as long as each individual accounts for their own opinion when they update their opinion on each topic. I will also summarize our proof that strong connectedness in ``source layers'' (which represent fundamental beliefs) eventually yields a consensus opinion in each layer. I will finally present numerical simulations of our multiplex DeGroot model on a two-layer network that we use to examine the effects on opinion dynamics of (1) different network structures and (2) different types of initial opinion data. This project is a collaboration with Kye Shi, Abigail Hickok, Weiqi Chu, and Mason A. Porter.", "id": "Paper/64652", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64652"}, {"title": " On Prime Cycle Lengths of Monomial Maps in <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.867ex\" height=\"2.843ex\" style=\"vertical-align: -1.005ex;\" viewBox=\"0 -791.3 1234.5 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbb {Q}_p</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJAMS-51\" d=\"M480 -10Q480 -13 486 -24T507 -50T541 -80T588 -104T648 -114Q666 -114 688 -110T714 -106Q724 -106 728 -114T729 -130Q723 -145 663 -163T548 -181Q503 -181 463 -169T395 -139T343 -97T307 -56T284 -19L280 -3L262 1Q188 24 131 81Q57 155 37 275Q34 292 34 342T37 410Q58 528 131 601Q179 652 248 676T388 701Q485 701 562 661Q698 595 731 448Q742 410 742 341T731 235Q707 141 646 81Q616 50 575 27T493 -5L480 -10ZM568 342Q568 613 437 659L395 666Q329 666 286 626Q232 570 213 439Q210 408 210 342T213 246Q231 113 286 57Q309 37 342 23Q357 19 389 19Q420 19 437 23Q469 38 491 57Q568 134 568 342ZM174 341V354Q174 393 175 419T183 484T205 561T246 635L249 639Q246 639 224 627T193 608Q189 606 183 601T169 589T155 577Q69 491 69 344Q69 133 231 52Q247 42 247 46Q247 46 246 48Q231 69 222 85T200 141T177 239Q174 269 174 341ZM708 341Q708 410 689 467T640 556T588 606T546 630Q532 638 531 638Q530 638 531 635Q563 590 577 543Q602 472 602 341V316Q602 264 599 230T580 144T531 48Q529 44 532 45T546 52Q575 68 596 84T642 128T683 200T706 299Q708 327 708 341ZM391 -17H333Q329 -15 326 -15Q324 -15 324 -17Q324 -21 362 -68Q424 -130 506 -143Q518 -144 544 -144Q569 -144 577 -143L589 -141L575 -139Q544 -127 509 -101T453 -37L442 -19L391 -17Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-70\" d=\"M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJAMS-51\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-70\" x=\"1100\" y=\"-308\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "cd9753a34981f780b1ba189d11d79bfe57480cf96aaa2d32ab1fa895f4575fda", "withdrawn": "", "abstract": "We consider cycles of a fixed length $p_0 \\geqslant 3$ of the monomial map $f(x) = x^n$ where $p_0$ is prime and $n \\geqslant 2$. We call $p$ a $p_0$-cycle yielding prime of $f$ if there exists a cycle of length $p_0$ in $f$ over $\\mathbb{Q}_p$. We derive a characterization of such primes $p$ using the prime divisors of the cyclotomic polynomial $\\Phi_{p_0}(n)$ in two different ways. The first method utilizes a classification of cycles as multiplicative orders of $n$ modulo divisors of $p-1$. The second method utilizes a direct argument from taking Nilsson's formula to be positive. We subsequently show a strict upper bound on the minimal such prime $p$ and give a formula for the asymptotic density of these primes in the set of all primes.", "id": "Paper/64654", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64654"}, {"title": " Maximum Likelihood Estimation for Statistical Models on the Grassmannain ", "webprogram_exclude": "0", "session_ids": ["Session/18115"], "source_sha256": "c6691232aa8c8e1e4c1b3026e70449d78b0f07545530f4317e29c9b724e11351", "withdrawn": "", "abstract": "In this talk, we will introduce the maximum likelihood estimation problem for three different statistical models related to the Grassmannian, namely the positive Grassmannian, the squared Grassmannian, and the configuration space of points in projective space. We use algebro-geometric methods to describe the complexity of these optimization problems via the maximum likelihood (ML) degree, and discuss the reality and positivity of the critical points.", "id": "Paper/64657", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64657"}, {"title": " Splitting the center of a Sylow subgroup ", "webprogram_exclude": "0", "session_ids": ["Session/18264"], "source_sha256": "4b9dd2b3c7832a3ac499cfa5ad7cbdaf81ed0c3bf13b1e7559480061f950f2bc", "withdrawn": "", "abstract": "(Joint work with Justin Lynd) Suppose p is a prime and S is a Sylow p-subgroup of a finite group G. If S is normal in G, then Z(S) is the direct product of S \\cap Z(G) with [Z(S), G]. We obtain an analogous result for all groups G except in some cases where p = 2 and G is not solvable, where we have counterexamples. It is an open problem to determine which groups are counterexamples.", "id": "Paper/64688", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64688"}, {"title": " Low Regularity Norm Inflation of Axisymmetric Hall Magnetohydrodynamics in Sobolev Space ", "webprogram_exclude": "0", "session_ids": ["Session/17952"], "source_sha256": "d6cd6257feed5c426cd708afd80ea6768268a45bb93f26f5c6efeb42be0cd73b", "withdrawn": "", "abstract": "It was shown by Oh and Jeong that Hall magnetohydrodynamics (MHD) in $\\mathbb R^3$ without dissipation exhibits norm inflation in $H^{\\sigma -1}\\times H^\\sigma$ for $\\sigma > 7/2$. We are going to discuss recent progress on low regularity norm inflation of axisymmetric Hall magnetohydrodynamics (MHD) where $u = u^re_r+u^ze_z$ and $B = B^\\theta e_\\theta$. For any short time interval, we constructed arbitrarily small initial data $(u_0,B_0) \\in H^{\\sigma-1} \\times H^{\\sigma}$ where $1<\\sigma<7/2$ such that the solution develops norm inflation. To be precise, $\\|B\\|_{\\dot H^{\\sigma}}$ becomes arbitrarily large while $\\|u\\|_{H^{\\sigma-1}}$ remains small. We could also generalize it to the case with fractional dissipation $(-\\Delta)^\\beta u$ and $(-\\Delta)^\\alpha B$, changing the range of $\\sigma$ to $1 < \\sigma < 7/2 - 2\\max\\{\\alpha,\\beta\\}$, $0 \\le \\alpha, \\beta < 5/4$.", "id": "Paper/64692", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64692"}, {"title": " Genus Distribution of Generalized Construction <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.743ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 750.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">A</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-41\" d=\"M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-41\" x=\"0\" y=\"0\"></use>\n</g>\n</svg> lattices ", "webprogram_exclude": "0", "session_ids": ["Session/18368"], "source_sha256": "fac11c7cb3382f9a9a9ba20ae8f22ccd3fb9ba64a503518ebba528d8c3fe7263", "withdrawn": "", "abstract": "Let $K$ be a CM-field and $\\mathfrak{o}$ denote its ring of integers. Let $\\mathfrak{p}$ be a nonzero integral ideal in $\\mathfrak{o}$ and $\\mathcal{C}$ be a free $[N,k]$-linear code defined over $\\mathfrak{o}/\\mathfrak{p}$. Define the Generalized Construction $A$ lattice $L(\\mathcal{C}):=\\{\\mathbf{v}\\in\\mathfrak{o}^N :\\mathbf{v}\\ \\mathrm{mod}\\ \\mathfrak{p}\\in\\mathcal{C}\\}$. In this talk, we will study the genus distribution of the generalized construction $A$ lattices.", "id": "Paper/64697", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64697"}, {"title": " A New Description of Torsion Units of Fibered Burnside Rings ", "webprogram_exclude": "0", "session_ids": ["Session/18264"], "source_sha256": "239d3d90535c411d4ffd9787895661ad44536127821595e59ed944c6dd0afc8b", "withdrawn": "", "abstract": "In 1971, Dress defined the $A$-fibered Burnside ring of a finite group $G$ and an Abelian group $A$, denoted by $B^{A}(G)$, a generalization of the Burnside ring of the finite group $G$. Of particular interest is the group of torsion units of $B^{A}(G)$, called the orthogonal unit group of $B^{A}(G)$ and denoted by $O(B^{A}(G))$. In 2019, Takegahara proved that $O(B^{A}(G)) = B(G)^{\\times} \\times K^{A}(G)$ where $B(G)^{\\times}$ denotes the unit group of the Burnside ring and $K^{A}(G)$ is a particular subgroup of $O(B^{A}(G))$. In this talk we provide three different descriptions of $K^{A}(G)$. This is joint work with Robert Boltje.", "id": "Paper/64700", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64700"}, {"title": " Unpacking the <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"6.865ex\" height=\"3.176ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -1006.6 2955.7 1367.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">B^{A}(G)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-42\" d=\"M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-41\" d=\"M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-47\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q492 659 471 656T418 643T357 615T294 567T236 496T189 394T158 260Q156 242 156 221Q156 173 170 136T206 79T256 45T308 28T353 24Q407 24 452 47T514 106Q517 114 529 161T541 214Q541 222 528 224T468 227H431Q425 233 425 235T427 254Q431 267 437 273H454Q494 271 594 271Q634 271 659 271T695 272T707 272Q721 272 721 263Q721 261 719 249Q714 230 709 228Q706 227 694 227Q674 227 653 224Q646 221 643 215T629 164Q620 131 614 108Q589 6 586 3Q584 1 581 1Q571 1 553 21T530 52Q530 53 528 52T522 47Q448 -22 322 -22Q201 -22 126 55T50 252Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-42\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-41\" x=\"1074\" y=\"513\"></use>\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"1390\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-47\" x=\"1779\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"2566\" y=\"0\"></use>\n</g>\n</svg>: An Introduction to the <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.743ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 750.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">A</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-41\" d=\"M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-41\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-fibered Burnside Ring ", "webprogram_exclude": "0", "session_ids": ["Session/18379"], "source_sha256": "1c6e3c04c2cfca76aab9179894588c5afad35fa3154737b6e8c233d5bee812cd", "withdrawn": "", "abstract": "In 1971, Dress defined the $A$-fibered Burnside ring of a finite group $G$ and an Abelian group $A$, denoted by $B^{A}(G)$, a generalization of the Burnside ring of $G$. But what is being generalized and what information does $B^{A}(G)$ capture? In this talk, we will begin with the definition of the Burnside ring before unpacking the $A$-fibered Burnside ring. Along the way we will emphasize what these algebraic objects encode about the groups $G$ and $A$.", "id": "Paper/64702", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64702"}, {"title": " Quantum White Noise Description of Quark-Gluon Interactions ", "webprogram_exclude": "0", "session_ids": ["Session/18321"], "source_sha256": "6fd37be1cff98d8700c27d42a6a5d47ad6cd1d1d3545a2ff1f8b8febe8378fca", "withdrawn": "", "abstract": "Representation theory of the Lie group Poincar´e is the mathematical\nbasis for describing the states of quantum particles moving at relativistic\nspeeds. The irreducible representations of the group that describe\nstates of such particles may be obtained using the tools of Mackey machinery.\nAlong with the second quantization methods from quantum probability,\nwe can set up a quantum field theory of fermions and bosons that are\nnon interacting. In this work, to incorporate interactions, we describe Irreducible\nRepresentations (IRR) of the extended Poincar´e group to describe\nthe states of subatomic particles that have ”color” as additional internal degrees\nof freedom. As the three-color degrees of freedom depend upon the\nspacetime coordinates of the particles we can describe entangled states for\nthe configuration space. The symmetry of the system then can be expressed\nby augmenting homogeneous Lorentz with SU(3) and the configuration space\nR4 by C3. Using the tools of systems of imprimitivity we can construct the\nsingle particle Hilbert space to describe the states of fermionic quarks that\nwe will then incorporate in the derivation of the colored Dirac equation. The\nHilbert space of massless bosonic gluons will lead to the fock space which will\nenable us to describe the asymptotic interaction between a quark and gluon\nfields as a white noise using the tools of quantum stochastic limits. Our construction\nresults in both states and operators of the fields (gauge) covariant\nwith respect to extended Poincar´e.", "id": "Paper/64718", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64718"}, {"title": " Regression to the Mean: A Practitioner’s Perspective on Mathematics, Policy, and Progress \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/17846"], "source_sha256": "a823f731721bfb43501b082f6f9ad32dc715d67876c45ea80430c84cd0d02b89", "withdrawn": "", "abstract": "As the United States marks the 250th anniversary of its founding, there are signs that many people who live here are unhappy with the way things are (policy). To the extent that people are unified in their disappointment, there seems to be less agreement on how we collectively got here, and by extention, how we might go from here (progress).  \n\nAt all levels of society, we can observe instances of existing processes, procedures, or policies that seem ineffective at best, and sometimes downright harmful. But for various reasons, the policies remain resistant to change, with the same lack of alignment on why they exist, and how to improve. \n\nThis talk will be a personal reflection on my background and education in mathematics has informed my work as a data and policy analyst, with the hope of provoking conversation, alignment, and collaboration within our community.  \n\nThe talk will center on a series of analyses and findings concerning race and equity in public schools; specifically, the outcomes from the public schools of a single, racially diverse, suburban community. Along the way, we will also motivate a framework for collaborative data-driven decision making, and perspective on getting unstuck when it comes to taking action.", "id": "Paper/64731", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64731"}, {"title": " Communicating Mathematical Norms Through Instructional Practices and Student Takeaways ", "webprogram_exclude": "0", "session_ids": ["Session/18068"], "source_sha256": "271116a8815bc668cb3fcbca8251ee6e3ba3d71c44be47419bf567506e2fea07", "withdrawn": "", "abstract": "Students encounter mathematical definitions throughout mathematics courses, but the norms and values that shape how mathematicians work with definitions may remain implicit. This project examines classroom activities designed to make these aspects of mathematical practice more explicit to students. Drawing on four activities implemented by an instructor in a calculus course and subsequent student interviews, we examine instructional practices used to communicate targeted definition norms and values and how students interpreted those messages. Findings highlight connections between instructional practices that foregrounded choice, comparison, and mathematical terminology and students’ takeaways about choice and variation in definitions, conceptual meaning in mathematical names, and the human role in creating mathematical definitions and terminology. These paired instructional practices and student takeaways illustrate ways that norms and values surrounding mathematical definitions can be communicated more explicitly to students.", "id": "Paper/64736", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64736"}, {"title": " The Associative Zesting of an Exact Factorization of Fusion Categories ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "e91d6d5b0f99108cb225c8110e7bfc5a34e014b0911ee21f4a6aae9c01fa46ca", "withdrawn": "", "abstract": "We explore how the associative zesting construction of fusion categories intertwines with the exact factorization of fusion categories. We begin by defining an induced zesting from a fusion category on a fusion subcategory when the zesting satisfies a certain property. With this restriction in place, we show that the induced zestings of an exact factorization preserve an exact factorization of the parent zesting. For a general zesting, we develop a general notion of induced zestings at the fusion ring level, and show that the induced zestings preserve an exact factorization of fusion rings. We present partial progress on extending these results to the fusion category level, and discuss potential directions for further exploration.", "id": "Paper/64747", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64747"}, {"title": " Gaussian-Type Integrals: A Study of Theory, Computation, and Applications ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "af06cf10c6c4b1bf6e10c4c4b591aecf36e666158c8953f8c0848b1d711a4ccd", "withdrawn": "", "abstract": "This project looks at Gaussian-type integrals and how the classical Gaussian integral can be extended by changing the exponent. I studied how these integrals are connected to the Gamma function and how their values change as the exponent changes. I also looked at convergence, more general forms of the integral, and the behavior of the results for different parameter values. Along with the theoretical work, I used numerical methods such as the Trapezoidal Rule and Simpson’s Rule to approximate the integrals and compare them with the exact values. The project also considers some applications of Gaussian-type integrals in probability, data analysis, and physics.", "id": "Paper/64749", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64749"}, {"title": " An Exploration of Interactions of Poetry and Mathematics in Teaching ", "webprogram_exclude": "0", "session_ids": ["Session/18216"], "source_sha256": "33a2336a9986622cc851ab28abd513afcc96ceeecd89ff9b82192eda6e907684", "withdrawn": "", "abstract": "Poetry and mathematics, seemingly distinct disciplines, share some common ground in the many forms of mathematical poetry. The interactions of the two disciplines within the framework of mathematical poems can sometimes result in unexpected synergy. In this presentation, a brief description comparing and contrasting aspects of the practices of poetry and mathematics are reviewed. Then a selection of a range of poems and excerpts of poems with mathematical themes, mathematical patterns, structures, and metaphors are introduced. A discussion follows for each poem with particular attention given to ways that unique facets of the each separate discipline add to the enrichment of the other. These poems may further serve as models for introducing or reviewing specific concepts in the classroom.", "id": "Paper/64758", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64758"}, {"title": " On the Existence of Hyperelliptic Curves over <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"5.254ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 2262 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbb {Q}(T)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJAMS-51\" d=\"M480 -10Q480 -13 486 -24T507 -50T541 -80T588 -104T648 -114Q666 -114 688 -110T714 -106Q724 -106 728 -114T729 -130Q723 -145 663 -163T548 -181Q503 -181 463 -169T395 -139T343 -97T307 -56T284 -19L280 -3L262 1Q188 24 131 81Q57 155 37 275Q34 292 34 342T37 410Q58 528 131 601Q179 652 248 676T388 701Q485 701 562 661Q698 595 731 448Q742 410 742 341T731 235Q707 141 646 81Q616 50 575 27T493 -5L480 -10ZM568 342Q568 613 437 659L395 666Q329 666 286 626Q232 570 213 439Q210 408 210 342T213 246Q231 113 286 57Q309 37 342 23Q357 19 389 19Q420 19 437 23Q469 38 491 57Q568 134 568 342ZM174 341V354Q174 393 175 419T183 484T205 561T246 635L249 639Q246 639 224 627T193 608Q189 606 183 601T169 589T155 577Q69 491 69 344Q69 133 231 52Q247 42 247 46Q247 46 246 48Q231 69 222 85T200 141T177 239Q174 269 174 341ZM708 341Q708 410 689 467T640 556T588 606T546 630Q532 638 531 638Q530 638 531 635Q563 590 577 543Q602 472 602 341V316Q602 264 599 230T580 144T531 48Q529 44 532 45T546 52Q575 68 596 84T642 128T683 200T706 299Q708 327 708 341ZM391 -17H333Q329 -15 326 -15Q324 -15 324 -17Q324 -21 362 -68Q424 -130 506 -143Q518 -144 544 -144Q569 -144 577 -143L589 -141L575 -139Q544 -127 509 -101T453 -37L442 -19L391 -17Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-54\" d=\"M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJAMS-51\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"778\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-54\" x=\"1168\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"1872\" y=\"0\"></use>\n</g>\n</svg> with Certain Jacobian Ranks ", "webprogram_exclude": "0", "session_ids": ["Session/19367"], "source_sha256": "cace638928509a8d0954d7f4679eaea853bb3f62c36023cae18b19b832616eae", "withdrawn": "", "abstract": "Let $y^2 = f(x,T)$ be a hyperelliptic curve of genus $g\\geq 1$, defined over $\\mathbb{Q}(T)$. We prove the existence of infinitely many imaginary hyperelliptic curves with a fixed genus $g$ having a certain rank for $5\\leq r\\leq 4g+2$, and a similar result for real hyperelliptic curves with a fixed genus $g$ having a certain rank for $6\\leq r\\leq 4g+4$. We begin by constructing such curves and prove the rank using two methods. First, we apply the generalized Nagao's conjecture, which relates the first moment and the rank of the Jacobian variety $J_\\mathcal{X}(\\mathbb{Q}(T))$, and that the conjecture holds for our curves, making the result unconditional. Furthermore, we explicitly construct rational points in the Mordell-Weil group and use Shioda-Tate to prove that the rank is equal to $r$.", "id": "Paper/64760", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64760"}, {"title": " Thick points of log-correlated Gaussian fields do not depend on the mollifier ", "webprogram_exclude": "0", "session_ids": ["Session/19364"], "source_sha256": "0ca54ccef9836e3e7d5d2d2d9dbe74aed91384a1fe381995b3a65696b1a48563", "withdrawn": "", "abstract": "The log-correlated Gaussian field (LGF) on $\\mathbb{R}^d$ ($d \\geq 2$) is a centered Gaussian random tempered distribution, defined modulo additive constants, whose covariance kernel is $\\log(1/|x-y|)$. In two dimensions, the LGF coincides with the whole-plane Gaussian Free Field (GFF). Because the field is a distribution, studying its pointwise behavior requires regularization via convolution with a mollifier. A point is called $\\alpha$-thick if the mollified field at that point grows like $\\alpha \\log(1/\\epsilon)$ as the mollification scale $\\epsilon \\to 0$. A natural question is whether the set of $\\alpha$-thick points depends on the choice of mollifier. We prove that for any two admissible mollifiers $\\rho$ and $\\sigma$ satisfying some mild conditions, the thick point sets coincide almost surely. The result holds in all dimensions $d \\geq 2$, and in the special case $d = 2$ extends to the zero-boundary GFF on any open domain with harmonically non-trivial boundary via the Markov property.", "id": "Paper/64761", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64761"}, {"title": " Analysis and Optimal Control of Multiscale Interface Couplings of Poroelasticity and Lumped Hydraulic Systems. ", "webprogram_exclude": "0", "session_ids": ["Session/18351"], "source_sha256": "6dac144045d080db130a4dc972d7ce29265271ae5887cf6a5725547487a4cf52", "withdrawn": "", "abstract": "Processes in the body, such as tissue perfusion, are governed by both local and global effects. Our proposed model uses a 3D system of partial differential equations to model the local area of tissue perfusion as fluid flowing through a deformable poroelastic medium. The corresponding global effects of the circulatory system are then modeled by a system of ordinary differential equations, using the electrical analog of hydraulic components to describe the system. The two systems are coupled across an interface of the porous medium via boundary conditions, which preserves the continuity of mass and the balance of stresses. For the optimal control problem, we utilize a quadratic cost functional with target values for the poroelastic displacement and pressure solutions minimized over a set of controls. The analysis of this multiscale interface coupling and control problem is important in the study of the development and progression of ocular diseases, as the development of these conditions is linked to local factors (intraocular pressure, tissue perfusion), but also global factors (blood pressure). Our goal is to better understand the relation between all these factors. For the multiscale system between linear poroelasticity equations and a non-linear hydraulic circuit, we give results on the wellposedness of solutions and existence of an optimal control to the minimization problem.", "id": "Paper/64764", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64764"}, {"title": " The Equitable Learning Inquiry Program: Supporting Faculty Adaptation Through SoTL ", "webprogram_exclude": "0", "session_ids": ["Session/18341"], "source_sha256": "44178a02c5993a99fc628adfdf16fbe6a173c3b9f522ef47181c8d1380446763", "withdrawn": "", "abstract": "The Equitable Learning Inquiry (ELI) program is a structured Scholarship of Teaching and Learning (SoTL) initiative in which faculty are supported by Center for Teaching and Learning (CTL) staff in investigating the impacts of socio-psychological interventions in their teaching. While faculty are free to identify and implement any intervention of their choosing, the investigations are situated within a program-level research question: how do such interventions impact student motivation and gaps in achievement in foundational courses? The year-long program consists of an initial institute where faculty dive deep into historical student outcome data, a pre-intervention implementation workshop, and a post-intervention data workshop followed by a community showcase. \n\nThis talk highlights the ELI program as a vehicle for both individual professional growth and institutional change. I will describe the structural framework of the ELI program, illuminate how participation shaped my own SoTL and instructional practice, and share how our findings are driving broader institutional SoTL engagement. Attendees will leave with practical insights about how to leverage CTL-faculty partnerships to support faculty inquiry into instructional practice and adaptations of high-impact practices.", "id": "Paper/64769", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64769"}, {"title": " A general-purpose sensitivity method for multiple simultaneous parameter perturbations in stochastic reaction networks ", "webprogram_exclude": "0", "session_ids": ["Session/17811"], "source_sha256": "06574f1a4635fde7cc509ea65470eb5fc8b2d1dbe0a53ef51e778ddfd85e8d61", "withdrawn": "", "abstract": "A central question for parameterized stochastic reaction networks is how expectations of quantities of interest change under parameter perturbations. We propose a multi-path stacked coupling (MSC) method and a corresponding simulation algorithm. This work extends the stacked-coupling framework of Anderson and Yuan to a genuinely multi-path setting. The resulting method provides a general-purpose framework for finite-difference sensitivity estimation whenever several nearby parameterized paths are used within the same estimator. We will also show how this viewpoint naturally applies in three representative settings: the simultaneous computation of many first derivatives, higher-order finite-difference estimation of a single first derivative using wider stencils, and the estimation of higher-order derivatives.", "id": "Paper/64774", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64774"}, {"title": " A Frattini Closure Property Applied to CLT Groups ", "webprogram_exclude": "0", "session_ids": ["Session/19362"], "source_sha256": "7e65f44435cbbda7159395160c0669f58d7cee464cfbce5409ec424e24efabd0", "withdrawn": "", "abstract": "A formation $\\mathfrak{F}$ is saturated if $G/\\Phi(G) \\in \\mathfrak{F}$, then $G \\in \\mathfrak{F}$.  This talk examines classes  of groups $\\mathfrak{C}$ that are not necessarily formations, but satisfy the condition that $G/\\Phi(G) \\in \\mathfrak{C}$ imply that $G \\in \\mathfrak{C}$.  More specifically, conditions are established for when $G/\\Phi(G)$ being a CLT group implies that $G$ is a CLT group.  A group $G$ is a CLT group if for all $d$ dividing the order of $G$, there exists a subgroup $H$ of $G$ such that $|H| = d$.", "id": "Paper/64778", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64778"}, {"title": " Positive autocorrelation at unit lag for stationary random walk Metropolis–Hastings in <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.77ex\" height=\"2.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -1006.6 1192.7 1152.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">{\\mathbb R}^d</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJAMS-52\" d=\"M17 665Q17 672 28 683H221Q415 681 439 677Q461 673 481 667T516 654T544 639T566 623T584 607T597 592T607 578T614 565T618 554L621 548Q626 530 626 497Q626 447 613 419Q578 348 473 326L455 321Q462 310 473 292T517 226T578 141T637 72T686 35Q705 30 705 16Q705 7 693 -1H510Q503 6 404 159L306 310H268V183Q270 67 271 59Q274 42 291 38Q295 37 319 35Q344 35 353 28Q362 17 353 3L346 -1H28Q16 5 16 16Q16 35 55 35Q96 38 101 52Q106 60 106 341T101 632Q95 645 55 648Q17 648 17 665ZM241 35Q238 42 237 45T235 78T233 163T233 337V621L237 635L244 648H133Q136 641 137 638T139 603T141 517T141 341Q141 131 140 89T134 37Q133 36 133 35H241ZM457 496Q457 540 449 570T425 615T400 634T377 643Q374 643 339 648Q300 648 281 635Q271 628 270 610T268 481V346H284Q327 346 375 352Q421 364 439 392T457 496ZM492 537T492 496T488 427T478 389T469 371T464 361Q464 360 465 360Q469 360 497 370Q593 400 593 495Q593 592 477 630L457 637L461 626Q474 611 488 561Q492 537 492 496ZM464 243Q411 317 410 317Q404 317 401 315Q384 315 370 312H346L526 35H619L606 50Q553 109 464 243Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-64\" d=\"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJAMS-52\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-64\" x=\"1021\" y=\"581\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18343"], "source_sha256": "21edfa1bd89b819de3c59922a95788b0d6d429b3d78b53f3c706edc663fa0fd7", "withdrawn": "", "abstract": "It is often asserted in the literature that one should expect positive autocorrelation for random walk Metropolis-Hastings (RWMH), especially if the typical proposal step-size is small relative to the variability in the target density. In this paper, we consider a stationary RWMH chain ${\\mathbf X}$ taking values in $d$-dimensional Euclidean space and (subject only to the existence of densities with respect to Lebesgue measure) with general target distribution having finite second moment and general proposal random walk step-distribution. We prove, for any nonzero vector ${\\mathbf c}$, strict positivity of the autocorrelation function at unit lag for the stochastic process $\\langle {\\mathbf c}, {\\mathbf X} \\rangle$, that is,\n\\[\n\\operatorname{Corr}(\\langle {\\mathbf c}, {\\mathbf X}_0 \\rangle, \\langle {\\mathbf c}, {\\mathbf X}_1 \\rangle) > 0,\n\\]\nand we establish the same result, but with weak inequality (which can in some cases be equality), when the state space for ${\\mathbf X}$ is changed to the integer grid ${\\mathbb Z}^d$.\nFurther, for ${\\mathbf c} \\neq {\\mathbf 0}$ we establish the sharp lower bound\n\\[\n\\operatorname{Corr}(\\langle {\\mathbf c}, {\\mathbf X}_0 \\rangle, \\langle {\\mathbf c}, {\\mathbf X}_1 \\rangle) > \\tfrac19\n\\]\non autocorrelation when we assume both that (i) the target density $\\pi$ is spherically symmetric and unimodal in the specific sense that $\\pi({\\mathbf x}) = \\hat{\\pi}(\\|{\\mathbf x}\\|)$ for some nonincreasing function $\\hat{\\pi}$ on $[0, \\infty)$ and that (ii) the proposal step-density is symmetric about ${\\mathbf 0}$.\n\nWe study the autocorrelation indirectly, by considering the incremental variance function (or incremental second-moment function) at unit lag. The same approach allows us also for $r \\in [2, \\infty)$ to upper-bound the incremental $r$th-absolute-moment function at unit lag.\n\nWe give also closely related inequalities for the total variation distance between two distributions on ${\\mathbb R}^d$ differing only by a location shift.", "id": "Paper/64808", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64808"}, {"title": " Constructing finite time singularities for some nonlinear PDEs ", "webprogram_exclude": "0", "session_ids": ["Session/18291"], "source_sha256": "70b517635a2ff42292e377071e19046d2277eecd2f2e7d51bc28899359a4de82", "withdrawn": "", "abstract": "In this talk, I will introduce the implosion blow-up results for the compressible Euler, the compressible Navier-Stokes equations, and the defocusing nonlinear Schr\\\"{o}dinger equation. We will discuss the existence of self-similar solutions and the stability near those solutions. During the talk, I will mention our work with Gonzalo Cao-Labora, Javier G\\'{o}mez-Serrano, and Gigliola Staffilani on the first non-radial implosion result for those three equations. If there is time, I will also mention our work on self-similar solutions of a hydrodynamic equation that may formally arise as potential blow-up profiles of the focusing NLS equation.", "id": "Paper/64827", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64827"}, {"title": " Traces of Rankin-Cohen brackets of Eisenstein series ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "3de76f52cb3733760a4a2ee93957944ad19774e9a70e71e89d504a9b91ec58b6", "withdrawn": "", "abstract": "We investigate modular forms obtained by taking the trace of the Rankin-Cohen bracket of two Eisenstein series twisted by a quadratic character. By using the Rankin-Selberg convolution method and analyzing the Fourier coefficients of such modular forms, we prove that they are not Hecke eigenforms for sufficiently large weight. We apply this result to show the non-vanishing of twisted central $L$-values of fixed weight and character for at least two Hecke eigenforms. Finally, we discuss improvements to these results under the assumption of Maeda's conjecture.", "id": "Paper/64829", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64829"}, {"title": " Any-Dimensional Polynomial Optimization via de Finetti Theorems ", "webprogram_exclude": "0", "session_ids": ["Session/18115"], "source_sha256": "c3c6e20b4bd28dd2acedcfbc60686326f105d991f7443a9e9ab3c70849ca0608", "withdrawn": "", "abstract": "There is growing interest in computationally proving mathematical theorems (e.g., using AI). Many theorems can be stated as inequalities that hold for infinitely-many dimensions, including inequalities in symmetric functions and graph parameters that arise in combinatorics. Taking an optimization perspective, we develop a framework for certifying any-dimensional inequalities by computing bounds on the limits of growing-sized optimization problems. Our key observation is a new and general connection between certifying any-dimensional inequalities and de Finetti-type theorems in probability. In particular, we prove new de Finetti theorems and use them to certify new any-dimensional inequalities inaccessible to previous approaches.", "id": "Paper/64833", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64833"}, {"title": " Global Existence of Solutions on the Quarter Plane for a Chemotaxis Model with Logistic Growth and Logarithmic Sensitivity ", "webprogram_exclude": "0", "session_ids": ["Session/18103"], "source_sha256": "533de91a4432fee407d4f86a49da6c8932b43619a5495c075290740609195897", "withdrawn": "", "abstract": "We study the initial-boundary value problem (IBVP) on the half-line\n\\begin{equation}\n\\begin{cases}\nv_t+u_x=0,\\\\\nu_t+(uv)_x=u_{xx}+ru(1-u),\n\\end{cases}\n\\qquad x\\in\\R^+,\\ t>0,\n\\tag{$\\ast$}\n\\end{equation}\nwith $u(0,t)=1$ and $r>0$ a fixed constant, arising as a viscous\nhyperbolic-parabolic balance law in which a conserved quantity $v$ is\ntransported by a diffusive, logistically self-limiting quantity $u$.\nAfter reformulating the problem around the constant equilibrium $u=1$\nvia $\\tilde u:=u-1$, we prove that for initial data\n$(v_0,u_0-1)\\in H^2(\\R^+)$ satisfying the compatibility condition\n$u_0(0)=1$ and sufficiently small in the $H^2(\\Rp)$ norm, the IBVP\nadmits a unique global-in-time solution\n\\[\n(v,u)\\in C\\bigl([0,\\infty);H^2(\\R^+)\\bigr)\\cap\nC^1\\bigl([0,\\infty);H^1(\\R^+)\\times L^2(\\R^+)\\bigr),\n\\]\nsatisfying a uniform-in-time energy estimate. The proof combines the\nclassical local existence theory of Kawashima for symmetrizable\nhyperbolic-parabolic systems with a uniform a priori estimate obtained\nby a half-line energy method in the spirit of Nakamura and Nishibata,\nitself an extension to the half-line of the whole-space method of\nMatsumura and Nishida. The chief technical obstruction --- boundary\nterms produced by repeated integration by parts on $\\R^+$ --- is\novercome by pairing the two equations of the system so that boundary\ncontributions either vanish identically, using the Dirichlet condition\n$\\tilde u(0,t)=0$, or cancel exactly between the transport and\ndiffusion equations.", "id": "Paper/64840", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64840"}, {"title": " Signal Deconvolution and Channel Identification on Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17908"], "source_sha256": "b7de6e41eafffc9cfdb13461e5d3e823173802cd200ad1a3328f0a2e4cc2b86f", "withdrawn": "", "abstract": "In multi-sensor scenarios, the source and received data can be considered as signals defined on graph structures with topologies governed by the data measurement strategy and the underlying physics of the problem. This talk addresses the blind deconvolution of nonstationary graph signals observed through a noisy and unknown shift-invariant graph channel. As a core component of the deconvolution process, a channel estimation method is proposed to obtain the spectral response of the unknown channel, where the presented approach assumes that the covariance structure of the source graph signal is known to the observer. To assess the performance of both the channel estimation and deconvolution methods, numerical experiments are performed on simulated data for cycle graphs, as well as real multi-station hourly temperature data with a user-defined graph topology according to neighborhoods of measuring stations.", "id": "Paper/64841", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64841"}, {"title": " Nonlinear Multiphase Advection Model with Flow-Attachment Phase Transition ", "webprogram_exclude": "0", "session_ids": ["Session/19369"], "source_sha256": "34a207dbddec17a6317bc0d293a154cf32667e07104e5206a9648993451bb004", "withdrawn": "", "abstract": "We study a diffusion-neglected, first-order hyperbolic PDE-ODE model for substrate transport, suspended biomass, and attached biomass, with a degenerate storage coefficient and an unbounded state-dependent characteristic speed in a tube reactor. In this talk, we present a priori estimate for a quasi-linear first-order hyperbolic system with volume exclusion. By utilizing a singularity transformation and the intrinsic local mass conservation law, we prove the global boundedness of the state variables under suitable physical conditions.", "id": "Paper/64844", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64844"}, {"title": " Bier spheres with nonrealizable central symmetries ", "webprogram_exclude": "0", "session_ids": ["Session/18072"], "source_sha256": "1bd4de86ab476aa2f67f59d5b957fb9bfc434a87cc2fc8a299954a2e5f686f76", "withdrawn": "", "abstract": "Bier spheres arise as deleted joins of simplicial complexes with their combinatorial Alexander duals and form one of the largest known families of simplicial spheres. We study centrally symmetric Bier spheres and give a simple criterion for when they cannot arise as boundaries of centrally symmetric polytopes. From this, we obtain a large new family of simplicial polytopes with combinatorial automorphisms that cannot be realized geometrically. Prior to our construction, the Bokowski--Ewald--Kleinschmidt polytope was the only known simplicial example exhibiting these properties. By Smith theory, these polytopes have noncontractible realization spaces.", "id": "Paper/64850", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64850"}, {"title": " Encouraging Metacognition Through Self-Assessment and Peer Feedback ", "webprogram_exclude": "0", "session_ids": ["Session/19349"], "source_sha256": "f3d2abfe0af7df5bd40cf7e854b5567b9d804a7256c0d23510ed8e56114cb56d", "withdrawn": "", "abstract": "Helping students recognize and improve their preparation habits can support greater reflection and engagement in mathematics courses. In this classroom study, students complete a brief daily self-assessment of their preparation using a three-level scale of plus, check, or minus, while a peer independently evaluates their preparation using the same scale. The study examines how closely students’ self-perceptions align with peer evaluations, how daily preparation relates to exam performance, and whether students change their preparation habits after receiving feedback from an initial exam. By comparing preparation patterns before the first and second exams, this study explores whether a simple routine of self-assessment and peer feedback can encourage students to become more aware of their learning behaviors. The presentation will focus on the educational implications of using regular reflection and peer feedback to promote student accountability, metacognition, and more intentional preparation for learning mathematics.", "id": "Paper/64852", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64852"}, {"title": " Borel classification and rigidity for higher rank lattices ", "webprogram_exclude": "0", "session_ids": ["Session/18213"], "source_sha256": "344f1509ab998eb911a83e5e52bc95ce28aa4376efedd1c78f649fa4797d8afd", "withdrawn": "", "abstract": "In the first part of this talk we will discuss the subject of Borel classification. We will review the main ideas and emphasize how it develops a solid framework to study classification problems across mathematics. This part is particularly suitable for a broad audience.\n\nIn the second half of the talk, we will discuss how this is related to the study of group actions and their rigidity properties. This is particularly related to rigidity theorems for lattices in higher lank Lie groups by Zimmer. Interestingly, some rigidity theorems of Zimmer admit a Borel counterpart as proved by Adams and Kechris. As time permits, we will present some new Borel rigidity theorems sharpening Adams and Kechris' results. This is joint work with Danae Rupp.", "id": "Paper/64853", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64853"}, {"title": " The Delta of a Variance Swap ", "webprogram_exclude": "0", "session_ids": ["Session/18328"], "source_sha256": "96a01edefa4507410e4dcf9cc84556d210e2e36a1131b3c72b80d37b69da0b82", "withdrawn": "", "abstract": "We define the variance swap total delta as the sensitivity of the price of variance to a change in underlying price.  We use Carr-Madan spanning formulas to analyze the total delta when the implied volatility smile curve may depend on the underlying price.  We show that the variance swap total delta is zero for the class of smile curves that are pure functions of (log) moneyness, which goes against the empirical observation that variance is up when the market is down.  We propose a simple modification of the smile to correct this issue.", "id": "Paper/64855", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64855"}, {"title": " Differentiable Magnetohydrodynamic Equilibria via Implicit Adjoints for Stellarator Optimization ", "webprogram_exclude": "0", "session_ids": ["Session/18104"], "source_sha256": "0b7ac82023ad5283d6ec857197cb385aa4cf642a2626ba337a6bbabf048b0dca", "withdrawn": "", "abstract": "Stellarators are fusion devices that confine a plasma using a external coils that create a magnetic field with a set of toroidal, nested surfaces. The magnetic field obeys magnetohydrodynamic equilibrium, so design efforts usually require many equilibrium solves to obtain the needed gradients using finite differencing, or high memory by auto-differentiating the nonlinear iterations. Here, the implicit adjoint formulation used in VMEX, a differentiable implementation of the VMEC equilibrium model, is described. Once the equilibrium has converged, sensitivities are obtained from the linearized equilibrium equations. For a scalar objective, one transposed solve gives derivatives with respect to all design variables. The adjoint systems are solved using structured linear solvers and matrix-free methods. Finally, combined coil and plasma optimization results will be shown for both fixed and free boundary conditions to identify optimized stellarators with good plasma confinement properties, such as omnigenity, low bootstrap current, and low turbulent transport.", "id": "Paper/64859", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64859"}, {"title": " Use of operator defect identities in multi-channel signal plus residual-analysis via iterated products and telescoping energy-residuals: Applications to kernels in machine learning ", "webprogram_exclude": "0", "session_ids": ["Session/19339"], "source_sha256": "c77f3ad4ec4c71451b681f56915e786626f64660dbf8844cd3c354c33c7e4fd7", "withdrawn": "", "abstract": "We present a new operator theoretic framework for analysis of complex systems with intrinsic subdivisions into components, taking the form of in general, and telescoping energy in particular. We prove new results which yield admissibility/effectiveness, and new a priori bounds on energy residuals. Applications include infinite-dimensional Kaczmarz theory for λn-relaxed variants, and λn-effffectiveness. And we give applications of our framework to generalized machine learning algorithms, greedy Kernel Principal Component Analysis (KPCA), which provides an exact telescoping residual identity and explicit finite-step energy decomposition, which are not usually available in standard PCA/KPCA analyses.", "id": "Paper/64860", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64860"}, {"title": " Global Existence of Weak Solutions to Chemotaxis Models with Porous-Medium Diffusion, Consumption, and Logistic Sources on <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"3.37ex\" height=\"2.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -1006.6 1450.8 1152.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbb {R}^N</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJAMS-52\" d=\"M17 665Q17 672 28 683H221Q415 681 439 677Q461 673 481 667T516 654T544 639T566 623T584 607T597 592T607 578T614 565T618 554L621 548Q626 530 626 497Q626 447 613 419Q578 348 473 326L455 321Q462 310 473 292T517 226T578 141T637 72T686 35Q705 30 705 16Q705 7 693 -1H510Q503 6 404 159L306 310H268V183Q270 67 271 59Q274 42 291 38Q295 37 319 35Q344 35 353 28Q362 17 353 3L346 -1H28Q16 5 16 16Q16 35 55 35Q96 38 101 52Q106 60 106 341T101 632Q95 645 55 648Q17 648 17 665ZM241 35Q238 42 237 45T235 78T233 163T233 337V621L237 635L244 648H133Q136 641 137 638T139 603T141 517T141 341Q141 131 140 89T134 37Q133 36 133 35H241ZM457 496Q457 540 449 570T425 615T400 634T377 643Q374 643 339 648Q300 648 281 635Q271 628 270 610T268 481V346H284Q327 346 375 352Q421 364 439 392T457 496ZM492 537T492 496T488 427T478 389T469 371T464 361Q464 360 465 360Q469 360 497 370Q593 400 593 495Q593 592 477 630L457 637L461 626Q474 611 488 561Q492 537 492 496ZM464 243Q411 317 410 317Q404 317 401 315Q384 315 370 312H346L526 35H619L606 50Q553 109 464 243Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4E\" d=\"M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJAMS-52\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-4E\" x=\"1021\" y=\"581\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18445"], "source_sha256": "3bccd5f68b6f56073f943004a8a1784a053be12409f7edd83db4a987b1cb5efb", "withdrawn": "", "abstract": "Abstract: This talk presents recent results on chemotaxis systems with nonlinear (porous-medium) diffusion, logistic growth, and chemical consumption on \\(\\mathbb{R}^N\\). For general, possibly non-integrable initial data, we establish the global existence of weak solutions that remain uniformly bounded for all time. We also discuss Hölder continuity and uniqueness of globally bounded weak solutions for \\(1<m\\le 3\\). Time permitting, I will briefly mention related results for chemotaxis systems with linear signal production.", "id": "Paper/64862", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64862"}, {"title": " The chromatic number of s-stable Kneser graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18359"], "source_sha256": "19b2e8ad4089ed97d9285e809cb5d6011f9b1e9d57385bfdb908cc4c48a9cdc2", "withdrawn": "", "abstract": "Generalizing theorems of Kneser and Schrijver, Meunier conjectured in 2011 that the chromatic number of $s$-stable $(n,k)$-Kneser graph  is $n - sk +s$ for all $n\\ge sk$. This conjecture was previously proven for all even $s$, and for $s \\ge 4$ and large enough $n$. We prove the conjecture in the cases $s=3$ and $n$ large enough, or $k=s=3$. To this end, we prove versions of the Hilton-Milner theorem for $s$-stable sets.", "id": "Paper/64870", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64870"}, {"title": " Diffusion Detection with Stochastic Excursion Statistics ", "webprogram_exclude": "0", "session_ids": ["Session/18008"], "source_sha256": "afb9af874e40b8e6a36102a34d49f244e29d146dc5d251088cb14c684e34cc88", "withdrawn": "", "abstract": "Distinguishing deterministic chaos from stochastic dynamics in discrete time series remains a fundamental and challenging problem, particularly in the presence of noise and limited data. Prior work has explored subjective metrics like entropy as a framework for capturing structural invariants between such signals---motivating the search for a robust, theoretically grounded method. In this work, we develop a nonparametric, theory-driven method based on excursion statistics of stochastic processes. Building on classical results on the persistent homology for continuous semimartingales, we exploit a universal scaling law relating the number of barcodes of size \n$\\epsilon$ to the quadratic variation of the signal. This yields a simple and interpretable diagnostic: stochastic diffusion processes exhibit an inverse-squared scaling in barcodes/excursion counts, while deterministic systems---periodic or chaotic---systematically violate this behavior. Using this principle, we construct a data-driven classification framework that operates directly on a single observed time series without embedding, symbolic transformations, or model training. We demonstrate the effectiveness of the method across a wide range of systems, including canonical stochastic diffusion, deterministic chaotic maps and flows, noisy hybrid systems, and real-world datasets including financial time series and audio signals.", "id": "Paper/64873", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64873"}, {"title": " Dynamics-Aware Sampling and Recovery for Tensor-Valued Dynamical Systems ", "webprogram_exclude": "0", "session_ids": ["Session/17945"], "source_sha256": "42f9e8ac603c32eaddcc2d9d0bb90bf16be830da693a72cc274d918ceb930dc4", "withdrawn": "", "abstract": "We study sampling and recovery for tensor-valued dynamical systems evolving under the t-product, with the goal of recovering an unknown initial tensor state from partial spatial observations over time. We show that, although the Fourier transform decomposes t-product dynamics into slicewise matrix systems, recovery is governed by aggregated spectral blocks that couple eigenspaces across slices sharing the same eigenvalues. This structure determines the space--time sampling tradeoff and leads to deterministic and randomized recovery guarantees based on spectral multiplicity, incoherence, and conditioning. We also show that temporal sampling plays a dual role: additional time samples can improve identifiability while worsening numerical stability through Vandermonde conditioning. Finally, we develop a Tensor Dynamical Sampling reconstruction framework and demonstrate its effectiveness on synthetic experiments, sea surface temperature data, and turbulence velocity data.", "id": "Paper/64874", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64874"}, {"title": " Orbits, Rational Maps, and Elliptic Curves; Where Dynamics Meets Number Theory ", "webprogram_exclude": "0", "session_ids": ["Session/18214"], "source_sha256": "0da0e31000b8c0c69f4bcd2e8f5eca6f95005889d5553cbb5c9c255ab039c512", "withdrawn": "", "abstract": "Arithmetic Dynamics lives at the intersection of dynamical systems and number theory. Motivated by results on elliptic curves, we ask ourselves if we replace elliptic curves with rational maps what are torsion points, canonical height, Galois actions, etc? Do these one to one translations of these elliptic curve theorems still hold over rational maps? and if not why not? For example, how could we go about proving the Uniform Boundedness Conjecture for rational maps, knowing that Merel's theorem is known for elliptic curves. Through this exploration, we develop our own field, expanding to new techniques, new questions, and an ever rich field of open questions. This session will give a general overview of what we've been thinking about in arithmetic dynamics and how it relates to elliptic curves in number theory.", "id": "Paper/64875", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64875"}, {"title": " On the number of distinct distance in sets of points in convex position in the plane ", "webprogram_exclude": "0", "session_ids": ["Session/18315"], "source_sha256": "5eb5612865d96aca3a6448aaa2d9f12d52357c805acccbcb7f26cd1685b8a42f", "withdrawn": "", "abstract": "We survey old and new results concerning the number of distinct distances in a set of points convex position in the plane. Joint work with Nivasch, Pach, and Pinchasi.", "id": "Paper/64876", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64876"}, {"title": " Plactic Stabilization and Row Content Formulas for Unshifted Rectifications of Superstandard Shapes ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "64f09c39ae339ea1f08fab2aa2f002f9872a24bb3bc2550ea123d8a07ae80da8", "withdrawn": "", "abstract": "\\begin{abstract}\nWe investigate the Robinson-Schensted-Knuth (RSK) insertion dynamics of unshifted $k$-fold concatenated reading words $W^{(k)} = w(T)^k$ generated by superstandard Young tableaux $T$. Evaluating these highly periodic words within the plactic monoid---or equivalently via jeu de taquin rectifications of unshifted disjoint skew tableaux---reveals strong structural rigidity for superstandard fillings, contrasting with the irregular insertion patterns observed in arbitrary shapes. We establish explicit, piecewise combinatorial formulas governing the exact multiset row contents of the resulting insertion tableaux. Specifically, we present precise closed-form content characterizations for three fundamental geometric families---superstandard rectangles, hooks, and staircases---completely determining their interval decompositions and modulo-boundary dynamics under arbitrary iteration parameters $k$.\n\\end{abstract}", "id": "Paper/64877", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64877"}, {"title": " On Rudenko’s Theorem for Discretely Valued Fields ", "webprogram_exclude": "0", "session_ids": ["Session/18193"], "source_sha256": "30a3b48c3b7b82489c03427ce4ffc628554c584f9795ad76cfae382b71fae80b", "withdrawn": "", "abstract": "S. Stein conjectured in 2000 that a balanced polygon in the plane cannot be dissected into an odd number of triangles of equal area. Significant progress has been made but the conjecture remains open in general. Recently Rudenko proved Stein’s conjecture for dissections with rational coordinates by proving a theorem about $\\mathbb{Q}^2$-flows on trivalent graphs. We show the limits of Rudenko's theorem by establishing a necessary condition for it to hold for $K^2$-flows, where $K$ is a valued field, and show that $\\mathbb{R}$ fails to meet this condition for any choice of valuation. Moreover, we prove that this condition is sufficient when the valuation is discrete, proving Stein’s conjecture for dissections with coordinates in a new class of number fields.", "id": "Paper/64879", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64879"}, {"title": " VECINA: Helping math be a good neighbor by mapping what matters ", "webprogram_exclude": "0", "session_ids": ["Session/17921"], "source_sha256": "c4ffce0bcdb3c49839343d83fe48864f71a2d24fe7019bffc609a4fe7c3016d8", "withdrawn": "", "abstract": "VECINA, or Visualizing Environmental and Community Information for Neighborhood Advocacy, is a collection of members of the Mathematics and Data Science Justice Collective (MDJC), community members of Olneyville, and the nonprofit Woonasquatucket River Watershed Council (WRWC). This project has allowed us to use a critical feminist lens of STEM and reflect on what are we doing that is changing the STEM (in particular math) mythos in the community and ourselves. This talk discusses what collaboration can look like as we consider how we can use art to understand and process data.", "id": "Paper/64884", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64884"}, {"title": " Hitomezashi: Stitching at Every Level ", "webprogram_exclude": "0", "session_ids": ["Session/18554"], "source_sha256": "7b8e307e3fce8c8b0c8c6c41577dbfd091f610f1c777440df6df1bc1f028d2b2", "withdrawn": "", "abstract": "Hitomezashi is a particular style of sashiko stitching characterized by crossing lines of stitches. A certain subset of hitomezashi designs can be generated with two binary strings—this means beautiful designs can be created with minimal instructions. In this talk, we discuss how hitomezashi can be introduced at many levels to promote mathematical investigation and engagement. We will discuss activities that have been implemented in an array of settings, including a 5th grade classroom, various undergraduate courses, and as inspiration for undergraduate research projects. From these implementations, we discuss broader lessons about what provides the “spark” in mathematical exploration.", "id": "Paper/64885", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64885"}, {"title": " A Whole New Side: The Duality Symmetries of Generalized Hitomezashi Patterns ", "webprogram_exclude": "0", "session_ids": ["Session/18232"], "source_sha256": "34e5d828a7337ddd2c213d5cc97e79ec194888015144aad69b833612325ba6ee", "withdrawn": "", "abstract": "Hitomezashi is a particular style of sashiko stitching characterized by crossing lines of stitches. Certain hitomezashi designs can be encoded with two binary strings and have been the subject of a wide-array of mathematical research. Dubbed generalized hitomezashi patterns (GHPs) by Sen & Martinez, these designs are reversible and can be “self-dual.” We investigate the possible “dual-” or “flip-symmetries” in GHPs; the inclusion of these symmetries is equivalent to considering two-color symmetry groups. In this talk we discuss the compatible two-color rosette symmetry types, describe the properties on binary strings that create these symmetries, and discuss why exactly 17 of the 46 two-color wallpaper groups are compatible with GHPs.", "id": "Paper/64886", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64886"}, {"title": " A New Look at Pólya Urn Processes ", "webprogram_exclude": "0", "session_ids": ["Session/17976"], "source_sha256": "2cd703ed5486f33d34a3edf309fa9cbadd2f9066f06fba0d61599349e8d583cf", "withdrawn": "", "abstract": "A P\\'{o}lya Urn Process, introduced by Athreya and Karlin (Annals of Mathematical Statistics, 1968), is a continuous-time variant of a discrete-time P\\'{o}lya Urn Model.  P\\'{o}lya Urn Processes are significantly more tractable than their discrete-time counterparts, and over the last 20 years, H. Mahmoud and his colleagues have established many interesting results pertaining to these processes.  In this talk, we will use methods differing from those used by Mahmoud to establish many results associated with various types of P\\'{o}lya Urn Processes:  most of our talk will focus on a significant generalization of the Triangular P\\'{o}lya Urn Process of Chen and Mahmoud (Annals of the Institute of Statistical Mathematics, 2018).", "id": "Paper/64887", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64887"}, {"title": " A Principal-Agent Mean-Field Game Model of Insurance with Risk Interdependence ", "webprogram_exclude": "0", "session_ids": ["Session/17800"], "source_sha256": "035095034776ea7e9ed288e69211fc9ad1ecbaabcda475db3cf3b019093ab98b", "withdrawn": "", "abstract": "We study an insurance contract-design problem under moral hazard, endogenous participation, and strategic risk interdependence. Because the resulting $N$-agent game suffers from the curse of dimensionality, we approximate the strategic interactions via a heterogeneous mean-field game. We rigorously establish the existence of a lower-level mean-field Nash equilibrium using measurable selection arguments and the Kakutani fixed-point theorem. By proving the $L^1$-Lipschitz continuity of the aggregate participation threshold, we further establish equilibrium uniqueness via a contraction mapping. We then embed this mean-field response into the insurer's upper-level Stackelberg optimization problem. We formulate the objective through general performance envelopes to accommodate potential equilibrium multiplicity, proving the existence of upper-level $\\varepsilon$-optimal contracts, and demonstrating the existence of an exact Stackelberg equilibrium under the uniqueness regime. We conclude by extending the model to finite contract menus, providing numerical evidence that multi-contract screening improves the principal's expected payoff in interdependent risk environments.", "id": "Paper/64888", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64888"}, {"title": " Overlap containment representations and the <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"3.54ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 1524 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">OC</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-43\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-4F\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-43\" x=\"763\" y=\"0\"></use>\n</g>\n</svg>-number ", "webprogram_exclude": "0", "session_ids": ["Session/18317"], "source_sha256": "69431e7cb18a1743112896aa67456024525c0ba86bd657cc5b383229ec968eee", "withdrawn": "", "abstract": "Given a collection of distinct, nonempty sets ${\\cal S}$, construct $G$, the overlap containment ($OC$) graph  of ${\\cal S}$, by adding a vertex for each set in ${\\cal S}$, where $S_x$ denotes the set associated with vertex $x\\in V(G)$.  Next, add edge $xy$ to the $OC$-graph if $S_x \\cap S_y \\not = \\emptyset$.  Finally, let $k: E(G) \\rightarrow \\{O,C\\}$ be a labeling of $E(G)$ so that \n\n\\smallskip\n$\\bullet$ $k(xy) = C$ if and only if $S_x\\subset S_y$ or $S_y \\subset S_x$, and\n\n$\\bullet$ $k(xy) = O$ if and only if $S_x \\cap S_y \\not = \\emptyset$ but $S_x \\not \\subset S_y$ and $S_y \\not \\subset S_x$.\n\n\\smallskip\nLet $G$ be a graph and $k: E(G)\\rightarrow \\{O,C\\}$.\nWe say $(G,k)$ is an $OC$-graph if there exists a collection of distinct, nonempty sets, ${\\cal S}$, for which $G$ with edge labeling $k$ is the $OC$-graph of ${\\cal S}$.  We give a characterization of $(G,k)$ that are $OC$-graphs.  The $OC$-number of an $OC$-graph is the minimum cardinality of $\\cup_{S\\in {\\cal S}} S$ where $(G,k)$ is the $OC$-graph for ${\\cal S}$. We give the $OC$-number for connected triangle-free graphs that are $OC$-graphs and for some complete graphs and cobipartite graphs where the edge labeling is restricted.", "id": "Paper/64890", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64890"}, {"title": " Multivariate Generalized Pólya Processes ", "webprogram_exclude": "0", "session_ids": ["Session/17976"], "source_sha256": "fb02bca2ee573b4af2995c01145a0ecd11d97b04213447b91dc1860269252994", "withdrawn": "", "abstract": "The Generalized P\\'{o}lya Process (GPP) is a type of self-excited point process defined on the nonnegative real line that has been studied recently within the reliability literature.  In this talk, we will show how elementary methods can be used to study many interesting properties associated with GPPs, as well as many multivariate variations of such GPPs.  Connections to recent work will be discussed.", "id": "Paper/64898", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64898"}, {"title": " An <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.024ex\" height=\"2.509ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -934.9 871.4 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\ell ^2</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2113\" d=\"M345 104T349 104T361 95T369 80T352 59Q268 -20 206 -20Q170 -20 146 3T113 53T99 104L94 129Q94 130 79 116T48 86T28 70Q22 70 15 79T7 94Q7 98 12 103T58 147L91 179V185Q91 186 91 191T92 200Q92 282 128 400T223 612T336 705Q397 705 397 636V627Q397 453 194 233Q185 223 180 218T174 211T171 208T165 201L163 186Q159 142 159 123Q159 17 208 17Q228 17 253 30T293 56T335 94Q345 104 349 104ZM360 634Q360 655 354 661T336 668Q328 668 322 666T302 645T272 592Q252 547 229 467T192 330L179 273Q179 272 186 280T204 300T221 322Q327 453 355 590Q360 612 360 634Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-2113\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-32\" x=\"590\" y=\"513\"></use>\n</g>\n</svg> Obstruction for Elementary Embeddings of Hyperbolic Groups ", "webprogram_exclude": "0", "session_ids": ["Session/19362"], "source_sha256": "3a413012fd22cb77320e0d6282b76d6a16f8daf51e9c8588775bbcd31aeca572", "withdrawn": "", "abstract": "Initially defined in work of Atiyah, the first $\\ell^2$-Betti number $\\beta_1^{(2)}(G)$ of a countable, discrete group $G$ has since become an invariant of great interest. In this talk, I’ll describe recent work (arXiv:2605.20397) in which I demonstrated two different inequalities in the first $\\ell^2$-Betti number arising from existential and elementary embeddings respectively in first order logic. In the case in which $H$ is an elementarily embedded subgroup of a torsion free hyperbolic group $G$, the proof leverages the rich structure of hyperbolic towers developed by Perin and Sela. In this setting, the resulting inequality $\\beta_1^{(2)}(H)+\\frac{1}{2} \\leq \\beta_1^{(2)}(G)$ presents a curious gap of at least $1/2$ between the first $\\ell^2$-Betti number of $G$ and that of $H$. I'll explain how this gap arises from the simple fact that the Euler characteristic $\\chi(\\Sigma)$ of a surface $\\Sigma$ must be an integer.", "id": "Paper/64906", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64906"}, {"title": " Analytic properties of Sato-Shintani zeta functions ", "webprogram_exclude": "0", "session_ids": ["Session/18010"], "source_sha256": "4926b410e4debda7c340c90e381e8866fea1f17ffac884c9c6985fb964f60444", "withdrawn": "", "abstract": "Sato-Shintani zeta functions enumerate integral orbits in prehomogenous vector spaces.  Their analytic properties, including the subconvexity, moments, functional equations and complete character sums have a fundamental arithmetic interest, with applications to counting arithmetic objects and equidistribution.  I will discuss recent work, some of it joint with Eun Hye Lee, developing the analytic theory.", "id": "Paper/64912", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64912"}, {"title": " Exploring the independence complexes of ternary graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18339"], "source_sha256": "cb13b3a9c5c65bf5e6196497c38dcd5c17c4a5944f4e1b7ef65ef3e1e088791e", "withdrawn": "", "abstract": "A result by Kim shows that a graph is ternary if and only if the independence complex of all induced subgraphs is either contractible or homotopy equivalent to a sphere. In this talk, we further explore properties of these independence complexes. Moreover, we take a closer look at the family of planar 1-well-covered graphs constructed by Pinter. We will explain how they fit into this context and investigate their independence complexes. This talk is based on joint work with Margaret Bayer, Richard Danner, Thiago Holleben, and Yirong Yang.", "id": "Paper/64915", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64915"}, {"title": " A new approach for fractional coloring ", "webprogram_exclude": "0", "session_ids": ["Session/18359"], "source_sha256": "f291c75d3521ad5fd6e520e2a51c55d5b139393ac8803c62faeaf2a0e930d6d7", "withdrawn": "", "abstract": "The fractional chromatic number of a hypergraph $H$, denoted $\\chi_f(H)$, is the minimum $k \\ge 1$ for which there exists a probability distribution $\\mathcal{D}$ over the independent sets of $H$ satisfying $\\Pr_{I \\sim \\mathcal{D}}[v \\in I] \\ge 1/k$ for every vertex $v$. In this talk, we present a new approach to sampling independent sets tailored for bounding the fractional chromatic number of $d$-degenerate graphs and hypergraphs. As a motivating application, we give an alternate, short proof of a recent result of Martinsson and Steiner showing that every $d$-degenerate triangle-free graph $G$ satisfies $\\chi_f(G) = O(d / \\log d)$. We then discuss extensions of this framework to broader graph and hypergraph classes, as well as to the setting of fractional coloring with local demands.\n\nThis talk is based on joint works with Peter Allen, Ewan Davies, David Gallardo, Lina Li, Ethan Luo, Abhishek Methuku, Huy Nguyen, Jonathan A. Noel, Jaehyeon Seo, Samuel Spiro, Minh-Quan Vo, and Kewen Yuan.", "id": "Paper/64916", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64916"}, {"title": " Two-Circle Problems for Harmonic Functions on Homogeneous Trees ", "webprogram_exclude": "0", "session_ids": ["Session/18255"], "source_sha256": "f55389c85e85de006258e547da56b22cb527ad60fe5b0d16c108835eada51bd5", "withdrawn": "", "abstract": "A complex-valued function $f$ on the vertices of a homogeneous tree $\\mathfrak{X}$ of degree $q+1$ is defined to be \\textit{harmonic} if $\\mu_1f=f$, where $\\mu_1$ is the spherical mean-value operator of radius 1. Motivated by Delsarte's Theorem in Euclidean space, we use algebraic methods to show that if $\\mu_k{f}=\\mu_{\\ell}f=f$, then for almost all $q$, a sufficient condition for $f$ harmonic is at least one of $k$ and $\\ell$ odd. In the case of $k$ and $\\ell$ relatively prime, using similar methods, we strengthen this condition to hold for all $q$.", "id": "Paper/64922", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64922"}, {"title": " Portfolio Optimization with Interacting Fast and Slow Latent Drift Factors ", "webprogram_exclude": "0", "session_ids": ["Session/18332"], "source_sha256": "0a18c009f31b433cea35fb5441a150495d71d0b81f1a8cac2d9c294f4fe6d4c1", "withdrawn": "", "abstract": "We consider a class of partial-information portfolio optimization problems where a traded spread exhibits short-run momentum and long-run mean reversion driven by latent Gaussian factors. Using Kalman–Bucy filtering, we derive and verify optimal portfolios under logarithmic, exponential, and power utility over arbitrary finite horizons. In each case, optimal demand decomposes into a myopic bet on expected price changes and, under power and exponential utility, an additional intertemporal hedging component. At finite times, we show that myopic demand is generated by a causal affine functional of current price and a filter adaptive MACD-type signal of price history. In the steady-filtering limit, we obtain a classification of the possible long-run forms of myopic demand. When effective fast–slow separation dominates filtering feedback, the myopic portfolio converges to a function of current price, an MACD-type signal, and, under logarithmic and power utility, current wealth. We exactly characterize when this MACD-type signal is a conventional MACD indicator.  When filtering feedback dominates separation, the MACD-type input is instead replaced by a signal with damped oscillatory price-history weights. Our theoretical work is complemented by numerical experiments which quantify the certainty-equivalent cost of approximating optimal myopic demand by simpler steady-state strategies, the portfolio value of retaining older price observations, and the horizons over which intertemporal hedging becomes quantitatively important.", "id": "Paper/64923", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64923"}, {"title": " The GIRAFFE Undergraduate Research Workshop ", "webprogram_exclude": "0", "session_ids": ["Session/17921"], "source_sha256": "fb9b5c69afa7dd92709295f8b3b295fa30384b00d1d10ec1760d42344b43c328", "withdrawn": "", "abstract": "The inaugural edition of the GIRAFFE Workshop was held at Winston-Salem State University in summer 2026. Undergraduates students and faculty mentors from their home institutions were brought together to initiate original research in graph theory (two projects) and data science (two projects). This week-long workshop was modeled on the Research Experiences for Undergraduate Faculty (REUF) program; a joint initiative of the American Institute of Mathematics and ICERM. In this presentation, we review the mathematical contributions of the workshop, plans for completing the projects, and lessons learned. We also share details of future iterations of the GIRAFFE workshop, including the application and award processes.", "id": "Paper/64926", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64926"}, {"title": " Distance Antimagic Labelings of Product Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17963"], "source_sha256": "3798dde008317ccd152ec28ab1687ba740eb8149089bc1ce2fc6028fd43c0753", "withdrawn": "", "abstract": "A distance antimagic labeling of a graph $G$ is a bijection $f:V(G)\\rightarrow \\{1,2,\\ldots, |V(G)|\\}$ satisfying the following condition. For every pair of distinct vertices $x$ and $y$, we have $w(x) \\neq w(y)$, where $w(x)=\\sum_{z\\in N(x)}f(z)$ and $N(x)$ is the neighborhood of $x$. A graph is called distance antimagic if such a labeling exists. In this talk, we develop distance antimagic labelings of various product graphs, particularly demonstrating the Cartesian and lexicographic products of several pairs of graphs are distance antimagic.", "id": "Paper/64927", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64927"}, {"title": " Numerics-Informed Neural Networks for Parabolic Partial Differential Equations ", "webprogram_exclude": "0", "session_ids": ["Session/19344"], "source_sha256": "8d52ccf2baeb72d1031b8d1ac606e5d809a84f93349312701e01509a56957871", "withdrawn": "", "abstract": "A physics-informed neural network (PINN) is trained by minimizing the residual of a strong-form PDE at collocation points. A numerics-informed neural network (NINN) is trained instead on the residual of a prescribed discretization of the same PDE, for example, a finite-difference scheme. The unknown is a nodal field on that mesh; Dirichlet conditions are imposed exactly by lifting, and no labeled solution data are used. For the two-dimensional heat equation with backward Euler time stepping, a lightweight U-Net learns the nodal update by minimizing the discrete residual of the five-point Laplacian. We prove a discrete $L^2$ error bound: the NINN error is at most a classical $O(\\tau+h^2)$ finite-difference term plus a sum of training residuals. If those residuals are small enough, the bound has the same order as the underlying scheme. The bound is conservative and does not explain observed rates above second order. Numerical tests on nineteen manufactured solutions show at least second-order convergence, and on selected smooth problems, the NINN error is smaller than that of the same finite-difference scheme. Training only on a subset of time steps, with a lifted forward pass on the rest, can retain this accuracy for some schedules.", "id": "Paper/64928", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64928"}, {"title": " A dynamical systems framework for personalized cardiovascular risk and intervention from longitudinal wearable data ", "webprogram_exclude": "0", "session_ids": ["Session/17688"], "source_sha256": "74889b66d081c9d55ef624d4316df409268c9baaf36d936686eaf6e74accf06f", "withdrawn": "", "abstract": "Wearable devices provide continuous measurements of cardiovascular and behavioral physiology, but translating these data into individualized and clinically interpretable measures of cardiovascular disease (CVD) risk remains challenging. In this work, we develop a subject-level mathematical framework that combines mechanistic dynamical modeling with statistical learning to estimate cardiovascular risk from longitudinal wearable data. Heart rate, physical activity, sleep duration, and sleep efficiency are incorporated into a coupled system of ordinary differential equations describing heart-rate dynamics, physiological recovery, and activity adaptation. Model parameters are estimated separately for each subject, providing an individualized representation of cardiovascular physiology. These subject-specific physiological characteristics are incorporated into a predictive framework to construct a positive CVD risk measure, which is subsequently adjusted for body mass index to obtain an individualized CVD risk score and corresponding risk category. The framework further uses the subject-specific dynamical model to evaluate changes in sleep and physical activity and identify personalized interventions predicted to improve cardiovascular dynamics. Application to wearable and clinical data demonstrates the ability of the framework to distinguish subject-level cardiovascular risk while providing mechanistically interpretable intervention recommendations. The resulting approach provides a mathematical framework for connecting continuously measured wearable physiology with personalized cardiovascular risk assessment and intervention.", "id": "Paper/64933", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64933"}, {"title": " Fast Fourier spectral method for kinetic equations: from particle to wave ", "webprogram_exclude": "0", "session_ids": ["Session/17702"], "source_sha256": "75007c6301ce42fe0df20d1dfa2ad53e248f759d55cf5bd135fe8dd8e2bd4230", "withdrawn": "", "abstract": "In this talk, I will present our recent progress on developing fast Fourier spectral methods for both classical kinetic equations and wave kinetic equations (WKE). In the first part, we focus on the Boltzmann equation, a fundamental model bridging many-particle system with macroscopic fluid dynamics. We introduce an efficient spectral formulation that approximates the non-cutoff Boltzmann collision operator and accelerates its computation through fast Fourier transforms (FFT), achieving accuracy and efficiency comparable to the cutoff case. Despite the practical success of the approaches, stability remains a significant challenge due to the lack of positivity and conservation. To address this, we develop a new analysis framework establishing spectral accuracy via a refined estimate of the negative part of the numerical solution. In the second part, we extend the fast spectral methodology to the WKE, the core equation in wave turbulence theory. By reformulating the high-dimensional nonlinear wave kinetic operator into a spherical integral — mirroring the structure of the Boltzmann operator — we reveal a double-convolution structure in Fourier space. This structure enables an efficient FFT-based evaluation of the wave interaction integral. Throughout the talk, I will demonstrate the accuracy, efficiency, and robustness of the proposed methods through a variety of 2D and 3D numerical experiments, and I will highlight several interesting phenomena and conjectures that emerge from these simulations.", "id": "Paper/64941", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64941"}, {"title": " If you give a mathematician a surface... ", "webprogram_exclude": "0", "session_ids": ["Session/18144"], "source_sha256": "3439f7ce71aa6b14d8b23c4bcae7f1b07d2b43e31b05d49dbbe96201a4a1ff9e", "withdrawn": "", "abstract": "If you give a mathematician a surface, their neighbor will give you another one. If their neighbor gives you another surface, you may start to wonder if they are the same. If you want to determine if two surfaces are the same, you will have algebraist, geometers, topologist and number theorists knocking at your door, asking them to show you how they think about surfaces. If you give me some time to talk, I’ll tell you about some fun ways to visualize and move between different representations of surfaces and the research inspired by these visualizations.\n\nIn this talk, I will describe some fun and intuitive ways to visualize Riemann surfaces and to move between their many representations. I will also discuss how these visual perspectives inspire new questions and directions in my research.", "id": "Paper/64951", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64951"}, {"title": " Crossing the Transcendental Divide: From Schottky groups to algebraic curves ", "webprogram_exclude": "0", "session_ids": ["Session/18355"], "source_sha256": "71d0c25600f3f3fe31e613420c28776d544786fc591605fde9bf1f451cf7d45f", "withdrawn": "", "abstract": "The transcendental divide refers to the inherent difficulty of passing between a Riemann surface and an algebraic curve. We construct a two-parameter family of non-hyperelliptic Riemann surfaces of genus at least 3 via Schottky uniformization, with dihedral symmetry and the maximal number of real components. For genera 3 through 6, we numerically recover explicit canonical equations and then verify them symbolically. We also discuss the numerical guarantees and computational limitations of this approach.", "id": "Paper/64952", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64952"}, {"title": " Unlearning to Teach Mathematics \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18770"], "source_sha256": "802142b6dbec0a4d007514ff716485c8372b5bae05964d50b8636df0c9dd06cd", "withdrawn": "", "abstract": "A challenge in improving students’ mathematics learning and identities is that their instructors come to teaching not as blank slates, but as people who have been immersed in mathematics since they were themselves students in school and through their graduate training. This means that instructors bring disciplinary expertise and experience, and skillful teaching depends on knowing the content. But instructors have also developed ideas about what learning math involves and what good mathematics teaching requires. They have formed ideas about learners and who is “bright” and capable and who “lacks background” and who struggles. Their mathematical knowledge is well-suited for professional mathematics work––proposing new ideas, tackling unsolved problems, proving conjectures––but inadequate for helping others learn mathematics. These ideas and habits that instructors have developed from their mathematical experiences present impediments to developing teaching practice that can support the range of students in their classes. This lecture will engage participants in specific examples of what is learned from experience, and show what is involved in a process of unlearning and rebuilding conceptions of math learning, habits of practice, views of students, and even the kind of mathematical understanding needed for teaching.", "id": "Paper/64966", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64966"}, {"title": " A Variational Neural Lagrangian Method for Generalized Diffusion via Displacement Parametrization ", "webprogram_exclude": "0", "session_ids": ["Session/19344"], "source_sha256": "934845517264988dd581b9011783f4a307a496312e29e01cc4323413f2c1b06f", "withdrawn": "", "abstract": "Generalized diffusions, including the Fokker-Planck and porous medium equations, share a common variational structure: each is a gradient flow driven by a free energy and damped by a dissipation mechanism. We present a structure-preserving, mesh-free Lagrangian scheme for this class, derived directly from the energy-dissipation law via the Energetic Variational Approach. Instead of evolving the density on a fixed grid, we transport a set of particles and update the density they carry, so that mass conservation is built into the representation. The transport over each time step is represented by a neural network that outputs a small displacement, $\\Psi(x) = x + \\tau U_\\theta(x)$, and is obtained by minimizing a single unconstrained energy functional. This avoids min-max training, input-convex architectures, and explicit Wasserstein distance computation, and it allows a compact network to be used at every step. We show that whenever the displacement gradient satisfies a verifiable smallness condition, the update is a local diffeomorphism, so the scheme conserves mass exactly and keeps the density positive, while a descent condition on the optimizer alone yields monotone decay of the discrete free energy. Numerical experiments on the porous medium equation, where the particles track the moving free boundary against the exact Barenblatt profile, and on Fokker-Planck problems in two and ten dimensions demonstrate accuracy, energy stability, and scalability to high dimensions where grid-based methods are infeasible.", "id": "Paper/64975", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64975"}, {"title": " Space-Filling Embroidery ", "webprogram_exclude": "0", "session_ids": ["Session/18232"], "source_sha256": "c1b424f51c96ecbdece26f3b0b1d35fe903f46c62291a29b6c91350fc848349f", "withdrawn": "", "abstract": "This talk will discuss insights gained through an interdisciplinary collaboration between a mathematician and a textile artist. In the project’s first year, we focused on space-filling curves, moving from drawing and analyzing to prototyping and to the creation of finished embroidery pieces. Working with two students, we designed a series of exploratory prompts which allowed us to develop a shared vocabulary and visual language, and to identify a series of questions to explore arising from mathematical, visual and materiality concerns.  This led to new mathematical ideas, new approaches to textile-making, and new ways to engage in interdisciplinary pedagogy.", "id": "Paper/64976", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64976"}, {"title": " Realization Spaces via Numerical Algebraic Geometry ", "webprogram_exclude": "0", "session_ids": ["Session/18239"], "source_sha256": "97bb39a86b8f5a6a58a126fdadcdf78282056ece849f677b94af20e4beb30856", "withdrawn": "", "abstract": "Matroid realization spaces are famously difficult to understand, yet they arise as components of varieties cut out by low-degree polynomials in many variables—precisely the setting where numerical algebraic geometry tools excel. We present RealizationSpaces.jl, a Julia package combining the symbolic capabilities of OSCAR with the numerical algebraic geometry engine of HomotopyContinuation.jl to study realization spaces of point configurations generally, including those of matroids.\n\nWe will discuss the general pipeline of the package's main algorithms and how symbolic and numerical methods come together to produce human-readable data summarizing invariants of realization spaces, such as their components, dimensions, degrees, and combinatorial shadows. The software also includes functionality for quotienting the space by certain symmetries, sampling real points on the space, and producing drawings of rank-3 matroids via constrained optimization.", "id": "Paper/64977", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64977"}, {"title": " A Bregman ADMM for Bethe variational problem ", "webprogram_exclude": "0", "session_ids": ["Session/17807"], "source_sha256": "61e4dccf9d4477319a39e83a6bd71bd37afd11aa138eb59eeb146d7041a08530", "withdrawn": "", "abstract": "In this work, we propose a novel Bregman ADMM with nonlinear dual update to solve the Bethe variational problem (BVP), a key optimization formulation in graphical models and statistical physics. Our algorithm provides rigorous convergence guarantees, even if the objective function of BVP is non-convex and non-Lipschitz continuous on the boundary. A central result of our analysis is proving that the entries in local minima of BVP are strictly positive, effectively resolving non-smoothness issues caused by zero entries. Beyond theoretical guarantees, the algorithm possesses high level of separability and parallelizability to achieve highly efficient subproblem computation. Our Bregman ADMM can be easily extended to solve the quantum Bethe variational problem. Numerical experiments are conducted to validate the effectiveness and robust- ness of the proposed method.", "id": "Paper/64984", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64984"}, {"title": " Kronecker graph monoid encodings of spectral properties in Boolean graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18255"], "source_sha256": "3335acab0891e3a71dcac8758cd684de2f9a49f42b1bd05f3c126dcd8368caa0", "withdrawn": "", "abstract": "The zero-divisor graph $\\Gamma(R)$ of a commutative ring $R$ is defined by taking vertices to be the nonzero zero-divisors of $R$, and two distinct vertices are adjacent if and only if their product equals zero. If $R$ is a finite Boolean ring, then the eigenvalues of the adjacency matrix of $\\Gamma(R)$ have been characterized as those of two Pascal-type matrices, one having spectrum that was computed by Carlitz in 1965. In this talk, the eigenspaces corresponding to the Carlitz-type eigenvalues of $\\Gamma(R)$ are described. With respect to the Kronecker graph product, a certain $2$-generated monoid of graphs supplies subgraphs of $\\Gamma(R)$ that determine the supports of bases for the eigenspaces of $\\Gamma(R)$, along with graphs whose eigenvectors provide the numerical values of these supports.", "id": "Paper/64985", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64985"}, {"title": " Partition Pairing Theorems ", "webprogram_exclude": "0", "session_ids": ["Session/17968"], "source_sha256": "fa88af605d32a398b0542868b67ccff845daba2dbe90f80866fe95186091ae5c", "withdrawn": "", "abstract": "(joint work with Manosij Dastidar)  For a given integer partition, p, let r(p) denote the part size of the largest part that repeats.  Let s(p) = u1 - u2 + u3 - u4 + ... where the u's (listed in non-increasing order) are the part sizes of parts that appear an odd number of times.  Define the pairing index T(p) of p to be r(p)+s(p).  Our main result is that for every n and k, the number of partitions of n with pairing index k equals the number of partitions of n with k parts.  Refinements of the theorem and related congruences will also be presented.", "id": "Paper/64986", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64986"}, {"title": " The CubeHarmonic, between combinatorics and music theory ", "webprogram_exclude": "0", "session_ids": ["Session/18233"], "source_sha256": "a1c9039953c498be988aad07b4446e82e8c3320e56c14790f117e7e5ce9b200e", "withdrawn": "", "abstract": "The CubeHarmonic is a musical instrument based on the Rubik’s Cube. It advances the tradition of combinatorics applied to music. In particular, the CubeHarmonic allows one to obtain different chord combinations starting from a few pitches. The CubeHarmonic is being developed as a physical, hybrid, and completely virtual musical instrument. The latter includes its 4D variant, the HyperCubeHarmonic. Here, we explore the mathematical behind the concept of this instrument: the unscrambled cube can be seen as a portion of tonnetz cut and folded, whose slices are then permutated one move after the other. If the Rubik’s cube provided a visualization of group transformations, the CubeHarmonic provides their sonification, and, considering artistic developments, its musification.", "id": "Paper/64988", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64988"}, {"title": " CANCELLED Inverse Eigenvalue of a Graph-Zero Forcing AIM Research Community \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/19354"], "source_sha256": "2e2d97bc7d1f80fedb5cf3e0c0fbed11bf2fa1e8550b0e29963677747146fdea", "withdrawn": "", "abstract": "This presentation will report on research conducted by various research groups in the Inverse Eigenvalue of a Graph-Zero Forcing AIM Research Community (IEPG-ZF ARC). This virtual research community began in 2021 with support from the American Institute of Mathematics (AIM) and the NSF. The IEPG-ZF ARC forms new research groups annually, which focus on combinatorial and linear algebraic problems related to inverse eigenvalue problems of graphs. Opportunities to join this community, other AIM research communities, or to form new AIM research communities will also be discussed.\n\nThe inverse eigenvalue problem for graphs (IEPG) is to determine if a given set of real numbers is the spectrum of a matrix with a given graph. This problem and related variants have been of interest for many years, and recently developed tools have accelerated progress and opened  new lines of inquiry. Zero forcing (ZF) is a propagation process on graphs that has become  fundamental for study of the IEPG, bridging combinatorics and linear algebra. ZF has also arisen independently in quantum information processing, monitoring electrical power networks, and graph search algorithms.", "id": "Paper/64989", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64989"}, {"title": " Asymptotic Limits of the Principal Spectrum Point of a Stage-Structured Population with a Mixed Dispersal Model ", "webprogram_exclude": "0", "session_ids": ["Session/19351"], "source_sha256": "33e17b86228cae1d52e1c096bf2be63349400d7b93597cee9f41fd2a22075516", "withdrawn": "", "abstract": "The principal spectrum point is typically used to characterize the long-term\nbehavior of solutions to linear differential systems. We consider a two-stage\nstructured population system consisting of immature juveniles who disperse\nrandomly and locally at the rate $\\mu_1$ and adults that have attained\nreproductive maturity who disperse nonlocally at the rate $\\mu_2$. Keeping one\ndispersal rate fixed, we find the limit of the principal spectrum point as the\nother dispersal rate goes to zero or infinity. These asymptotic results help\ndescribe how extreme dispersal rates of either life stage affect the persistence\nor extinction of the population. We shall also address the applications to the\nlong-term dynamics of the solutions of the corresponding nonlinear system.", "id": "Paper/64990", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64990"}, {"title": " Post-Quantum Threshold Cryptography from Group Actions ", "webprogram_exclude": "0", "session_ids": ["Session/18307"], "source_sha256": "a9f59b948e984d15361de4bda474769d4cc682f2e0c5247d3cbdde508a88b34a", "withdrawn": "", "abstract": "Macaw and Kea are, respectively, group action-based threshold digital signature and public-key encryption schemes submitted to NIST's multiparty threshold cryptography (MPTC) competition. I will discuss these constructions, paying particular attention to structural features that arise because of a lack of efficiently-computable module structure which make these protocols more difficult to instantiate than Schnorr-based analogues.", "id": "Paper/64996", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64996"}, {"title": " Correlation inequalities over congruence-uniform lattices ", "webprogram_exclude": "0", "session_ids": ["Session/18138"], "source_sha256": "694d22f5ec85598c09da5b454a2c7618202a50c0ff9f913575d18569a635bf3f", "withdrawn": "", "abstract": "Any two increasing functions on a finite lattice are positively correlated with respect to a given setwise log-supermodular measure. A classic theorem of Fortuin, Kasteleyn, and Ginibre beautifully characterizes setwise log-supermodularity when the lattice is distributive. Their result inspired many additional correlation inequalities over distributive lattices, most notably the Four Functions Theorem by Ahlswede and Daykin. In this work, we present a natural generalization of the Four Functions Theorem that applies to the broader class of congruence-uniform lattices. Using this result, we derive several new correlation inequalities over congruence-uniform lattices.", "id": "Paper/64999", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/64999"}, {"title": " Coupling size structure and competition in coral-algal dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/18023"], "source_sha256": "34d4eee7980e3452210df53ad496f77233f68f6b1979d9d4b5638c7c1e4e9563", "withdrawn": "", "abstract": "Caribbean coral reefs have faced long-term decline driven by compounding stressors, including anthropogenic pressures such as the overharvesting of herbivorous reef fish. This negatively impacts grazer-mediated space competition by allowing macroalgal overgrowth to suppress coral recruitment, increase coral mortality, and drive reefs toward an algal-dominated state. Systems of ordinary differential equations (ODEs) have been used to capture these coral-algal dynamics and support the existence of alternative stable states, but they treat coral homogeneously without accounting for how colony size distributions affect competitive performance. Conversely, integral projection models (IPMs) of coral dynamics project population trajectories based on continuous size distributions but omit competitive coral-algal feedback. We integrate a coral IPM with a discrete-time model of coral-algal interactions to capture both size-dependent vital rates and interspecific competition, establishing a framework to investigate the interactions between coral size distributions and algal competitive pressure.", "id": "Paper/65004", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65004"}, {"title": " A finite volume discretization of the multi-layer shallow water equations as a Hamiltonian system ", "webprogram_exclude": "0", "session_ids": ["Session/17757"], "source_sha256": "70cf5e1f77248830d4398a44da7c11dc1f6ba8552afb91b0af3665ce083cdf6b", "withdrawn": "", "abstract": "The system of multilayer shallow water equations is an important\nmodel for large-scale geophysical flows, namely the ocean and\natmosphere. Without frictional forces, the model is reversible, and\ncan be reformulated as a Hamiltonian system. In this work, we exploit\nthe finite volume discretization techniques and the\nskew-symmetry of the Hamiltonian system to derive an energy\nconserving scheme for the shallow water equations. Outcropping is a common problem\nfor multilayer geophysical \nmodel, where the thickness of fluid layers can go to zero or even\nbecome negative.  In this work, we demonstrate, within the Hamiltonian\nframework, how outcropping can be \nprevented with the addition of an artificial potential energy term that is\nbased on the slope of the interior layer interfaces. Numerical\nexperiments will be carried out to assess the effectiveness of\nthis approach.", "id": "Paper/65017", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65017"}, {"title": " Parameter-robust preconditioning for hybridizable symmetric discretizations ", "webprogram_exclude": "0", "session_ids": ["Session/17962"], "source_sha256": "31259b907a9f2825c153435e036b3d28eff50b9f22dc863d40c8cfded5e0546a", "withdrawn": "", "abstract": "The Hybridizable Discontinuous Galerkin (HDG) method effectively reduces the size of global linear systems by allowing for the elimination of local degrees of freedom. While this reduction is computationally efficient, designing robust solvers for the resulting condensed systems remains a significant challenge. In this talk, we introduce a novel, parameter-robust preconditioning framework specifically designed for the reduced linear systems arising from HDG discretizations.\n\nOur approach relies on the operator preconditioning framework to first construct a parameter-robust preconditioner for the full system. We then eliminate the local degrees of freedom of this preconditioner to derive a preconditioner for the reduced system. Because reduced preconditioners obtained in this manner do not automatically inherit robustness, we establish rigorous theoretical conditions that guarantee parameter independence at the condensed level.\n\nFinally, we apply this theoretical framework to a variety of parameter-dependent PDEs. To demonstrate the practical versatility and scalability of the approach, we present comprehensive 2D and 3D numerical results for several PDE models confirming the robust performance of the proposed preconditioners.", "id": "Paper/65018", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65018"}, {"title": " Kimura’s Neutral Law Is Not as Simple as One Might Think: Simulations of the Moran Process ", "webprogram_exclude": "0", "session_ids": ["Session/18350"], "source_sha256": "2b578d336971a0cf1e1060dd9fa03c77c1cadaa6c9879092fecf582e0304cf3a", "withdrawn": "", "abstract": "One of the important tasks of genomic analysis of the SARS-Cov-2 virus is determination of selection forces acting on the genome. \nTo accomplish this, it is crucial to determine a model under neutrality. \nSuch model is potentially provided by the Kimura law.\nKimura's neutral theory predicts that the rate of neutral molecular substitution equals the mutation rate, $C = \\mu$, \nindependent of population size $N$. This property was employed by Paradis and Wu to test neutrality of non-coding\nregions of SARS-CoV-2 genome (Paradis \\& Wu, 2024, \\textit{Virus Evolution})).\nWe revisit this identity using four simulators of the infinite alleles Moran model: \na discrete time birth and death chain, a continuous time algorithm with exponential waiting times, \na Poisson scheme, and a parametrisation with independent mutation and replacement processes. \nAll four simulators recover $C \\approx \\mu$ in the small $\\mu$ regime, but the observed substitution rate systematically falls below $\\mu$ as mutation grows large: \nincoming mutants disrupt ongoing fixation sweeps, and the more mutations that arrive during the fixation window, \nthe fewer sweeps complete cleanly. We explain this shortfall analytically in two complementary ways. \nFirst, a heuristic argument that treats disruption arrivals as independent yields the closed form $C_H(N,\\mu) = \\mu\\,(1 - 1/N)^{(N^2 - N)\\mu}$, \nwhich recovers $C = \\mu$ as $\\mu \\to 0$ and captures the decay at large $\\mu$. \nSecond, we identify fixations with the single step transition out of the \"critical\" allelic partition and evaluate its stationary weight under the \nEwens sampling formula with $\\theta = N\\mu$, giving the per-generation fixation flux $\\Phi(N,\\mu) \\propto N!\\,\\theta^{2} / (\\theta^{(N)}\\, N)$, where $\\theta^{(N)}$ is the rising factorial.\nThis comprehensive analysis helps delineate the conditions in which Kimura’s classical result applies and where it fails, \nproviding a more nuanced framework for modeling the evolutionary dynamics of SARS-CoV-2.", "id": "Paper/65019", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65019"}, {"title": " Comparing Full Covariance and Single-Index Approaches to Mean-Variance Portfolio Optimization ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "dfb5894ebd75d87131685d9b64f74ffb123f07b22ff7568398ffdb583f6ab5b6", "withdrawn": "", "abstract": "Mean-variance portfolio optimization provides a mathematical framework for allocating wealth among risky assets by balancing expected return and portfolio variance. However, implementation becomes increasingly difficult as the number of assets grows because the classical Markowitz framework requires estimation of a large covariance matrix. This project investigates the Single Index Model as a parsimonious alternative to full covariance estimation in portfolio optimization.\nBeginning with the classical mean-variance framework, we formulate the Global Minimum Variance Portfolio, efficient frontier, and tangency portfolio using matrix methods. We then estimate asset returns using the Single Index Model, Rᵢ = αᵢ + βᵢ · Rᴹ + eᵢ, which decomposes risk into systematic and idiosyncratic components and substantially reduces the number of parameters required to model asset co-movement. Using historical equity-market data, portfolios constructed from the full sample covariance matrix are compared with those constructed from the Single Index Model. The comparison examines portfolio weights, volatility, expected return, Sharpe ratio, and efficient-frontier behavior. Out-of-sample testing is used to evaluate how portfolios formed under each approach perform on data not used for estimation.\nThe study investigates whether the reduction in estimation complexity provided by the Single Index Model can preserve the principal risk-return characteristics of classical mean-variance optimization while producing portfolios that remain effective out of sample. The project connects optimization, matrix algebra, regression, and financial modeling to address a practical challenge in large-scale portfolio construction.", "id": "Paper/65021", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65021"}, {"title": " Fourier restriction to hyperbolic rectangles and an application ", "webprogram_exclude": "0", "session_ids": ["Session/19336"], "source_sha256": "97a03714208d038f89fdd71a1677fc562a1ff7d4ed286915dff021ce36dea435", "withdrawn": "", "abstract": "We study the Lebesgue space inequalities for extension operators associated with hyperbolic surfaces in $\\mathbb R^3$ over rectangular regions. In the polynomial-method range, we characterize the corresponding operator norms in terms of the side lengths. As an application, we obtain new restriction estimates for a class of hypersurfaces with additive structure.", "id": "Paper/65026", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65026"}, {"title": " Uncrowding the 5-Vertex Model: RSK and Crystal Structures ", "webprogram_exclude": "0", "session_ids": ["Session/18376"], "source_sha256": "59eab4be45b78bbb96268a64672686c82fd01b15744c486d43290d88ca7d625b", "withdrawn": "", "abstract": "While the uncrowding algorithm on set-valued tableaux has long been instrumental in proving the Schur positivity of stable symmetric Grothendieck polynomials, lattice models have emerged as a modern framework for investigating symmetric functions, in particular symmetric Grothendieck polynomials. In this work, we synthesize these combinatorial and lattice-theoretic approaches by defining both the Robinson--Schensted--Knuth (RSK) correspondence and the uncrowding operation directly on a 5-vertex model of Motegi and Sakai and its subsequent reinterpretation by Buciumas, Scrimshaw, and Weber. Our lattice-based RSK formulation yields a powerful new result: the direct construction of the associated crystal structure on the states of the 5-vertex model. \n\nThis talk is based on the preprint  \t\nhttps://doi.org/10.48550/arXiv.2606.02972.", "id": "Paper/65029", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65029"}, {"title": " Contractions and applications of crystal skeletons: Young quasisymmetric and Stanley symmetric functions ", "webprogram_exclude": "0", "session_ids": ["Session/18067"], "source_sha256": "e0df1a9c09b7d562ac1688379ccace0074ef5e0c741c6015ef2f6341d59b39b9", "withdrawn": "", "abstract": "The character of a connected $\\mathfrak{sl}_n$-crystal is a Schur polynomial; the crystal can be further decomposed into quasicrystals, whose characters are the Gessel quasisymmetric functions. Crystal skeletons are obtained by contracting quasicrystals within crystal graphs. They generalize dual equivalence graphs, and can be used to prove the Schur expansion of a symmetric function when the quasisymmetric expansion is known. In this paper, we show that the crystal skeleton can be tiled further into components which we call quasicrystal skeletons, whose characters are Young quasisymmetric Schur functions. We characterize which edges in the crystal skeleton move between quasicrystal skeleton components. Contracting the quasicrystal skeleton components yields Bruhat order. We illustrate how these tools can be applied to symmetric functions by analyzing the Stanley symmetric functions.\n\nThis is based on the preprint  \t\nhttps://doi.org/10.48550/arXiv.2607.12232.", "id": "Paper/65031", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65031"}, {"title": " Composition operators and Rational Inner Functions on the bidisc: A geometric approach ", "webprogram_exclude": "0", "session_ids": ["Session/17377"], "source_sha256": "362a5b751b03e7c5e58a91e6a73fcdf74d8a3867d4e71d179016379847ec87bb", "withdrawn": "", "abstract": "In this talk, we will study composition operators acting on the weighted Bergman\nspaces on the bidisc, i.e.\n\\[\nC_{\\Phi}: A^2_{\\beta}(\\mathbb{D}^2)\n\\longrightarrow\nA^2_{\\beta}(\\mathbb{D}^2),\n\\]\nwhere $\\Phi$ is induced by rational inner functions (RIFs), or by a RIF and a smooth\nfunction in the mixed case. Our approach is geometric. Our main result is a uniform\ncriterion for all $\\beta\\in(-1,0]$ that can be summarized as follows: boundedness of\nthe composition operator is equivalent to transversal intersection of the level sets\nfor non-smooth symbols, under the assumption that if any tangential intersection\noccurs at the singularity, it must be of high order. This extends the characterization\nof Bayart--Kosiński to non-smooth self-maps of the bidisc. To reach our conclusions,\nwe utilize results obtained by Anderson, Bergqvist, Bickel, Cima, and Sola on Clark\nmeasures associated to RIFs and Puiseux factorizations.", "id": "Paper/65032", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65032"}, {"title": " An unstable parabolic free boundary problem ", "webprogram_exclude": "0", "session_ids": ["Session/18378"], "source_sha256": "aca67219ea76dfb9e48d8fa60d8e2b52bc2ccc1b157ee61d84bee4e95f6b1012", "withdrawn": "", "abstract": "We will discuss a parabolic PDE that arises in models for combustion and wildfire. Our main concern is the fire front or free boundary. In this problem, at a fixed time the spatial free boundary may have singularities. However, we show that the space-time free boundary is $C^{1,\\alpha}$. This is joint work with Gilles Bokolo-Tamba.", "id": "Paper/65036", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65036"}, {"title": " Hecke <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.852ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 1228 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">C^*</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-43\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2217\" d=\"M229 286Q216 420 216 436Q216 454 240 464Q241 464 245 464T251 465Q263 464 273 456T283 436Q283 419 277 356T270 286L328 328Q384 369 389 372T399 375Q412 375 423 365T435 338Q435 325 425 315Q420 312 357 282T289 250L355 219L425 184Q434 175 434 161Q434 146 425 136T401 125Q393 125 383 131T328 171L270 213Q283 79 283 63Q283 53 276 44T250 35Q231 35 224 44T216 63Q216 80 222 143T229 213L171 171Q115 130 110 127Q106 124 100 124Q87 124 76 134T64 161Q64 166 64 169T67 175T72 181T81 188T94 195T113 204T138 215T170 230T210 250L74 315Q65 324 65 338Q65 353 74 363T98 374Q106 374 116 368T171 328L229 286Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-43\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-2217\" x=\"1094\" y=\"513\"></use>\n</g>\n</svg>-Algebras via Schlichting Completions ", "webprogram_exclude": "0", "session_ids": ["Session/18381"], "source_sha256": "cfdb8c3e4300c7e9b5b1824b60673a98b22b11cf6f3e5208ec682dece7f93bd0", "withdrawn": "", "abstract": "Hecke $C^*$-algebras arise from Hecke pairs $(G,H)$, where $H$ is an almost normal subgroup of $G$, and encode convolution on double cosets $H\\backslash G/H$.\nIn this expository talk, we introduce Hecke pairs, Hecke algebras, and their $C^*$-completions, focusing on the role of Schlichting completions. This construction replaces $(G,H)$ by a locally compact group with compact open subgroup, allowing the Hecke algebra to be viewed as a corner of a group $C^*$-algebra. We will explain how this perspective connects Hecke $C^*$-algebras with Morita equivalence, crossed products, groupoid $C^*$-algebras, and $K$-theoretic invariants.", "id": "Paper/65038", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65038"}, {"title": " Understanding SELEX Dynamics Through Machine Learning Techniques ", "webprogram_exclude": "0", "session_ids": ["Session/18239"], "source_sha256": "ff554390efef29f26df54a7ff20cc23cf1e9df5799c8555c8bc03399823568d0", "withdrawn": "", "abstract": "Single-stranded DNA and RNA sequences are known as oligonucleotides. When oligonucleotides exhibit high binding affinity and specificity to target molecules, they are known as aptamers. Systematic Evolution of Ligands by Exponential Enrichment (SELEX) is the standard experimental procedure used to identify candidate aptamers. SELEX is an iterative process in which a large library of randomized sequences are exposed to the target molecule. Sequences that bind to the target molecule advance to the next round of SELEX while the remaining non-binding sequences are discarded. The end of each round results in a large pool of successful sequences. Experimentalists can identify the sequences present in the pool along with the number of times that particular sequence appears. Despite its well-defined experimental procedure, the results of SELEX remain poorly understood. Polymerase chain reaction (PCR) used in the SELEX process introduces transcription errors that can interrupt the enrichment of the\nbest-performing aptamers. Furthermore, there is no efficient method for downselecting from large post-SELEX pools to aptamer candidates. We first investigate these pools through raw sequence analysis and propose an in silico stochastic model of SELEX that reproduces the mutational landscape of SELEX rounds. We also create and apply new unified oligonucleotide descriptors that encode folding topology and nucleotide-type organization to identify changes in the geometric space across SELEX rounds through estimating a PDE using deep learning methods.", "id": "Paper/65042", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65042"}, {"title": " Time Inconsistent Linear Quadratic Optimal Control for Mean Field Games in Hilbert Spaces ", "webprogram_exclude": "0", "session_ids": ["Session/17781"], "source_sha256": "fdb1ba7fde44737f485cbfb0d419d2ae108a86cb7d87a3d76dc45db76763d099", "withdrawn": "", "abstract": "This talk considers time-inconsistent linear-quadratic mean-field games governed by stochastic evolution equations in Hilbert spaces. Time inconsistency arises from the explicit dependence of the cost functional on the initial time, so that the classical notion of optimal control based on Bellman’s principle is no longer applicable. We formulate the problem through a multiperson differential game approach and study closed-loop equilibrium strategies. In the linear-quadratic setting, the equilibrium strategy admits an affine feedback representation characterized by an operator-valued Riccati equation coupled with a forward-backward equilibrium system. We establish well-posedness of the resulting system under suitable conditions and obtain the existence of a closed-loop equilibrium strategy. The framework provides a characterization of time-consistent decision making for infinite-dimensional mean-field models with time-inconsistent preferences.", "id": "Paper/65046", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65046"}, {"title": " Asymptotic Enumeration of Singular Meanders ", "webprogram_exclude": "0", "session_ids": ["Session/19346"], "source_sha256": "119b6b93c8efd972561e18bb803e6a07ac06b173cad1cbf8e9b0096eb072bad4", "withdrawn": "", "abstract": "A meander is a pair of self-avoiding curves in a disk, each with its endpoints on the boundary circle, which intersect each other transversely $n$ times. Counting meanders (up to homeomorphism of the disk) is an open problem: no closed form is known, although there exist upper and lower bounds on the exponential growth rate. A singular meander generalizes this notion to allow $k$ additional non-transverse intersections. In this talk we show that for fixed $k$, the number of singular meanders with $n$ transverse and $k$ non-transverse intersections has the same exponential growth rate in $n$ as the number of meanders. Also that for fixed $n$, this count grows like $4^k$ as $k \\to \\infty$. We also give upper and lower bounds on the number of singular meanders with $N = n + k$ total intersections.", "id": "Paper/65047", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65047"}, {"title": " Realized Variance Disagreement ", "webprogram_exclude": "0", "session_ids": ["Session/18332"], "source_sha256": "7e43922d4e8a4f1e3a4cdc3860957c80cc83c28405d8fd50cd552da1dea44470", "withdrawn": "", "abstract": "We propose realized variance disagreement as a nonparametric measure of segmentation between equity and options markets over a fixed time interval. Defined as the aggregate difference between  diffusive variance components of high-frequency asset returns and their risk-neutral conditional  expectations recovered from options  expiring at the end of the trading day, this statistic captures realized violations of the  fundamental no-arbitrage condition that diffusive variance coincides under the physical and risk-neutral probability measures. We derive a central limit theorem that enables feasible inference on  integrated variance disagreement  between equity and options markets. We further develop  market integration tests that can detect  spot   and integrated variance disagreements. Empirically, we find evidence for episodes of disagreement between equity and options markets. These periods exhibit mild persistence and differ in magnitude across assets.", "id": "Paper/65062", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65062"}, {"title": " Nonexistence of Cube-Centered Powerful Triplets with Asymmetric Prime-Exponent Profiles ", "webprogram_exclude": "0", "session_ids": ["Session/19361"], "source_sha256": "e7a94cac22f660e5fc5fd577d2e6ec37c438fbf47947f1329c28d6ef66bbe044", "withdrawn": "", "abstract": "The celebrated Erd\\H{o}s-Mollin-Walsh conjecture asserts that no three consecutive positive integers are all powerful; despite sustained work, it remains a notoriously difficult open problem. Recent progress has come from studying cube-centered triplets $x^3-1, x^3, x^3+1$ with prescribed prime-exponent profiles for the two neighbors. Chan (2025) and our 2025 work settled the symmetric profiles $(3,3)$ and $(2,2)$. Son (2026) obtained further nonexistence results under coprimality hypotheses. The asymmetric profiles $(3,2)$ and $(2,3)$, however, have not previously been resolved. We prove that, for primes $p,q$, neither the system $x^3-1=p^3y^2, x^3+1=q^2z^3$ nor the system $x^3-1=q^2z^3, x^3+1=p^3y^2$ has an integer solution. Unlike related results, our theorems require neither positivity nor coprimality assumptions. We also prove that the mixed-exponent hexic equation $x^6-1=p^3q^2a^6$ has no integer solution with $a\\ne0$ for primes $p,q$, not necessarily distinct. The main technical innovation lies in treating the neighboring equations as a coupled system in the non-coprime cases. Their interaction, exploited through Pell addition formulas and $p$-adic valuation analysis, provides the structural constraints that both enable the quartic results of Ljunggren, Cohn, and Bennett-Walsh to restrict the possible Pell indices to a finite set and support integral-point analysis on Mordell curves. Together with the symmetric results, our theorems complete the classification of all four square/cube prime-exponent profiles around a perfect cube, eliminating a notable structured family of potential counterexamples to the Erd\\H{o}s-Mollin-Walsh conjecture.", "id": "Paper/65065", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65065"}, {"title": " Oriented Graphs with DDM Labelings ", "webprogram_exclude": "0", "session_ids": ["Session/17921"], "source_sha256": "ec104cb3a3226f7f25b22b8dd63f79fa881e67f15c2b50ddf8d77dccbab60f04", "withdrawn": "", "abstract": "In a difference distance magic (DDM) labeling, each vertex of a graph is given a unique value from 1 up to the number of vertices such that for each vertex the sums of the labels of vertices in the in-neighborhood minus the sums of the labels of vertices in the out-neighborhood equals zero. We present constructive methods that create DDM oriented graphs. Each method uncovers details about the structure of oriented graphs that admit such labelings.", "id": "Paper/65070", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65070"}, {"title": " Multi-objective Bayesian Inference for Stochastic Agent-Based Models via Topological Data Analysis ", "webprogram_exclude": "0", "session_ids": ["Session/18303"], "source_sha256": "65d3808335a54f4556d94d1da48cc59576877536f3affacdf574f757187e6365", "withdrawn": "", "abstract": "Stochastic agent-based models provide a natural framework for describing emergent behavior arising from local interactions among individual agents, such as cells. A central mathematical challenge is to infer model parameters from model simulations, which is difficult due to the stochastic, complex, and high dimensional nature of such models. We develop a multi-objective Bayesian inference framework that combines approximate Bayesian computation with topological data analysis (TDA). We demonstrate this framework on a stochastic agent-based model of zebrafish skin pattern formation, and show that by characterizing model outputs using multiple objectives arising from TDA that provide complementary information, we are able to accurately recover ground-truth parameter values. Our work demonstrates how multi-objective inference with TDA, combined with Bayesian methods, is a computationally efficient method for performing parameter inference and identifiability analysis for complex, high dimensional models.", "id": "Paper/65087", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65087"}, {"title": " The hereditary closure of unigraphs ", "webprogram_exclude": "0", "session_ids": ["Session/18141"], "source_sha256": "0eb513b12e378b5e9ad1040ef9362637cdcad9aa4f2ea7afe6115fc73f8b8797", "withdrawn": "", "abstract": "A graph with degree sequence $\\pi$ is a \\emph{unigraph} if it is isomorphic to every graph that has degree sequence $\\pi$.  The class of unigraphs is not hereditary and in this talk we discuss the related hereditary class HCU, the hereditary closure of unigraphs, consisting of all graphs induced in a unigraph. Our work characterizes the class HCU in multiple ways making use of the tools of a graph decomposition due to Tyshkevich.", "id": "Paper/65091", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65091"}, {"title": " Mean-Field Actor-Critic Flow: A Reinforcement Learning Algorithm for Mean-Field Games ", "webprogram_exclude": "0", "session_ids": ["Session/18274"], "source_sha256": "3d110516b0dc1a34e16b04e47d096bb245274693424e69b40e78bb9354039a99", "withdrawn": "", "abstract": "Mean-field games (MFGs) have emerged as a powerful framework for modeling strategic interactions among a large number of agents, with important applications in quantitative finance, including systemic risk, optimal execution, and market impact modeling. In this talk, we introduce the mean-field actor-critic flow (MFAC), a reinforcement learning (RL)-based algorithm for solving MFGs, and establish its validity through both theoretical analysis and numerical experiments.\n\nUnlike traditional RL approaches, our method employs partial differential equations (PDEs) to model the continuous learning dynamics of the actor, critic, and population distribution.\nInspired by optimal transport, the distributional dynamics evolve along a novel geodesic flow, and we prove the convergence of MFAC under a single time scale. \nFurthermore, drawing on ideas from generative modeling, we parameterize the distribution using score functions, enabling sampling through Langevin Monte Carlo driven by the learned score.\nNumerical experiments on financial models demonstrate that MFAC effectively computes the MFG equilibrium and achieves state-of-the-art performance.\n\nThis is joint work with Mo Zhou (UCLA) and Ruimeng Hu (UCSB).", "id": "Paper/65093", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65093"}, {"title": " Summarizing and Reconstituting Ballot Profiles ", "webprogram_exclude": "0", "session_ids": ["Session/18097"], "source_sha256": "206a6f6e2b84be39f2bfb65a1bc7135abe5c208de957fff2355db6e72cb483a0", "withdrawn": "", "abstract": "Given a profile $P$ of ballots (complete or partial rankings), we consider various compact summaries of $P$ together with ways to use the summary to build a synthetic profile $\\tilde{P}$ that is similar to $P$ in salient ways.", "id": "Paper/65097", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65097"}, {"title": " The Effect of Visualization Tools on Conceptual Understanding in multivariable Calculus ", "webprogram_exclude": "0", "session_ids": ["Session/18091"], "source_sha256": "0384f0bdf3d4b4510ef1171d2f531cdce5e92ea48daebf9d30bbbb2e0795d5f2", "withdrawn": "", "abstract": "Calculus IV at the Lebanese American University includes abstract multivariable concepts that students often find difficult to visualize. Visualization tools are commonly used by students to support understanding, yet limited data exists on their effect on student performance at the undergraduate level. This study aims to compare student performance on selected concepts with and without the use of visualization tools. A draft analysis of results will be shared based on various data sets collected throughout the semester.", "id": "Paper/65100", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65100"}, {"title": " Mutant Fixation for a Stochastic Evolutionary Model in Fragmented Populations ", "webprogram_exclude": "0", "session_ids": ["Session/17811"], "source_sha256": "290bc6e7f20144bce31b57d782373e6567c9673ded4175d25d64e67acb9d9af0", "withdrawn": "", "abstract": "Population fragmentation is a common feature of many biological systems. Understanding mutant fixation in such systems is challenging because the underlying stochastic dynamics are high-dimensional. In this work, we develop a general mathematical framework for analyzing stochastic evolution in fragmented populations connected by rare migration. The framework is sufficiently general to accommodate heterogeneous deme sizes, deme-dependent birth and death processes, and migration on arbitrary strongly connected directed networks with asymmetric migration rates. We show that, in the limit where migration occurs on a much slower timescale than within-deme dynamics, the full stochastic process can be reduced to a lower-dimensional Markov chain whose states correspond to configurations of fully mutant and fully wild-type demes. The reduction theorem establishes that fixation probabilities and absorption times of the original process are asymptotically determined by the corresponding quantities of a reduced chain. As an application, we derive explicit formulas for mutant fixation probabilities and fixation times in fragmented populations initiated by the introduction of a single mutant. The results provide a general and tractable approach for studying evolutionary dynamics in complex fragmented populations.", "id": "Paper/65110", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65110"}, {"title": " Stability of the Homeotropic State in Cholesteric Liquid Crystals ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "90c2cc8c54eaae217b5fbea8ece1cbf1c66e297c8c78aacc797035d364ec0921", "withdrawn": "", "abstract": "Cholesteric liquid crystals naturally favor twisted molecular configurations, while homeotropic boundary anchoring favors alignment perpendicular to the confining surfaces. We investigate the competition between these effects in a three-dimensional slab using the Landau–de Gennes Q-tensor model.\n\nTo study stability, we first derive the weak formulation and evaluate the first variation at the constant homeotropic configuration. We find that the first variation vanishes under periodic or compatible Dirichlet conditions on the lateral faces. For free lateral boundaries, however, nonzero chirality generally leaves a nonvanishing boundary term, so the constant homeotropic configuration is not stationary, regardless of the anchoring strength imposed only on the top and bottom surfaces. We then derive the second variation of the free-energy functional. We estimated the chiral elastic term and the Hessian of the bulk potential, these estimates yield sufficient conditions on the chirality $\\tau_0$, anchoring strength $w_0$, and slab height $H$ that ensure the second variation has a positive quadratic lower bound. \n\nWe also implemented a three-dimensional finite element simulation in Firedrake to study the evolution of the liquid crystal under gradient flow. To analyze the numerical results, we developed a measure of the average vertical alignment on horizontal cross-sections at different heights. This allowed us to compare the behavior near the anchored surfaces with that in the interior rather than relying only on visual inspection. We find that stronger anchoring produces nearly vertical alignment near the top and bottom surfaces, while significant deviations from the homeotropic configuration may remain in the interior. Thus, strong surface alignment does not necessarily force the entire liquid crystal into a uniformly vertical state.", "id": "Paper/65111", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65111"}, {"title": " Uniform Factor-Balancedness in Arnoux–Rauzy Words ", "webprogram_exclude": "0", "session_ids": ["Session/19345"], "source_sha256": "ba016622fc00ad68c04e81a85655ab82e98b054e26c5439608049a22a5567722", "withdrawn": "", "abstract": "In this talk we characterise uniform factor-balancedness in Arnoux--Rauzy words, generalising the work of Espinoza, Popoli, and Stipulanti on ternary alphabets to finite alphabets of any size. In particular we prove that an Arnoux--Rauzy word $\\mathbf{x}$ is uniformly factor-balanced if and only if $\\mathbf{x}$ has bounded weak partial quotients.", "id": "Paper/65113", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65113"}, {"title": " AC Theorem: The Function ", "webprogram_exclude": "0", "session_ids": ["Session/19368"], "source_sha256": "53f6393a346b3f4d99e588377aa1f3fcfe4845fb809a12b2c2d830b4b8194b75", "withdrawn": "", "abstract": "AC Theorem: The function\n\n$f(x) \\equiv a_0x^n$ + $a_1x^{n-1}$ + $a_2x^{n-2} + a_3x^{n-3}$ +......+ $a_{n-2}x^2$ + $a_{n-1}x$ + $a_n$\n\nhas all the coefficients real\n(1) If all zeros of the function $f(x)$ are real and different, then the function $\\phi(x) \\equiv f(x) f^{\\prime\\prime}(x)$ -$[f^\\prime (x)]^2$ has all imaginary zeros; and\n(2) If all zeros of the function $f(x)$ are real and two zeros are equal, then that equal zero is also zero of the function\n$\\eta (x) \\equiv $ $a_1x^{n-1}$ + $2 a_2x^{n-2}$ + $3 a_3x^{n-3}$ +...+ $(n-2)a_{n-2}x^2$ + $(n-1)a_{n-1}x$ + $na_n$", "id": "Paper/65121", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65121"}, {"title": " Approximation analysis of structured neural networks ", "webprogram_exclude": "0", "session_ids": ["Session/17945"], "source_sha256": "bc42f794d85b226a265b46a06031e4b5bd93c030f8f6495ed36962e57722875d", "withdrawn": "", "abstract": "Deep learning has been widely applied and brought breakthroughs in speech recognition, computer vision, natural language processing, and many other domains. The involved deep neural network architectures and computational issues have been well studied in machine learning. But not much is known about the modelling, approximation or generalization abilities of deep learning models with network architectures and structures, due to some  differences between the classical fully-connected neural networks and structured ones used in deep learning. \n\nAn important family of structured deep neural networks are deep convolutional neural networks (CNNs) induced by convolutions. It is believed that local shift-invariance of natural images and speeches plays an essential role in the efficiency of CNNs. Another family of structured deep neural networks are transformers based on attention structures where variable dependence is believed to be crucial in processing natural language data. This talk describes approximation and generalization analysis of deep CNNs, transformers, and related structured deep neural networks.", "id": "Paper/65122", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65122"}, {"title": " A Signature Generalization of MacMahon’s Theorem and other <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.056ex\" height=\"1.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -576.1 454.5 721.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbf {s}</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAINB-73\" d=\"M38 315Q38 339 45 360T70 404T127 440T223 453Q273 453 320 436L338 445L357 453H366Q380 453 383 447T386 403V387V355Q386 331 383 326T365 321H355H349Q333 321 329 324T324 341Q317 406 224 406H216Q123 406 123 353Q123 334 143 321T188 304T244 294T285 286Q305 281 325 273T373 237T412 172Q414 162 414 142Q414 -6 230 -6Q154 -6 117 22L68 -6H58Q44 -6 41 0T38 42V73Q38 85 38 101T37 122Q37 144 42 148T68 153H75Q87 153 91 151T97 147T103 132Q131 46 220 46H230Q257 46 265 47Q330 58 330 108Q330 127 316 142Q300 156 284 162Q271 168 212 178T122 202Q38 243 38 315Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAINB-73\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Catalan Impressions ", "webprogram_exclude": "0", "session_ids": ["Session/18286"], "source_sha256": "f8024eb9177b6f36c4c1adeed6586048e9f969a959e8e3994d7bca0f28ef3e0f", "withdrawn": "", "abstract": "In 1915 Percy MacMahon proved that the number of sequences of $n$ distinct integers that can be partitioned into two decreasing subsequences is the Catalan number $C_n = \\frac{1}{2n+1}{2n+1 \\choose n}$.\nDonald Knuth framed this as a pattern avoidance result $|\\mathsf{Av}_n(123)| = C_n$ and established the same enumeration for stack sortable permutations $|\\mathsf{Av}_n(231)| = C_n$.\n\nWe extend MacMahon's result to the $k$-Catalan numbers $C_n^k = \\frac{1}{kn+1}{kn+1 \\choose n}$ that count $k$-ary trees with $n$ internal nodes.\nOur generalization involves \\emph{$r$-regular words} where each value in $[n] = \\{1,2,\\ldots,n\\}$ appears $r$ times.\nWe show that $C_n^k$ counts the $(k-1)$-regular words that become non-increasing after deleting their left-to-right minima.\nFor example, $331221$ is a \\emph{MacMahon word} for $k=3$ and $n=3$ as it contains $(k-1)=2$ copies of each value in $[n]=\\{1,2,3\\}$ and deleting its left-to-right minima leaves $3221$ which is non-increasing.\nMore generally, the MacMahon words with $s_i$ copies of $i \\in [n]$ are counted by the \\emph{signature Catalan number} $C_{s}$.\n\nThe $k$-Catalan numbers have previously been observed in regular word pattern avoidance.\n\n$|\\mathsf{Av}_n^{k-1}(231,221)| = C_n^k$ by Defant and Kravitz (Australas.\\ J.\\ Comb.\\ 2020) in the context of stack sorting words.\n\n$|\\mathsf{Av}_n^{k-1}(231,121)| = C_n^k$ by Kuba and Panholzer (Discrete Math. 2012) when investigating pattern avoidance in $k$-Stirling words.\n\n$|\\mathsf{Av}_n^{k-1}(123,112)| = C_n^k$ describes our result and was previously observed by Williams (PP 2023).\n\nThese three cases generalize the Knuth-MacMahon theorem to regular words and more broadly $s$-words.\n\nWe also discuss the $s$-associahedron by Ceballos and Pons (FPSAC 2019).\nIt has $C_{s}$ vertices labeled by $\\mathsf{Av}_{s}(312,212)$ and its edges correspond to minimal $(\\alpha > \\beta)$-swaps (i.e., a subword of larger values $\\alpha$ is swapped with an adjacent subword of smaller values $\\beta$).\nQian and Williams (CCCG 2026) create a Hamilton path from $1^{s_1} 2^{s_2} \\cdots n^{s_n}$ by greedily moving to the next vertex by maximizing $\\min(\\alpha)$.\nThe Hamilton path provides new Gray codes for $s$-Catalan objects.\nIts construction also mirrors the Hamilton path of the wigglyhedron by Pilaud and Williams (WADS 2025).", "id": "Paper/65124", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65124"}, {"title": " Topological Transforms for Shape Comparison ", "webprogram_exclude": "0", "session_ids": ["Session/18357"], "source_sha256": "b794ab52b4678e4b23aa041a770a28765c430ca07094789e83d1eafe8a3d57dd", "withdrawn": "", "abstract": "The goal of the field of topological data analysis (TDA) is to quantitatively encode and measure shape using Algebraic Topology. The available tools encompass both algebraic constructions (such as persistence diagrams and Euler characteristics) as well as graph based representations (such as Reeb graphs, mapper graphs, and merge trees). Applications of TDA have exploded in recent years, finding use in a diverse array of domains including plant biology, neuroscience, mechanical engineering, and many more. In this talk, we will focus on the family of transforms that have shown great promise in shape analysis applications, with the Persistent Homology Transform and the Euler Characteristic Transform at the helm. These tools have both practical interest, as we will show with examples from plant biology applications, as well as many open theoretical questions, such as the existence of monodromy and the generalization to the recently defined canopy for generalizing vineyards.", "id": "Paper/65128", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65128"}, {"title": " Helping clinicians actually understand statistical tests. ", "webprogram_exclude": "0", "session_ids": ["Session/18064"], "source_sha256": "e92a1065d388ab47a1784eb4c4c5ef6ccae21fe4b9c49d04c7c4cad4ba21fd8e", "withdrawn": "", "abstract": "Graduate biomedical trainees in Mexico usually meet statistics as a list of formulas to memorize before facing a thesis committee, and most of them arrive convinced that they are bad at math. The stakes of that arrangement are high. Clinicians make life or death decisions and give advice with lifelong consequences, and they base both on evidence they frequently cannot evaluate for themselves.\n\nUnderstanding Data is a one semester course whose first cohort runs from August to December 2026 with 16 graduate students and junior clinical researchers. Every inferential idea is introduced as a resampling procedure that the student writes and runs, and the closed form test appears afterward as a shortcut. We translated the full LS 40 lab sequence from Python into R, the language our trainees already need for their own protocols, and we replaced the textbook examples with de-identified data from our own metabolic disease cohorts.\n\nI will present what we measured: pre and post assessments of statistical reasoning, the change in self reported confidence for analyzing one's own data, and the end of course evaluations. I will also describe what needed redesign after the first run and what I would do differently with the second cohort.\n\nSuccesses and learning points will be shared openly, together with the R lab sequence, so that faculty building a modeling-first class can shorten their own implementation curve and judge what is likely to transfer to their student population.\n\nI will present what we measured. Pre and post assessments of statistical reasoning,  the change in self reported confidence for analyzing one's own data, and the end of course evaluations.\n\nI will also describe what needed redesign after the first run. \n\nOur successes and learning points will be shared openly so faculty building a modeling-first class can shorten their own implementation curve and get insights to adapt to their own student population.", "id": "Paper/65129", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65129"}, {"title": " Gradient Flows of Immersions near Equilibria — local incompressibility and global penalization ", "webprogram_exclude": "0", "session_ids": ["Session/18244"], "source_sha256": "0a767d9df5a82b435f62ead08b54f467cd5c8a80ff2be7c886fe381462d8c731", "withdrawn": "", "abstract": "We present an analysis of gradient flows of complex energies of `fluidic’ surfaces — those with no reference configuration, such as membranes formed from lipid bilayers. From a dynamical systems perspective there is a key obstacle to overcome: energy assigned to the surface is naturally expressed in terms of the first and second fundamental forms of the surface, while the flow is naturally expressed in terms of a normal and tangential velocity.  We develop a closed system for the gradient flow in terms of the natural coordinates of the tangent plane of the set of admissible (closed) surfaces near quasi-equilibrium of the energy. This leads to a minimal dynamical system framework with a symmetrized linear structure. Linear stability analysis is reduced to understanding familiar operators subject to explicit geometric constraints. We present the results for complex energies and simple geometries, restricting attention to immersions in $R^2$, showing that either global length penalty or local incompressibility increase the stability of equilibrium.", "id": "Paper/65134", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65134"}, {"title": " Randomized Quasi-Monte Carlo Approximate Control Variates ", "webprogram_exclude": "0", "session_ids": ["Session/17807"], "source_sha256": "30e654d28b4ce5ff42d51f6f7631e2bd4f3d25b2f1eb090274573d72f0fc08ad", "withdrawn": "", "abstract": "Multifidelity model ensembles and quasi-Monte Carlo sampling are two established but largely separate routes to reducing the cost of forward uncertainty quantification. Their combination has so far been confined to multilevel quasi-Monte Carlo, which requires the models to form a strict hierarchy of discretizations and fixes the control variate coefficients in advance. We present a randomized quasi-Monte Carlo (RQMC) extension of the approximate control variate (ACV) framework of Gorodetsky et al.\\ that removes both restrictions. The estimator is unbiased for an arbitrary ensemble of models, and its variance separates into a model-correlation part and a sample-allocation part combined through a Hadamard product, exactly as in the Monte Carlo case. Using an ansatz of model-dependent variance decay rates, multilevel and multifidelity quasi-Monte Carlo arise as particular choices of the auxiliary sample sets, yielding tridiagonal and diagonal structure matrices respectively, and a new RQMC-ACV estimator with a dense structure matrix and freely optimized coefficients arises alongside them. We give a greedy algorithm that allocates samples over the dyadic lattice by maximizing predicted variance reduction per unit work. Numerical experiments verify the efficacy of our method.", "id": "Paper/65137", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65137"}, {"title": " Weyl’s polarization theorem in positive characteristic ", "webprogram_exclude": "0", "session_ids": ["Session/18030"], "source_sha256": "688578e3efb267f18d4c19c99270b9f45fb507fae13c13b8b091577c9f1c9f2f", "withdrawn": "", "abstract": "Weyl's theorem on polarizations is a landmark result of classical invariant theory: it says that the polynomial invariants of an arbitrary direct sum of copies of a representation $V = \\mathbb{Q}^n$ of a group $G$ are all obtained, by polarization, from the invariants of just $n$ copies of $V$. In the 1990s, Richman showed that polarization always fails for finite groups in the modular setting. I will explain how to extend Weyl's theorem to positive characteristic in the simplest case, that of multisymmetric polynomials (i.e., the case when $G = S_p$ acts on $k^p$ over a field $k$ of characteristic $p > 0$). In particular, our result easily implies the existence of non-noetherian $GL_{\\infty}$-algebras over fields of positive characteristic.", "id": "Paper/65138", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65138"}, {"title": " Comparing Clinical Profiles of Adolescents and Adults with Epilepsy Using Statistical and Exploratory Topological Data Analysis ", "webprogram_exclude": "0", "session_ids": ["Session/18239"], "source_sha256": "8369be53b8a565c72bceecd437d6ecc3688fefc4d065f16b91a7cca7f4e2950f", "withdrawn": "", "abstract": "Epilepsy can present through a wide range of seizure types, symptoms, and associated factors, some of which may be difficult to recognize in adolescents. This study compares epilepsy characteristics in adolescents ages 12–19 and adults and investigates whether combinations of these characteristics reveal age-related patterns in epilepsy presentation. A publicly available epilepsy dataset containing demographic, diagnostic, seizure, symptom, medication, and potential risk-factor information is analyzed. Descriptive and inferential statistical methods are used to identify characteristics that differ between the two age groups. Initial findings indicate that seizure type and epilepsy classification differ significantly between adolescents and adults, while most individual symptoms and reported risk factors do not. In particular, absence seizures are more common among adolescents, while focal seizures are more common among adults.\n\nExploratory Topological Data Analysis using Mapper complements the statistical analysis by examining how multiple characteristics occur together rather than evaluating each characteristic independently. This approach represents patients as multivariable profiles based on seizure classifications, symptoms, and reported risk factors. The analysis investigates whether adolescents and adults occupy distinct or overlapping regions of the resulting data structure and whether particular combinations of characteristics are more prominent among adolescents. This presentation will highlight the primary statistical differences identified between the two age groups and examine the clinical profiles revealed through the exploratory Mapper analysis. It will also demonstrate how traditional statistical methods and Topological Data Analysis can provide complementary perspectives on complex health data.", "id": "Paper/65144", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65144"}, {"title": " Gromov–Wasserstein Geometry and Ricci Curvature for Evolving Spatial Transcriptomic Networks ", "webprogram_exclude": "0", "session_ids": ["Session/17908"], "source_sha256": "0985ce174721bb34cc2b02d9f284fe8909822d7aacb78bbc9976842455928e3a", "withdrawn": "", "abstract": "Developmental analysis of independently sampled, unaligned spatial transcriptomic data motivates geometric tools for characterizing changes in relational network structure across stages. We present a framework for analyzing the spatiotemporal evolution of gene-expression networks in Gromov--Wasserstein (GW) space. Each developmental stage is represented by a graph integrating gene expression and spatial proximity. This representation enables structural comparison across stages, continuous interpolation through GW geodesics, and quantification of network-level changes using Ollivier--Ricci curvature. Applied to a spatiotemporal transcriptomic \\textit{Drosophila} dataset, the GW-geodesic interpolants reproduce the main trends in curvature dynamics observed in empirical networks. Agreement with higher-order Co-Optimal Transport distances, which jointly incorporate spatial and temporal information, further suggests that the framework captures salient developmental changes. The approach connects optimal transport, graph curvature, and higher-order network representations for studying evolving structured biological data.", "id": "Paper/65146", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65146"}, {"title": " The non-peripheral curve graph and distance estimates in big mapping class groups ", "webprogram_exclude": "0", "session_ids": ["Session/19362"], "source_sha256": "bddb1e369aaba8c95d157704ecf96f0532cda62727d79c9dd752c4226688ca4e", "withdrawn": "", "abstract": "We recall the construction and properties of the non-peripheral, simple closed curves for surfaces of infinite type.  We present two applications of this graph concerning asymptotic dimensions and divergence of big mapping class groups. if time permits, we discuss an example where the non-peripheral arc and curve graph is used to construct distance estimation (in the sense of Masur-Minsky) for big mapping class groups.  This is a progress report of on-going work.", "id": "Paper/65147", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65147"}, {"title": " Combinatorial Architectures for Franklin Magic Squares: Sharp Criteria for Higher-Order Dyadic Constructions ", "webprogram_exclude": "0", "session_ids": ["Session/17963"], "source_sha256": "c8cb0b9d17d57ca73f6e1854da82c1975e3911babbd8b30a205198847a78fc97", "withdrawn": "", "abstract": "A Franklin magic square is a bijective labeling of the cells of an $N\\times N$ grid by $1,\\ldots,N^2$, subject simultaneously to half-row and half-column sums, toroidal $2\\times2$-block sums, bent-diagonal sums, and concentric-corner sums. Recent approaches to this coupled grid-labeling problem use Hilbert bases, polyhedral cones, and matrix constructions. We instead develop explicit dyadic placement architectures that force Franklin’s identities directly. For every $N=8n$, the Parallel Dyadic Weave (PDW) places consecutive labels in layered diagonal dyads and propagates them through reflection and stitching rules. We prove a sharp characterization: the resulting labeling is a Franklin magic square if and only if its sign sequence satisfies two bipartite zero-sum conditions. Hence Franklin’s reversal-symmetric patterns constitute only a proper subfamily of the admissible class. An extension based on a bijective chronological map encompasses reversed, permuted, and interleaved assignments. Under inter-layer complementarity, intra-layer half-balance, and admissible signs, the resulting labelings preserve Franklin's identities. Independently, the Knight-PDW replaces the scaffold with noncontiguous knight dyads; for every $N=16m$, the weighted layer-polarity criterion is necessary and sufficient for all prescribed sums to hold. Together, these results establish a placement-level framework for constructing and characterizing magic labelings on structured grids: global arithmetic identities follow from dyadic pairing, discrete symmetries, and finite algebraic balance conditions.", "id": "Paper/65149", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65149"}, {"title": " Machine Learning and Statistical Methods for Survival Prediction in Oncology: A Multi-Cohort Comparative Study ", "webprogram_exclude": "0", "session_ids": ["Session/19338"], "source_sha256": "4b89cf33a2eb405189aa1bc19dc851bba39086ca8533f931f31658e90ef3827b", "withdrawn": "", "abstract": "Accurate survival prediction is important for prognostic assessment and risk stratification in oncology. This study compared statistical and machine learning approaches for analyzing right-censored survival outcomes across three clinical cancer cohorts: the Veterans’ Administration Lung Cancer Study, the German Breast Cancer Study Group 2 (GBSG2), and the North Central Cancer Treatment Group Lung dataset. Kaplan–Meier analysis was used to characterize survival patterns, and four modeling approaches—Cox proportional hazards (Cox-PH), Random Survival Forest (RSF), Survival Decision Tree (SDT), and DeepSurv—were evaluated for survival prediction. Model performance was assessed using the concordance index (C-index) and integrated Brier score (IBS), reflecting discrimination and overall prediction error, respectively. RSF showed the most consistent performance across the three cohorts, achieving C-indices of 0.735, 0.701, and 0.744 in the Veteran, GBSG2, and Lung datasets, respectively, with corresponding IBS values of 0.064, 0.120, and 0.139. Cox-PH yielded C-indices of 0.706, 0.558, and 0.653 and IBS values of 0.076, 0.161, and 0.147, respectively. DeepSurv showed competitive performance but did not consistently outperform RSF, whereas SDT had the weakest overall performance. Beyond prediction, Cox-PH provided directly interpretable estimates of covariate effects through hazard ratios, highlighting the continued value of conventional statistical modeling for identifying prognostic factors. Overall, RSF provided the most consistent predictive performance across these heterogeneous oncology cohorts, while Cox-PH offered greater interpretability of covariate–survival associations. These findings underscore the complementary strengths of statistical and machine learning approaches and suggest that survival-model selection should consider both predictive performance and clinical interpretability. \\\\\\\\\n\\textbf{Keywords:} Survival analysis; Time-to-event data; Machine learning; Cox proportional hazards; Random survival forest; DeepSurv; Prognostic modeling; Oncology", "id": "Paper/65150", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65150"}, {"title": " Non-Asymptotic Confidence Intervals for Randomized Quasi-Monte Carlo (RQMC) ", "webprogram_exclude": "0", "session_ids": ["Session/17807"], "source_sha256": "b096338e7eba9c406b3796ee08d1ea2457da53e725fa745087e44d7639c399a7", "withdrawn": "", "abstract": "Quasi-Monte Carlo (QMC) methods provide better estimation for integration by replacing IID samples with deterministic low-discrepancy sequences such as the Sobol sequence. Randomized QMC (RQMC) methods retain the advantage of QMC while providing unbiased estimates by adding randomizations to the QMC points.  For RQMC, we take $R$ independent randomizations, or replicates, of $n$ RQMC points, averaging the $n$ function evaluations within each replicate.\n\nWe present two novel methods for finite-sample RQMC CIs, extending upon established CIs for IID samples. Our theory uses the variance model $\\sigma^2_n = \\gamma n^{-r}$, where $\\gamma$ is a constant and $r \\ge 1$. The $r$ typically equals $1, 2,$ or $3$, with higher $r$ corresponding to smoother functions.\n\nOur first approach is for bounded integrands in $[0,1]$ by adapting the Hedged Betting and Empirical Bernstein CIs of Waudby-Smith and Ramdas (2024). Given a fixed budget $N = nR$, we investigate the optimal $n$ minimizing the CI width. Our theory yields $n^* = O(N^{1/(r + 1)})$ for $r > 1$ ($n^* = 1$ for $r = 1$), with this slow growth of $n$ with $N$ being reflected in our empirical investigations. For sufficiently large $N$, our simulations show improved performance over the IID case ($n=1$) when compared with RQMC ($n>1$). %\\aleksei{Don't think you need ``when $n>1$''.} \\aadit{I think it adds more clarity without taking much space.}\n\nOur second approach uses the weaker assumption of a bounded kurtosis and we empirically bound the kurtosis as $10$. In stage 1, we use $R_1$ replicates to bound the sample variance and in stage 2, we use $R_2$ new replicates to deliver the estimate $\\hat \\mu$ s.t $\\Pr( |\\hat\\mu-\\mu|\\le\\varepsilon)\\ge1-\\alpha$ for the given uncertainty requirement $\\varepsilon$. We obtain $R_2$ using the minimum of Chebyshev's and Berry-Esseen's inequalities. We get $n^* = O(\\varepsilon^{-2/r})$ for $r > 1$ ($n^* = 1$ for $r = 1$) and a similarity is seen to the first approach where $n^*$ seems to grow faster for smaller $r$, with $r = 1$ being an exception. \n\nA crucial difference is that the first approach specifies the budget but not the desired CI width, while the second approach does the opposite. Both approaches are conservative as they tend to give $100\\%$ coverage empirically for a $95\\%$ CI, with this being a common problem of non-asymptotic CIs.", "id": "Paper/65159", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65159"}, {"title": " Beckner and Logarithmic Sobolev inequalities and stability of the Poincaré inequality with weighted Gaussian measures. ", "webprogram_exclude": "0", "session_ids": ["Session/17749"], "source_sha256": "e7c4cc6c8537ae41e09f7b5caf7bffcc11248f6401ac3deedb03d2115f510f9a", "withdrawn": "", "abstract": "We employ a Markov semigroup approach combined with the \\( \\Gamma \\)-calculus to establish a generalized Beckner inequality associated with weighted Gaussian measures. As a direct consequence, we derive the corresponding Poincaré inequality in the same setting. Subsequently, by means of a duality argument, we investigate gradient and \\(L^2\\) stability estimates of the Poincaré inequality. Furthermore, we formulate a scale-dependent version of the Poincaré inequality for homogeneous Gaussian-type measures and apply it to analyze the stability of the Heisenberg Uncertainty Principle with homogeneous weights. Finally, we establish a Logarithmic Sobolev inequality for weighted Gaussian measures and utilize it to derive the Euclidean Logarithmic Sobolev inequality with homogeneous log-concave weights.", "id": "Paper/65161", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65161"}, {"title": " Berezin Ranges of Composition Operators on H^{2} ", "webprogram_exclude": "0", "session_ids": ["Session/19339"], "source_sha256": "4644b89418e036bb3b6d6264dec26e71354055c2883b6c0cdf8576405feb6b18", "withdrawn": "", "abstract": "Following work initiated by Felder and Cowen, we investigate Berezin ranges of composition operators on the Hardy space induced by linear-fractional symbols. We show a variety of surprising facts: some are envelopes of families of circles, some are open while some include different amounts of boundary, and some have a corner point. For several linear-fractional classes, we identify the Berezin range exactly, and prove the exact conditions under which they are convex. Joint work with Trieu Le and Paul Bourdon.", "id": "Paper/65162", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65162"}, {"title": " Cycles of Life – Geometrically and Polar ", "webprogram_exclude": "0", "session_ids": ["Session/17091"], "source_sha256": "8d599396925c000335c61a8a8512001f821afd54a783ef40feea42f5347c4330", "withdrawn": "w", "abstract": "The course of life can be seen in cycles, including some people’s beliefs of birth and rebirth, but also as a combination of linearity and cyclicity in spirals and other curves that can be described in polar coordinates. Two solo dance pieces explore both options – geometrically through the conic sections, and through diverse polar curves generated by a Mathematica program.", "id": "Paper/65165", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65165"}, {"title": " Assessing Mathematical Communication with Presentations ", "webprogram_exclude": "0", "session_ids": ["Session/19349"], "source_sha256": "da192d99825ee56a79d7459b54a5a0ded01008fe41c304da81117905ebfd1b90", "withdrawn": "", "abstract": "Oral exams seem daunting, but when we give the students the questions in advance and phrase it as a ``presentation'' of the solutions, the assessment takes a whole new direction. In this talk, I will explain how I implemented presentations, with an emphasis on mathematical communication, as an alternative form of assessment in a Calculus 1 class. Reframing the focus from ``getting math right'' to clearly explaining a mathematical thought process had far-reaching consequences. Specifically, preparing for these presentations helped the students do better group-work, increased in-class engagement, fostered more connections, and gave students a different means by which to demonstrate their understanding. Join us for an overview of how these presentations were run, what impact it had, what went well, and what I will change in future iterations; all with an eye towards how you could adopt this in your own courses.", "id": "Paper/65170", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65170"}, {"title": " A mathematical analogy between certain hollow vortex and bubble flows ", "webprogram_exclude": "0", "session_ids": ["Session/18444"], "source_sha256": "ce483e813abdb5d7d4aa6d0b547db9cb0639a03d5896c5f6b010b5c5f0a389ec", "withdrawn": "", "abstract": "Following earlier work by Hur and Wheeler, Crowdy and Tanveer recently elucidated a mathematical analogy between two sets of apparently distinct free boundary problems in 2D inviscid fluid dynamics. These include a hollow vortex in simple shear/straining flow and a translating bubble in the presence of surface tension. In this talk, we will discuss how to extend this mathematical analogy to the following problems: An equilibrium hollow vortex with no surface tension in a third order straining flow, with first order strain component along with simple shear, and a bubble with surface tension in a first order straining flow allowing for circulation at infinity.\n\nWe obtain new local existence, uniqueness, and analyticity results concerning both, the vortex and the bubble problem, and give an analytic criterion for when the vortex and bubble shapes are identical, even though the ambient flows differ. Numerical computations supplementing our theoretical results are given, and we provide explicit solutions in the abscence of shear (vortex), and zero Bernoulli constant (bubble).\n\nThis is joint work with D. Crowdy and S. Tanveer", "id": "Paper/65180", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65180"}, {"title": " Spike patterns in multi-species Keller-Segel models ", "webprogram_exclude": "0", "session_ids": ["Session/18445"], "source_sha256": "419ab8d9b98a7e4f8e6e6cc05898ea019b761185d023c3dee2658ba5790a11e3", "withdrawn": "", "abstract": "Among the fundamental features of Keller--Segel models is the existence of spatially concentrated steady-state solutions, which capture chemotaxis-driven cellular aggregation and offer a mechanistic explanation for important biological and pathophysiological phenomena, such as morphogenesis and tumor growth. In this talk, we present our recent results on spiky steady states in multi-species Keller--Segel models. By combining the inner–outer gluing method with bifurcation analysis, we establish the existence of such states and characterize several classes of spike configurations, including synchronized and segregated patterns.", "id": "Paper/65211", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65211"}, {"title": " New algorithms for the convergence of solutions to non-monotone variational inequalities ", "webprogram_exclude": "0", "session_ids": ["Session/19368"], "source_sha256": "82138c6978099f8c2a8d800ed7aab84ac89ea0d8601b5238705a80b54a276d60", "withdrawn": "", "abstract": "We introduce new algorithms to study the convergence of solutions to quasi-monotone variational inequalities with Lipschitz continuous operators in a Hilbert space. We consider two new algorithms, the first one without the knowledge of the Lipschitz constant of the operator, and the second one with its knowledge. In both cases, we show the strong convergence of the generated sequence to a solution of the problem. We compare also the convergence speed for the two algorithms by providing some examples of applications and numerical experiments.", "id": "Paper/65217", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65217"}, {"title": " The conjugacy action of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"10.165ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 4376.7 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\textrm {Aut}(X,\\mu )</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-41\" d=\"M255 0Q240 3 140 3Q48 3 39 0H32V46H47Q119 49 139 88Q140 91 192 245T295 553T348 708Q351 716 366 716H376Q396 715 400 709Q402 707 508 390L617 67Q624 54 636 51T687 46H717V0H708Q699 3 581 3Q458 3 437 0H427V46H440Q510 46 510 64Q510 66 486 138L462 209H229L209 150Q189 91 189 85Q189 72 209 59T259 46H264V0H255ZM447 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x=\"3383\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"3987\" y=\"0\"></use>\n</g>\n</svg> is not unbalanced ", "webprogram_exclude": "0", "session_ids": ["Session/18213"], "source_sha256": "5c9599e325cbe092471060504e3b97730ba9f2a74a851d31ca51f0732059d464", "withdrawn": "", "abstract": "Generic unbalancedness is a property of group actions introduced by Panagiotopoulos and Allison. They showed that if a group action is generically unbalanced, then the orbit equivalence relation on any generic invariant class cannot be Borel reducible to an orbit equivalence relation induced by a TSI group action. In this talk, we show that the conjugacy action of ${\\rm Aut}(X,\\mu)$ is not generically unbalanced, answering a question of Le Maître.", "id": "Paper/65234", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65234"}, {"title": " A birth-death process with limited nutrients and its implications on mutation dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/19370"], "source_sha256": "7af3e305b85ebcc56b24ad2e543f4a6e6916ce2e29f1367f4f08302198737d86", "withdrawn": "", "abstract": "The conditions that support sustained bacterial growth at a constant rate are rarely encountered in natural environments. In contrast, bacteria cultured under optimal laboratory conditions, such as in nutrient-rich media, can often exhibit relatively stable growth. In natural environments, bacteria typically inhabit physically structured environments in which spatial constraints limit mobility and produce localized variations in nutrient availability. As cells grow and increase their population through nutrient consumption, they progressively deplete nutrients within their local environment. In this work, we present a birth–death process (BDP) model in which state-dependent transitions are directly coupled to resource availability, thereby integrating stochastic population dynamics with the gradual depletion of the nutrients. The model captures the key growth phases observed in bacterial populations under nutrient-limited conditions, including the progression from population growth to nutrient depletion and the subsequent reduction in growth. Because mutations arise during cell division, the cumulative number of divisions provides a basis for estimating the potential mutation supply within the population. Although mutations are not explicitly incorporated into the model, the model approximates the number of mutation opportunities by tracking the cumulative number of cell divisions. This provides a connection between population dynamics and the potential for evolutionary change without introducing an explicit mutation process. The model also demonstrates clear dependence of population dynamics on the governing parameters. In particular, changes in the initial nutrient concentration, initial population size, nutrient consumption rate, and death rate alter the timing and magnitude of population growth and nutrient depletion. These parameter dependencies highlight how environmental conditions and population characteristics jointly influence the number of cell divisions and, consequently, the potential for mutation and evolutionary change.", "id": "Paper/65236", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65236"}, {"title": " <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"3.54ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 1524 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">OC</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-43\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-4F\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-43\" x=\"763\" y=\"0\"></use>\n</g>\n</svg>-Interval Representations of Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18317"], "source_sha256": "d4987eebecc57f1a3d7e9044fbf5dd3b8e62d48439334ffc6e0f1f9454f5f427", "withdrawn": "", "abstract": "Let $\\mathcal{I}$ be the collection of all nonempty closed intervals of $\\mathbb{R}$, excluding $\\mathbb{R}$ itself. An {\\it interval graph} is a graph $G$ such that there is a map $I:V(G)\\to \\mathcal{I}$ satisfying the following property: $uv\\in E(G)$ if and only if $I(u)\\cap I(v)\\neq \\emptyset$. We call the map $I$ an {\\it interval representation}. Interval graphs are very well-studied, and they have nice characterization theorems. We now consider a variation of this problem. Given an interval graph $G$, let $\\ell : E(G)\\to \\{O,C\\}$ be an edge-labeling that either assigns a label of $O$ (short for ``overlap\") or a label of $C$ (short for ``contain\"). We call $\\ell$ an {\\it $OC$-interval labeling} if there exists an interval representation $I:V(G)\\to \\mathcal{I}$ such that $\\ell(uv) = O$ if and only if $I(u)$ and $I(v)$ have an overlap relationship and such that $\\ell(uv) = C$ if and only if $I(u)$ and $I(v)$ have a containment relationship. The central research question is to characterize the edge-labelings of interval graphs that are $OC$-interval labelings. Specifically, we discuss algorithms and structural characterizations for this problem.", "id": "Paper/65244", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65244"}, {"title": " Explainable Machine Learning for Functional Data ", "webprogram_exclude": "0", "session_ids": ["Session/18314"], "source_sha256": "5cc7791d02b82877a66f7667bfb2a7a759ca578a1f375a1877563f886118b891", "withdrawn": "", "abstract": "Black-box machine learning models are recognized as useful tools for prediction applications,\nbut the algorithmic complexity of some models causes interpretation challenges. Explainability\nmethods have been proposed to provide insight into these models, but there is little research\nfocused on supervised modeling with functional data inputs. We argue that, especially in appli-\ncations of high consequence, it is important to explicitly model the functional dependence in a\nblack-box analysis to not obscure or misrepresent patterns in explanations. As such, we discuss a method using variable importance under the Elastic Shape Analysis (ESA) framework for training supervised machine learning models with functional inputs. The methodology is an analysis process\nthat includes the data preprocessing, modeling, and post-hoc explanations. The preprocessing\nis done using elastic functional principal components analysis, which accounts for vertical and\nhorizontal variability in functional data and, ultimately, allows for explanations in the origi-\nnal data space that identify the important functional variability without bias due to correlated\nvariables. Here, we demonstrate the methodology on two high-consequence applications: explosives\nclassification for national security and inkjet printer identification in forensic science. The appli-\ncations exhibit the method's ability to provide an understanding of the characteristics\nof the functional data useful for prediction. Code for implementing the pipeline is available in\nthe veesa R package (and supplemental python code).", "id": "Paper/65247", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65247"}, {"title": " Intrinsic Cellular Organization Shapes Rhythmogenesis and Modulatory Responses in Respiratory Networks ", "webprogram_exclude": "0", "session_ids": ["Session/18320"], "source_sha256": "2e86fdb28f02510f1c42dcae9bba35b21db20d379d8b7c1652d317b14944a2c2", "withdrawn": "", "abstract": "The preB\\\"{o}tzinger complex (pBC) in the mammalian brainstem generates inspiratory rhythm. Experimental studies have identified two intrinsic biophysical mechanisms, a persistent sodium current (INaP) and a calcium-activated non-selective cation current (ICAN), as important contributors to rhythm and pattern generation. Although ICAN modulation is known to have differential effects on different intrinsic firing phenotypes in the pBC, including intrinsic bursting pacemaker neurons and silent followers, its network-level consequences in heterogeneous populations remain poorly understood. Here, using a computational model of a synaptically coupled excitatory pBC network, we show that ICAN can exert fundamentally different effects on network amplitude and synchrony depending on how it is expressed across intrinsic phenotypes. In networks with uniformly distributed intrinsic properties, population activity amplitude shows minimal sensitivity to ICAN modulation. In contrast, when intrinsic properties are organized into distinct rhythogenic and pattern-forming subpopulations, the same modulation yields pronounced changes in network dynamics, despite comparable overall parameter ranges. Thus, the network-level effects of ICAN depend critically on the structural organization of intrinsic cellular properties across the population. By combining large-scale simulations with dynamical systems analysis, we uncover the mechanisms underlying this differential modulation. Together, our findings highlight the organization of intrinsic cellular properties as a key determinant of circuit robustness and flexibility in generation and modulation of respiratory rhythms.", "id": "Paper/65250", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65250"}, {"title": " Tools for Studying Pattern Formation in Systems Involving Nonlocal Interactions ", "webprogram_exclude": "0", "session_ids": ["Session/17883"], "source_sha256": "00def3e225caae4b45dfa6bad744df33b7d6cd9ad1cc79631e937484b307e51c", "withdrawn": "", "abstract": "We show that tools from functional analysis used in reaction diffusion systems to study of pattern formation can be extended to models where diffusion is replaced by a nonlocal operator. We illustrate this point by considering a nonlocal version of the Klausmeier model, a system of equations describing the interaction between plant biomass and water availability in arid ecosystems. Modeling the spread of plants as a nonlocal process, we derive an amplitude equation for this system and prove the existence of periodic patterns. Using continuation methods we explore how these patterns change as the width of the nonlocal kernel expands and provide an approach for finding a second order approximation describing the resulting structures.", "id": "Paper/65251", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65251"}, {"title": " Rethinking High School Mathematics Pathways: Implications for College Readiness and Undergraduate Mathematics Education ", "webprogram_exclude": "0", "session_ids": ["Session/19341"], "source_sha256": "254ad23b9822777ae74470a4df8b73973612ab48e847981644647d79f9eb437a", "withdrawn": "", "abstract": "High school mathematics is undergoing significant change, with direct implications for undergraduate mathematics. Developments such as AP Precalculus, expanded access to AP Statistics without Algebra II, evolving state standards beyond the Common Core State Standards for Mathematics, and the growing influence of artificial intelligence are reshaping what it means to be “college ready.” At the same time, research calls for moving beyond a single, calculus-driven sequence toward multiple, flexible pathways aligned with students’ goals and careers for both college- and non-college-intending students.\n\nThese shifts raise pressing questions: Who will enroll in calculus? What preparation will students bring? What mathematical ideas should be assumed? What role should data science, computational science, and statistics play in high school?\n\nThis session synthesizes current changes and introduces a design perspective grounded in the problem-based middle school mathematics curriculum, Connected Mathematics®4 (CMP4). Grade 8 serves as a bridge to high school, covering key ideas from both Grade 8 and Algebra 1. In this pathway, CMP4 uses a functions-based approach to help students formalize patterns of change, relationships, and transformations. Uniquely, students in Grade 8 and Algebra 1 use the same instructional materials rather than separate courses or texts. This structure reduces barriers, supports equity, and allows more flexible course movement, positioning students to pursue advanced mathematics.\n\nBuilding on this design perspective, participants will engage in small-group discussions to identify essential “big mathematical ideas” for all high school students, consider preparation for STEM and non-STEM pathways, and reflect on how high school and undergraduate expectations may need to evolve. The session invites undergraduate mathematicians to help shape the secondary–postsecondary transition.", "id": "Paper/65253", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65253"}, {"title": " Towards an Optimal Bound for the Interleaving Distance on Mapper Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18324"], "source_sha256": "bb9c90c3948edbe7c129a50b2ce1a152041edd41f98a0d9fe09fa294aec550c7", "withdrawn": "", "abstract": "Mapper graphs are widely used in topological data analysis and visualization. They can be understood as discrete approximations of Reeb graphs, providing insight into the shape and connectivity of complex data. Given a point cloud together with a real-valued function, a mapper graph summarizes the structure: each node represents a local neighborhood, and edges connect nodes whose corresponding neighborhoods overlap. Our focus is the interleaving distance for mapper graphs, arising as a discretized analogue of the interleaving distance for Reeb graphs-a quantity known to be NP-hard to compute. This distance measures similarity of two mapper graphs by quantifying how much ``stretching'' is necessary to be made comparable. Recent work introduced a loss function that gives an upper bound on this distance which evaluates how far a given collection of maps, called an assignment, is from being a true interleaving. Importantly, the loss is computationally tractable, offering a practical way to bound the distance; however the quality of the bound is dependent on the choice of assignment.\n\nIn this work, we develop the first computational framework for bounding the interleaving distance on mapper graphs in two ways: first, by formulating an integer linear program (ILP) that determines whether an $n$-interleaving exists; and second, by constructing an ILP that identifies an assignment with minimal loss for that $n$. We also evaluate the method on small examples where the interleaving distance is known, and on benchmark and simulated datasets, demonstrating the utility of the approach for classification tasks based on mapper graphs.", "id": "Paper/65254", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65254"}, {"title": " Forest webs and pattern avoidance ", "webprogram_exclude": "0", "session_ids": ["Session/17943"], "source_sha256": "1c0f56889761aa542aa027f3275ddc914ef88a3d7588aca9b0784dae01f459bc", "withdrawn": "", "abstract": "In a recent preprint, Mike Cummings showed that the smooth components of suitably parametrized Springer fibers are in bijection with contracted, fully reduced Pl\\\"ucker degree-two $\\mathfrak{sl}_r$-webs of standard type and that are forests. He showed these are enumerated by sequence A116731 in the OEIS, which is equinumerous with permutations avoiding the patterns {321,2143,3124}. Cummings posed the problem of strengthening this enumerative result by finding a bijection between these webs and a collection of pattern-avoiding permutations. Here we solve this problem, although notably not with the collection of patterns that Cummings had proposed. Rather, we give a bijection between this class of webs and permutations avoiding the patterns {132,4321,3214}.", "id": "Paper/65258", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65258"}, {"title": " A Graduate Student Perspective on Math Circles ", "webprogram_exclude": "0", "session_ids": ["Session/18211"], "source_sha256": "594f367d931afa63d57672884e47678df97b1aaf52f6e11bc196f7198c806682", "withdrawn": "", "abstract": "Math Circles is a program designed to demonstrate the breadth and beauty of mathematics through collaboration on difficult math and logic problems. Many people view math as a rigid subject, in which there are only two types of answers: right and wrong. This program showed students who had previously experienced math in this way that math can indeed be a creative endeavor. Throughout the last year, we facilitated weekly sessions with middle school students, supported by the MAA Neff Outreach Grant. Our role as facilitators was primarily to work with the kids, and engage in productive struggle alongside them. A core piece of this program was the students presenting their solutions and explaining them to their peers. After each presentation, we always asked the question, “Did anyone else think about this differently?”. The answer was almost always yes. In this session, we will share our experience and methodology with Math Circles, and lead an activity where participants will work on some of these problems. We believe that learning happens best through collaborative experiences, so this session will be highly interactive.", "id": "Paper/65259", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65259"}, {"title": " Weighted Syzygies of Pointed Curves ", "webprogram_exclude": "0", "session_ids": ["Session/18347"], "source_sha256": "5da4a99041c2fb74432c4c4f74c8af5f7943a6b58cb7520d08e67d90f1d5a940", "withdrawn": "", "abstract": "Let $C$ be a smooth projective curve of genus $g$. When a line bundle $L$ on $C$ is sufficiently positive (i.e. when $\\deg L \\geq 2g+1$), the graded section is generated in degree 1 and a complete linear series on $L$ induces a closed embedding into projective space. Many classical theorems investigate the syzygies of such an embedding as $\\deg L$ grows. In contrast, less is known when $L$ is \\emph{not} guaranteed to be very ample; that is, when $\\deg L < 2g+1$. In this setting, one may still choose a \\emph{weighted} minimal generating set of the section ring which minimally embeds $C$ into a weighted projective space. In this talk, I will show that in the case $L=\\mathcal{O}_C(dP)$, where $P$ is a point on $C$, we can obtain many tight bounds regarding the syzygies and ambient spaces of the weighted embedding by understanding the combinatorics of the Weierstrass semigroup of $P$ and using nice degenerations.", "id": "Paper/65260", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65260"}, {"title": " Modeling the migratory patterns of humpback whales sighted off Guatemala ", "webprogram_exclude": "0", "session_ids": ["Session/18023"], "source_sha256": "9f7c8a4f32a4367c8ac84c0c79d30620b116d04ed5d55ad3ea9df0d99bbdad0a", "withdrawn": "", "abstract": "Northern Pacific humpback whales (\\textit{Megaptera novaeangliae}) migrate seasonally between northern feeding areas, extending from California to Alaska, and southern breeding grounds in Mexico and Central America. We analyze the migratory dynamics of whales observed off the coast of Guatemala, using a dataset spanning approximately 40 years and containing more than 5,000 observations of 229 individual whales. We model the trajectories of individual whales using Fourier regression and group the resulting trajectories into clusters using Ward’s hierarchical clustering algorithm. Our analysis identifies three main migratory clusters, distinguished by both their geographic distributions and the timing of migration between feeding and breeding grounds. We further investigate the potential effects of the 2014-2016 North Pacific marine heatwave on humpback whale movement by examining residuals between observed and model-predicted locations. We find statistically significant differences in the residuals among the pre-, during, and post-heatwave periods, indicating possible changes in movement patterns associated with the marine heatwave. This work contributes to the understanding of humpback whale migration and may inform conservation efforts by identifying critical habitats and assessing how environmental changes may affect migratory populations.", "id": "Paper/65261", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65261"}, {"title": " Clonal rosette composition of a Bromeliaceae genet ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "a22fd4ddf9ac987c0980d605c74eae08601b4d0e38dedc0daffb8a6d72f6c592", "withdrawn": "", "abstract": "Bromeliaceae, a neo-tropical plant family encompassing over 3,500 species, exhibit two modes of reproduction: sexual reproduction via flowers and seeds and asexual reproduction through the production of genetically identical clonal rosettes. In previous work, we constructed a combinatorial model that produces the probability that a bromeliad genetic individual, or genet, is comprised of at least $n$ clonal rosettes. This research aims to develop an agent-based model for the clonal trajectory of one bromeliad genet, informed by environmental and species-specific data. We use a modified beta-binomial distribution as the core determinant of clonal reproduction, and we use greenhouse data from collaborators to test the model accuracy. Since many bromeliad species are threatened or endangered, this model can be leveraged by conservationists and natural resource managers to promote population growth and implement conservation strategies.", "id": "Paper/65262", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65262"}, {"title": " Linear Asymptotic Stability of the Smooth 1-Solitons for the Degasperis-Procesi Equation ", "webprogram_exclude": "0", "session_ids": ["Session/18109"], "source_sha256": "9621d9ec0acb06dd9ab192160efbbdccd4081592983b5d3decbc4899d710528a", "withdrawn": "", "abstract": "In this paper, we study the asymptotic stability of smooth 1-solitons in the Degasperis-\nProcesi (DP) equation. Such solutions necessarily exist on a non-zero background, and their\nspectral and orbital stability has previously been verified by Li, Liu & Wu and by Lafortune &\nPelinovsky. Using the complete integrability of the DP equation to establish the strong spectral\nstability of smooth solitary waves, namely that the origin is the only eigenvalue of the associated\nlinearized operator acting on L2(R) and that, moreover, in appropriate exponentially weighted\nspaces the non-zero spectrum for the linearized operator admits a spectral gap away from the\nimaginary axis. This spectral gap result is then upgraded to an exponential decay estimate on\nthe semigroup associated with the linearized operator, establishing a linear asymptotic stability\nresult in exponentially weighted spaces.", "id": "Paper/65264", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65264"}, {"title": " When Number Theory Drives an Oscillator: Energy, Power, and 2-Adic Resonance ", "webprogram_exclude": "0", "session_ids": ["Session/18867"], "source_sha256": "c42fc99755234d92bb639b339db7c67b3380772aed2091dfcda5a9bc0526638a", "withdrawn": "", "abstract": "What happens when a familiar linear oscillator is driven by an arithmetic function? We study the damped oscillator\n$$\nmy''+cy'+ky=\\nu_2(\\lceil t\\rceil),\n$$\nwhere $\\nu_2(n)$ is the $2$-adic valuation of the integer $n$.  By decomposing the forcing into periodic dyadic layers, we obtain explicit Fourier coefficients and show how the arithmetic structure of the forcing affects the oscillator response. This leads to closed-form expressions for long-time average mechanical energy and average power, and a hierarchy of resonant responses at dyadic frequencies.  Numerical simulations agree closely with the analytical energy predictions, and we also investigate the corresponding power response and the effect of damping on the resonance structure. This linear problem is intended as a first step toward a broader study of arithmetic oscillators: dynamical systems driven by forcing functions arising from number theory.", "id": "Paper/65266", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65266"}, {"title": " Cylindric growth diagrams, walks in simplices, and exclusion processes ", "webprogram_exclude": "0", "session_ids": ["Session/18286"], "source_sha256": "1cf4b18710bf00f8a5eee46f64a82795798891d448b60cda37dbee1eb4203bda", "withdrawn": "", "abstract": "We describe bijections between three different classes of combinatorial objects: lattice walks in simplicial regions as introduced by Mortimer--Prellberg, standard cylindric tableaux as introduced by Gessel--Krattenthaler and Postnikov, and sequences of states in the totally asymmetric simple exclusion process on a cycle. \n\nWith this new perspective, we show that a recent bijection of Courtiel et al. between certain simplicial walks with forward and backward steps is equivalent to a cylindric analogue of the Robinson--Schensted correspondence, originally defined by Neyman by iterating an insertion operation. We show that this correspondence has a more natural description by introducing a cylindric version of Fomin's growth diagrams. Our description elucidates the symmetry of the correspondence, extends to the semistandard case, and allows us to interpret the above walks as oscillating cylindric tableaux.", "id": "Paper/65267", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65267"}, {"title": " Inverse Eigenvalue Problems, Floquet Isospectrality and the Hilbert–Chow Morphism ", "webprogram_exclude": "0", "session_ids": ["Session/18292"], "source_sha256": "b4197bcb287786031b081bce47173a08b4970db31852e3f85f93591440c95908", "withdrawn": "", "abstract": "A central question in inverse spectral theory asks how much a periodic potential can change without changing the Floquet spectrum. This is closely related to the additive inverse eigenvalue problem: Friedland proved that the diagonal of a complex matrix can be adjusted to realize any prescribed spectrum, and we ask the complementary question—when can the diagonal be changed while leaving the spectrum completely unchanged? In joint work with Matthew Faust and Andreas Kretschmer, we obtain a clean characterization: a complex matrix admits a nonzero diagonal perturbation preserving its characteristic polynomial if and only if it has two unequal principal minors of the same size. Applied to periodic discrete Schrödinger operators, this reveals a sharp transition: the zero potential is rigid for sufficiently small periods, whereas nontrivial Floquet-isospectral potentials appear as soon as one period exceeds three. Our main tools combine ideals of spectral invariants, degeneration techniques from commutative algebra, and the geometry of the Hilbert–Chow morphism.", "id": "Paper/65268", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65268"}, {"title": " What the literature says...about students’ learning of inferential statistics ", "webprogram_exclude": "0", "session_ids": ["Session/18064"], "source_sha256": "4bd90375b006b372bc6a123d756ce83faf076813921632416f56be4eb334f61b", "withdrawn": "", "abstract": "Traditional introductory statistics education is heavily constrained by what Cobb (2007) called “the tyranny of the computable.” For decades, our curriculum content has been dictated by what can be calculated rather than by what is conceptually essential to statistical inference – or conceptually accessible to our students. As a result, students routinely fall into two common traps of “anti-statistical thinking”: the bog of over confidence and the bog of disbelief (Tintle, et al., 2015). We draw on empirical research from statistics education studies to show how traditional statistics creates and reinforces misconceptions about p-values and how teaching randomization and resampling can remedy them. This presentation addresses how transforming your statistics class into one based on resampling and simulation-based inferential methods can liberate the introductory curriculum. Let’s pull ourselves up by our bootstraps and help our students understand data!", "id": "Paper/65270", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65270"}, {"title": " Topological Analysis of Zebrafish Larvae Brain Dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/18320"], "source_sha256": "3a5d5e4e8f474d3c9c13575ad5abb45ddb0bec8fa8aaf0ece1b707f35b915bc1", "withdrawn": "", "abstract": "Even in the absence of visual stimuli, assemblies of neurons in the visual system of zebrafish larvae collectively activate.  These assemblies are each spatially localized and together cover the optic tectum along its retinotopic axis.  Yet functionally, less is known about the assemblies, including how these subnetworks of neurons generate and maintain spontaneous dynamics.  To better understand the dynamics of neural assemblies in zebrafish larvae optic tectum, we recorded calcium imaging of ~2000 neurons for 1 hour at 15 Hz for 12 fish, and then identified glutamatergic, GABAergic, and cholinergic neurons using immunostaining.  We applied a topological data analysis (TDA) to the correlations of assembly neurons during and outside of spontaneous activity.  Using Betti curves to summarize the persistent homology, we identified a plausible low-rank structure to the correlations agnostic to spectral analyses.  Incorporating TDA into a sliding window analysis allowed us to cluster spontaneous activations into distinct dynamic profiles, ultimately leading us to hypothesize about the role of cholinergic neurons in recruiting and maintaining assembly activity, and more broadly, visual attention.", "id": "Paper/65272", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65272"}, {"title": " Semialgebraic Conditions for Identifying Triangles in Phylogenetic Networks ", "webprogram_exclude": "0", "session_ids": ["Session/18115"], "source_sha256": "b65283ea65ec50098df8d311daf22871cafe6e06ae9b2b0931753f5826eb0f3b", "withdrawn": "", "abstract": "An important consideration for a model-based method of phylogenetic network inference is the identifiability of the network parameter of the model. A recurring theme in previous works exploring this issue is that it is often difficult to identify the orientation of edges in a triangle of the network. In this talk, we examine the identifiability of triangles in Jukes—Cantor phylogenetic network models. We give a semialgebraic description of the simplest 3-leaf network models, from which we see that despite being algebraically indistinguishable, these network models are not identical, nor are they generically identifiable. We will also discuss the implications of these results for practical phylogenetic inference.", "id": "Paper/65274", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65274"}, {"title": " Designing transversal gates through quantum code composition ", "webprogram_exclude": "0", "session_ids": ["Session/18387"], "source_sha256": "2eee9b92aafcfb8fc7ae6d83cb2d214076a7898f81abea4526fee47ab8384140", "withdrawn": "", "abstract": "Transversal gates are the simplest form of fault-tolerant gates and are relatively easy to implement in practice. Yet designing codes that support useful transversal operations---especially non-Clifford or addressable gates---remains challenging. We show that some of these limitations can be overcome using the so-called quantum lego formalism, where transversal gates naturally appear as symmetries of the individual quantum code blocks. By composing such code blocks and tracking their symmetries during these transformations, this approach enables the systematic construction of codes with addressable transversal single- and multi-qubit gates targeting specific logical qubits regardless of whether the gate is Clifford or not.", "id": "Paper/65276", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65276"}, {"title": " Rook Characters as Symmetric Functions ", "webprogram_exclude": "0", "session_ids": ["Session/18375"], "source_sha256": "e9b33ec724ce23dae9815e4b205be994d3375172937bd4f448005364437c4c52", "withdrawn": "", "abstract": "We define an inhomogeneous basis of the ring of symmetric functions with the property that evaluations of this basis at roots of unity produce the irreducible characters of the rook monoid (also known as the symmetric inverse semigroup). Through Schur-Weyl duality, we show that the transition coefficients of this basis with the power sum basis are the characters of the propagating partition algebra and that the structure coefficients of this basis are equal to the coefficients in the smash (or Heisenberg) product of Schur functions.", "id": "Paper/65279", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65279"}, {"title": " A characterization of all nonbipartite well-edge-dominated graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18317"], "source_sha256": "0f9ac1f4c4e4e3ae662e588710fd5b4b3d00e5209ad3d8948e5f8d0237beb76c", "withdrawn": "", "abstract": "A set $F\\subseteq E(G)$ is an edge dominating set of $G$ if every edge in $E(G)\\setminus F$ shares a vertex with some edge $f \\in F$, and the edge domination number of $G$, $\\gamma'(G)$, is the minimum cardinality among all edge dominating sets of $G$. $G$ is said to be well-edge-dominated if all minimal edge dominating sets have the same cardinality. Continuing the work of Berg et al. from 2024, we finish the characterization of all nonbipartite well-edge-dominated graphs.", "id": "Paper/65281", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65281"}, {"title": " A two-stage point process framework for spatio-temporal forecasting of urban crime ", "webprogram_exclude": "0", "session_ids": ["Session/19338"], "source_sha256": "bdcff0ae04ac962ee0ffdfe3d0f824c20bb2d8d90a04971c0e9253a772f386ae", "withdrawn": "", "abstract": "We study the spatio-temporal dynamics of urban crime using a two-stage point-process framework, applied to more than 8 million incidents recorded by the Chicago Police Department between 2001 and 2025. Discretizing time into weekly intervals represents the data as a sequence of spatial point patterns over the city. At each time point, we assess competing spatial models using Ripley's $K$-function diagnostics, composite likelihood criteria, and residual analysis. Under the selected family we carry out estimation and inference, obtaining weekly parameter estimates with uncertainty assessment. The resulting parameter sequence is then treated as a multivariate time series, to which we fit seasonal ARIMA and state-space models that propagate the estimation uncertainty from the spatial stage. Forecasts of future parameters reconstruct predicted crime-intensity surfaces, which we evaluate using rolling-origin cross-validation with held-out point-process log-likelihood, cell-count error, and the predictive accuracy index. We compare the framework against kernel density hotspotting and self-exciting point process benchmarks, and discuss the trade-off between the interpretability and modularity of the two-stage approach and jointly specified spatio-temporal models. The results illustrate how classical point process inference, combined with time series methods, yields interpretable and competitive forecasts of urban crime patterns.", "id": "Paper/65290", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65290"}, {"title": " Higher-order Singularities of Pentads ", "webprogram_exclude": "0", "session_ids": ["Session/18042"], "source_sha256": "29915ab75af5b8cc4ec48b135c06ace72c5767430fed056b0c37308e83d6885b", "withdrawn": "", "abstract": "A pentad is a five-bar planar mechanisms consisting of two triangles connected by three line segments, also known as a 3(RR) mechanism. It is the unique five-bar arrangement that is not decomposable into triangles. A general pentad is a structure, that is, its links can only be assembled in at most six configurations, these being nonsingular isolated solutions of the pentad ideal. However, for special pentads, singular assemblies exist. These are called \"shaky\" structures, because with joint clearance or link elasticity, significant motion away from the singularity becomes possible. Classical methods from kinematics can construct pentads with singular assembly configurations of multiplicity up to~3. We derive conditions for singularities up to order~6, the maximum possible for an isolated solution, and use numerical algebraic geometry to describe the solution sets. This includes finding the multiplicity 4 singularities of planar 3(RPR) robots and determining how to add a fifth link to a given four-bar linkage to construct pentads of multiplicity 4, 5, or 6. Furthermore, an unexpected symmetry leads to the construction of a six-bar 4(RR) linkage with multiplicity 6. The motion capability of a multiplicity 6 pentad will be demonstrated using a physical model.", "id": "Paper/65293", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65293"}, {"title": " Width, Intersection, and Index ", "webprogram_exclude": "0", "session_ids": ["Session/17803"], "source_sha256": "b83ed1a81f5b7e03f3d56d6cbc3b686e3abce7e5257e7157bcd6d34f553968db", "withdrawn": "", "abstract": "Gromov's p-widths, $\\{\\omega_p\\}_{p=1}^{\\infty}$ are a set of invariants on Riemannian manifolds that have played an important role in the construction of minimal hypersurfaces via min-max. Deemed the \"volume spectrum\", each invariant gives rise to an embedded minimal hypersurface in dimensions $3$ and higher, generically with multiplicity $1$. In dimension $2$, the story is different, as the p-widths yield only immersed geodesics. Moreover, many of the index bounds associated to the p-widths in higher dimensions fail on surfaces. In this talk, I will present some inequalities relating the parameter $p$, the index of the geodesics associated to $\\omega_p$, as well as the number of intersections between such geodesics.", "id": "Paper/65294", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65294"}, {"title": " The chromatic symmetric function of graphs glued at a single vertex ", "webprogram_exclude": "0", "session_ids": ["Session/18359"], "source_sha256": "72819c20549cfbfb333ab1351748330b52a998b894e9321ff7f1a2280a057a42", "withdrawn": "", "abstract": "We describe how the chromatic symmetric function of two graphs glued at a single vertex can be expressed as a matrix multiplication using certain information of the two individual graphs. We then prove new $e$-positivity results by using a connection between forest triples, defined by the first author, and Hikita's probabilities associated to standard Young tableaux. Specifically, we prove that gluing a sequence of unit interval graphs and cycles results in an $e$-positive graph. We also prove $e$-positivity for a graph obtained by gluing the first and last vertices of such a sequence. This generalizes $e$-positivity of cycle-chord graphs and supports Ellzey's conjectured $e$-positivity for proper circular arc digraphs.", "id": "Paper/65295", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65295"}, {"title": " Robust rank adaptive factorization of kernel matrices by interpolation and sketching ", "webprogram_exclude": "0", "session_ids": ["Session/18032"], "source_sha256": "dc4ea4ef6200943d46ae493d70f52bcbaeb942dec6edc40f7de012f6f07a127c", "withdrawn": "", "abstract": "Kernel matrices arise in a wide array of applications including integral equations, spatial statistics, and machine learning. We consider the common setting in which one can evaluate entries of a kernel matrix $A \\in \\mathbb{C}^{m\n\\times n}$ given by $A(i,j) := K(x_i, y_j)$, where $\\{y_j\\}_{j=1}^n \\subset \\Omega_s$ is a set of \\textit{source points} and $\\{x_i\\}_{i=1}^m \\subset \\Omega_t$ is a set of \\textit{target points}. For many common kernels $K$, the matrix $A$ is numerically low-rank if the source and target domains $\\Omega_s, \\Omega_t \\subset \\mathbb{R}^d$ are sufficiently well separated.\n\nWe introduce a novel randomized algorithm for computing low-rank approximations of kernel matrices $A$ which combines the robustness of sketching methods such as the recently-introduced IterativeCUR with the efficiency of entry evaluation methods such as adaptive cross approximation. The central idea of our approach is to introduce a set of interpolation points $\\{z_i\\}_{i=1}^R$ in the target domain $\\Omega_t$ with $r < R < \\min(m,n)$, sketch the map from sources to interpolation points, then interpolate the sketch to the target points. This reduces the cost of computing a sketch $AG$ where $G \\in \\mathbb{R}^{n \\times \\ell}$ is a random matrix with i.i.d. standard Gaussian entries from $\\mathcal{O}(mn\\ell)$ to $\\mathcal{O}\\big(\\ell R(m + n)\\big)$ operations. We then use this approximate sketch both to choose pivots in an incomplete LU factorization of $A$ and to estimate the residual error iteratively. This results in a robust low-rank approximation algorithm with $\\mathcal{O}\\big(\\ell (R + r^2)(m + n)\\big)$ total complexity.\n\nWe derive probabilistic guarantees for the accuracy of our approach, provide numerical comparisons to adaptive cross approximation and the proxy point method, and illustrate several applications to integral equations and kernel learning.", "id": "Paper/65297", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65297"}, {"title": " Cohomology of matrix points on varieties ", "webprogram_exclude": "0", "session_ids": ["Session/17954"], "source_sha256": "5e90c36ef11531f51917e2ace8bb9659412c96dc5616b48f8c1c6a4b53036ed8", "withdrawn": "", "abstract": "In algebraic geometry, we are used to studying the geometry of solutions of polynomial equations in real numbers, complex numbers, other fields, and other commutative rings. But how about solutions in non-commutative algebras, such as the matrix algebra? We show that while the space of ``matrix points'' over a vareity can be very complicated, its (singular) cohomology ring can be uniformly determined in terms of that of the base variety.", "id": "Paper/65304", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65304"}, {"title": " A DNN Biophysics Model with Topological and Electrostatic Features ", "webprogram_exclude": "0", "session_ids": ["Session/18026"], "source_sha256": "ee71e22120cf1c09c71fcc480639210d8b09a4ef34e125487f7d3cc216bc455e", "withdrawn": "", "abstract": "In this project, we present a deep neural network (DNN)-based biophysics model that uses multi-scale and uniform topological and electrostatic features to predict protein properties, such as Coulomb energies or solvation energies. The topological features are generated using element-specific persistent homology (ESPH) on a selection of heavy atoms or carbon atoms.  The electrostatic features are generated using a novel Cartesian treecode, which adds underlying electrostatic interactions to further improve the model prediction. The optimal models trained on more than 17,000 proteins for predicting Coulomb energy and trained on more than 4,000 proteins for predicting solvation energy show the efficiency and fidelity of these features in representing the protein structure and force field. The feature generation algorithms also have the potential to serve as general tools for assisting machine learning based  prediction of protein properties and functions.", "id": "Paper/65305", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65305"}, {"title": " The Sharp Discrete Hardy Inequality on <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.605ex\" height=\"2.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -1006.6 1121.4 1152.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbb {Z}^3</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJAMS-5A\" d=\"M39 -1Q29 9 29 12Q29 23 60 77T219 337L410 648H364Q261 648 210 628Q168 612 142 588T109 545T97 509T88 490Q85 489 80 489Q72 489 61 503L70 588Q72 607 75 628T79 662T81 675Q84 677 88 681Q90 683 341 683H592Q604 673 604 666Q604 662 412 348L221 37Q221 35 301 35Q406 35 446 48Q504 68 543 111T597 212Q602 239 617 239Q624 239 629 234T635 223Q635 215 621 113T604 8L597 1Q595 -1 317 -1H39ZM148 637L166 648H112V632Q111 629 110 622T108 612Q108 608 110 608T116 612T129 623T148 637ZM552 646Q552 648 504 648Q452 648 450 643Q448 639 266 343T77 37Q77 35 128 35H179L366 339L552 646ZM572 35Q581 89 581 97L561 77Q542 59 526 48L508 37L539 35H572Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJAMS-5A\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-33\" x=\"943\" y=\"581\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/17804"], "source_sha256": "2fc14d600720631183786b30aceb0960840dcb40cc194ee8efd067d72fed8460", "withdrawn": "", "abstract": "We establish the sharp Hardy inequality for the standard discrete Laplacian on $\\mathbb{Z}^3$. For every finitely supported function $u:\\mathbb{Z}^3\\to\\mathbb{C}$, \\[ \\langle u,\\mathcal{L}_3u\\rangle = \\sum_{x\\in\\mathbb{Z}^3}\\sum_{j=1}^3 |u(x+e_j)-u(x)|^2 \\geq \\frac14\\sum_{x\\neq 0}\\frac{|u(x)|^2}{|x|^2}. \\] The constant $1/4$ is optimal and coincides with the sharp constant in the classical three-dimensional Hardy inequality. Equivalently, it gives the sharp coupling constant for the nonnegativity of the discrete Schrödinger quadratic form associated with the Euclidean inverse-square potential. In fact, we prove a stronger inequality with an explicit strictly positive remainder, which also implies that equality is not attained by any nonzero finitely supported function. The proof is constructive: we introduce an explicit reciprocal edge field and use an edgewise completion of squares to produce a lattice Hardy weight. A concavity argument yields the required inverse-square lower bound, while an explicit minimizing sequence establishes sharpness.", "id": "Paper/65306", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65306"}, {"title": " Isogeny-Torsion Graphs of Some Quadratic Number Fields ", "webprogram_exclude": "0", "session_ids": ["Session/19356"], "source_sha256": "e797483a4ef88c475dd87d5cca5891875b3f22d73c73cfeb595c602b9c00c150", "withdrawn": "", "abstract": "An elliptic curve over a number field $K$ is a smooth projective curve E with a point defined over $K$. By the Mordell-Weil theorem, the $K$-rational points on elliptic curves form a finitely generated abelian group. Isogenies of elliptic curves are maps between elliptic curves which are also group homomorphisms. We can organize isogeny classes into graphs and label the vertices with the torsion structure of corresponding elliptic curves. These graphs are called isogeny-torsion graphs, and in 2021, Chiloyan and Lozano-Robledo classified all isogeny torsion graphs over $\\mathbb{Q}$. In this talk, we explore progress on this classification question over other number fields, using work done by Banwait, Najman, and Padurariu extending Mazur's theorem. Of particular interest is the quadratic field $K = \\mathbb{Q}(\\sqrt{213})$. This talk is based on joint work with Clayton Boothe, Michael Logal, and Lance E Miller.", "id": "Paper/65307", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65307"}, {"title": " On diassociative graphs of finite loops ", "webprogram_exclude": "0", "session_ids": ["Session/17954"], "source_sha256": "3213db472f7822de8a26209c7ff3bdcb54145f1a0f316cb61b2cb657431a53bc", "withdrawn": "", "abstract": "The diassociative graph of a loop encodes diassociativity combinatorially: vertices are elements, and edges join pairs that generate a group. This construction turns the algebraic question ``which pairs generate a group?'' into a graph-theoretic one, revealing the distribution of group-generating pairs in nonassociative loops. In this talk, I will present a systematic study of diassociative graphs, with a particular focus on loops that arise naturally from the quaternion groups. I will then introduce the diassociative number of a loop, which counts the number of its non-group-generating pairs, and present bounds for loops of a fixed order. Finally, I will identify families of loops that attain extremal values, and outline open questions for future work.", "id": "Paper/65314", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65314"}, {"title": " Complex Stochastic Gradient Descent: Convergence and Directional Bias in Reproducing Kernel Hilbert Spaces ", "webprogram_exclude": "0", "session_ids": ["Session/18272"], "source_sha256": "b5adc26f0fd809adca3450d0ac2b03de9c8b5cddbdef16128a509538f22111ee", "withdrawn": "", "abstract": "Complex-valued models arise naturally in many areas of applied mathematics and learning, but the theory of gradient-based optimization in complex spaces is still less developed than in the real setting. In this talk, we develop a framework for gradient descent and stochastic gradient descent (SGD) on complex Hilbert spaces. Using the real Hilbert space structure hidden inside a complex Hilbert space, we obtain convergence results that closely mirror the classical real-valued theory. We then turn to complex reproducing kernel Hilbert spaces and study the solutions selected by the optimization dynamics. We show that familiar directional-bias phenomena continue to hold in this setting, revealing a direct connection between the geometry of the RKHS and the long-time behavior of the learning algorithm. The framework applies naturally to classical spaces from complex analysis, including Fock and Hardy spaces. In these examples, kernel regression leads to constructions involving the superoscillations sequences arising in quantum mechanics and the finite Blaschke products, illustrating how optimization, kernel methods, and complex function theory can interact within a single learning-theoretic framework. This is joint work with Emeric Battaglia.", "id": "Paper/65318", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65318"}, {"title": " Stability in an inverse spectral problem for the magnetic Schrödinger operator ", "webprogram_exclude": "0", "session_ids": ["Session/17965"], "source_sha256": "19d797932a69827315ef9cd07dc897c77d3a32248df92f44d31fb277344f0a62", "withdrawn": "", "abstract": "We show that on a simple Riemannian manifold, the electric potential and the solenoidal part of the magnetic potential appearing in the magnetic Schrödinger operator can be recovered Hölder stably from the boundary spectral data. This data contains the eigenvalues and the Neumann traces of the corresponding sequence of Dirichlet eigenfunctions of the operator. Our proof contains two parts: (1) We show that the boundary spectral data can be stably obtained from the Dirichlet-to-Neumann map associated with the respective initial boundary value problem for a hyperbolic equation, whose leading order terms are a priori known. (2) We construct geometric optics solutions to the hyperbolic equation, which reduce the stable recovery of the lower order terms to the stable inversion of the geodesic ray transform of one-forms and functions.", "id": "Paper/65332", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65332"}, {"title": " A middle order on permutations ", "webprogram_exclude": "0", "session_ids": ["Session/18138"], "source_sha256": "8d138b9110b459012c24121467408cd1461f253027fbf253c892bd3589c18c54", "withdrawn": "", "abstract": "We define a partial order on permutations of a fixed size, which is the image of a natural partial order on inversion sequences. We call this a \"middle order\" because it refines the weak order on permutations and admits the Bruhat order as a refinement. These middle orders are distributive lattices, and they have many nice combinatorial properties. We characterize and enumerate intervals and boolean intervals (in general, and of any given rank), and give a combinatorial interpretation of their Euler characteristic. The restriction of this poset to involutions is less well-behaved, but there is a simple formula for the Möbius function of principal order ideals in that setting.", "id": "Paper/65334", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65334"}, {"title": " CANCELLED A topological view of algebraic structures in <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"6.51ex\" height=\"3.009ex\" style=\"vertical-align: -1.005ex;\" viewBox=\"0 -863.1 2803 1295.7\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\r\n<title id=\"MathJax-SVG-1-Title\">C_p(X)</title>\r\n<defs aria-hidden=\"true\">\r\n<path stroke-width=\"1\" id=\"E1-MJMATHI-43\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"></path>\r\n<path stroke-width=\"1\" id=\"E1-MJMATHI-70\" d=\"M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"></path>\r\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\r\n<path stroke-width=\"1\" id=\"E1-MJMATHI-58\" d=\"M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z\"></path>\r\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\r\n</defs>\r\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\r\n <use xlink:href=\"#E1-MJMATHI-43\" x=\"0\" y=\"0\"></use>\r\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-70\" x=\"1011\" y=\"-213\"></use>\r\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"1171\" y=\"0\"></use>\r\n <use xlink:href=\"#E1-MJMATHI-58\" x=\"1561\" y=\"0\"></use>\r\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"2413\" y=\"0\"></use>\r\n</g>\r\n</svg> \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/19358"], "source_sha256": "32d938455d329f874f1de8cc5a7d70e01992cded71eb0b216c82e31c1e23af5f", "withdrawn": "w", "abstract": "For a Tychonoff space $X$, $C(X)$ denotes the ring of real-valued continuous functions on $X$. This ring, equipped with the topology of pointwise convergence, is denoted by $C_p(X)$. In this article, we investigate the connection between the algebraic structure of $C(X)$ and the function space $C_p(X)$ by studying various properties of idelas and subrings of $C(X)$. For any ideal $I$ of $C(X)$, we establish that its closure in this space is of the form\n$$cl(I)=\\{f\\in C(X): \\bigcap\\limits_{g\\in I}Z(g)\\subseteq Z(f)\\}$$\nwhere $Z(f)$ denotes the zero set $\\{x\\in X:f(x)=0\\}$ of $f$. Using this result, we characterise several well-known topological spaces. For instance, $X$ is locally compact if and only if the ideal $C_K(X)$ of all continuous functions with compact support is dense in $C_p(X)$. It follows that every closed ideal is a $z$-ideal. However, the converse does not hold, since every free ideal is dense. Moreover, a principal ideal is closed if and only if it is a $z$-ideal. We eventually find out that every closed ideal is a $z^0$-ideal if and only if $X$ is an almost $P$ space. We further show that every essential ideal is dense if and only if $X$ is discrete, whereas every essential ideal is closed if and only if $X$ is finite. We obtain that a subring of $C(X)$ containing all constant functions is dense in $C_p(X)$ if and only if it separates points. Furthermore, we establish that every intermediate ring is closed (or, open) in $C_p(X)$ if and only if $X$ is pseudocompact. Beyond ideals and subrings, we also determine the closures of several well-known subsets of $C(X)$ in $C_p(X)$. The set of all divisors of zero is either closed or dense, according as $X$ is finite or infinite. Moreover, the set of units is dense if and only if $X$ is totally separated.\n\\begin{enumerate}{References:}\n\\item L. Gillman and M. Jerison, Rings of Continuous Functions, Springer, London (1976).\n\\item V. V. Tkachuk, A $C_p$-Theory Problem Book - Topological and Function Spaces, Springer, New York (2011).\n\\end{enumerate}", "id": "Paper/65336", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65336"}, {"title": " Anomaly Wars 4: A New Hope ", "webprogram_exclude": "0", "session_ids": ["Session/18097"], "source_sha256": "98e329005ca358049395dbed069331e2d819224d2bbbab246e99e0c362e35166", "withdrawn": "", "abstract": "Necessary and sufficient conditions are useful for the identification of ranked-choice voting anomalies, both for theoretical and computational purposes.  Unfortunately, such conditions are often hard to find and are not always useful in real-world elections where not all criteria are met.  In this talk, we show how computational tools can expand both the discovery and applicability of necessary and/or sufficient conditions, with a focus on monotonicity anomalies in instant runoff elections.", "id": "Paper/65341", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65341"}, {"title": " Using Graph Theory to Analyze Two-Way Train Tracks ", "webprogram_exclude": "0", "session_ids": ["Session/19366"], "source_sha256": "35e6183295d1dd83f1d30b296fa58e1c7e9aebe8a4361eb8f5b71948140007c2", "withdrawn": "", "abstract": "In this talk we introduce ever-changing directed graphs as a way to model train track configurations.  We see that there are many challenges that arise using such a model, as ever-changing directed graphs are neither directed nor undirected in the conventional sense.  To address this, we develop a method for constructing truly directed graphs to model a train's movement in a configuration.  This technique will allow us to determine the characteristics that are necessary of certain train track configurations so that tracks can be traversed in both directions - regardless of starting position and direction.", "id": "Paper/65342", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65342"}, {"title": " Only finitely many modular Jacobians are supersingular modulo a given prime ", "webprogram_exclude": "0", "session_ids": ["Session/18276"], "source_sha256": "2bfb33f75e5fa41796bbc5899ad35294647cd68b824aec06fb3a7ddc2f763fbc", "withdrawn": "", "abstract": "We study supersingularity of modular Jacobians $J_0(N)$ and abelian varieties $A_f$ of $\\mathrm{GL}_{2}$-type from both the vertical perspective (where the prime $p$ is fixed, and the level $N$ varies) and the horizontal perspective (where the newform $f$ is fixed, and the prime $p$ varies). Vertically, we prove that for any given prime $p$, $J_{0}(N)$ is supersingular modulo $p$ for only finitely many levels $N$. Horizontally, we show that for sufficiently large $p$, the reduction of $A_f$ modulo $p$ is supersingular if and only if it isogenous to a power of a supersingular elliptic curve.", "id": "Paper/65363", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65363"}, {"title": " Murmurations in Short Intervals for Elliptic Curves ", "webprogram_exclude": "0", "session_ids": ["Session/18239"], "source_sha256": "1a925c0f6d743e1f91c088aa8344c246198a3c99fd019c6c8a640b768e8c0a79", "withdrawn": "", "abstract": "Murmurations are the phenomenon that the average value of $\\epsilon(E) a_p(E)$, the $p$-th $L$-function coefficient weighted by the root number, over elliptic curves of conductor in some range $N(E) \\in [N_1, N_2]$ seem to approximate a continuous, oscillating function. Recent work by Sawin and Sutherland uses an alternative formulation of murmuration where curves are ordered by naive height instead of conductor. For murmurations to appear in this setting, one has to first average $\\epsilon(E) a_p(E)$ for a single curve over $p \\in (C_1, C_2)$ and then average over elliptic curves of bounded height. However, currently known results average over all of $\\mathbb{N}$ instead of a small interval $(C_1, C_2)$. Our work explores how small the interval $(C_1, C_2)$ can be for the conclusion to still hold.", "id": "Paper/65369", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65369"}, {"title": " Eigenvalue statistics for elements in the group ring of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.499ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 645.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">S</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-53\" d=\"M308 24Q367 24 416 76T466 197Q466 260 414 284Q308 311 278 321T236 341Q176 383 176 462Q176 523 208 573T273 648Q302 673 343 688T407 704H418H425Q521 704 564 640Q565 640 577 653T603 682T623 704Q624 704 627 704T632 705Q645 705 645 698T617 577T585 459T569 456Q549 456 549 465Q549 471 550 475Q550 478 551 494T553 520Q553 554 544 579T526 616T501 641Q465 662 419 662Q362 662 313 616T263 510Q263 480 278 458T319 427Q323 425 389 408T456 390Q490 379 522 342T554 242Q554 216 546 186Q541 164 528 137T492 78T426 18T332 -20Q320 -22 298 -22Q199 -22 144 33L134 44L106 13Q83 -14 78 -18T65 -22Q52 -22 52 -14Q52 -11 110 221Q112 227 130 227H143Q149 221 149 216Q149 214 148 207T144 186T142 153Q144 114 160 87T203 47T255 29T308 24Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-53\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-arithmetic groups associated with a quaternion orders ", "webprogram_exclude": "0", "session_ids": ["Session/17954"], "source_sha256": "45a8c611e2d0173037c6bca0e960ca6c0f22d89355a719292a3fc7c1eed8f879", "withdrawn": "", "abstract": "Let $\\Gamma = \\langle g_0, \\ldots, g_d\\rangle$ be a subgroup of $G = \\frac{D^*}{Z(D^*)}$ where $D$ is a quaternion algebra over an algebraic number field $k$ and let \n\\[z = a_0 g_0 +\\cdots +a_d g_d = \\overline{a_0}g_0^{-1} + \\cdots + \\overline{a_d}g_d^{-1} = z^*\\in \\mathbb{C}[\\Gamma]\\]\n be a self adjoint formal linear combination of elements of $\\Gamma$ then a unitary representation $\\pi:\\Gamma\\rightarrow U(V)$ gives rise to a linear operator $\\pi(z) = a_0\\pi(g_0) + \\cdots a_d\\pi(g_d)$ on $V$ and we may study its spectral measure. When $V = \\ell^2(\\Gamma)$ and $\\pi$ is the regular representation we call this measure the Kesten measure of $z$. \n\nViewing $z$ at the infinite place yields a compact group that decomposes into finite dimensional irreps via the Schur-Weyl theorem. At the finite places one gets family of operators which are slight generalizations of adjacency operators for Cayley graphs on projective linear groups.\n\nWe will discuss the bulk, spacing, and edge statistics for the families associated with a few elements, $z\\in\\mathbb{C}[G]$. Including the element giving rise to the famous Ramanujan Graphs of Lubotzky, Phillips, and Sarnak which is an element of $\\mathbb{Z}[F_k]$ and an element associated with the Quaquaversal Tiling of Conway and Radin living in $\\mathbb{Z}[G_{4,6}]$. We will show that the bulk statistics converge to the Kesten measure in the weak-* sense for a large class of elements; We will prove Ramanujan type bounds for a smaller class of elements; And we will make some conjectures about local eigenvalue spacing statistics.", "id": "Paper/65371", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65371"}, {"title": " The quaternion Brauer monoid ", "webprogram_exclude": "0", "session_ids": ["Session/18336"], "source_sha256": "fdabc52f24753dc5d46c3b42d5af702f6d18232c549f42abb6ead9740f33dfb4", "withdrawn": "", "abstract": "Quaternion algebras generate the 2-torsion in the Brauer group of a field, and two quaternion algebras may be composed whenever they are linked by a common separable quadratic subalgebra.  We extend this composition to quaternion rings, and we describe the resulting monoid in cases of arithmetic interest.", "id": "Paper/65375", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65375"}, {"title": " Towards a better understanding of airborne transport of Infectious respiratory particles ", "webprogram_exclude": "0", "session_ids": ["Session/19343"], "source_sha256": "7209cf0d76d50203a81cb29a372bddc988c3a7db8410073b4cab2571e20d2647", "withdrawn": "", "abstract": "Emerging and re-emerging respiratory pathogens are known to continually pose major public health hazards with adverse implications as conclusively evidenced by the recent SARS-CoV-2 pandemic.  Mathematical modeling must continue to provide insights into the mechanisms of virus transmission and help develop strategies for effective treatment and mitigation. As the challenges are multifaceted, our multidisciplinary approach brings together dynamical systems/fluid flow perspectives, computational fluid dynamics simulations, and optimization techniques.  The aim is to better understand the transport of infectious respiratory particles in a standard classroom and extend the understanding to predicting beyond the simulated classroom scenario.", "id": "Paper/65379", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65379"}, {"title": " Arithmetic Triangle Groups and their Topographs \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18336"], "source_sha256": "8ebbacfeba7c4a3dd715e15350074b7cef4628c8fdc03dc9337e627c7543b76e", "withdrawn": "", "abstract": "When one thinks of \\textit{triangle groups}, one likely thinks of triangular tessellations. Such triangular tessellations may be of the sphere, Euclidean plane, or hyperbolic plane - depending on the sum of the interior angles of the triangles. So on one side of the spectrum, triangle groups correspond to geometry, on the other side we see number theory. This beautiful connection often arises when the triangle group is \\textit{arithmetic} (commensurable with the norm-$1$ unit group of an order in a quaternion algebra). Takeuchi classified and tabulated exactly which hyperbolic triangle groups are arithmetic, but his classification does not provide a direct construction for the algebra or order based on the defining relations of the triangle group itself. We will provide such a construction.\n\nThis research is also inspired by John H. Conway. He built a surprising geometric arrangement of numbers --- called a \\textit{topograph} --- which describes the arithmetic structure for $M_2(\\mathbb{Z})$ through symmetries, incidence relations, and other geometric aspects. In this spirit, we build \\textbf{triangular topographs}: geometric structures describing the relationship between a triangle group, a triangular tiling, and the arithmetic of the related quaternion order and algebra. We will provide examples for several spherical cases.\n\nThis work is joint with Martin Weissman.", "id": "Paper/65389", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65389"}, {"title": " Topology and Geometry of Neural Connectivity of Eating and Drinking Behaviors under Deprivation ", "webprogram_exclude": "0", "session_ids": ["Session/18320"], "source_sha256": "b6004d336d54337cec56fb78c194601734a4933b5f58fc69f65db31148118fff", "withdrawn": "", "abstract": "In a joint project with the Stern Lab at the Max Planck Florida Institute for Neuroscience, we performed various analyses on neural and behavioral datasets obtained from the insular cortex of food-deprived and water-deprived mice. Our findings suggest that there are two different underlying neural manifolds for neural point clouds associated to the two ingestion behaviors and that neural connectivity happening around ingestion events are rather influenced by the corresponding behaviors than by the types of deprivation.", "id": "Paper/65399", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65399"}, {"title": " Topological Data Analysis and Dynamical Systems for Robust, Trustworthy, and Adaptive Intelligence ", "webprogram_exclude": "0", "session_ids": ["Session/18114"], "source_sha256": "cd6e38f830bd75d0b64546d5913dae07f102559b3a8e883af9b99414733e367e", "withdrawn": "", "abstract": "Time-evolving point clouds are common in scientific data. Their geometric structure has meaning in a range of AI/ML applications, but modeling the evolution of this structure over time remains challenging. For many models in topological and geometric machine learning, the heart of this challenge lies with the introduction of a second parameter, time, to the classical concept of single-parameter persistent homology across distance. Time brings a range of theoretical and algorithmic complexities which are compounded by the need to model successive time steps using a zigzag of interconnected simplicial complexes, rather than a simple filtration. Nevertheless, multiple research efforts have recently made headway on this problem.\n\nThis talk presents a new tool for the challenge: a flexible algorithm to compute zigzag homology barcodes for arbitrary connected paths through 2d space of parameters (filtration value and time). Domain scientists can use these paths to identify homological features which persist along both dimensions. Model developers can use them to access new data primitives, e.g. induced maps on homology and cycle representatives, which have been difficult to obtain historically, using existing software. This algorithm scales similarly to classical single-parameter persistent homology, both asymptotically and in practice.", "id": "Paper/65402", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65402"}, {"title": " Multi-subspace power method for decomposing partially symmetric tensors ", "webprogram_exclude": "0", "session_ids": ["Session/18355"], "source_sha256": "d2e1bf177ac639491250b2a64652d76f03c9ce785f5aff831d019620e8937f17", "withdrawn": "", "abstract": "We present an algorithm for low rank decomposition of tensors of any symmetry type, from fully asymmetric to fully symmetric. It recovers the decomposition one summand at a time via the higher-order power method. This approach is known to fail in general: there need not be a relationship between the summands of a decomposition and the (partially symmetric) singular vector tuples (pSVTs) of the tensor. Our approach overcomes this problem by transforming the input to a tensor with orthonormal slices, via orthogonalization of a flattening. The summands of the decomposition of the original tensor can be recovered from the pSVTs of this new transformed tensor. We introduce a shifted power method for computing pSVTs and prove its global convergence. Numerical experiments demonstrate that our algorithm achieves higher accuracy and faster runtime than existing methods.", "id": "Paper/65405", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65405"}, {"title": " A sharp analysis of Root-MUSIC: locations of correct and extraneous roots ", "webprogram_exclude": "0", "session_ids": ["Session/18305"], "source_sha256": "524df0179ed9cc4b9a2d5c328cac365f79cf8fab97e08db655043c39158af1d0", "withdrawn": "", "abstract": "Spectral estimation is an area of research within signal processing concerned with determining the frequencies of a signal based on finite uniform samples disrupted by noise. There exists a family of highly celebrated spectral estimation algorithms referred to as subspace methods which are widely known and readily available to the general public. Root-MUSIC is one such algorithm that approximates the signal's frequencies by constructing a high-degree polynomial and finding a subset of roots which are closest to the complex unit circle. We prove that the selection process chooses the relevant roots of the polynomial, and provide sharp, non-asymptotic, and explicit error bounds for the accuracy of the selected roots in terms of fundamental model parameters. All results hold under a natural separation condition on the correct signal frequencies and are applicable to several versions of the problem which are used in practice.", "id": "Paper/65410", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65410"}, {"title": " Definable Poems ", "webprogram_exclude": "0", "session_ids": ["Session/18216"], "source_sha256": "66faf4c76b6ddf61bf104699cf6e1d38aeb0140653b5fae1da8c88fb9c623d37", "withdrawn": "", "abstract": "Mathematical logicians and poets share a preoccupation: what can be said in a restricted, and typically impoverished, language? The logician asks which objects and relations are definable in a given formal language, and finds that severe restrictions often leave surprising expressive power intact. The poet working under constraint takes up a version of the same question, in a setting where an answer is judged by what it does to a reader.\n\nWe pursue this question in both settings, with some attention to definability in restricted languages and with examples drawn from constrained poetry. Mathematics and poetry are forms of symbolic manipulation, and each, at its best, changes the way we experience what it touches.\n\nWe close with remarks on teaching, where this shared question can invite students into an appreciation of both subjects.", "id": "Paper/65411", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65411"}, {"title": " From Particle Diffusion to Mixture Dynamics: Quantitative Hydrodynamic Limits for the Vlasov–Fokker–Planck/Navier–Stokes System ", "webprogram_exclude": "0", "session_ids": ["Session/18445"], "source_sha256": "42033fdd5e8310a1ccee2249d2897adbc9d107404b30e2e0f65c6469236cdf38", "withdrawn": "", "abstract": "The fluid–particle suspensions can be modeled by a Vlasov–Fokker–Planck kinetic equation coupled with the incompressible Navier–Stokes fluid equations. In this talk, I will present the quantitative hydrodynamic limits of this kinetic–fluid system under the light and fine particle scalings.\nIn the light-particle regime, relaxation toward a centered Maxwellian leads to the Navier–Stokes–Kramer–Smoluchowski system, in which the particle density satisfies an advection–diffusion equation. A Hilbert expansion and refined macro–micro energy estimates yield global-in-time pointwise convergence with an explicit rate near equilibrium. In the fine-particle regime, relaxation occurs toward a moving local Maxwellian centered at the fluid velocity, and the limit is an inhomogeneous incompressible Navier–Stokes system for the fluid–particle mixture. An weighted macro–micro energy method, together with a hidden damped wave structure, gives quantitative pointwise convergence without requiring the limiting profile to be necessarily small. The talk will emphasize how different scalings of the same model determine distinct equilibrium structures, macroscopic limits and analytical mechanisms.", "id": "Paper/65420", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65420"}, {"title": " So-Thompson‘s Proof of Upper Bild Convexity via Convex Optimization ", "webprogram_exclude": "0", "session_ids": ["Session/17942"], "source_sha256": "aa8f4614fa4a603ba26d33cac14ac442b4f52fae538b35adc6d61f63a03fc628", "withdrawn": "", "abstract": "The quaternionic numerical range of a matrix is generally nonconvex.\nNevertheless, So and Thompson [1] proved that its intersection with the\nclosed upper half of the complex plane, called the upper bild,\nis always convex. Their proof reduces the problem to the\n\\(2\\times 2\\) case and relies on an explicit analysis of the boundary\ncurves. In particular, the upper boundary is identified with a portion\nof the boundary of the complex numerical range of the associated\ncomplex representation and is therefore concave, while the convexity\nof the two nonreal branches of the lower boundary is established by\nshowing that their derivatives are monotonically increasing.\n\nIn this talk, we present an alternative geometric proof. We first use\nthe fact that the intersection of the upper bild with any vertical line\nis either empty or connected. Consequently, its convexity follows once\nthe upper boundary is shown to be concave and the lower boundary to be\nconvex. The main new ingredient is a geometric treatment of the lower\nboundary in the generic \\(2\\times 2\\) case. We reformulate the relevant\nminimization problem as the distance from an affinely moving point to a disk whose radius is a concave function of the vertical-fiber\nparameter. This reformulation yields the convexity of the lower\nboundary directly and provides a more geometric alternative to the\nderivative-based argument of So and Thompson.\n\n\\vspace{3em}\n \n[1] W. So and R. C. Thompson, “Convexity of the upper complex plane part of the numerical range of a quaternionic matrix,” Linear and Multilinear Algebra, vol. 41, no. 4, pp. 303–365, 1996.", "id": "Paper/65421", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65421"}, {"title": " Forced condensation and anti-condensation on heavy-tailed networks ", "webprogram_exclude": "0", "session_ids": ["Session/19351"], "source_sha256": "3e3bd4c44d19b9d64b0d873501e35367927a45663534d8ddfc0fce7d299910b9", "withdrawn": "", "abstract": "We study a driven selection mechanism on a fixed heavy-tailed network. At each step fresh mass is injected, its direction is recomputed from the current mass profile by a power-normalization rule, and the combined mass is transported by a primitive mixing matrix. The exponent $\\theta$ controls the feedback. Positive values give more weight to larger coordinates, while negative values favor smaller ones. When $\\theta=0$, the injected mass is distributed uniformly. After deterministic growth of the total mass is scaled out, an explicit mixing--forcing condition ensures that the injection profile converges to a nonlinear Perron--Frobenius-type fixed point on the simplex. Hilbert's projective metric gives a simple way to understand the stability of the system. The discounted network response brings positive profiles closer together, while the escort map scales their projective distance by $|\\theta|$. On heavy-tailed networks this fixed point separates three effects that are often conflated: response or degree tilt, anomalous inverse-participation-ratio scaling, and genuine few-node localization. Positive feedback selects high-response nodes and, when response follows degree, a hub-directed branch. Negative feedback selects low-response nodes and typically produces a broad peripheral cloud unless the lower tail of the response field is itself thin. Numerical calculations on finite networks illustrate convergence, forcing-rate dependence, and the sign law. Monte Carlo calculations for truncated heavy-tailed response profiles illustrate the predicted participation-ratio crossover, while a uniform comparison bound states when this benchmark scaling transfers to the full fixed point. This mechanism is different from both conserved-mass condensation and graph growth. Instead, feedback selects a non-equilibrium profile on a fixed, heterogeneous network.", "id": "Paper/65426", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65426"}, {"title": " From Tool to Participant: Reconsidering AI Chatbots’ Roles in Mathematical Proving Activities ", "webprogram_exclude": "0", "session_ids": ["Session/18137"], "source_sha256": "1f7f0697601c4652ca776fc441743441bf797aa682f6aaeceea5313c2b26cbd5", "withdrawn": "", "abstract": "A central question in AI chatbot-mediated mathematics classrooms is whether an AI chatbot is merely a tool for students or can become a participant in mathematical activity. This talk explores this question through the lens of collective argumentation, focusing on how students and AI chatbots interact by proposing, explaining, justifying, comparing, rebutting, or evaluating ideas toward the shared goal of producing mathematical proofs. Drawing on students’ experiences with AI chatbot-mediated proof revision, we examine how students understand and position the chatbot as they interact with its contributions. Students first constructed mathematical arguments independently and then engaged with an AI chatbot to evaluate and revise their arguments, attending to mathematical validity and completeness. Their written reflections following these interactions suggest that students’ perceptions and positioning of the chatbot are dynamic and evolve through engagement with its responses. Across their reflections, students positioned the chatbot as a source of ideas, an evaluator of their arguments, or an unreliable contributor whose responses required scrutiny and verification. We will present perspectives from two groups of college students: non-STEM majors in a mathematics pathway course and prospective K-6 teachers in a mathematics content course. Rather than focusing solely on whether AI chatbots improve students’ arguments, this talk centers on how students interact with AI-generated contributions. It examines how students challenge, accept, or reject these inputs and how these actions relate to their perceptions of chatbots’ roles in their proof work. The talk concludes with implications for designing AI chatbot-mediated proof-writing activities that support students in constructing, evaluating, and revising mathematical arguments while also encouraging them to examine AI chatbots’ contributions and limitations critically.", "id": "Paper/65429", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65429"}, {"title": " Stability of Finite-Batch Particle Mean-Field Variational Inference Beyond Strong Convexity ", "webprogram_exclude": "0", "session_ids": ["Session/18280"], "source_sha256": "f11820e60efb632c5451f5445cd53450a9e046a5cfe12b8e7f038e237c129716", "withdrawn": "", "abstract": "We study the implementable finite-batch particle algorithm for mean-field\nvariational inference as a fully discrete stochastic approximation of the\nprojected Wasserstein dynamics.  The target potential is globally smooth but\nneed not be strongly convex.  The departure from contractivity is quantified by the curvature defect\n\\[\n\\mathfrak d_\\alpha(x,y)\n=\n\\bigl[\\alpha\\|x-y\\|^2-\n\\langle\\nabla V(x)-\\nabla V(y),x-y\\rangle\\bigr]_+,\n\\]\nwhich is the additive loss in the one-step Euler contraction estimate.  We prove a\nnon-asymptotic Wasserstein stability bound that separates\ninitialization, product-empirical approximation, finite-batch drift error,\ntime discretization, and the defects accumulated along the coupled\ntrajectories.  Under the uniform bound $\\mathfrak d_\\alpha\\leq\\beta$, the\nparticle iterates remain within $O(\\sqrt{\\beta/\\alpha})$ of any MFVI\nminimizer, up to explicit errors in the particle number, batch size, and step\nsize.  The proof uses a stationary comparison array whose population law is\nan MFVI minimizer but whose particle-level law is a random product empirical\nmeasure, and it controls the resulting projected-drift discrepancy\nexplicitly.  We also give coordinatewise defect estimates and structural\nconditions for dimension-independent projected-drift sensitivity, construct\nan arbitrary-dimensional smooth nonconvex benchmark with a closed-form MFVI\nminimizer, and explain why polynomially growing drifts require a modification\nof the untamed explicit scheme. This is a joint work with Vinh Nguyen at UC Berkeley.", "id": "Paper/65431", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65431"}, {"title": " Resolution of Coquaternion Singularities in Transformation of Biologic Functions ", "webprogram_exclude": "0", "session_ids": ["Session/18336"], "source_sha256": "9f9eaaa29b506c123a0add03906e01c2fe80c0ee4c0ca824ca8d4cc82f556930", "withdrawn": "", "abstract": "In biologic systems only three universal regulatory elements are known: negative feedback, positive feedback and reciprocal links. These elements provide functional regulation of biologic systems on molecular, cellular and organ level.  In dynamical systems the second order matrices are the simplest form determining a regulatory structure of these functional patterns, represent a basis of the Lie algebra of a special linear group sl(2,R). A unit matrix being added to this basis endows the space spanned by four basis elements with the algebraic structure of coquaternion. States of a BS are visualized as points of the space R3, obtained as the projection along the coordinate related to the unit matrix. The space of indefinite metric is presented by the three families of surfaces obtained as quadratic functions of coquaternion basis.  One- sheet and two-sheet hyperboloids are separated by a null cone presented by vectors of “zero lengths”. Null cone separates two different regulatory mechanisms of a BS - negative feedback and positive feedback. Positive feedback requires much more energy than negative feedback to perform its function. In the conditions of permanent cell renewal processes the energy levels and structural stability are maintained by functional mechanisms when the system bifurcates and switches the structural mechanisms of regulation. When the system undergoes bifurcation it goes through the singularity when crosses the null cone. It seems that physiologic mechanisms are able to resolve singularity by activating the underlying molecular level of biological cells such that it provides smooth transformation of the molecular flows, while on the macro, a biological cell, level it will appear as a jump like process attributed to a bifurcation.", "id": "Paper/65432", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65432"}, {"title": " Mathematical modeling of spatial evolution with applications to biomedical systems ", "webprogram_exclude": "0", "session_ids": ["Session/18350"], "source_sha256": "634983c548b4ecca06cc7efbc4757d0bd51501be0178ddd405c57ce36df68a13", "withdrawn": "", "abstract": "Evolutionary dynamics permeates life and life-like systems. Mathematical methods can be used to study evolutionary processes, such as selection, mutation, and drift, and to make sense of many phenomena in life sciences. Mass-action (or mean-field) evolutionary dynamics have been studied over the last 100 years, and produced an enormous wealth of useful results. In this talk, however, I will discuss how spatial interactions may change the laws of evolution, giving rise to a number of interesting and counterintuitive findings. I will discuss both explicitly spatial systems and metapopulations, and demonstrate a number of scaling laws that describe production and spread of disadvantageous, neutral, and advantageous mutants. Applications of these laws to bacterial growth and carcinogenesis will be discussed.", "id": "Paper/65434", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65434"}, {"title": " Mathematical structure induced by scaled Grasmann numbers ", "webprogram_exclude": "0", "session_ids": ["Session/17954"], "source_sha256": "2832b31877192349d360df8dd0ec200a5ee63b461b22800a4dc2d6522a4dd33f", "withdrawn": "", "abstract": "We introduced generalized Grassmann numbers scaled by the real numbers. The underlying algebraic structures are presented. Analytic, and operator-algebraic properties of such systems are also studied.", "id": "Paper/65435", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65435"}, {"title": " Complexity in Fields and Semifields ", "webprogram_exclude": "0", "session_ids": ["Session/18387"], "source_sha256": "0ce9b1037960c7ee20b5364eff4a2b6a00f1409c6d02799c5a7db790e20d3518", "withdrawn": "", "abstract": "The rank of a tensor has many points of relevance to coding theory. In one direction, it can be studied as the metric for codes consisting of tensors, or as an invariant for rank-metric codes. In the other direction, results from classical coding theory in the Hamming metric provide bounds on the tensor rank and multiplicative complexity of finite field extensions, through for example the results of Brockett and Dobkin from the 1970s. In recent years, this has been extended to consider also finite semifields, which correspond to certain types of MRD codes.\n\nIn this talk we will show new connections between classical coding theory and the tensor rank, providing new bounds and results on the tensor rank of some fields and semifields. We will also discuss the additive complexity of these extensions, link this to to the complexity of encoding in the Hamming metric, and provide new best-known algorithms for field and semifield operations in terms of overall complexity.", "id": "Paper/65440", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65440"}, {"title": " Platonov’s Conjecture on Weak Approximation ", "webprogram_exclude": "0", "session_ids": ["Session/18076"], "source_sha256": "70a9aa6078f05fb2724d1a21eee7946ae46eabe11dc74eee58572fbce1124aaf", "withdrawn": "", "abstract": "Platonov, around 1978, conjectured that all semisimple adjoint groups over arbitrary fields have weak approximation. In this talk I will show that there is an infinite family of fields, with each field admitting infinitely many adjoint groups that fail weak approximation, hence disproving the conjecture. More generally, I will give a criterion for the failure of weak approximation using R-equivalence.", "id": "Paper/65443", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65443"}, {"title": " Invariance of rowmotion for variants of the Tamari lattice ", "webprogram_exclude": "0", "session_ids": ["Session/18334"], "source_sha256": "cbf502ee8936ab188635fd136b2c9088ebadc6f29b99e2aae51557c7db6b591a", "withdrawn": "", "abstract": "Rowmotion is an invertible operator that was originally defined on the set of order ideals of a finite poset and has more recently been extended to act on broader classes of finite lattices, such as semidistributive lattices, trim lattices, and beyond. We show that the rowmotion operator behaves the same on all alt $\\nu$-Tamari lattices for a fixed lattice path~$\\nu$. We use this invariance of rowmotion theorem to establish cyclic sieving and homomesy results in the particular case of the rational Tamari lattices. This is joint work with Ben Adenbaum, Emily Barnard, Cesar Ceballos, Cl\\`ement Chenevi\\'ere, Colin Defant, Sam Hopkins, Matthias M\\\"uller, and Martin Rubey.", "id": "Paper/65444", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65444"}, {"title": " Progress toward generalized action-angle variables for guiding center motion in 3D toroidal fields ", "webprogram_exclude": "0", "session_ids": ["Session/18316"], "source_sha256": "4ee2a2e75ab59060fc64314a129b1377b2a575458c0e5bd7f1e1bf2a6d544291", "withdrawn": "", "abstract": "Action-angle variables simplify the analysis of integrable Hamiltonian systems by transforming phase-space variables into constant actions and linearly evolving conjugate coordinates. These variables are foundational for understanding resonance structures, transport phenomena such as resonant island overlap, and many other applications. Previous work (e.g., Tao et al., Physics of Plasmas, 2007) developed action-angle coordinates for the adiabatic guiding center motion of librating particles in strong magnetic fields with general geometry. In this work, we present progress on extending the perturbative construction to circulating particles in toroidal fields with no symmetry angle.\n\nThis material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Department of Energy Computational Science Graduate Fellowship under Award Number DE-SC0024386.", "id": "Paper/65450", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65450"}, {"title": " Weak-type inequalities and endpoint blowup of the Bergman projection on non-smooth domains ", "webprogram_exclude": "0", "session_ids": ["Session/17887"], "source_sha256": "1fd4c71f10b8c91500e927083db7f4dc560dc4f990f390a2f2fa3b61b0a56489", "withdrawn": "", "abstract": "In this talk, we explore recent results concerning endpoint weak-type regularity of the Bergman projection on Hartogs-like domains in $\\mathbb{C}^n$. We show that the Bergman projection on different generalizations of the Hartogs triangle fails to be well-defined as an integral operator on the entire $L^p$ space, when $p$ is the lower endpoint of the open interval for which the Bergman projection is \nbounded. We then explore this problem in the context of generalized Forelli-Rudin integral operators. This work is joint with L. Chen (ERAU).", "id": "Paper/65452", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65452"}, {"title": " An Algorithm for Computing the Smallest Elated Number of a Given Height ", "webprogram_exclude": "0", "session_ids": ["Session/17921"], "source_sha256": "9d18011b3bdd9ebcda0f74a7efe4ab26e1fa54499c4194ac227a9956f1409ebf", "withdrawn": "", "abstract": "The elated function maps a positive integer to the sum of the squares of its digits, multiplied by the integer's leading digit. A number is elated if it eventually reaches 1 under iteration of the elated function, and the height of a elated number is the number of iterations required to reach 1. The elated function is a variant of the happy function, which has been studied for many years.\nIn 2008, Cai and Zhou published a method for efficiently computing the smallest happy number of any given height.\nIn this talk, we discuss an algorithm to accomplish the same task in the setting of elated numbers, where the landscape is significantly more complicated.\nThis work was started at REUF 2023 at ICERM, and will be presented by Nathan Fox and Rachel Lynn.", "id": "Paper/65453", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65453"}, {"title": " A sharp upper bound on cohomological dimension in unra ", "webprogram_exclude": "0", "session_ids": ["Session/17929"], "source_sha256": "c56e5a5d1117baf7bb2780a541950fd2004009ad0094d8d59a51e184a0bb33df", "withdrawn": "", "abstract": "Given an ideal $I$ in a regular local ring $A$, the cohomological dimension of $I$ in $A$ is the index of the highest non-vanishing local cohomology of $A$ supported at $I$. Determining effective upper bounds on the cohomological dimension in terms of topological invariants of $\\text{Spec}(A/I)$ is a central problem in commutative algebra: foundational results include the Hartshorne--Lichtenbaum Vanishing Theorem and the Second Vanishing Theorem.\n\nIn equal characteristic, Faltings established in 1980 a general bound on the cohomological dimension of an ideal in terms of its “big height”. In this talk, we extend Faltings’ results to the unramified mixed characteristic setting and show that the resulting bound is sharp.", "id": "Paper/65455", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65455"}, {"title": " Observability of Schrödinger equations in Euclidean space ", "webprogram_exclude": "0", "session_ids": ["Session/18326"], "source_sha256": "d5493a8f5ec9cf759a0c9ae22d2a8771c7867daf4fd4c41c3ffd7ae4b4478b20", "withdrawn": "", "abstract": "The Schr\\\"odinger equation is observable from a set if there is a uniform positive probability that\na quantum particle will enter the set in finite time. On the flat torus, the Schr\\\"odinger equation\nis observable from any open set. These results have previously been extended to show periodic\nopen sets can be used to observe the Schr\\\"odinger equation in Euclidean space. In this talk we\nprove observability from non-periodic sets in Euclidean space. The proof uses a propagation of\nsingularities approach to replace the observation set by its average along a direction.", "id": "Paper/65456", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65456"}, {"title": " Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties ", "webprogram_exclude": "0", "session_ids": ["Session/18355"], "source_sha256": "04eb669d0fc83cea067621c2cd05f5203055dbe3c6f42b23552caa72d099d6b8", "withdrawn": "", "abstract": "Minimizing the Rayleigh quotient of a Hamiltonian matrix over a tensor train variety is a fundamental yet computationally intensive task in quantum chemistry. We investigate this problem through the lens of applied algebraic geometry, introducing the Rayleigh-Ritz degree (the number of complex critical points) and the Rayleigh-Ritz discriminant (the discriminant of this optimization problem). \nWe present recent foundational results on the algebraic geometry of tensor train varieties, and conclude by reporting on our numerical experiments.\nThis is based on joint work with Viktoriia Borovik, Serkan Hoşten, and Max Pfeffer.", "id": "Paper/65457", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65457"}, {"title": " Student research on the damped wave equation ", "webprogram_exclude": "0", "session_ids": ["Session/17442"], "source_sha256": "a8a10ce7b0405c75b9bcabdc42265866ba5445f053769900af0b5b9de95e3786", "withdrawn": "", "abstract": "The damped wave equation describes the evolution of a vibrating system that comes to rest due to the presence of a damping force. In this talk I will discuss research work by undergraduate and graduate students on energy decay rates for the damped wave equation. I will discuss two results on the flat two-torus that provide very precise information about the polynomial rate of decay from the geometry of the support of the damping and its growth behavior near 0. I will discuss a result proving that unbounded damping satisfying the geometric control condition can still produce exponential energy decay, so overdamping does not occur. On the other hand, I will discuss a result proving that for time-dependent damping that increases in time, overdamping does occur.", "id": "Paper/65458", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65458"}, {"title": " Harmonic Analysis of the Ternary Hypercube ", "webprogram_exclude": "0", "session_ids": ["Session/17945"], "source_sha256": "5683e1d39529608ac0b414e59aa0eea27217f32266ae35cb831105423afce145", "withdrawn": "", "abstract": "The ternary hypercube in dimension $N$ consists of all vectors whose coordinates are from the set $\\{-1, 0, 1\\}$.  We build a theory of harmonic analysis on this space using Hadamard matrices as the Fourier transform.  We consider questions regarding sparsity in the Fourier basis, sparsity in the Euclidean-Fourier dictionary, fast algorithms, and extremal cases in the hypercube.  This is joint work with Enrique Alvarado, Vale Ferb, and Nikita Raman as part of the Research Experiences for Undergraduates at Iowa State University.", "id": "Paper/65461", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65461"}, {"title": " Mathematical Analysis of Many-Body Quantum Simulation with Coulomb Potentials ", "webprogram_exclude": "0", "session_ids": ["Session/18246"], "source_sha256": "e173bc16cbe8041fbfeaa75ae98416d6cb5b35f49cf2437ac0947e7e8368aac9", "withdrawn": "", "abstract": "Efficient simulation of many-body quantum dynamics is central to advances in physics, chemistry, and quantum computing. A fundamental question is whether the simulation cost can scale polynomially with system size in the presence of realistic interactions. In this talk, we focus on many-body quantum systems with Coulomb interactions, which play a central role in electronic and molecular dynamics. We prove that first-order Trotterization for such unbounded Hamiltonians admits a polynomial dependence on the number of particles in the continuum limit, with a convergence rate of order 1/4--in contrast to prior Trotter analyses for bounded operators, which diverge in this limit. The result holds for all initial wavefunctions in the domain of the Hamiltonian. This 1/4-order rate is optimal, as previous work shows that it can be saturated by the ground state of the hydrogen atom. Moreover, higher-order Trotter formulas do not improve the worst-case scaling. We also discuss additional regularity conditions on the initial state under which the original Trotter convergence rate can be recovered. Finally, we discuss our recent development on the spatial error and algorithm complexities. The main analytical challenges arise from the many-body structure and the singular nature of the Coulomb potential.", "id": "Paper/65462", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65462"}, {"title": " Within-Host Modeling of Host–Pathogen Interactions in Pneumococcal Infection and Chagas Disease ", "webprogram_exclude": "0", "session_ids": ["Session/19371"], "source_sha256": "d88b30f9c7481aef85c02c5b66239940ecec15251b09e7005e4897dcafeeb6f2", "withdrawn": "", "abstract": "Mathematical models can help clarify how interactions between pathogens and the immune system influence infection outcomes. In this work, we study two within-host infection models using parameter-estimation and dynamical-systems approaches. For \\textit{Streptococcus pneumoniae}, we build on an existing mechanistic model of pneumococcal lung infection and focus on estimating host-pathogen interaction parameters by fitting the model to bacterial and immune-response data using simulated annealing. The goal is to improve parameter quantification and assess uncertainty and correlation among fitted processes. For \\textit{Trypanosoma cruzi}, we study how immune-response structure affects long-term infection dynamics. A five-dimensional model is reduced to two planar systems that differ in their CD8\\(^+\\) T-cell dynamics. Model I exhibits a forward bifurcation, bistability, and oscillatory dynamics, while Model II retains these behaviors and can additionally exhibit backward bifurcation.", "id": "Paper/65467", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65467"}, {"title": " A Decade of Undergraduate Research in Analysis ", "webprogram_exclude": "0", "session_ids": ["Session/17442"], "source_sha256": "92c240875a0e7109f58522852f9678f6222a393e91ce9b8c56dc94392b3764d1", "withdrawn": "", "abstract": "This presentation showcases work with Butler students – sophisticated analysis collaborative research results that have happened each year for more than a decade, skipping only the Covid year. Its overwhelming success developed from three components that any mathematics department can implement: its establishment as a strategic department goal; a corresponding undergraduate course development and curricular design; and the formation of a nine-day summer research camp in which every department major is invited to participate. Out of these three pillars flow peer-reviewed publications, student posters for MathFest and JMM, and student presentations. Come see how.", "id": "Paper/65471", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65471"}, {"title": " Dual reflection groups for three-dimensional Artin–Schelter regular algebras ", "webprogram_exclude": "0", "session_ids": ["Session/18278"], "source_sha256": "a440c080614f3f21b5f7f3e83653609fe5218fc060ac810b2a9685bb859161f0", "withdrawn": "", "abstract": "Recent efforts in noncommutative invariant theory have sought to generalize the Chevalley--Shephard--Todd theorem by replacing commutative polynomial rings with Artin--Schelter (AS) regular algebras and group actions with Hopf actions. One possibility of Hopf algebra is a \\emph{dual group algebra} $H = (\\Bbbk G)^*$: a $(\\Bbbk G)^*$-action on an algebra $A$ is the same as a $G$-grading of $A$. In this framework, a finite group $G$ is called a \\emph{dual reflection group} if there exists a $G$-graded AS regular algebra $A$ such that its identity component $A_e$ is also AS regular. While gradings on two-dimensional AS regular algebras are completely understood, higher-dimensional cases have previously yielded only scattered examples.\n\nIn this talk, I will provide a classification of group gradings on three-dimensional AS regular algebras, focusing specifically on nonabelian grading groups. This is because an abelian group grading is the same as an action by an abelian group, which is better understood in the literature. Our main result proves that there are 6 infinite families and 7 exceptional 3-dimensional quadratic AS regular algebras graded by nonabelian groups, alongside 4 infinite families and 2 exceptional 3-dimensional cubic algebras. The classification is achieved through a detailed analysis of the superpotential and the Nakayama automorphism associated with the algebras. Thanks to our classification, we provide a complete list of nonabelian dual reflection groups for 3-dimensional AS regular algebras.", "id": "Paper/65476", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65476"}, {"title": " Polar Derivative Inequalities for Self-Reciprocal Polynomials ", "webprogram_exclude": "0", "session_ids": ["Session/19368"], "source_sha256": "5a1b95a1f2de772b8dc2afaf15cf495d7f47f2646c01f96314ed7942f7f3e513", "withdrawn": "", "abstract": "A polynomial (f) of degree (n) is called self-reciprocal if it satisfies\n$\nf(z)=z^n f(1/z).\n$\nLet $f$ be a self-reciprocal polynomial of degree $n$ whose zeros all lie in the left half-plane, with each zero in the second quadrant having modulus at most 1. Under these hypotheses, it is known that\n$\n\\left|f'\\left(e^{-i\\theta}\\right)\\right|\n\\leq\n\\left|f'\\left(e^{i\\theta}\\right)\\right|,\n\\qquad 0\\leq\\theta\\leq\\pi.\n$\nWe extend this result to the polar derivative\n$\nD_\\alpha f(z)=nf(z)+(\\alpha-z)f'(z).\n$\nSpecifically, we prove that\n$\n\\left|D_\\alpha f\\left(e^{-i\\theta}\\right)\\right|\n\\leq\n\\left|D_\\alpha f\\left(e^{i\\theta}\\right)\\right|\n$\nfor real $\\alpha$ satisfying $|\\alpha|\\geq 1$ and $0\\leq\\theta\\leq\\pi$. The inequality is reversed when $|\\alpha|\\leq 1$; consequently, equality holds when $|\\alpha|=1$. As applications, we derive several sharp inequalities for the polar derivatives of self-reciprocal polynomials.", "id": "Paper/65477", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65477"}, {"title": " Coordinated Alternative Grading in Calculus I ", "webprogram_exclude": "0", "session_ids": ["Session/18440"], "source_sha256": "bd93f563629ba3a12cb59d0c2607da29dd0524460253b3988dac8d3d7458bb6a", "withdrawn": "", "abstract": "The implementation of alternative grading in mathematics education has been increasingly documented since the 2020 PRIMUS special issue on alternative grading (Campbell et al., 2020). At the same time, coordinated mathematics courses are receiving increased attention (e.g., Villalobos et al., 2025), particularly as institutions face pressure to standardize course content and delivery. Much of the existing discussion of alternative grading, however, focuses on its implementation within individual courses, with less attention given to students’ transitions from alternatively graded courses into subsequent, traditionally graded coursework.\n\nThis report describes a department’s implementation of standards-based grading in loosely coordinated Calculus I courses and considers the subsequent performance of students who continued into traditionally graded Calculus II. In Fall 2025, three instructors at a large metropolitan community college in the South-Central United States coordinated standards-based grading across all 16-week sections of Calculus I. Prior to the semester, the instructors negotiated course standards, a grading table, assessment guidelines, and a common grading rubric. During the semester, coordination consisted primarily of informal discussions to normalize marking criteria and the development of a mostly uniform final exam.\n\nWe found that frequent discussion of expectations for student work helped maintain both consistent marking across sections and consistent messaging to students. At the same time, minor differences in pedagogical approach resulted in different student experiences, particularly with regard to reattempts. Of 76 students enrolled, 53 (70%) earned passing grades in the course.\n\nPreliminary institutional data, however, indicate that students who subsequently enrolled in traditionally taught and graded Calculus II were successful at a rate lower than the historical average. Although several factors may account for this difference, this result highlights an additional consideration for instructors implementing alternative grading: how students navigate the transition from alternatively graded courses to more traditionally graded coursework.", "id": "Paper/65485", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65485"}, {"title": " A Persistent-Homology Approach for Identifying Knowledge Gaps ", "webprogram_exclude": "0", "session_ids": ["Session/18105"], "source_sha256": "e7ba25b4a2ec2fd1224e4c9b5f2fb8bda2ce22e059c35f23b9ab56a3ae586ff7", "withdrawn": "", "abstract": "In recent years, researchers have begun embedding scientific knowledge and concepts into high-dimensional Euclidean space. These embeddings represent semantic differences between concepts as pairwise distances between points, offering a novel lens for studying the structural properties of scientific knowledge. In this talk, we present our use of persistent homology to identify topological holes in these embedding spaces. In addition to analyzing these holes, we identify academic works (if any) that “bridge the gaps' represented by these holes. We will discuss how these holes are bridged, as well as the recognition, novelty, and impact of the works that bridge them.", "id": "Paper/65486", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65486"}, {"title": " A Dynamical Lifting Problem for Additive Polynomials ", "webprogram_exclude": "0", "session_ids": ["Session/18214"], "source_sha256": "7f0daeadf590ead7b512899e73402c3dd04fff23aa55bd1d6167bf3510ac7770", "withdrawn": "", "abstract": "In this talk, we introduce a dynamical analogue to the lifting problem for Galois covers of algebraic curves. We use the classification of finite subgroups of $\\mathrm{Aut}(\\mathbb{P}^1)$ to find a negative solution for the families of additive and semi-additive polynomials over $\\overline{\\mathbb{F}}_p$. We also compute the dimension of the space of (semi-)additive polynomials in the moduli space of dynamical systems, and find that they contradict a well-known finiteness property of dynamical systems in characteristic zero.", "id": "Paper/65488", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65488"}, {"title": " On Bubbling Diagrams and Grothendieck Polynomials ", "webprogram_exclude": "0", "session_ids": ["Session/18308"], "source_sha256": "45434c315429261fc88471b07d95bcdb62ab4cba62b0e2779fac119bd8bf19cc", "withdrawn": "", "abstract": "Grothendieck polynomials represent K-theoretic classes of the complete flag variety and can be thought of as a non-homogeneous generalization of Schubert polynomials.  In this talk, we discuss bubbling diagrams, a combinatorial tool which can be used to compute supports of certain Grothendieck polynomials.  Bubbling diagrams were originally introduced in a joint paper with M{\\'e}sz{\\'a}ros, St.~Dizier, and Setiabrata (2024) for Grothendieck polynomials associated to vexillary permutations, but variants can also be used to compute supports in certain other cases.  We discuss the strengths and limitations of the bubbling diagram model along with some possible strategies to extend it.", "id": "Paper/65489", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65489"}, {"title": " Finiteness and Liftability of Post-Critically Finite Bicritical Maps ", "webprogram_exclude": "0", "session_ids": ["Session/17755"], "source_sha256": "6e512ff8388b57df697833977e0846fb2a5789bda2b20120ae4a49838882f205", "withdrawn": "", "abstract": "In a well-known, but unpublished paper from 2013, Pink showed that PCF quadratic maps in characteristic $>2$ satisfy Thurston rigidity and admit lifts to characteristic zero which preserve dynamically significant algebraic and combinatorial invariants. In this talk, we generalize Pink's results to the family of PCF degree $n$ bicritical maps in characteristic $>n$. We use techniques of Silverman to extend Milnor's characterization of the moduli space of bicritical maps to fields of positive characteristic. We then use this characterization to establish finiteness via a result of Benedetto-Ingram-Jones-Levy, and derive liftability using methods of Pink.", "id": "Paper/65497", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65497"}, {"title": " Hybrid SINDy-EnKF in Learning Chikungunya Dynamics from Incomplete, Noisy, or Partially Observed Data ", "webprogram_exclude": "0", "session_ids": ["Session/19365"], "source_sha256": "0f5789e268245b9c94c91c15db3ff3a5cbcf498b4612b411c00df3ba8b6b819a", "withdrawn": "", "abstract": "Current mechanistic models for the transmission dynamics of the Chikungunya virus (CHIKV) rely on uncertain parameters or partially observed data. This limitation challenges the use of theoretical models for understanding and forecasting disease spread. Here we present a hybrid, data-driven model framework that combines Sparse Identification of Nonlinear Dynamics (SINDy) with the Ensemble Kalman Filter (EnKF) for sequential data assimilation. Our numerical experiments show that this approach improves prediction accuracy and provides a good reconstruction of unobserved trajectories under partial observability, a common constraint in real-world epidemiological surveillance. SINDy can be applied to epidemic trajectories, recovering the underlying equations in noise-free conditions. However, standalone SINDy is highly sensitive to noise, leading to spurious terms and poor performance.  Hence, we embed the identification procedure within an EnKF framework, which assimilates noisy observations to correct forecast states from the SINDy-derived model and to infer unobserved state variables.", "id": "Paper/65499", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65499"}, {"title": " Axisymmetric Navier-Stokes Equations with Swirl: Computer-assisted proofs of steady states with an eye towards richer dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/18244"], "source_sha256": "aa400d07d017a421721ac6f0476dda0e4f9de4e059fe88d6de7046ebcc9991d4", "withdrawn": "", "abstract": "The global regularity of solutions to the 3D Navier–Stokes equations is famously unknown, and the axisymmetric case with swirl is perhaps the simplest geometry in which blowup may occur. We study this setting on a periodic cylinder with no-slip boundary conditions and time-independent body forcing, where weak solutions are guaranteed to have a global attractor and computer-assisted proofs are uniquely positioned to give rigorous results in a non-perturbative regime. In this geometry the equations reduce to a system in a periodic axial variable and a radial variable. Our approach for developing computer-assisted proofs of steady states of the Navier-Stokes equations in a cylindrical domain uses a Fourier–Jacobi (Zernike) basis.\n\nIn any problem one wants the basis used to express solutions to have several desirable properties: easy to express differential operators, easy to compute products, and rapid convergence properties. Fourier series are best for periodic domains, but there is no uniformly best option for radial variables. A Fourier–Jacobi basis has its advantages --- the differential operators act as sparse ladder and conversion operators between Jacobi families; multiplication via interpolation may be computed accurately and relatively quickly; the spectral coefficients of solutions converge geometrically --- however laborious quantitative estimates are required for the computer-assisted proof. For example, the derivative nonlinearity requires bilinear estimates from multiplying different polynomial bases, and inverting the Stokes operator on this basis and recovering explicit decay estimates requires significant effort. With this infrastructure in place we prove the existence of non-perturbative steady states, and we expect the framework to apply more broadly to PDEs in cylindrical geometries, and to richer dynamics.", "id": "Paper/65504", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65504"}, {"title": " Resonant Vector Bundles, Conjugate Points, and the Stability of Pulse Solutions to the Swift Hohenberg Equation Using Validated Numerics ", "webprogram_exclude": "0", "session_ids": ["Session/18008"], "source_sha256": "3488aff4596fc07de7ffa1dcfacd8cc83fcbe5112f534d61127415dd95692cfa", "withdrawn": "", "abstract": "In this talk we present a computer-assisted proof\nfor the stability of pulse solutions to the Swift-Hohenberg equation, generalizing\nthe framework based on counting conjugate points / the Maslov index developed\nin Beck & Jaquette (2022). \n\nThe general set up is to first compute a homoclinic orbit of a 4D Hamiltonian\nODE. Next one evolves unstable vector bundles of the linearized system from\none end of the homoclinic to the other. These vector bundles define a heteroclinic orbit in the space of Lagrangian Grassmanians (limiting from a point to a periodic orbit), and the number of conjugate points counts the number of times\nthe heteroclinic orbit passes through a fixed reference frame. To get a validated\ncount of the conjugate points -- a topological index of the heteroclinic-- one must show that they only occur in a compact\nregion, which requires a careful analysis of the limiting behavior of this path of\nLagrangian subspaces, and the taming of external resonances in an application\nof the parameterization method.", "id": "Paper/65509", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65509"}, {"title": " Simple smooth modules over Lie algebras ", "webprogram_exclude": "0", "session_ids": ["Session/17666"], "source_sha256": "220e7c8573c0c57fe625612db60f72343cd518ae8a8ef5747bc93aa8781d43ce", "withdrawn": "", "abstract": "In this talk, I will show you the recent progress on simple smooth modules over various Lie algebras and list some open problems.", "id": "Paper/65510", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65510"}, {"title": " Positive Intermediate Ricci Curvature and Symmetry ", "webprogram_exclude": "0", "session_ids": ["Session/18290"], "source_sha256": "7f4b8bdc0b199bf5498e4be84a6b49c2d3862e0d5c3d5a6c3ace752cf0bfa6f8", "withdrawn": "", "abstract": "While Ricci curvature can be thought of as a trace of sectional curvatures, intermediate Ricci curvatures interpolate between sectional and Ricci curvatures as partial traces, bridging the gap between two classical areas of study. In the study of positive sectional curvature, there are a number of results which classify positively curved manifolds with large symmetry rank. This talk will focus on recent work in which we extend such results to positive second intermediate Ricci curvature.", "id": "Paper/65513", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65513"}, {"title": " <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.07ex\" height=\"2.009ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -576.1 460.5 865.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">q</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-71\" d=\"M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-71\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-series and quantum modularity ", "webprogram_exclude": "0", "session_ids": ["Session/18333"], "source_sha256": "86e94551d19e13159b4045b36fc65a48d4c651472baa3da44479a7a0d6fcc31b", "withdrawn": "", "abstract": "$q$-series identities within the unit disk and at roots of unity on its boundary are central to the intersections of $q$-hypergeometric series, partition theory, and modularity. For example, Ramanujan’s original 1920 characterization of his mock theta functions implies that they are $q$-hypergeometric series whose exponential singularities, as $q$ approaches  roots of unity radially from within the disk, are compensated for by theta functions. More recently, Cohen, Zagier, and others have established related identities across various contexts.  Following a brief overview of this area, we introduce new results that establish quantum modularity of related $q$-series and identities. This includes preliminary joint work with J. Dousse (Geneva) and J. Lovejoy (Paris), and joint work with D. Metacarpa (UIUC).", "id": "Paper/65516", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65516"}, {"title": " Distinguishing elliptic curves modulo <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.259ex\" height=\"2.009ex\" style=\"vertical-align: -0.671ex; margin-left: -0.089ex;\" viewBox=\"-38.5 -576.1 542 865.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">p</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-70\" d=\"M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-70\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>: a case study in computation-informed conjectures ", "webprogram_exclude": "0", "session_ids": ["Session/17808"], "source_sha256": "9bfe40ced2e9dd58b01b685af48ade65bf8a9d29362e32e3520c24abc7d3b0aa", "withdrawn": "", "abstract": "A pair of elliptic curves are said to be congruent modulo $p$ if their $a_\\ell$ invariants are equal modulo $p$ for all \"good\" primes $\\ell$. This prompts a natural question: when the curves are not congruent mod $p$, what proportion of good primes $\\ell$ witness this non-congruence?\n\nTo investigate this question, we gathered computational data, primarily with SageMath, and analyzed it. We will discuss how SageMath's open-source nature enables advanced users to write efficient code for computing large amounts of data, how software packages such as SageMath frequently must make a trade-off between efficiency and ease-of-use, and how this experience may be used to inform future enhancements to the SageMath library. We will also discuss how we used the data we generated to form conjectures about our original question.\n\nTo keep this talk accessible to a general computational mathematics audience, we will not discuss the proofs of our conjectures, and no advanced number theory knowledge will be required.", "id": "Paper/65517", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65517"}, {"title": " Frames Associated with <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.716ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 1169.4 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">C_0</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-43\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-43\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-30\" x=\"1011\" y=\"-213\"></use>\n</g>\n</svg>-Semigroups ", "webprogram_exclude": "0", "session_ids": ["Session/18305"], "source_sha256": "03572e3091fe01b6a8766dfa40448738720a8b8255b15a6035a8a47859b03e0f", "withdrawn": "", "abstract": "Due to Christensen, Hasannasab, and Philipp  we have a necessary and sufficient condition for a system $\\{T^n \\varphi\\}_{n \\in \\mathbb{Z}_+}$ to be a frame, for a separable infinite-dimensional Hilbert space $H$, which exhibits the connection between frame theory and operator theory as the bounded operators $T$ that can be used to generate a frame for $H$ must be similar to a compression of the shift operator on $H^2(\\mathbb{T})$ to a particular coinvariant subspace of the shift in $H^2(\\mathbb{T})$. \n Similarly, in recent work by Bailey, Han, Kornelson, Larson, and Liu it is shown that every frame representation for a countable, unital, left-cancellation semigroup $S$ must be equivalent to a compression of the left regular representation on $\\ell^2(S)$ to a certain coinvariant subspace of the left regular representation in $\\ell^2(S)$. \n\n\nWhen considering continuous frames given by a $C_0$-semigroup of operators $\\{T(t)\\}_{t \\geq 0}$ we may ask whether a similar characterization for such frames can be obtained. Moreover, for a $C_0$-semigroup $\\{T(t)\\}_{t \\geq 0}$, there is an associated bounded operator known as the cogenerator $C = (A+I)(A-I)^{-1}$ of the semigroup whenever $1 \\notin \\sigma(A)$ (where $A$ is the infinitesimal generator of the semigroup). It can be shown that $\\{T(t)\\varphi\\}_{t \\geq 0}$ is a continuous frame for $H$ if and only if $ \\{C^n (A-I)^{-1}\\varphi \\}_{n \\in \\mathbb{Z}_+}$ is a discrete frame for $H$ so that studying the frame properties of the frames by iterations of the cogenerator will shed light on the properties of the continuous frames given by the associated semigroup $\\{T(t)\\}_{t \\geq 0}$. In this talk, we will address the aforementioned questions as well as provide some results on frame properties of the frames obtained from iterations of operators defined in terms of the infinitesimal generator of a given $C_0$-semigroup. This is joint work with Eva Gallardo-Gutierrez and Jonathan Partington.", "id": "Paper/65520", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65520"}, {"title": " Rajchgot-Additive Factorizations and Irreducible Permutations ", "webprogram_exclude": "0", "session_ids": ["Session/17943"], "source_sha256": "913becb4aa5afb13bf5d285cf104d1baac9c41905fac70a9b0e2eb8a31f5db82", "withdrawn": "", "abstract": "The Rajchgot index, introduced by Pechenik, Speyer, and Weigandt and named after Jenna Rajchgot, is a permutation statistic defined using longest increasing subsequences. We study how this statistic behaves under permutation multiplication and prove that it is subadditive. We then show that Rajchgot additivity implies Coxeter-length additivity. These results motivate a new enumerative family. We call a permutation Raj-irreducible if it admits no nontrivial Rajchgot-additive factorization. We present some enumerative results and investigate the patterns that emerge.", "id": "Paper/65522", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65522"}, {"title": " Maximum nullity and compatible forts ", "webprogram_exclude": "0", "session_ids": ["Session/17911"], "source_sha256": "f6671a004bb97dac242fe16ac8019b4c4fdfcb3886a7f84ce8b3a40f25ca82c7", "withdrawn": "", "abstract": "The graph parameter ${\\mathrm N}(G)$ is the maximum nullity among all matrices with symmetric zero/nonzero pattern associated to a graph $G$.  The zero forcing number ${\\mathrm Z}(G)$ is a well-known upper bound for ${\\mathrm N}(G)$, and it is known that a zero forcing set of $G$ is exactly a set that intersects each fort of the graph.  So the zero forcing number can be defined as the size of a minimum set that intersects every fort of $G$.  We provide a similar characterization of ${\\mathrm N}(G)$ that is purely combinatorial.  The value ${\\mathrm N}(G)$ can be seen to be the rank of a representable matroid having minimum rank for such matroids all of whose circuits are forts for $G$.  Using this connection to matroid theory and collections of forts that are compatible in a certain sense, we characterize  ${\\mathrm N}(G)$.", "id": "Paper/65523", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65523"}, {"title": " How much confidence can you get from list decoding? ", "webprogram_exclude": "0", "session_ids": ["Session/18020"], "source_sha256": "76227f00adb29675655b46966c7975b69b14d4f3e7b4fe38d235d95de07269f5", "withdrawn": "", "abstract": "In error correction decoding, the difference between the decoded codeword and the received signal, which we call the noise sequence, carries valuable reliability information on the confidence of the decoding. If noise sequences are ranked in decreasing order of likelihood, a noise sequence with low rank indicates high confidence in the decoding. Building on the development of Soft-Output Guessing Random Additive Noise Decoding, we explore the relationship between the likelihood ranks arising in list decoding and the posterior probability of correctness.\n\nWe show that the ranks associated with subsequent list entries carry reliability information unobtainable from the first rank alone.  More than any absolute rank, it is the relative positioning of the ranks to each other that determines the reliability. In the large-blocklength limit, a sufficiently late second rank can imply that the first codeword in the list is asymptotically correct, even when the rank associated with the first codeword viewed in isolation would suggest otherwise. Perhaps more surprisingly, the asymptotic reliability of the first codeword depends only on the first, second, and last ranks. In this talk, we detail these results as well as explaining the key concepts behind establishing them.", "id": "Paper/65528", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65528"}, {"title": " Uniform representation stability for ordered Hurwitz spaces ", "webprogram_exclude": "0", "session_ids": ["Session/18297"], "source_sha256": "253ef7ec893a2a49a37ddd68a3d470c12a3977e31f3a83dd2a9a569943d4aa4c", "withdrawn": "", "abstract": "\"Ordered Hurwitz spaces\" are moduli spaces of branched covers of the Riemann sphere with a choice of ordering on the branch points. Motivated by applications to number theory, Jordan Ellenberg conjectured that the cohomology of these spaces satisfies a condition called \"representation stability\" with respect to the action of the permutation group of the branch points. In this talk I will explain this conjecture, and a resolution due to work joint with Z. Himes and J. Miller.", "id": "Paper/65529", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65529"}, {"title": " From QBD Processes to Eigenfunctions: Approaches to Proving Convergence ", "webprogram_exclude": "0", "session_ids": ["Session/17976"], "source_sha256": "9ec4dd50ff1edf12ae596e099e2dfa7898588b3f7e5cc86e08b39b048ebeea4f", "withdrawn": "", "abstract": "Eigenfunction representations provide a useful description of the behavior of time-dependent queueing processes. For several classes of queues, including the periodic ($M_t/M_t/c$) queue and the ($M_t/M_t/c$) queue with catastrophes and repair, such representations arise naturally from the associated generating functions. The quasi-birth-and-death (QBD) framework provides a substantially more general setting in which to investigate these representations.\n\nThis talk examines several possible approaches to establishing the convergence of the QBD generating-function representation to an eigenfunction expansion. The analysis involves the analytic structure of the generating function, the zeros of the associated matrix-valued function, and the spectral properties of the periodic evolution operator (monodromy matrix). Contour integration and residue methods provide one possible route, while spectral and operator-theoretic arguments suggest others.\n\nParticular attention will be given to the issues that arise in passing from the analytic generating-function representation to a convergent expansion in eigenfunctions, including the location and multiplicity of the relevant zeros, the cancellation of singularities inside the unit circle, and the control of the resulting infinite series. The goal is to compare several possible approaches, identify the principal analytical obstacles, and assess which features of the QBD structure may lead to a rigorous convergence result.", "id": "Paper/65531", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65531"}, {"title": " Phylogenetic networks evolving under G-equivariant models ", "webprogram_exclude": "0", "session_ids": ["Session/18115"], "source_sha256": "54f21d6b87fdec1c6ddd9b688968ed63dc35a16b439bdcb39b5b0aa5837265bf", "withdrawn": "", "abstract": "Phylogenetic network models extend evolutionary structures from trees to more complicated networks.  This perspective is useful because it allows to account not only for speciation, but also for other evolutionary events, including hybridization and lateral gene transfer.   We aim to study the algebraic geometry of phylogenetic network models, with the goal of proving identifiability results, specifically for the displayed tree phylogenetic network model.  Our focus is on producing results for broad classes of phylogenetic models, specifically widely used models that are G-equivariant.  We prove new identifiability results for level-1 networks in this class of models.  This is joint work with Marta Casanellas, Elizabeth Gross, Ben Hollering, and Jesus Fernandex-Sanchez.", "id": "Paper/65535", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65535"}, {"title": " Randomized truncation of quantum states ", "webprogram_exclude": "0", "session_ids": ["Session/18294"], "source_sha256": "9a56bc134405834dfa8426fbf00f67670ac7e8595ff87494ad065147dff22a62", "withdrawn": "", "abstract": "A fundamental task in quantum information is to approximate a pure\n  quantum state in terms of sparse states or, for a bipartite system,\n  states of bounded Schmidt rank. The optimal deterministic\n  approximation in each case is straightforward, and maximizes the\n  fidelity: keep the largest entries or singular values.  On the other\n  hand, random mixtures of sparse states can achieve quadratically\n  improved trace distances, and yield nontrivial bounds on other\n  distance measures like the robustness.\n\n  In this work, we give efficient algorithms for finding mixtures of\n  sparse states that optimally approximate a given pure state in\n  either trace distance or robustness.  These algorithms also yield\n  descriptions of efficiently samplable ensembles of sparse, or\n  less-entangled, states that correspond to these optimal mixed\n  approximations. This can be used for the truncation step of\n  algorithms for matrix product states, improving their accuracy while\n  using no extra memory and no asymptotic increase in runtime, and we\n  demonstrate this improvement numerically.\n\n  Our proofs use basic facts about convex optimization and zero-sum\n  games, as well as rigorous gurarantees for computing and sampling\n  from maximum-entropy distributions. In particular, a key step in our\n  construction is {\\em conditional Poisson sampling}, which is the\n  well-studied problem of drawing fixed-size subsets from a population\n  with known inclusion probabilities. We give improved algorithms for\n  carrying out this sampling, which may be of independent interest.", "id": "Paper/65536", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65536"}, {"title": " New properties of random plane graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18369"], "source_sha256": "e2ff4fe57282bdbe1c5eea312575d27b56dad7b26de14cce5b3d5c52682ff507", "withdrawn": "", "abstract": "In \\emph{plane graphs}, the vertices are fixed points in the plane, and the edges are non-crossing straight-line segments. Such graphs model many real-world situations, in when the vertices are not allowed to be moved (for example, in maps and computer graphics). \n\nOne might say that random graphs are well-understood, but much less is known for random plane graphs. We improve the current best bounds for several properties of a random plane graph. \n\nFor example, let $P$ be a set of $n$ points and let $t$ be the maximum number of edges that a plane graph of $P$ may have. It was known that a random plane graph of $P$ is expected to have at least $t/2+n/16$ edges. We improve this bound to $t/2+n/12$ (we further improve this bound in the case where $P$ has a large convex hull).\n \nWe obtain additional new bounds for random plane graphs, such as lower bounds for the expected number of vertices of degree $i$ in a random plane graph, where $i\\ge 4$. We also obtain a first lower bound for the expected number of leaves in a random plane spanning tree.", "id": "Paper/65537", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65537"}, {"title": " Families of Ramanujan Graphs of Brandt Matrices from Quaternion Algebra ", "webprogram_exclude": "0", "session_ids": ["Session/17954"], "source_sha256": "bbcff740c7d372d6a8f297f7c0a9498254ff4b62ce372b6f5b44a92a3e6a89b4", "withdrawn": "", "abstract": "It is known that certain Brandt Matrices associated with quaternion algebra over rational are adjacency matrices of Ramanujan Graphs. It has been demonstrated that very often these graphs are regular graphs. We work on interconnecting these families of Ramanujan Graphs with Projective Fraisse families of finite connected graphs. To study the corresponding graph of Projective Fraisse limit, we work on creating confluent bonding epimorphism between those finite graphs, that are Ramanujan Graphs. The inverse limit of an inverse sequence of cycles often forms Graph-Solenoids, with respect to the winding number of the underlying wrapping maps. We work on finding Graph-Solenoid from these families of Ramanujan Graphs associated to various prime numbers.", "id": "Paper/65541", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65541"}, {"title": " Identifiability of a simple model of lateral gene transfer ", "webprogram_exclude": "0", "session_ids": ["Session/18039"], "source_sha256": "eefc2f1db479875f6c145de02ba9f55ab99caae596d48136a98f800f3edb11d0", "withdrawn": "", "abstract": "In evolutionary biology, factors like lateral gene transfer complicate the tree of life, making inference of a species tree more difficult. \nThe phenomenon of lateral gene transfer allows genetic material to be passed between organisms as opposed to inheritance, causing the tree for a particular gene to differ from the species tree. \nIn this work, we define a model of lateral gene transfer\non site patterns.\nIn the case where lateral gene transfer is restricted to occur only between\nclosely related species, we show that the unrooted topology of the species tree is identifiable from SNP data on the taxa.\nOur proof involves showing a connection between our lateral gene transfer\nmodel and graphical models on a related tree, and uses ranks of flattenings\nto identify splits in the tree.  We also report on results of using\nthe singular value decomposition on flattening matrices to identify\nthe unrooted topology in simulated data.", "id": "Paper/65542", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65542"}, {"title": " Model Theory of Valued Fields: From Ax-Kochen to Formal Verification \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18573"], "source_sha256": "e3457f5b444cc00f172a153bdc99ccb044059726fc5cd2e90cb0cfefde7ce3ff", "withdrawn": "", "abstract": "As the discipline of applied model theory has developed since the middle of the last century, ideas have arisen from the natural examples of \n algebraically closed fields and real closed fields. These concepts have then been considered for fields with a valuation, where the interaction between the field, the value group and the residue field forced a more thorough understanding of the concepts. We see this from model-theoretic tests for quantifier elimination, to elimination of imaginaries, to notions of minimality and now the process of formal verification. In this talk, I will review some of this history.", "id": "Paper/65548", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65548"}, {"title": " A Jump-Diffusion Model for Pricing Catastrophe Bonds Under Exchange Rate and Interest Rates ", "webprogram_exclude": "0", "session_ids": ["Session/18332"], "source_sha256": "36db508b80d3f5d7ca66d8c9680dca6bf9ceae9a9f68d1919e187b2dd8253c9e", "withdrawn": "", "abstract": "We develop a stochastic pricing model for catastrophe (CAT) bonds that combines interest-rate risk, exchange-rate risk, and jump risk in one arbitrage-free framework. Standard CAT bond models rely on continuous diffusion only, which misses sudden extreme losses and does not capture the joint behavior of interest rates and exchange rates. We model these three rates as a coupled three-dimensional system of stochastic differential equations, with both diffusion terms and compensated compound Poisson jumps. Consequently, we derive CAT bond pricing formulas by incorporating zero-coupon bonds and foreign currency call options. We validate the formulas against Monte Carlo simulation using calibrated parameters and show that adding jumps improves the fit to observed prices compared to the standard diffusion model. We further extend the framework to multiple currency pairs, showing that the jump calibration adapts to both stable and volatile exchange-rate economies.", "id": "Paper/65550", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65550"}, {"title": " Universality of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.395ex\" height=\"1.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -576.1 600.5 721.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">n</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-6E\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-categories of cospans ", "webprogram_exclude": "0", "session_ids": ["Session/18210"], "source_sha256": "5a2ef051e07aa4716ee757c518093e6b0c271933a9a092ab7136bf04b7a49c0a", "withdrawn": "", "abstract": "Following Haugseng, given a category $C$ with pushouts and a non-negative integer $n$ we can form an $n$-category $\\mathrm{Cospan}_n(C)$ whose $k$-morphisms are iterated cospans of height $k$ in $C$ and whose composition operations are given by taking pushouts. This construction gives a limit-preserving functor $\\mathrm{Cat}^{\\mathrm{po}} \\to \\mathrm{Cat}_n$. Does this functor admit a left adjoint?\n\nIn this talk we will show that there is a natural extension of $\\mathrm{Cat}^{\\mathrm{po}}$, namely a category $\\mathbb{AC}_n\\mathrm{Cat}$ of ``categories with admissible $n$-cospans'' into which $\\mathrm{Cat}^{\\mathrm{po}}$ embeds fully faithfully, and an extension $\\mathrm{Cospan}_n : \\mathbb{AC}_n\\mathrm{Cat} \\to \\mathrm{Cat}_n$ of the cospan construction which does admit a left adjoint. This left adjoint is 1. explicit enough to be computable in many cases (it is a generalization of the twisted arrow category construction) and 2. fully faithful, so that the objects of $\\mathbb{AC}_n\\mathrm{Cat}$ can be used to model $n$-categories. Time permitting we will use this theory to discuss a strategy to prove the cobordism hypothesis.", "id": "Paper/65551", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65551"}, {"title": " Success Stories in Data-Driven Undergraduate Research ", "webprogram_exclude": "0", "session_ids": ["Session/17921"], "source_sha256": "e763d83b6d00e13023812dc0a0cebe0bfa2c49f6c66ec306ff5ee28098ed79ca", "withdrawn": "", "abstract": "This presentation showcases a collection of research projects conducted by undergraduate students at a primarily undergraduate institution through three-semester senior theses and a week-long departmental research camp. The projects apply a range of supervised and unsupervised machine learning techniques to investigate questions arising from diverse real-world applications. The talk will highlight selected research questions, the methods used to address them, and key findings from these projects.\n\nBeyond the individual research results, the presentation will discuss accessible approaches to engaging undergraduates in data driven research at a primarily undergraduate institution. Students participate in the full research process, including formulating research questions, conducting literature reviews, preparing and exploring data, selecting appropriate methods, interpreting computational results, and communicating their findings. The presentation will also describe strategies for structuring both short-term research experiences and longer-term undergraduate thesis projects, with particular attention to helping students progress from guided exploration to conducting independent research and presenting their work in national forums.", "id": "Paper/65552", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65552"}, {"title": " Topology-Guided Deep Learning for Spatio-Temporal Data ", "webprogram_exclude": "0", "session_ids": ["Session/18026"], "source_sha256": "8b3e16a0a0ee8ba9d6cd2d3a1b3de8368cc2046534970940db1142b1c3d35146", "withdrawn": "", "abstract": "In recent years, artificial intelligence (AI) has emerged as a new powerful machinery that enables to harness the rich information encoded in complex real-world phenomena, from climate sciences to the spread of infectious diseases. However, the existing models still tend to be limited in their capabilities to explicitly account for higher-order relations within the encoded knowledge, especially in conjunction with multi-granular and multimodal datasets which are the inherent characteristics in various real-world applications. In this talk, I will introduce the emerging approaches of topological deep learning (TDL), i.e., the new arsenal of tools at the interface of statistical topological data analysis, computational topology, machine learning, deep learning, and data science, and demonstrate how TML can help in addressing fundamental knowledge gaps on the way of the more systematic, reliable, and trustworthy applications of AI in intelligent transportation, biosurveillance, climate science, and bioinformatics. In particular, I will showcase the applications of our new TML machinery to the challenging problems in digital finance, intelligent transportation, biosurveillance of infectious diseases, and molecular graph analysis.", "id": "Paper/65554", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65554"}, {"title": " A lower bound on the number of edges in DP 4-critical graphs ", "webprogram_exclude": "0", "session_ids": ["Session/16805"], "source_sha256": "edc689d1ac9b79f2e8cdf55f545c2ef8b3b0fe9fa7fd1d3fd196742aa335173c", "withdrawn": "", "abstract": "A graph $G$ is $k$-critical (list $k$-critical,  DP $k$-critical) if $\\chi(G)= k$ ($\\chi_\\ell(G)= k$, $\\cDP(G)= k$) and for every proper subgraph $G'$ of $G$, $\\chi(G')<k$ ($\\chi_\\ell(G')< k$, $\\cDP(G')<k$). \r\nLet $f(n, k)$ ($f_\\ell(n, k), \\fDP(n,k)$) denote the minimum number of edges in an $n$-vertex\r\n$k$-critical (list $k$-critical, DP $k$-critical) graph. \r\nThe main result of this talk is that if  $n\\geq 6$ and $n\\not\\in\\{7,10\\}$, then\r\n$\\fDP(n,4)>\\left(3 + \\frac{1}{5}  \\right) \\frac{n}{2}.$\nThis is the first bound on $\\fDP(n,4)$ that is asymptotically better than the well-known bound  $f(n,4)\\geq \\left(3 + \\frac{1}{13}  \\right) \\frac{n}{2}$ by Gallai from 1963,  and it is\nexact for  every $n\\geq 15$ divisible by 5.\nThe result also yields a  better bound on $f_{\\ell}(n,4)$ than the ones known before.\n\nThis is joint work with P. Bradshaw, I. Choi and J. Xu.", "id": "Paper/65558", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65558"}, {"title": " A Modified Chinese Postman Approach to Laser Cutting Trajectories ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "b5d7ee5177ed6cdb140a76a7a637fe184d7b923c7202f0fd48a5ff4c024a00c4", "withdrawn": "", "abstract": "In collaboration with the Makerspace at the University of the Pacific, we studied the paths generated by their laser cutter using LightBurn software. We exported the machine's G-Code and modeled the cutting process as a Chinese Postman Problem (CPP) to determine efficient routes that traverse all required cutting edges.\n\nWhile LightBurn includes optimization settings through its Cut Planner, these paths do not always minimize non-cutting travel moves. By modifying the CPP to reflect laser cutter behavior, we identified a route that reduced non-cutting travel distance from 223.61 mm to 99.91 mm, a reduction of approximately 55%.", "id": "Paper/65561", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65561"}, {"title": " Foliations forcing closed orbits ", "webprogram_exclude": "0", "session_ids": ["Session/18267"], "source_sha256": "54ca8cad2c41afb3feda7a3b1ad5bfae18e0b68d2a7e7242e7249e3d1a9c1921", "withdrawn": "", "abstract": "The topology and geometry of foliations on 3-manifolds inform the dynamics of transverse flows. In this vein, we address the following question: What properties of a foliation force all transverse flows to have closed orbits? We fully resolve this question for finite depth foliations on hyperbolic 3-manifolds. These foliations generalize finite-type fibrations by allowing a hierarchy of spiraling behavior. For the foliations which don’t force closed orbits, we construct aperiodic transverse flows. This is joint work in progress with Audrey Rosevear.", "id": "Paper/65567", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65567"}, {"title": " Visual Analysis of Neural Representations with Mapper Graphs: From Explanation to Alignment ", "webprogram_exclude": "0", "session_ids": ["Session/18353"], "source_sha256": "600481604f8b40cdc1c7c34d6fd3e9e7629537c0f9b6efc0e9f36ab975123e76", "withdrawn": "", "abstract": "Neural networks learn high-dimensional representations that capture rich semantic and structural relationships, yet interpreting these representations remains a fundamental challenge for explainable AI. This talk will present how Mapper graphs can serve as interactive visual abstractions that help domain experts explore, interpret, and compare neural representation spaces. \n\nFirst, I introduce Explainable Mapper, a framework for interpreting Mapper graphs constructed from language-model representations. By combining Mapper-based exploration with LLM-assisted explanation and perturbation-based verification, the framework enables users to automatically generate and validate hypotheses about the linguistic properties encoded in Mapper elements, including nodes, edges, paths, connected components, and trajectories. \n\nSecond, I present TopoAlign, which extends the interpretation of a single Mapper graph to the comparison of Mapper graphs built from representations of different models, layers, training epochs, and modalities. Through topology-aware alignment and coordinated visualizations, TopoAlign enables users to compare global structures, identify corresponding local subgraphs, and inspect fine-grained alignment patterns, such as feature splitting, merging, and disentanglement. \n\nTogether, these works demonstrate how Mapper-based visual analysis can support the study of neural representations, from explanation within a single model to comparative alignment across representation spaces.", "id": "Paper/65569", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65569"}, {"title": " VIPERS: A Model of Measles Epidemics Incorporating Vaccination and Commuting Rates ", "webprogram_exclude": "0", "session_ids": ["Session/18159"], "source_sha256": "cd749c76e3bcdef54cc85529549a7e7a091501851e7faf7c9b06406bebc26f8e", "withdrawn": "", "abstract": "Measles is an extremely contagious disease where a single infected individual is likely to infect many others. In epidemiology, this represents a high basic reproduction number, $\\mathcal{R}_0$. Recent decreasing vaccination rates are correlated with an increase in measles cases. An outbreak could be exacerbated by under-vaccinated communities acting as a breeding ground for measles that later spreads to other communities. This could put highly vaccinated communities at higher risk. \n  \n  We developed and analyzed a new compartmental ODE model that we call VIPERS, which tracks sub-populations in different stages of measles: Vaccinated, Infected, Pre-symptomatic, Exposed, Recovered, and Susceptible. We calculate $\\mathcal{R}_0$ to better understand the severity of a measles epidemic for any number of communities with differing vaccination coverage and interconnectedness, and validate our model using real-world data. Additionally, we incorporate interventions such as social distancing into our model to find an optimal strategy for decreasing an epidemic's impact based on the multi-city structure. For larger, highly vaccinated communities connected to much smaller, under-vaccinated communities, we find that social distancing minimizes the number of cumulative infections if the intervention does not start until around day 70, whereas for two similar neighboring cities the social distancing should be implemented in the first few days of an epidemic.", "id": "Paper/65571", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65571"}, {"title": " Eigenvalues of Higher-Order Quaternion Tensors with Applications in Color Video Compression and Facial Recognition ", "webprogram_exclude": "0", "session_ids": ["Session/17942"], "source_sha256": "34943e060e5b9def1b289605179c5a88acdd2badfe1b40c21cb06923d1c43505", "withdrawn": "", "abstract": "In this talk, we investigate the eigenvalue problem for higher-order quaternion tensors under the T-product. We introduce the notion of $p$th-order T-eigenvalues and develop an efficient algorithm for computing right $p$th-order T-eigenvalues and their associated eigentensors by means of complex representation tensors. Several fundamental properties of $p$th-order T-eigenvalues are also established. \n\t\t\n\t\t\nThe proposed framework is further applied to color video compression and color facial recognition. Numerical experiments and comparisons with existing methods demonstrate that our approach achieves competitive compression quality with lower computational cost and provides higher recognition rates with improved efficiency in color facial recognition.", "id": "Paper/65581", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65581"}, {"title": " Fronts and patterns with parameter ramps ", "webprogram_exclude": "0", "session_ids": ["Session/18244"], "source_sha256": "0e0f9243e6cf46547aaa48ede55dac11e794b008ff914e935b8baa685738328d", "withdrawn": "", "abstract": "Pattern formation in the presence of slowly-varying spatio-temporal heterogeneities has application in diverse areas, including biology, chemistry, and fluid dynamics.  Using prototypical PDE models, this talk will discuss front and patterned solutions in the presence of parameter ramps which moderate the instability of a homogeneous equilibrium state.  We will discuss ramps which vary slowly in space, and rigidly propagate in time, as well as those which are slowly-vary in time, but are homogeneous in space. We will discuss how techniques from dynamical systems, geometric singular perturbation theory, modulational approximation, and numerical continuation reveal a variety of novel phenomena.", "id": "Paper/65591", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65591"}, {"title": " Not That Kind of Group: The Origin and Spread of the Core Group in Mathematical Models of STIs ", "webprogram_exclude": "0", "session_ids": ["Session/18374"], "source_sha256": "1918cb74149e134a0eeadaaac8981cef40150c5ad9e30187ffc06d63d7909f9a", "withdrawn": "", "abstract": "Historians and medical practitioners have long perceived the causal relationship between the dissemination of sexually transmitted infections (STIs) and military exploits in particular. For instance, health practitioners from centuries ago understood the social dimensions of diseases such as syphilis: that it migrated with soldiers across oceans and nations as they fornicated with local women and sex workers alike, assigning hierarchies of risk to their behavior. Yet, with the emergence of epidemiology in the 1800s and as its codification took hold in the 1900s, the mathematical models of diseases and epidemics were slower to adopt these social characteristics of disease transmission. However, at the behest of the Public Health Service, American soldiers returning from the Vietnam War with high rates of gonorrhea spurred mathematicians in the late 1960s and throughout the 1970s to examine facets of STIs beyond biological determinants of the host and contagion. Thus, the concept of the core group emerged with mathematical models of gonorrhea. Members of the core group are considered the most \"efficient\" transmitters of disease: they represent less than two percent of the sexually active population, but can be responsible for up to sixty percent of STI transmission. How? How did mathematicians' designation of gonorrhea as a \"social disease\" transform the mathematical models of STIs? How did they use the core group as a quantification of risk? And, ultimately, how did the shifting definitions of the core group impact the mathematical models of HIV/AIDS? Through analyzing the mathematical models of gonorrhea that mathematicians and epidemiologists developed between the 1960s and 1990s, this talk will examine the origination of the core group, the epistemological boundaries of who and what comprises a core group member, and how this concept eventually proved vital for modeling the HIV/AIDS pandemic.", "id": "Paper/65609", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65609"}, {"title": " Adding inputs and outputs to achieve structural identifiability in linear compartmental models ", "webprogram_exclude": "0", "session_ids": ["Session/18039"], "source_sha256": "017249ae1405243ef28c79f485b37037fd9c1ecb9c2268f03e9afbf14f5b786c", "withdrawn": "", "abstract": "Linear compartmental models are used heavily in many application areas, including pharmacology,\ncell biology, toxicology, and ecology; and they typically involve many parameters. In a typical setup,\nthere are some known inputs (controls) and outputs (measured variables), but the other state variables\nare unknown. Sometimes this results in a structurally identifiable model, which means that the parameter\nvalues can be determined (globally or locally) from experimental data, but sometimes this results in an\nunidentifiable model, where one or more parameters can take on an infinite number of values yet yield the\nsame input-output data. In this case, the modeler must decide what to do with their unidentifiable model.\nOne approach is to add inputs and/or outputs to make the model structurally identifiable. However, there\nis no general theory that describes which inputs or outputs are most appropriate to add. Accordingly, we\npropose an algorithm to step-by-step add inputs or outputs to the model to make the model structurally\nidentifiable. Our approach uses computational algebra and matroid theory to determine the dependent\nsets of unidentifiable parameters so that these parameters can be made identifiable one-by-one in an\nefficient way.", "id": "Paper/65611", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65611"}, {"title": " Some new results on quaternion matrix equations ", "webprogram_exclude": "0", "session_ids": ["Session/17942"], "source_sha256": "26b2e5b4d1ed45109290624ca8840277b949f0d6eef2750ca2f8d3153e780fd7", "withdrawn": "", "abstract": "In this talk, we consider some quaternion matrix equations with arbitrary number of equations and unknowns. We derive some practical necessary and sufficient conditions for the existence of a solution to these equations. We also give the general solutions to the equations. Moreover, we propose the applications to the encryption and decryption of color videos using the quaternion matrix equations.", "id": "Paper/65617", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65617"}, {"title": " A mathematical modeling and Epidemiology-Informed Neural Networks framework for uncertainty-aware COVID-19 forecasting ", "webprogram_exclude": "0", "session_ids": ["Session/17972"], "source_sha256": "6890438d7698226537c78abcbe718a886ae7270f5680c182e9d8e547b933e5aa", "withdrawn": "", "abstract": "COVID-19, a respiratory disease caused by the novel coronavirus SARS-CoV-2, has resulted in over 779 million reported cases and approximately 7.1 million associated reported deaths worldwide. Changes in human behavior, policy interventions, population immunity, vaccinations, and the circulation of disease variants continuously trigger new epidemic waves, emphasizing the importance of understanding the complex transmission dynamics of COVID-19. In particular, identifying temporal changes in transmission is essential for accurately reconstructing epidemic patterns and reliably forecasting disease burden. In this talk, I will present an integrated mathematical modeling framework, called Epidemiology-informed Neural Networks (EpINNs), which combines a mechanistic model of COVID-19 transmission with Physics-informed Neural Networks (PINNs). The framework demonstrates how mechanistic mathematical modeling and scientific machine learning can be combined to improve our understanding of the evolving transmission dynamics of COVID-19 and support uncertainty-aware epidemic forecasting.", "id": "Paper/65622", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65622"}, {"title": " From the renormalization group to a Galois group: On the rigor and labor of renormalization, physical and mathematical ", "webprogram_exclude": "0", "session_ids": ["Session/17978"], "source_sha256": "635114ad1b77044c9de1cd103ae80ced5aea0c713089801e07a814d3854b24c9", "withdrawn": "", "abstract": "Arguably, the greatest obstacle to establishing a maximally mathematically rigorous model of QFT, beginning with its inception in QED, has been the presence of divergencies, arising in calculated quantities by altering values of these quantities to compensate for effects of the self-interactions of elementary particles in high-energy regimes. These difficulties were eventually handled by the renormalization procedure. The procedure remains a crucial part of QFT, because all QFTs currently used in high-energy physics contain these divergencies. Remarkably effective as it has proven to be, the legitimacy of the procedure has always been under the debate and have been seen as a problem by many physicists and philosophers of physics. This discontent also led to arguing for the necessity of discrete finite theories (definitionally free of divergencies) replacing QFTs.\nThis talk advocates a different view, building on the use of Galois theory, originating in abstract algebra, in the workings of the renormalization group, which recasts renormalization in terms of effective QFTs, which allow one to investigate the changes of a quantum system at different energy scales. This approach, as developed by A. Connes and M. Marcolli, combines Galois theory with another mathematical theory, the motive cohomology theory, originating in algebraic geometry. The approach leads to a new perspective on renormalization. It suggests that the divergences of QFT are a structured phenomenon, defined by an action of a specific motivic Galois group (governing the renormalization group) on a set of effective theories. This implies that these divergences are not an artifact of the formalism but reflects the existence of new symmetries in nature. The theory, while rigorous mathematically, is hypothetical as concerns its physical viability. The contribution of this talk is twofold. First, it offers a new view of the relationships between the mathematics of QFT and physical reality in high-energy regimes that make this approach to renormalization viable. Secondly, this talk suggests that, if the divergencies of QFT manifest deeper symmetries in nature itself, it may not be possible to replace the current, mathematically continuous, QFTs with discrete finite theories, free from divergencies.", "id": "Paper/65623", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65623"}, {"title": " Quaternion methods for proving theorems about transversals in a spherical triangle ", "webprogram_exclude": "0", "session_ids": ["Session/18336"], "source_sha256": "60fb508da73939ea11f717ba48bc88c1fe669cd8606dd6446a85051152f22589", "withdrawn": "", "abstract": "Quaternions can be used to prove theorems in spherical geometry. Here we use quaternions to show how to prove theorems about the lengths of transversals in spherical triangles.  This technique is featured in the speaker's book \"Spherical Geometry and its Applications,\" with CRC Press.", "id": "Paper/65625", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65625"}, {"title": " Operator-Guided Efficient Transition Path Sampling via Stochastic Optimal Control up to an Exit Time ", "webprogram_exclude": "0", "session_ids": ["Session/18282"], "source_sha256": "11e728bc1b9b04ba9b852c46beb4e3299a598b5a1145034df56620416f24f8c7", "withdrawn": "", "abstract": "Sampling transitions between metastable states is a central problem in dynamical system theory and molecular dynamics in particular. A key challenge is the existence of high free-energy barriers that separate the states, making transitions extremely rare. Recent machine learning-based cast transition path sampling (TPS) as stochastic optimal control (SOC) over a fixed time horizon, and parameterize the drift bias with a neural network trained by simulation-in-the-loop, where training requires repeated biased rollouts. We instead develop a new \\emph{operator-theoretic} approach for the problem based on the Koopman operator. Because Koopman operators are linear, their leading eigenfunctions reveal the metastable sets and provide an estimate of the committor function with no transition path information required. We formulate TPS as an SOC problem up to an \\emph{exit time}. Our time horizon is the first hitting time of the target set, and our running cost penalizes time spent in nonreactive regions by encoding the estimated committor function. We derive the optimal controller in closed-form, and approximate it in a reproducing kernel Hilbert space (RKHS). This reduces the problem of constructing the optimal controller to solving a single equality-constrained convex quadratic program, whose solution is characterized by a linear KKT system. On the two-channel double well, our controller raises the transition hit probability from $0\\%$ to $98.7\\%$ over a time horizon $T=10$.", "id": "Paper/65626", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65626"}, {"title": " A Delayed Smoking Model with General Response and Nonlinear Initiation ", "webprogram_exclude": "0", "session_ids": ["Session/17860"], "source_sha256": "0996f5dda2218cc218bbdc13d55cc0808ca9528643c66d7da4b114a609c4f05c", "withdrawn": "", "abstract": "We study a delayed smoking model with general nonlinear initiation functions\nand a general nonnegative coefficient for the education-modified delayed\npathway. Mass-action incidence and exponential delay attenuation are special\ncases. We prove positivity, boundedness, global existence, and a reproduction\nthreshold. The smoking-free equilibrium is locally stable below the threshold\nand globally stable under a global incidence bound. Above the threshold, a\nsmoking-present equilibrium exists; saturation assumptions ensure uniqueness\nand delay-independent local exponential stability. We also prove uniform\npersistence above the threshold. Two complementary sufficient conditions for\nglobal convergence to the smoking-present equilibrium are obtained: a\nverifiable Lyapunov--Krasovskii matrix inequality and an equilibrium-ratio\ndissipation condition. These global conclusions are relative to histories\ncontaining a nonzero smoking seed and require more structure than the basic\narbitrary-incidence formulation.", "id": "Paper/65627", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65627"}, {"title": " The Berlin Ostraca Revisited ", "webprogram_exclude": "0", "session_ids": ["Session/17713"], "source_sha256": "a526c7f7d6ab30a7697aaf4172d03c076fd434ac45e4e7be0d66948187812a56", "withdrawn": "", "abstract": "Since Jürgen Mau and Wolfgang Müller’s 1962 publication, the Berlin Ostraca have been an anomaly among ancient mathematical sources; the third-century BCE collection of ostraca displays mathematical work in stereometry, similar to Euclid’s \\textit{Elements} Book XIII, far more advanced than any mathematics, geometric or otherwise, in almost all papyrological sources. The provenance, furthermore, is Elephantine, a small island on the southern river Nile about which little is understood of the administrative or intellectual culture. In light of recent scholarship on mathematical diagrams and on the vast antique sources from Elephantine, I revisit the ostraca with a focus on the deceptively simple diagrams. As a result, I reveal the Berlin Ostraca may contain direct references to Euclid’s \\textit{Elements} and further material from the \\textit{Elements} Book III. In my talk, I will discuss these potential new findings, how they relate to the stereometric material in the text, and suggest future research on the Elephantine island.", "id": "Paper/65628", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65628"}, {"title": " Adopting and Assessing Impacts of Alternative Grading Practices in Introductory Mathematics Courses ", "webprogram_exclude": "0", "session_ids": ["Session/18440"], "source_sha256": "aeb11973b7bfd6b1b85d4e84bb3a843f3bd2f6cf3205c39f594fab684a8a4255", "withdrawn": "", "abstract": "In this session, we present work-in-progress addressing two significant challenges in the alternative-grading movement in our local context: implementing practices at scale and generating research-backed insights on student impacts. First, we share our experience implementing a hybrid model of mastery-based and specifications-based grading in introductory linear algebra (300 students) and multivariable calculus (180 students), each offered in coordinated sections. Second, we present the research design of our ongoing study examining how these practices influence students’ basic psychological needs—grounded in Self-Determination Theory—and their perceptions of alternative versus traditional grading. Ultimately, this work seeks to advance broader understanding of how students navigate, internalize, and respond to alternative grading in large-enrollment courses.", "id": "Paper/65629", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65629"}, {"title": " On a thermoelastic Shear: Well-posedness and stability ", "webprogram_exclude": "0", "session_ids": ["Session/19363"], "source_sha256": "26ab2c8b053c7403420ba4586aea317ae73b061d7241689f4b27f57afb901296", "withdrawn": "", "abstract": "In this talk we present, in a bounded interval, a one-dimensional linear thermoelastic shear Bresse system, where the heat effect is given by Fourier’s law.\nFirst, we consider one problem, in some details, by establishing the well posedness, using the semigroup theory and with the help of non-classical deferential operators. After that, we discuss the stability of the system, in the case of equal and nonequal speed of wave propagation. \nFinally, we shade some lights on two other similar systems.", "id": "Paper/65638", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65638"}, {"title": " Structure of Linear Extensions of Partially Ordered Sets ", "webprogram_exclude": "0", "session_ids": ["Session/19340"], "source_sha256": "032b38daa2aef5246b167680ad44e5072fd3d3840073a4b08ca023c371e82671", "withdrawn": "", "abstract": "We study the structure of linear extensions of a finite poset $P$ by investigating partial orders on the maximal chains of the lattice of order ideals $J(P)$. These partial orders on the maximal chains of $J(P)$ are called maximal chain descent orders (MCDOs) introduced by Lacina. MCDOs come from EL-labelings of finite bounded posets and encode the structure of shellings arising from EL-labelings. Every linear extension of $P$ gives an EL-labeling of $J(P)$, and so generates an MCDO. Our main question is: when do different linear extensions of $P$ result in isomorphic MCDOs? We give partial answers to this question. In particular, we prove that linear extensions that are related by an automorphism of $P$ result in isomorphic MCDOs. Additionally, we show that, for a certain family of posets, a linear extension $l$ and Stanley's evacuation of $l$ generate isomorphic MCDOs. In this case the isomorphism comes from a well known isomorphism of weak order on permutations.", "id": "Paper/65639", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65639"}, {"title": " The Banach–Mazur distance between <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"9.73ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 4189.3 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">C([1,\\omega ^n])</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-43\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 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xlink:href=\"#E1-MJMAIN-29\" x=\"3275\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18364"], "source_sha256": "b9c291680ddfea08629a9644864a7fa63adb611959e69c58028e4e2e718e94fc", "withdrawn": "", "abstract": "We give precise values of the Banach--Mazur distance between spaces $C([1,\\omega^n])$ and $C([1,\\omega])$ of all continuous real-valued functions on ordinal intervals endowed with the order topology.\nThis solves a long-lasting problem posed by Bessaga and Pełczyński. Joint work with Łukasz Piasecki.\n\n\\noindent\\textbf{References}\n\nMarek Malec, Łukasz Piasecki,\n\\emph{The Banach--Mazur distance between $C([1,\\omega^n])$ and $C([1,\\omega])$}, Studia Math. 285 (1), 91--104 (DOI: 10.4064/sm250120-15-7).", "id": "Paper/65641", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65641"}, {"title": " Energy-Based Physics-Informed Form Finding for Clustered Tensegrity Structures ", "webprogram_exclude": "0", "session_ids": ["Session/18305"], "source_sha256": "01edeb6e4def736819a7118e646b1f2ff6825de51106181fea8691a8e330e309", "withdrawn": "", "abstract": "Tensegrity form-finding and physical property prediction are fundamental problems in structural mechanics, which aim to determine equilibrium configurations and internal force distributions. These problems are challenging due to strong nonlinearity arising from the coupling between geometry and forces, and the need to satisfy equilibrium, stability, and structural constraints. This paper proposes an energy-based learning approach for clustered tensegrity form finding and physical property prediction. The proposed approach incorporates total potential energy minimization and constitutive relations into the training objective, enabling the prediction of equilibrium nodal configurations and the reconstruction of physical quantities such as member forces and force densities. By integrating energy-based physical losses directly into the learning process, the method promotes physical consistency while combining data-driven learning with physics-based constraints. Numerical experiments on tensegrity prism and lander structures demonstrate accurate prediction of equilibrium configurations and internal forces across different training-data ratios, indicating the potential of the proposed approach for nonlinear tensegrity form finding and structural analysis.", "id": "Paper/65642", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65642"}, {"title": " Counting Schreier Sets Under Neighborhood Conditions ", "webprogram_exclude": "0", "session_ids": ["Session/17106"], "source_sha256": "4d7a6770dcf2c99ecbab8d285bf93bdaf69f72caab69b05c5db587c757067753", "withdrawn": "", "abstract": "We count Schreier sets that satisfy a neighborhood condition, including $k$-clustered, $k$-consecutive-free, $k$-neighbored, $k$-isolated, and closed under integral $2$-averages. For\nthe first four conditions, we determine the initial counts and prove linear recurrence relations.\nFor the last condition, we prove a recurrence that involves the divisor counting function.", "id": "Paper/65647", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65647"}, {"title": " Minimax Optimal Estimator and Improved Error Rate for the MLE in Logistic Regression with Gaussian Design ", "webprogram_exclude": "0", "session_ids": ["Session/17718"], "source_sha256": "8d579b8fd9f867a7cdfd608bdb36e3155146b883728f8b01e1c04bb476f8e3a4", "withdrawn": "", "abstract": "We study finite-sample parameter estimation in logistic regression with Gaussian design, where the goal is to estimate $\\btheta^*\\in \\mathbb{R}^d$ with $R=\\|\\btheta^*\\|_2\\ge 1$ from i.i.d. samples $\\{(\\bx_i,y_i)\\}_{i=1}^n,$ $\\bx_i \\sim N(\\bm{0},\\bI_d)$, $y_i\\mid \\bx_i \\sim \\Bern((1+\\exp(-\\bx_i^\\top \\btheta^*))^{-1})$. In this paper, we provide the first minimax optimal estimator, and improve on the best known finite-sample error rate for the maximum likelihood estimator (MLE). These two accomplishments are due to a minimax optimal estimator for the parameter norm $R$. First, we establish the minimax lower bound $\\Omega(\\sqrt{R^3/n})$ for norm estimation. We then improve the best known norm estimation error rate of the MLE, i.e., $O(\\sqrt{R^3d/n})$ from Chardon, Lerasle, and Mourtada (2024), to $\\tilde{O}(\\sqrt{R^3/n}+R^2d/n)$. The additional term, $R^2d/n$, appears to be the intrinsic bias of the MLE, as evidenced by the high-dimensional asymptotic theory Zhao, Sur, and Candes (2022) and numerical examples. We show that, however, this additional term is not information-theoretically necessary. To this end, we construct  an efficient debiased norm estimator that achieves the error rate $O(\\sqrt{R^3/n})$   and is therefore minimax optimal. Combining this with the optimal direction estimator given by the MLE, we establish the minimax optimal rate $\\Theta(\\sqrt{Rd/n}+\\sqrt{R^3/n})$ for estimating $\\btheta^*$, as well as the improved finite-sample error rate $\\tilde{O}(\\sqrt{Rd/n}+\\sqrt{R^3/n}+R^2d/n)$ for the MLE. Numerical experiments demonstrate that the proposed minimax optimal estimators outperform the MLE.", "id": "Paper/65648", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65648"}, {"title": " Exotic Worm Domains in Complex Manifolds ", "webprogram_exclude": "0", "session_ids": ["Session/17887"], "source_sha256": "3b2ff0027e8b5d3f23f32854ecdbee99fd3f070cb6c56c716d9b9df1aa670d86", "withdrawn": "", "abstract": "Worm domains were first constructed by Diederich and Fornaess in 1977 as examples of smoothly bounded pseudoconvex domains in $\\mathbb{C}^n$ that do not admit a Stein neighborhood base.  Since then, worm domains have provided counterexamples to many other phenomena in Several Complex Variables.  By \"exotic\" worm domains, we mean pseudoconvex domains exhibiting worm-like behavior (as measured by a particular cohomology class) which do not admit Stein neighborhoods.  We will provide examples of exotic worm domains in different complex manifolds and discuss some preliminary results and open problems on such domains.", "id": "Paper/65653", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65653"}, {"title": " Folding Paper to Explore the Locus of Points Beyond Conics. ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "ce7f4942fda51a7e68f7ed72c136ae5c75e84713630d55034fba2e8904955d3c", "withdrawn": "", "abstract": "The classical question that starts “the locus of points equidistant between a point and ...” has many interesting generalizations, where the second object need not be a point or a line, but a “generalized directrix.” This was easy to explore with patty paper and fold lines, but it quickly became difficult to see exactly what curves were being produced and some hidden nuances in the notion of “distance to a curve.” I became interested in how this could be done recursively, where fixing an initial point $O$ and curve $C_0$ uniquely defines a whole sequence of curves $C_i$. Reframing this question intrinsically, it became clear that we did not need to look at all of $C_0$ at a time, but we were able to map the orbit of a single point through each step in the sequence. After implementing this in Python just to see what it looked like, this yielded beautiful pictures and surprising results. Clearly articulating these patterns as conjectures, we were able to prove that they were not coincidental, but consequences of the underlying geometry.", "id": "Paper/65659", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65659"}, {"title": " Mapping Performance Metrics Over Time to Monitor Program Development: An Application of NCAA Track & Field Data  ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "b1829878d44cd643817886e95bcec154146da2cd2ff365051bfc9454801f5712", "withdrawn": "", "abstract": "When evaluating schools in the collegiate track and field system, athletes often consider team performance, coaching, and program reputation; however, there is limited publicly available information that objectively measures these factors. This project uses NCAA track and field performance data to address the lack of accessible data-driven insights by identifying which schools have progressing programs, and which develop their athletes on a year-to-year basis.\nPerformance data points are collected from the Track & Field Results Reporting System (TFRRS) to construct a database of NCAA athletes and their performances across their collegiate career. The project develops statistical methods and models for measuring individual athlete progression, which are then aggregated at the program level to compare patterns of athlete development across schools and conferences.\nThe analysis aims to differentiate programs that consistently improve athlete performance from those whose success may primarily reflect recruiting already accomplished athletes, especially by allowing athletes to see their own expected improvement percentages as their data is synthesized through our own predictive modeling. The project provides recruits, transfers, and high school athletes with a more transparent and objective way to evaluate collegiate opportunities.", "id": "Paper/65660", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65660"}, {"title": " Optimal Hardness of Online Algorithms for Large Common Induced Subgraphs ", "webprogram_exclude": "0", "session_ids": ["Session/18002"], "source_sha256": "f5d83ee73e60721cc0b028096a7edb45203dc48d6194a4dc24368a7ebb6efaeb", "withdrawn": "", "abstract": "We study the problem of efficiently finding large common induced subgraphs of two independent $\\mathbb{G}(n, 1/2)$ graphs. We show that a simple greedy online algorithm finds a common induced subgraph of half-optimal size with high probability, and use the Overlap Gap Property to show that no online algorithm can do better than half-optimal with probability bounded away from zero. This work is joint with David Gamarnik and Mikl\\'os Z. R\\'acz.", "id": "Paper/65670", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65670"}, {"title": " Optimal Learning of Linear Operators ", "webprogram_exclude": "0", "session_ids": ["Session/18447"], "source_sha256": "1562ae8c26f3ad8ab440b54e69c7f71625ebd27b4f3ba973df914a0032d58f56", "withdrawn": "", "abstract": "Operator learning is an emerging paradigm at the intersection of scientific computing and machine learning. Its central objective is to learn operators between function spaces from data. Although operator learning has found broad applications across science and engineering, its theoretical foundations remain underdeveloped. In this talk, I will present recent progress on the statistical and computational limits of operator learning, focusing on several fundamental operator classes: bounded linear operators between Sobolev spaces, pseudo-differential operators central to the analysis of partial differential equations (PDEs) and mathematical physics, and Fourier integral operators associated with hyperbolic systems and wave propagation. Across these settings, a common multiscale framework yields minimax-optimal statistical rates together with computationally efficient estimators. These results contribute to a unified theory of operator learning at the interface of analysis and PDEs, computational mathematics, statistics, and data science.", "id": "Paper/65682", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65682"}, {"title": " Any-dimensional metanetworks ", "webprogram_exclude": "0", "session_ids": ["Session/18036"], "source_sha256": "64f5ced2b656a8bfb4d9b1b1e3752768ab5f0365ab90d0e0cf9a29fc4e545efc", "withdrawn": "", "abstract": "Any-dimensional machine learning models can be defined on a fixed set of parameters and be evaluated on inputs of varying sizes. This idea was common for many models, including graph neural networks, but was recently formalized by Eitan Levin using algebraic ideas related to symmetries and representation stability. In this talk, we explain its mathematical formulation and apply these ideas to \"graph metanetworks\". \n\nGraph metanetworks are neural networks that take the weights of another neural network as input and predict useful properties of it.\nExisting metanetworks are trained and tested on input networks of a single fixed size, yet operating across sizes is what one usually wants in practice: training on small networks and evaluating on large ones is far cheaper, provided that generalization holds.\nWe show that strong out-of-distribution size generalization across model widths is possible with the right architecture on the suitable test data distribution (in particular, input networks trained with $\\mu P$).", "id": "Paper/65683", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65683"}, {"title": " Instructional Support of Student Prior Knowledge in Calculus Classrooms ", "webprogram_exclude": "0", "session_ids": ["Session/18068"], "source_sha256": "46a54b5e17d735c91ab490928a0985264aae8a9adbb892906e30ca9d82896e62", "withdrawn": "", "abstract": "Postsecondary mathematics is well documented as a stumbling block for STEM (science, technology, engineering, and mathematics) major college students (Bressoud, 2015; Rasmussen et al., 2014). The Mathematical Association of America (MAA) has called for a transformation of postsecondary mathematics requirements (Burn & Zoellner, 2024) focused on offering major dependent pathways. While these pathways more closely match mathematics content to intended majors, if the mathematics instruction does not support students, they may still struggle. For this reason, it is important that as we look at transforming postsecondary mathematics we also focus on understanding and strengthening postsecondary mathematics classroom instruction.\nThis manuscript reports on a secondary analysis of survey and interview data from postsecondary mathematics instructors to understand the frequency with which they report engaging in ‘good’ instructional practices (e.g., Fenstermacher & Richardson, 2005) in their introductory calculus courses. Interview data is used to provide detail and depth to the survey responses. Survey data was collected from 148 self-selected introductory calculus instructors at postsecondary institutions across the United States. Using a cluster analysis based on their reported instructional practices, 6 instructors were recruited for interviews to describe their instruction both generally and specifically when they introduce the definition of the derivative to students. Survey data is used to better understand the frequency of specific best teaching practices and comparative tests are used to see if differences exist between groups of instructors. Interview data is analyzed thematically to provide examples of what these self-reported practices may look like in the classroom. \nBy understanding what reported instructional practices look like in postsecondary introductory calculus classrooms - and if and how often instructors engage in ‘good’ teaching practices, we may better support them in strengthening their instruction. These results can illuminate how mathematics teacher educators might support current and future postsecondary mathematics instructors.", "id": "Paper/65686", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65686"}, {"title": " The Rogers–Ramanujan–Slater Data Base ", "webprogram_exclude": "0", "session_ids": ["Session/18333"], "source_sha256": "6af125aca2e8ce8799fbcfe4b20e134f8cf8cc0b7e9031cdbdd1ba67d0c2821d", "withdrawn": "", "abstract": "The RRSDB (Rogers—Ramanujan—Slater Data Base) has been under development for a few years now, and will continue to be a work in progress.   The RRSDB is inspired by the OEIS, LMFDB ($L$-functions and modular forms database), Atlas of Finite Groups, and other mathematical databases that have become standard tools for students and practitioners, combined with the famous list of 130 Rogers--Ramanujan type identities published by Lucy Slater in 1952, and subsequent attempts to publish expanded versions of Slater's list.   The speaker will demonstrate current features and content, and speculate on possible future developments.  Contributors to the database include the speaker, Hunter Waldron, Kevin ``KG\" Gomez, Shashank Kanade, and Robert Schneider.   Interested audience members are invited to join the project development team.", "id": "Paper/65687", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65687"}, {"title": " Reduced-Order and Machine-Learning Methods for Multiscale Reactive Transport ", "webprogram_exclude": "0", "session_ids": ["Session/17926"], "source_sha256": "158ba164f75a8788e78f6b6635f79ad37de300418ea5875ae25a7cf1d8d5fa0d", "withdrawn": "", "abstract": "Reactive transport plays an important role in many applications, including contaminant transport, nuclear waste disposal, geochemical processes, and carbon dioxide sequestration. These models typically involve the coupling of fluid flow, transport of multiple chemical components, and complex reaction processes. We consider such coupled systems in heterogeneous multiscale media, where strong variations in material properties and nonlinear reactions can make direct numerical simulations computationally expensive. We develop a hybrid reduced-order and machine-learning framework based on iterative coupling between the flow and reactive transport problems. Within the reactive transport solve, an operator-splitting strategy is used to decouple the transport and reaction subproblems. The transport equations are solved implicitly and projected onto a reduced-order space designed to capture the dominant multiscale features of the heterogeneous medium, while the nonlinear reaction step is approximated using a data-driven model that learns the local reaction dynamics. Numerical examples are used to study the accuracy and computational efficiency of the proposed approach.", "id": "Paper/65688", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65688"}, {"title": " On Fast-Slow Mean-Field Forward-Backward Stochastic Systems ", "webprogram_exclude": "0", "session_ids": ["Session/18274"], "source_sha256": "b2d9e3dc4cfbff78f079bf1db0a219fabe9854849db765e96d427928e31ebb59", "withdrawn": "", "abstract": "We establish an averaging principle for a class of multiscale mean-field forward-backward stochastic differential equations and identify several mechanisms that are absent from classical slow-fast systems. In particular, the classical procedure of freezing the slow variables at deterministic values and averaging with respect to the invariant measure of the resulting fast dynamics is no longer valid. The correct averaging mechanism is instead governed by a frozen fast dynamics in a random environment and its associated conditional invariant measures, which preserve the dependence between the slow state and its distribution.\n\nThe forward-backward structure creates a further obstruction: local averaging estimates need not remain stable when propagated over an arbitrary time horizon. We identify a stability condition formulated through the decoupling field of the averaged system under which this obstruction can be overcome. Using a joint lifted semigroup for the state-law dynamics, together with a two-scale discretization and a Gordin-type decomposition, we prove strong averaging for both the forward and backward components with the optimal convergence rate \\(O(\\varepsilon^{1/2})\\).\n\nAs an application, we apply the general theory to a class of mean-field stochastic control problems and develop an efficient algorithm for solving the resulting control problems.", "id": "Paper/65719", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65719"}, {"title": " Parity of the partition function in quadratic progressions ", "webprogram_exclude": "0", "session_ids": ["Session/18333"], "source_sha256": "9957549c0a3024fbf45432d749e643c79cb1adf9d46a5c75b2694e816a07acd9", "withdrawn": "", "abstract": "The parity of the partition function $p(n)$ is one of the most\nstubborn problems in number theory.  In 2010, the first author conjectured, for square-free $1<D\\equiv 23\\pmod{24}$, that the values\r\n$$p\\!\\left(\\frac{Dm^2+1}{24}\\right),$$\r\nas $m$ ranges over positive integers with $(m,6)=1$, include infinitely\r\nmany even and infinitely many odd terms.  We prove\r\nthis conjecture.\r\nThe key new idea is geometric.  Logarithmic derivatives of\r\n\\emph{twisted Borcherds products} built from Ramanujan's third-order\r\nmock theta functions recast the problem in terms of CM points of\r\ndiscriminant $-D$ on $X_0(6)$.  \r\nThese results imply that\r\n\\[\\#\\{0\\leq n\\leq X: p(n)\\text{ is odd}\\}\\gg\\sqrt X,\\]\r\nwhich is now the best known lower bound for odd values of $p(n)$. The algebraic identities at the heart of this paper, as well as the improved lower bound for odd partition numbers, have been formalized in Lean by AxiomProver.", "id": "Paper/65723", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65723"}, {"title": " Two-Color Rado Numbers for Equal-Coefficient Non-Homogeneous Equations ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "2c30c37f86bd79e67bab96bfe11312e22f04831f385087e2ed6db1c56064435e", "withdrawn": "", "abstract": "A two-color Rado number asks how far one must color the positive integers before a monochromatic solution to a given equation is unavoidable. Here, we study the equal-coefficient non-homogeneous equation $t x_1+t x_2+\\cdots+t x_m=x_{m+1}+c$, \nwhere $m\\ge2$, $t\\ge1$, and $c\\le mt-2$. Write\n$S=mt,\\ D=S-1-c.$\nIf $S$ and $c$ are both odd, the odd-even coloring shows that the\nRado number is infinite. In every remaining parity case we determine the\nRado number exactly: $R_2(m,t,c)=1+(mt-1-c)(mt^2+t+1).$\nThe lower bound comes from an explicit three-block coloring. For the upper\nbound, we shift the positive integers to start at $0$.  In these coordinates,\nthe defect $D$ is an additive constant. A minimal-counterexample scaling\nargument reduces the problem to the primitive defects $1$ and $2$.\nThe primitive problem becomes a question about sums of $m$ same-colored integers. A\ncollision between a red $m$-sum and a blue $m$-sum forces the same output\nto have both colors. A short case analysis proves that such a collision is\nunavoidable. The formula recovers the previously known homogeneous and\nunit-coefficient cases.", "id": "Paper/65725", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65725"}, {"title": " Exact weight filtrations of half the theta cycle modulo <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.313ex\" height=\"2.843ex\" style=\"vertical-align: -0.671ex; margin-left: -0.089ex;\" viewBox=\"-38.5 -934.9 995.9 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">p^2</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-70\" d=\"M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-70\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-32\" x=\"712\" y=\"513\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18276"], "source_sha256": "3dba8305bf3e5c36cd259cb96c218af2eb82a5f0968c9fda35f86212a8b331a7", "withdrawn": "", "abstract": "Congruences between modular forms play many important roles in number theory. Examining repeated derivatives of a modular form yields the theta cycle, which has been a major tool when working with modular forms modulo a prime $p$. The theta cycle modulo $p$ is known, but the theta cycle modulo higher powers of primes remains mysterious. Previous work has provided exact values for a proportion of the theta cycle modulo $p^2$, but this proportion diminishes when the weight $k$ is near to the prime $p$. We remove the dependency on $k$ to understand at least 49\\% of every theta cycle modulo $p^2$ for all $p$ and all $k < p$. This is joint work with Martin Raum and Olav Richter.", "id": "Paper/65726", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65726"}, {"title": " Professional Development and Its Influence on Mathematics Faculty ", "webprogram_exclude": "0", "session_ids": ["Session/18091"], "source_sha256": "15e607c8932631356fe73ceb02faab65e784c5073a0826a15281757ea243ad85", "withdrawn": "", "abstract": "Professional development (PD) experiences of mathematics faculty at a public research university and the conditions influencing whether learning translates into instructional practice. Semi-structured interviews were conducted with two mathematics faculty members and analyzed using thematic analysis through a framework of PD effectiveness. Findings indicate that faculty perceive extended, immersive experiences as most effective, particularly when coupled with accountability for classroom implementation and disciplinary relevance. Collaborative learning and concrete guidance facilitated implementation, while time constraints, overwhelming communication, and difficulty translating ideas into practice emerged as barriers", "id": "Paper/65728", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65728"}, {"title": " On the classification of the seven-dimensional Lie algebras with five-dimensional nilradical ", "webprogram_exclude": "0", "session_ids": ["Session/19342"], "source_sha256": "1f56b412214acd5a9f46b62f4fb01b624502797efed07ef99685a484f30a475b", "withdrawn": "", "abstract": "In this talk, we will give an overview of the classification problem of the seven-dimensional solvable Lie algebra. We present a complete list of solvable algebras with five-dimensional nilradical.", "id": "Paper/65730", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65730"}, {"title": " Arithmetic growth in partially commutative semigroups of endomorphisms ", "webprogram_exclude": "0", "session_ids": ["Session/18259"], "source_sha256": "1fe651f5965ce45a71f7237fd53ee708d68dcb51c5fbf9008053226cd0a13ba7", "withdrawn": "", "abstract": "We establish asymptotics for the degree and height growth rate functions of partially commutative semigroups of endomorphisms of varieties, i.e., semigroups where the only relations between generators, if any, are commuting ones.", "id": "Paper/65732", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65732"}, {"title": " Exit Times and Location Detection ", "webprogram_exclude": "0", "session_ids": ["Session/17442"], "source_sha256": "12633cc1cd412364a2a513c6a85db8741de3dab42713b3d3d213ef144b30c7aa", "withdrawn": "", "abstract": "In 2023, Wyman and Xi asked ``Can you hear your location on a manifold?'' We pose a related question, asking if probabilistic data can be used to recover location within a manifold. More precisely, we ask if location can be recovered from the distribution of exit times of Brownian sample paths. We show that exit time moments determine location up to symmetry for a variety of two-dimensional domains. We also establish detection results on general planar domains. The key tool driving our work is a ``Poisson hierarchy,'' which establishes a connection between exit time moments of Brownian motion and solutions to a family of Poisson problems.", "id": "Paper/65733", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65733"}, {"title": " Identifiability of Directed-Cycle and Catenary Linear Compartmental Models ", "webprogram_exclude": "0", "session_ids": ["Session/18127"], "source_sha256": "0ca9a0c1cb728e9d4d8c84512f173ca47596a46bc7ef0a7d63d335fb09fd440d", "withdrawn": "", "abstract": "A parameter of a mathematical model is structurally identifiable if it can be determined from noiseless experimental data. We examine the identifiability properties of two important classes of linear compartmental models: directed-cycle models and catenary models (models for which the underlying graph is a directed cycle or a bidirected path, respectively). Our main result is a complete characterization of the directed-cycle models for which every parameter is (generically locally) identifiable. Additionally, for catenary models, we give a formula for their input-output equations. Such equations are used to analyze identifiability, so we expect our formula to support future analyses into the identifiability of catenary models. Our proofs rely on prior results on input-output equations, and we also use techniques from linear algebra and graph theory.", "id": "Paper/65734", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65734"}, {"title": " Toric compactifications of periodic graph operators ", "webprogram_exclude": "0", "session_ids": ["Session/18292"], "source_sha256": "7fe3fe509744ff152ec8877d0311a2b639ae6a6e7e9614c59358f3199adb74b8", "withdrawn": "", "abstract": "A periodic graph operator is a Laplacian plus potential acting on functions on the vertices of a periodic graph. The spectrum of this operator is the projection of an affine algebraic variety called the Bloch variety. We complexify and compactify this variety in a suitable toric variety and ask under what conditions we can extend operators to this toric variety. We outline a few spectral-theoretic consequences of this compactification.", "id": "Paper/65736", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65736"}, {"title": " An exploration of zero forcing variants through reconfiguration graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18207"], "source_sha256": "cd70f739ccb19f3c0588323d392d8930b68347317164e3b3cf6f32e2d7eb48c8", "withdrawn": "", "abstract": "Reconfiguration graphs are used to study how sets with a chosen property are related to each other.  For example, a token jumping reconfiguration graph represents the sets as vertices and indicates with edges when pairs of sets are related by an exchange of an element in one set for a different element in the other.\n\nIn zero forcing, we use token reconfiguration graphs to examine the relational structure of minimum forcing sets.  Interesting aspects of such reconfiguration graphs can reflect interesting behaviors of the forcing rules with respect to the base graphs that the reconfiguration graphs are derived from.\n\nIn this talk, we explore the positive semidefinite (PSD) and skew zero forcing rules through the lens of token jumping and token sliding reconfiguration graphs.  We encounter a few of those `interesting' things along the way, including a curious identity between PSD forcing on block graphs and skew forcing on a certain family of trees.", "id": "Paper/65737", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65737"}, {"title": " Classifying Possible Density Degree Sets for Hyperelliptic Curves ", "webprogram_exclude": "0", "session_ids": ["Session/18379"], "source_sha256": "52267b7cea3573af29e9c99ef2ba2c5499ae0ceefa6cd3c829507812e5fb8962", "withdrawn": "", "abstract": "Let $C$ be a smooth, projective, geometrically integral hyperelliptic curve of genus $g \\geq 2$ over a number field $k$. We provide a classification of the possible density degree sets $\\delta(C/k)$ for such curves, focusing on the subset of points that arise from morphisms to $\\mathbb{P}^1$, which we refer to as $\\mathbb{P}^1$-parameterized points, denoted as $\\delta_{\\mathbb{P}^1}(C/k)$. As a framework, we utilize the notion of $\\mathbb{P}^1$-parameterized points, which arise from natural geometric constructions first introduced by Bianca Viray and Isabel Vogt which result from pulling back rational points on $\\mathbb{P}^1$. In particular, we determine the structural constraints on the density degree sets imposed by the arithmetic of the Jacobian, detailing when these sets are restricted to solely even integers or contain odd degrees.", "id": "Paper/65738", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65738"}, {"title": " Great Expectations for the Determinant, Trace, Characteristic, and Minimal Polynomials ", "webprogram_exclude": "0", "session_ids": ["Session/17855"], "source_sha256": "9198528a814517b24de7ff8bd90b8e126257e86c7b1b8da797dd2a2d547755dc", "withdrawn": "", "abstract": "The minimal polynomial of a square matrix $M$, $\\mu_M$, is typically introduced with a \"mission\"—something to do: provide the \"smallest\" polynomial that $M$ satisfies. Its peer concepts of Trace, Determinant, and Characteristic polynomial are typically not so introduced, but they can be, working over $\\mathbb R$ or $\\mathbb C$. The Trace of $M$ is, scaling aside, the \"smallest\" similarity-invariant way to \"put a number on a matrix\". The Characteristic polynomial is the unique invariant way to assign to an $n \\times n$ matrix $M$ a degree $n$ polynomial $\\chi_M$ (depending polynomially on $M$), so that when $\\mu_M$ is of degree $n$, $\\chi_M=\\mu_M$. The determinant, with its longer history, carries a rich collection of competing missions. Historically, the determinant put a number $\\det (M)$ on $M$ so that the number is nonzero when and only when corresponding linear systems are consistent, with unique solutions. The axiomatic treatment of the determinant, often attributed to Karl Weierstrass, provides an indirect sense of mission. But constructing the determinant function is awkward to motivate in an elementary context. This can be abetted by the Last-Mile variant of (Gauss-Jordan) Elimination, and the Faddeev-LeVerrier algorithm can help tie things together, as we will detail.", "id": "Paper/65741", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65741"}, {"title": " On Directional Curvature Methods for Efficient Word2Vec Optimization ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "ff45f2ad7ee5bbd32da227c73b1a10981994fe5d6bda232fb92fccb89bee7e91", "withdrawn": "", "abstract": "Word embeddings are important in many natural language processing applications, but their training is still dependent on first-order optimization methods (e.g., Adam, SOAP). This raises the question of whether second-order curvature information can improve training efficiency without being computationally expensive in the long run. In this work, we study the application of second-order methods to the Continuous Bag-of-Words (CBOW) and Skip-gram objectives of the word2vec model. In particular, we derive explicit expressions for the directional curvature in the CBOW and Skip-gram objectives, and we show that these directional curvature quantities can be evaluated with essentially the same asymptotic computational cost as a gradient. These results motivate the use of computationally efficient curvature-aware optimization methods, which we investigate experimentally with the Rescaled Exponential Decay (RED) optimizer, two variants that we introduce (RED-M and RED-Hessian), and several established baselines. Our experiments show that curvature-aware optimization can improve convergence behavior and, in some settings, reduce overfitting, but does not consistently translate into higher-quality semantic embeddings. Together, our results clarify both the applications and the practical limitations of incorporating second-order information into word embedding training.", "id": "Paper/65743", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65743"}, {"title": " Differentiability and Mode Selection in Modal-Based Structural Optimization ", "webprogram_exclude": "0", "session_ids": ["Session/18069"], "source_sha256": "a8d8d84b2119418d83e2c61937e176fac8f10fc566ec4185f032c78085be4d3e", "withdrawn": "", "abstract": "Design, model calibration, and non-destructive testing require objective functions that compare computed and target vibrational modes. Standard mode-matching objectives become fragile near repeated eigenvalues, where eigenvectors are not uniquely defined and may fail to be differentiable with respect to multiple design variables. Building on classical spectral-projector perturbation results, we identify a practical framework for differentiable modal optimization: least-squares objectives that depend on isolated modal subspaces rather than on individual eigenvectors. The resulting adjoint sensitivities avoid the difficult nullspace term required by classical repeated-eigenvalue eigenvector sensitivity methods.\n\nWhile this subspace formulation resolves important local differentiability issues, global optimization still requires selecting the correct modes or modal subspaces when the current design is far from the target. We discuss two strategies for this mode-selection problem. The first segregates modes by type and uses alternating minimization to update design variables and mode assignments. The second introduces nonsmooth regularization to encourage sparse or structured mode selection to avoid overfitting. Together, these ideas provide a promising framework for gradient-based modal optimization in settings with repeated eigenvalues, mode switching, and mode-selection challenges far from the desired design.", "id": "Paper/65747", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65747"}, {"title": " Numerical Investigation of Heat and Mass Transfer in a Non-Newtonian Quaternary Hybrid Nanofluid over a Stretching Sheet ", "webprogram_exclude": "0", "session_ids": ["Session/19343"], "source_sha256": "cb8dce3132a02ca96d450817e0af19ffaaecf8692b5c7d9449daea36c5ce4ddd", "withdrawn": "", "abstract": "This study presents a numerical investigation of heat and mass transfer in a three-dimensional non-Newtonian quaternary hybrid nanofluid flow over a stretching sheet. The quaternary hybrid nanofluid consists of single-wall carbon nanotubes (SWCNT), multi-wall carbon nanotubes (MWCNT), alumina (Al$_2$O$_3$), and titania (TiO$_2$) nanoparticles dispersed in ethylene glycol. The non-Newtonian behavior of the fluid is modeled using the Upper Convected Maxwell (UCM) model. The governing partial differential equations for momentum, energy, and concentration are transformed into a system of nonlinear ordinary differential equations using similarity transformations. The resulting equations are solved numerically with MATLAB's \\texttt{bvp4c} solver. The effects of key dimensionless parameters, including the Deborah number, Prandtl number, Schmidt number, Brownian motion parameter, thermophoresis parameter, and Soret parameter, on velocity, temperature, and concentration profiles are analyzed. The study also compares the transport performance of simple nanofluid, hybrid, ternary hybrid, and quaternary hybrid nanofluids. The results show that the quaternary hybrid nanofluid significantly enhances heat and mass transfer characteristics, producing higher Nusselt and Sherwood numbers compared to other nanofluid compositions. The findings demonstrate the potential of quaternary hybrid nanofluids in advanced thermal engineering and industrial heat transfer applications.", "id": "Paper/65748", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65748"}, {"title": " On the Spectral Synthesis of Lipschitz Persistence Diagram Vectorizations ", "webprogram_exclude": "0", "session_ids": ["Session/19336"], "source_sha256": "a5c716c704c88dcb3924dc9af33edcbdaeceb248bab38143941ee53e91c51d71", "withdrawn": "", "abstract": "A persistence diagram represents the birth and death of homology classes along a filtration as a multiset of intervals, and we consider persistence diagram vectorizations to be maps \\( D(X,A) \\to E \\) sending persistence diagrams over a metric pair $(X,A)$ to values in a Banach space \\( E \\). We prove an isometric isomorphism between Lipschitz extensions of vectorizations, modulo constants, on the Grothendieck completion \\( K(X,A) \\) of \\( D(X,A) \\) and the bounded \\( 1 \\)-cocycles for the translation action of \\( K(X,A) \\) on \\( \\ell ^ \\infty ( K(X,A), E ) \\). We then prove that if every bounded linear functional on \\( E \\) maps a Lipschitz extension of a vectorization to the sum of an additive homomorphism from \\( K(X,A) \\) to \\( \\mathbb C \\) and a Fourier--Stieltjes transform of a finite complex regular Borel measure on \\( \\widehat{K(X,A)} \\), then the associated cocycle generates a synthesizable variety. We extend spectral synthesis to Lipschitz vectorizations of persistence diagrams on separable metric pairs and show whether examples of persistence diagram vectorizations in the literature have Lipschitz extensions with spectral synthesis.", "id": "Paper/65751", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65751"}, {"title": " Dynamics of perturbed elliptical billiard tables ", "webprogram_exclude": "0", "session_ids": ["Session/18065"], "source_sha256": "2e0a0f7acc37169f376b5e9e849befbe0a5b7253fa8350f80c30823fe585585e", "withdrawn": "", "abstract": "Dynamical billiards consist of a particle on a two-dimensional table, bouncing elastically off the boundary. The state of the system is given by the bounce location along the boundary and the incoming angle, and tracking these over successive bounces defines a two-dimensional area-preserving map first studied by Birkhoff. While generic strictly convex billiards are known to be chaotic, determining genericity for a given table is difficult, so one often resorts to numerical computation. In this talk, we use the parameterization method to compute high-order Taylor expansions of local stable/unstable manifolds attached to periodic orbits of billiard maps. Globalizing appropriate fundamental domains locates transverse intersections, giving insight into chaotic invariant sets. A key step, composing a polynomial with the implicitly defined billiard map, is done efficiently via the discrete Fourier transform, which requires extending the billiard map to a complex domain. We address this extension from a computational perspective.", "id": "Paper/65759", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65759"}, {"title": " A Formative Assessment Framework with Student-Led Discussions and Peer-Generated Questions ", "webprogram_exclude": "0", "session_ids": ["Session/19349"], "source_sha256": "4e5e1f61420d10023994b9eb192ece3df099a2cb74595b87975ca51908966dc4", "withdrawn": "", "abstract": "Student-led scored discussions, combined with peer-generated questions, offer an innovative approach to formative assessment that fosters meaningful student learning and success. For student-led discussions, using the Spider Web Discussion method, inspired by the Socratic seminar, places students at the center of the learning process by encouraging them to lead discussions, collaborate, and critically engage with course material. To prepare for these discussions, the instructor provides guiding questions based on the content covered. Students lead the scored discussions in analyzing, synthesizing, and challenging ideas, while also sharing references to support their points. During the student-led discussions, the instructor serves as an observer, facilitator, and monitors student interactions and participation using a scoring rubric that assesses collaboration, engagement, and critical thinking. The instructor creates a physical web-like diagram during the discussions to map the conversation flow to illustrate the collaboration and interaction between students.  This addition shows the visual representation of the discussion and provides a valuable tool for both students and instructors to reflect on the group dynamics and individual participation.\nThe peer-generated questions component, in addition to the instructor-provided questions, enhances this method by requiring students to create their own open-ended questions based on assigned readings or topics.\nTo promote further discussions, the peer-generated questions are shared with the group, encouraging students to think deeply about the material and connect it to broader concepts. \nCombining these components promotes higher-order thinking and also aligns with formative assessment principles by providing students with opportunities to reflect on their understanding of the content and improve through feedback. This dual approach supports student success by fostering ownership of learning, encouraging collaboration, promoting critical thinking, and providing real-time feedback. By encouraging students to actively participate in their learning, this framework illustrates how formative assessment can enhance engagement, build confidence, and promote significant academic growth.", "id": "Paper/65766", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65766"}, {"title": " Improved Algorithms for the Separation-Preserving Transition Between Least-Squares Assignments ", "webprogram_exclude": "0", "session_ids": ["Session/19352"], "source_sha256": "72bab19f7345fd989d9a3f718f66f5e49d974eb41e6c4209efdd1baa5195b0bd", "withdrawn": "", "abstract": "Balanced least-squares assignments (LSAs) of a dataset to a set of sites are one of the common methods for partitioning a dataset, as their clusters satisfy a valuable separation property, each pair being separated by a hyperplane in a cell complex. We are interested in applications where there is a need to gradually transition from an initial LSA to a target LSA while retaining separability throughout. Such applications naturally arise in resource redistribution efforts and can be modeled as a sequence of balanced LSAs. The computation of each step of the transition is possible through classic, but expensive parametric optimization techniques where a linear program (LP) is solved to identify the next LSA.\n\nWe devise a routine to combine progress in the linear transition of sites with a desired change in cluster sizes. The corresponding \\emph{combined algorithm} shortens the sequence of balanced LSAs by eliminating extraneous steps in the sequence. Additionally, we improve upon the size of LPs being solved in each iteration. Through a collection of upper-envelope computations, we identify a small candidate set of data points that can be moved between clusters. This leads to a \\emph{coreset algorithm} in which one may restrict the setup and solution of LPs in each iteration to that candidate set. Computational experiments confirm that our approaches reduce the number of steps in the transition and improve the computational efficiency of each iteration, yielding a significant improvement over the state of the art.", "id": "Paper/65772", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65772"}, {"title": " Image and Invertibility of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.395ex\" height=\"1.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -576.1 600.5 721.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">n</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-6E\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-tuple Vertex Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "e2a08a6a8b9df193540b67e10a3cb4b74eddb23b37c7fe0b32afbc5ab4b7d78b", "withdrawn": "", "abstract": "Erdős, Alavi, Behzad, and Lick introduced the concept of a double vertex graph$^{[1]}$, which was then generalized to the $n$-tuple vertex graph by Wright as follows: For a graph $G$ with vertex set $V(G)$ and edge set $E(G)$, its $n$-tuple $U_n(G)$ has vertex set $U_n(V(G))$ consisting of all $n$-element subsets of $V(G)$ and edge set $U_n(E(G))$ consisting of pairs of vertices matching all but one element where the distinct elements are adjacent vertices in $V(G)$$^{[2]}$.\n\nIn the paper summarized by this poster, I explore the $n$-tuple vertex graph as an operation over the space of connected, finite graphs (write $\\mathbb{G}$), focusing on the questions:\n\n(1) What is the image of $U_n$ in $\\mathbb{G}$?\n\n(2) How can we define $U_n^{-1}$?\n\nI establish some properties of graphs in the image of $U_n$ and hence show a way to determine whether certain types of graphs are $n$-tuples of a graph $G\\in\\mathbb{G}$ for some $n$. I then develop a procedure to deconstruct $n$-tuples into their inverse image.\n\nThe $n$-tuple operation has applications in combinatorics and Ramsey theory, and is particularly useful in coloring problems$^{[2]}$.\n\nThis poster assumes rudimentary knowledge of graph theory and set theory.\n\nPapers referenced:\n\n1. Alavi, Y., Behzad, M., Erdős, P., & Lick, D. R. (1991). Double vertex graphs. \\textit{Journal of Combinatorics, Information, and System Sciences}, 16(1), 37–50. \n\n2. Wright, V. (1992). \\textit{N-tuple vertex graphs} (Masters thesis).", "id": "Paper/65773", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65773"}, {"title": " Embedded contact homology and obstructing Anosov dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/18267"], "source_sha256": "10220712d111dd3c61fe02d308c9097fa182c73a176ea0312002ce01050a68b2", "withdrawn": "", "abstract": "We discuss some recent work using embedded contact homology and its associated ECH capacities to obstruct Anosov flows. This includes a Floer-theoretic obstruction to a 3-manifold admitting any Anosov flow, as well as obstructions to Reeb flows and Hamiltonian flows being Anosov; the latter addresses a question of M. Herman. We also consider some implications for symplectic geometry in dimension 4.", "id": "Paper/65774", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65774"}, {"title": " Pyranim: A Combinatorial Game of Doom and Despair ", "webprogram_exclude": "0", "session_ids": ["Session/19321"], "source_sha256": "abdfb66ad91fd2eef6fd4afe41d8f72fd461cc52f5657df4daff9b07f1e7122a", "withdrawn": "", "abstract": "Motivated by the work of Curran, Gray, Locke, and Low in \\textit{Pyramid Nim} (2022), we study Pyranim, an impartial combinatorial game on a triangular poset of chips. On each turn, a player removes a chip that does not support two chips immediately above it. The removal then propagates recursively, removing every chip that consequently becomes unsupported. The player making the final move wins. We construct bijections among supported Pyranim positions on the \\(n\\)-pyramid, Dyck paths of semilength \\(n\\), and unlabeled unit interval graphs on \\([n]\\). We then prove that this correspondence descends to isomorphism classes: two supported Pyranim positions are recursively game-isomorphic if and only if their associated unit interval graphs are isomorphic. Consequently, the number of game-isomorphism classes of supported positions on the \\(n\\)-pyramid equals the number of unlabeled unit interval graphs on \\(n\\) vertices.", "id": "Paper/65775", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65775"}, {"title": " Thriving despite toxicity: microbial pacifists often win in boom-and-bust environments even against antagonists aided by the optimal control theory. ", "webprogram_exclude": "0", "session_ids": ["Session/17688"], "source_sha256": "c4b17d918c4a291188f4cbdf76c85234768b38287f9e01efe741d4eaa617a0bf", "withdrawn": "", "abstract": "In this project, our goal was to resolve a fascinating puzzle: why toxin-producing microbes almost always win against toxin-sensitive microbes in idealized environments such as a lab, but the situation is often reversed in the real world? Finding an answer required a combination of wet lab experiments, mathematical models, and optimal control theory.  It turns out, frequent environmental disruptions such as \"dilutions\" (e.g., flushing of the gut, or brushing of the teeth, or dry soils experiencing heavy rains) give non-antagonistic microbes a good chance to win.  This is the case for a fairly broad range of model parameters and remains true whether the dilutions are periodic or randomly timed, and even if antagonistic microbes can use population sensing to produce toxin selectively.  We verified the latter by solving non-local Hamilton-Jacobi-Bellman PDEs, encoding the optimal control of toxin production for antagonistic microbes, with dilutions modeled as discontinuous jumps in population trajectories.  More broadly, our results also offer some caution about limitations of dynamic models with time-averaged rates.  Joint work with MingYi Wang and Andrea Giometto.", "id": "Paper/65776", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65776"}, {"title": " Rational Points Near Space Curves ", "webprogram_exclude": "0", "session_ids": ["Session/18279"], "source_sha256": "9b70f9919b0af1865931c286239677e1b0fadf45511f8cbeb35b585f09e3c1e6", "withdrawn": "", "abstract": "How many rational points are near a space curve? This talk reports on a recent work which provides a sharp answer. The method is entirely Fourier analytic.", "id": "Paper/65779", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65779"}, {"title": " Sum of parts in partitions, overpartitions and partitions without repeated odd parts ", "webprogram_exclude": "0", "session_ids": ["Session/18333"], "source_sha256": "3e9f908a0f0a0cdee9c030fb46641c601e2d1de8446ff4090c10185aff83e159", "withdrawn": "", "abstract": "In this talk, we first obtain several Ramanujan-type congruences modulo 5 and 7 for sum of certain non-overlined parts in overpartitions classified by parity and sum of certain parts in partitions without repeated odd parts classified by parity. Secondly, we give a new combinatorial refinement explaining a modulo 5 congruence due to Andrews and Dastidar for weighted sum of parts in partitions classified by parity. This refinement involves a new sum of parts vector partition function and the vector crank introduced by Garvan in 1986. This is joint work with Frank Garvan.", "id": "Paper/65780", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65780"}, {"title": " Finding Littlewood–Richardson Coefficients using Peelable and Shuffle Tableaux ", "webprogram_exclude": "0", "session_ids": ["Session/19366"], "source_sha256": "436789c8038a6eedddbe46293fb750c5184a1067e7af43e9cede01f76d8b8aff", "withdrawn": "", "abstract": "We present a new combinatorial rule for computing Littlewood--Richardson coefficients $c_{\\lambda/\\mu,\\nu/\\rho}^{\\kappa}$ using peelable tableaux compatible with shuffle tableaux, which is analogous to the Remmel--Whitney rule. Given two skew shapes $\\lambda/\\mu$ and $\\nu/\\rho$, their shuffle diagram $D = (\\lambda/\\mu) \\circledast (\\nu/\\rho)$ is formed by interlacing their squares. While these coefficients count Yamanouchi shuffle tableaux in a type $A$ Kashiwara crystal, verifying them with lowering crystal operators is computationally intensive. We establish a bijection between Yamanouchi shuffle tableaux and $D$-peelable tableaux of shape $\\kappa$, providing an efficient method to compute generalized Littlewood--Richardson coefficients for Temperley--Lieb immanants of Jacobi--Trudi matrices without testing crystal operators. Furthermore, a composition of odd Bender--Knuth involutions gives a shape-preserving bijection that yields the symmetry $c_{\\lambda/\\mu,\\nu/\\rho}^{\\kappa} = c_{\\nu/\\rho,\\lambda/\\mu}^{\\kappa}$.", "id": "Paper/65787", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65787"}, {"title": " Seeing dynamics with topology: recent progress on Anosov flows ", "webprogram_exclude": "0", "session_ids": ["Session/17364"], "source_sha256": "c3f79f718bba813fd75fe3638746a360cdc3901471f402b0aa598ebe65fb80cf", "withdrawn": "", "abstract": "Trajectories of a vector field in a 3 (or 4, 5,...) dimensional space can be very complicated and tangled, winding around each other.  What restriction on the vector field could allow us to describe these trajectories qualitatively and say something about the \"shape\" of the flow?  \n\nThis talk is about one great success story in this area, the study of Anosov systems. These are, in some sense, the simplest examples of \"chaotic\" dynamics, and so fascinating to study.  At the same time, their qualitative behavior is robust under perturbation. This  means a topologist (who likes things floppy and deformable!) can talk meaningfully about them.  \n\nI hope to give you -- likely a total outsider! -- a taste of this subject, and show you how perspectives from low-dimensional and geometric topology have led to exciting recent breakthroughs in understanding these dynamical systems.", "id": "Paper/65788", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65788"}, {"title": " Quantitative Morse Theory on Free Loop Spaces on Riemannian <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.162ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 500.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">2</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-32\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-spheres ", "webprogram_exclude": "0", "session_ids": ["Session/18290"], "source_sha256": "d8c03558b7b158054af1e776dc8faf4e4a5d832a3794ecc62254b24142d092c5", "withdrawn": "", "abstract": "Suppose that $M$ is a is a Riemannian $2$-sphere with diameter $d$. In this talk, we demonstrate that if some closed curve of length $l$ on $M$ cannot be contracted to a point through closed curves of length at most $l+Cd$ for some constants $l>0,C>0$, then there exist exponentially many stable simple closed geodesics on $M$ of length at most $2d$. We also show that if some map $f$ from $S^m$, $m\\geq 1$, to the space of free loops of length at most $l$ on $M$ cannot be contracted to a point in the space of free loops of length at most $l+Cd$, then there exist exponentially many stable simple closed geodesics on $M$ of length at most $2d$.", "id": "Paper/65790", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65790"}, {"title": " Pointwise behavior of NLFT ", "webprogram_exclude": "0", "session_ids": ["Session/18279"], "source_sha256": "b345717b2f3060a180ebe90bc8c0a3e794586d8e8794e9a821840a4ad22349e0", "withdrawn": "", "abstract": "We discuss the pointwise behavior of the $SU(1,1)$ nonlinear Fourier transform (NLFT) in discrete and continuous settings. In particular, we establish the divergence of NLFT for the critical case when the input is square-summable, answering negatively  the strong version of the celebrated nonlinear Carleson conjecture. Additionally, we analyze convergence of NLFT for some special cases.", "id": "Paper/65792", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65792"}, {"title": " Interactive Oral Assessment in an Introductory Proof Course ", "webprogram_exclude": "0", "session_ids": ["Session/18440"], "source_sha256": "b6dc36dfbb257ff30fdf29b0b2aaa921010ee92011dc0b24b35b3e170d018c43", "withdrawn": "", "abstract": "In an introductory proof course, we want students to do more than produce correct written proofs: we want them to explain their reasoning, respond to questions, evaluate mathematical arguments, and reflect on their own understanding. These goals can be difficult to assess through traditional written exams alone—and adding richer forms of assessment can seem prohibitively time-consuming.\n\nIn this talk, I will describe an alternatively graded assessment structure for a Foundations of Advanced Mathematics course that, in addition to regular homework with re-attempts, combines short student-created screencasts, structured peer review, and an interactive oral assessment. Students used a simple specifications rubric to guide their work and feedback, and they completed a self-assessment following the oral assessment. Together, these components provided multiple opportunities for students to demonstrate and reflect on their mathematical understanding while emphasizing communication and revision rather than point accumulation. I will share how the pieces of the assessment fit together, examples of the rubric and assessment process, and practical choices that kept the system manageable.", "id": "Paper/65793", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65793"}, {"title": " Combinatorial Topological Dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/18008"], "source_sha256": "928425ec5730c2fa63a644319e882318bbba10df564a47a669207777787902a0", "withdrawn": "", "abstract": "In recent years, topological methods that had been developed for classical\ndynamics, such as Conley's theory, have been carried over to a discrete,\ncombinatorial setting, thereby opening the door to a purely combinatorial\nversion of dynamical systems. The first step in this direction was\nForman's discrete Morse theory on simplicial complexes, and it has found\nnumerous applications in data science and other application areas.\n\nIn this talk, I will present an overview over recent results in combinatorial\ntopological dynamics, which generalizes and extends these early results in a\nnumber of directions. The notion of multivector fields on Lefschetz complexes\nwill be introduced in detail, as well as an extension of Conley's theory in this\nsetting.  This includes topics such as isolated invariant sets, their Conley\nindex, Morse decompositions, and connection matrices. In addition, applications\nof the theory to establishing recurrence in classical dynamics, and to obtaining\ncomputer-assisted proofs for global dynamics will be presented.", "id": "Paper/65797", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65797"}, {"title": " Connected Cospectral Irregular Graphs with Identical Invariants and Distinct Lovász Numbers ", "webprogram_exclude": "0", "session_ids": ["Session/19354"], "source_sha256": "c65a08a215b940b625cf9d28f3e22fe1e6b0c4086f44e5cf45700b2c9af5759c", "withdrawn": "", "abstract": "For every integer \\(n\\geq 11\\), we construct a pair of connected,\nirregular, nonisomorphic graphs on \\(n\\) vertices that are cospectral\nwith respect to the adjacency, Laplacian, signless Laplacian, and\nnormalized Laplacian matrices and have equal independence, clique,\nchromatic, complement chromatic, and maximum-cut numbers, but distinct\nLov\\'{a}sz \\(\\vartheta\\)-numbers. The graphs are obtained by joining\neach member of a fixed pair of cospectral, nonisomorphic regular graphs\non ten vertices, due to van Dam and Haemers~(2003),\nwith the complete graph \\(K_{n-10}\\). We prove that this construction\npreserves the equality of the four spectra and the stated\ninteger-valued combinatorial invariants within each pair, while leaving\nthe respective Lov\\'{a}sz numbers unchanged. We derive exact formulas\nfor these Lov\\'{a}sz numbers and prove that they are distinct. We also\ndetermine the cardinality-constrained maximum-cut profiles of the two\nbase graphs and their complements. These profiles yield exact formulas\nand establish equality of the maximum-cut numbers within each pair,\nboth for the joins of the base graphs with \\(K_{n-10}\\) and for the\njoins of their complements with \\(K_{n-10}\\). For \\(n=10\\), we first\npresent a regular pair satisfying all the stated properties except\nirregularity, and then a connected, irregular, nonisomorphic pair that\nshares all four spectra and all the stated integer-valued combinatorial\ninvariants, but has distinct Lov\\'{a}sz numbers. An exhaustive SageMath\ncomputation shows that no pair of connected, irregular, nonisomorphic\ngraphs on at most nine vertices shares all four spectra and has equal\nvalues of all these invariants. Hence, ten is the smallest possible\norder, and pairs with all the stated properties exist for every\n\\(n\\geq 10\\). This extends and strengthens an earlier result for \\emph{even}\n\\(n\\geq 14\\) (Sason, 2024), which also did not address complement\nchromatic numbers, the maximum-cut numbers of the graphs, or the\nmaximum-cut numbers of the corresponding joins formed from their\ncomplements. Thus, the Lov\\'{a}sz number provides an efficiently computable\ncertificate of nonisomorphism even when the four spectra and all the\nstated integer-valued combinatorial invariants coincide. The full version is available at \\texttt{arXiv:2609.10884}.", "id": "Paper/65799", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65799"}, {"title": " Coordinating Change: Implementing Alternative Grading at Scale ", "webprogram_exclude": "0", "session_ids": ["Session/18250"], "source_sha256": "ea2e0202bc2b37cddfa51fdbb3eeed11dbe914a4e2d1135edb230b33d0521b76", "withdrawn": "", "abstract": "Coordinating a large, multi-section course involves more than ensuring that students encounter common content and assessments. It also creates opportunities—and challenges—for implementing meaningful pedagogical change at scale. Over the past few years, I have coordinated a large Calculus I course serving hundreds of students each year and taught by a team of instructors with varied backgrounds, experiences, and approaches to teaching. During that time, we transitioned from a traditional points-based assessment system to an alternative grading structure organized around clearly defined learning outcomes and multiple opportunities for students to demonstrate proficiency.\n\nIn this talk, I will share lessons learned from implementing and refining this grading structure across a coordinated course. In particular, I will discuss strategies for supporting instructors through a substantial change in assessment practices, establishing consistency without eliminating instructor autonomy, and communicating a new and unfamiliar grading system to a large student population. I will also describe structures we developed to support students and instructors throughout the semester and ways that feedback from both groups informed subsequent iterations of the course.\n\nMore broadly, this case study illustrates how course coordination can provide infrastructure not only for consistency across sections, but also for sustainable pedagogical innovation. I will share practical strategies, challenges, and lessons that may be useful to others coordinating large multi-section courses or considering course-wide changes to assessment.", "id": "Paper/65800", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65800"}, {"title": " A Data-Free Discontinuous Galerkin Finite Element Operator Network for Obstacle Problems and Optimal Control ", "webprogram_exclude": "0", "session_ids": ["Session/17926"], "source_sha256": "56fae26f1abf68a9fc3f9202c5a5fb7109c6ec570524d50a6dc91f5c8891dec0", "withdrawn": "", "abstract": "Obstacle problems arise in applications involving contact, free boundaries, and inequality constraints. Solving these problems repeatedly can be expensive, especially when the coefficients are discontinuous and the contact region changes with the input parameters. In this work, we develop a discontinuous Galerkin finite element operator network (DG-FEONet) for parameterized obstacle problems and a related optimal control problem. The network directly predicts the discontinuous Galerkin finite element coefficients and is trained without labeled solution data. The training loss is constructed using the discrete energy and optimality conditions, while the obstacle constraint is enforced directly in the predicted solution. For the optimal control problem, DG-FEONet predicts the state, and the corresponding control is then recovered from the discrete system. Numerical experiments show that DG-FEONet accurately predicts the solution, contact region, and optimal control for unseen inputs. The proposed method provides an efficient approach for solving nonsmooth and constrained PDE problems with discontinuous coefficients.", "id": "Paper/65801", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65801"}, {"title": " ArguAgent: Voice-Based AI Support for Enhancing Development of Mathematical Argumentation Through Small Group Discussions ", "webprogram_exclude": "0", "session_ids": ["Session/18262"], "source_sha256": "6b5f07f931e74da9cadc1d1e89689700a2824711192e3cc80287d42b1764a50f", "withdrawn": "", "abstract": "ArguAgent, one of the learning applications in the GENIUS platform (AI4STEM Education Center, University of Georgia), is an AI-supported environment for face-to-face mathematical discussion. Students discuss a problem in small groups while the system listens, tracks the structure of the argument each group is building (claims, evidence, and logical reasoning), and makes that structure visible to the teacher and group in near real-time. ArguAgent works over voice rather than typing, on the premise that typing and screen interaction introduce extraneous cognitive load that can interfere with mathematical reasoning. Recognizing small-group speech in noisy classrooms is not easy, but this approach allows discussions to unfold naturally. Where a group stalls, the system may intervene and send an intervention prompt, such as \"Are there none, one, or lots of fractions between 4/7 and 5/7, and why?\" The system is built to leave space for productive struggle, and to leave important pedagogical judgments to the teacher.\n\n\nPiloting the system with a fraction-density task exposed a problem mathematicians will recognize. We initially used a widely-cited argumentation rubric from science education research that gated its levels on cited evidence, but the rubric scored a structural argument (that one can always construct another fraction between any two) below a list of worked examples. We rebuilt the scoring on Stylianides's (2008) reasoning-and-proving framework so that a general argument outranks a list of cases. In April 2026, ten preservice teachers, standing in for the middle-school students who are the eventual audience, piloted the system in small groups. Post-session surveys gave the interventions poor ratings for timing, but credit for being generally helpful. The hard problem, so far, is not getting the mathematics right but knowing when to intervene. This talk presents the design, pilot findings, and preliminary results from classroom trials planned for fall 2026.", "id": "Paper/65803", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65803"}, {"title": " Fourier transform, neural networks and complexity ", "webprogram_exclude": "0", "session_ids": ["Session/18279"], "source_sha256": "22e4bfb67bb193d3481a4231bf33313ecbe5c6605d63180395a4a9326b173bb5", "withdrawn": "", "abstract": "We are going to discuss the connection between Bourgain's and Talagrand's celebrated results on orthogonal functions and neural networks. In particular, we are going to see that the Fourier ratio, the ratio of the L1 to the L2 norms of the Fourier transform, which has been shown to play an important role in several problems in harmonic analysis in recent years, is also one of the key factors in the learning process of the neural networks.", "id": "Paper/65804", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65804"}, {"title": " Differential coinvariants ", "webprogram_exclude": "0", "session_ids": ["Session/18308"], "source_sha256": "ca665c46c6a23bcb07ff605df1d3c8c5eaaf5f2052142d682b897f17f1eabc8d", "withdrawn": "", "abstract": "Let $V$ be a vector space, let $\\Omega$ be the bigraded algebra of regular differential forms on $V$, and let $W$ be a subgroup of $GL(V)$. The natural action of $W$ on $V$ induces an action of $W$ on $\\Omega$. Let $I \\subseteq \\Omega$ be the ideal generated by $W$-invariants with vanishing constant term and write $SR_W := \\Omega/I$ for the corresponding quotient ring. We outline progress and problems pertaining to the combinatorial and geometric structure of $SR_W$. Joint with Robert Angarone, Sutanay Bhattacharya, Patricia Commins, Trevor Karn, Satoshi Murai, and Andy Wilson.", "id": "Paper/65805", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65805"}, {"title": " Temporal Graph Classification with Topological Machine Learning ", "webprogram_exclude": "0", "session_ids": ["Session/18026"], "source_sha256": "d69dc57a27ae22b8653a564a435d80b5858fc0f70380f554efae93e6654e528f", "withdrawn": "", "abstract": "Temporal graph classification arises in applications such as cybersecurity, brain connectivity analysis, and traffic networks, yet remains less studied than temporal link prediction and node forecasting. Existing methods often lose fine-grained temporal information or struggle with long-range dependencies.\n\nIn this talk, we present T3former, a Topological Temporal Transformer that incorporates sliding-window topological and spectral descriptors through a novel Descriptor-Attention mechanism. By combining topological, spectral, and temporal information, T3former captures complex evolving graph structures while maintaining robustness and temporal fidelity. Experiments on social, brain, and traffic network benchmarks demonstrate state-of-the-art performance, supported by theoretical stability guarantees under temporal and structural perturbations.", "id": "Paper/65810", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65810"}, {"title": " Symmetry Induced Bifurcation Points in Nonlinear Diffusion Problems ", "webprogram_exclude": "0", "session_ids": ["Session/18008"], "source_sha256": "8a712ddd6598896d7106af7daab5b2fe36e6eb335f4cdd5abac69a389207ec7e", "withdrawn": "", "abstract": "Nonlinear parabolic partial differential equations frequently occur in the modeling of applied phenomena. They often exhibit complicated dynamics which is organized by their associated equilibrium solutions. As a function of the involved model parameters, the equilibria can be detected using a bifurcation analysis, which in turn is centered around a deeper understanding of bifurcation points. Yet, in many applied systems establishing these organizing centers rigorously is difficult to achieve using traditional mathematical techniques. In this paper, we propose a theoretical framework for computer-assisted proofs of symmetry-induced transcritical and pitchfork bifurcations in nonlinear problems. This is accomplished by reformulating the existence question via a zero finding problem for an associated extended nonlinear system. The approach is general and allows for a wide variety of underlying symmetries. We demonstrate how these results can be\napplied in the setting of parabolic systems and higher-order equations, on both one- and two-dimensional domains.\n\nThis talk is based on joint work with Maxime Breden and Thomas Wanner", "id": "Paper/65811", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65811"}, {"title": " Nonuniqueness for the Cubic Nonlinear Schrödinger Equation ", "webprogram_exclude": "0", "session_ids": ["Session/18306"], "source_sha256": "e7e3439932b5d86b7bc66fd3722a2284c3624ffe90fa633a2e4fc99e7d2d54a2", "withdrawn": "", "abstract": "We construct by convex integration a nonzero singular weak solution of the one-dimensional periodic cubic nonlinear Schr\\\"odinger equation that is compactly supported in time, has zero initial datum, and satisfies\n\\[\nu\\in\\bigcap_{\\alpha<1/6} C_t^0 H_x^\\alpha\n\\cap\n\\bigcap_{1\\leq p<3} C_t^0 L_x^p.\n\\]\nThe key new ingredient is a two-carrier perturbation: its zero-output interaction cancels the previous error, without introducing any zero Fourier\nmode, which is crucial in the cubic NLS. For a singular solution, every admissible Fourier cutoff gives the same limit for the nonlinear term. Whenever a singular solution belongs to \\(C_t^0L_x^3\\), this nonlinearity agrees with the ordinary product \\(|u|^2u\\). Together with unconditional uniqueness at \\(H^{1/6}\\), this makes the threshold sharp within the singular solution class considered here.", "id": "Paper/65817", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65817"}, {"title": " A Rubik’s Style Rational Tangle Cube ", "webprogram_exclude": "0", "session_ids": ["Session/18240"], "source_sha256": "2a2f021932b1f286ffa8f424088f83e65d4a20f27f4d042e62c41d5fe24c65d2", "withdrawn": "", "abstract": "In this talk we will describe and share a new Rubik's style puzzle that incorporates Conway's Rational Tangles. We will study several groups of symmetries associated with this, possible configurations, and solution techniques.", "id": "Paper/65827", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65827"}, {"title": " The Vertex Subforest Polynomial Is Not Log-Concave ", "webprogram_exclude": "0", "session_ids": ["Session/18369"], "source_sha256": "cb9144dc975f5f50b0fdc18ce9464a80151a15867728429a3e185a7aee6656fd", "withdrawn": "", "abstract": "We use an AI architecture called PatternBoost to produce counterexamples to the log-concavity condition in the vertex subforest sequence. The i-th element of the sequence is the number of vertex subsets of size i whose induced subgraph is a forest. We look only at bipartite graphs to reduce our search space, we encode them as one-dimensional objects by flattening the top-right block of the adjacency matrix. We train a transformer to generate high-scoring objects, where our scoring function is the log-concavity inequality on one side. We locally optimize the objects we get back from the transformer, and repeat. Our computation found 12 counterexamples. Our findings show how far combinatorial log-concavity extends beyond matroid-like settings. This has implications for knowing stronger conditions under which log-concavity holds.", "id": "Paper/65828", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65828"}, {"title": " Edge Clustering on Temporal Hypergraphs ", "webprogram_exclude": "0", "session_ids": ["Session/18324"], "source_sha256": "5dccba07b8bd569b9dcce961ba2d5270182906b21b0cc6ceeb7e6a09a76c1291", "withdrawn": "", "abstract": "Finding densely connected subsets of vertices in an unsupervised setting, called clustering or community detection, is one of the fundamental problems in network science. The edge clustering approach detects communities by clustering the edges of the graph and then assigning a vertex to a community if it has at least one edge in that community, thereby allowing for overlapping clusters of vertices. We apply the idea behind edge clustering to temporal hypergraphs, an extension of a graph where a single edge can contain any number of vertices and each edge has a timestamp. There is significant interest in hypergraph mining, including several recently proposed methods for community detection, but the added complexity often makes extending traditional network science techniques a non-trivial task.\n\nGiven a temporal hypergraph $H$, we build its line graph $G = LG(H)$ where edge weights in $G$ are a combination of two components: an intersection-based structural similarity score and a temporal similarity score. We then cluster $G$ using hierarchical single linkage clustering from HDBSCAN. The extension to hypergraphs allows for many different patterns of interaction between edges. By defining a suitable structural similarity function coupled with temporal information, our edge clustering algorithm can find meaningful motifs in higher order relational datasets. \nStructural similarity between edges is generally based on the edges having some intersection, and we examine several variations.\n\nWe test the algorithm on a collaboration hyper-network based arXiv pre-print papers posted between January 2018 and October 2025. Using various similarity functions, we show that we can find several persistent interaction motifs (cluster structures) that can help understand such complex data structures. We conclude by presenting ideas for incorporating random walk methods to our temporal hypergraph analysis.", "id": "Paper/65829", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65829"}, {"title": " CANCELLED Cuppable Implies Low Cuppable in the Enumeration Degrees \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/19340"], "source_sha256": "eeb3e9d77874ae4124325973023145a2f0ac3cce606846aa0eb8f584ed38fa83", "withdrawn": "i", "abstract": "A degree $\\mathbf{0} < \\mathbf{a} < \\mathbf{0}'$ is \\emph{cuppable} if there exists an incomplete degree $\\mathbf{b}$ such that $\\mathbf{a} \\vee \\mathbf{b} = \\mathbf{0}'$. We show that any cuppable $\\Sigma_2^0$ degree is low-cuppable in the enumeration degrees. This extends Soskova and Wu's result showing that all nonzero, incomplete $\\Delta_2^0$ sets are low-cuppable in the enumeration degrees.", "id": "Paper/65830", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65830"}, {"title": " Spatial discretization for nonlinear Schrödinger equations with low regularity or singular potential ", "webprogram_exclude": "0", "session_ids": ["Session/17702"], "source_sha256": "c52c0ab87e7787f10121d2c60af1296532d7e0a995e9d7ff30935261956f6009", "withdrawn": "", "abstract": "The (time-dependent) nonlinear Schr\\\"odinger equation with low regularity or singular potential arises widely in applications of quantum physics and chemistry. Typical examples include the piecewise constant potentials or the singular Coulomb-type potentials. Such potentials have very low regularity and also limit the regularity of the underline solutions, posing significant challenges in accurate and efficient numerical simulation. For the spatial discretization, we analyze the standard Fourier spectral method and demonstrate its favorable convergence behavour under low regularity potentials. Furthermore, we propose a potential projection Fourier pserudospectral method that shares the same accuracy as the Fourier spectral method with much lower computational cost and better sturcture preservation.", "id": "Paper/65832", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65832"}, {"title": " Proper Additive Edge Colorings of Regular Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18106"], "source_sha256": "b7108d44b35f34d41e537d5e62bee2e8843bbdcd45c9e66d106cb27955acd0c3", "withdrawn": "", "abstract": "An additive coloring of a graph $G$ is a labeling $c:V(G)\\rightarrow \\mathbb{N}$ such that if $vw$ is an edge of $G$, then $\\sum_{u\\in N(v)}c(u)\\neq \\sum_{u\\in N(w)}c(u) $. In 2009, Czerwi\\'{n}ski et al. conjectured that if $G$ is a graph with chromatic number $k$, there exists an additive coloring of $G$ such that for all vertices $v$, $c(v)\\in\\{1,2,\\dots, k\\}$. We verify that a strengthening of this conjecture holds for line graphs of d-regular Vizing-class-1 graphs. We present bounds on the proper additive chromatic index of d-regular Vizing-class-2 graphs and demonstrate an edge-recoloring procedure that can convert proper edge colorings of d-regular Vizing-class-2 graphs into proper additive edge colorings.", "id": "Paper/65834", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65834"}, {"title": " Real Monodromy Action of the 3RPR Mechanism ", "webprogram_exclude": "0", "session_ids": ["Session/18042"], "source_sha256": "8558c6c458f79f7502fafecdaadc26982d88972d763a3634b99afdec531dce1b", "withdrawn": "", "abstract": "The algebraically defined Galois group directly corresponds to the geometric monodromy group, which studies how solutions permute along loops in parameter space. Rather than studying the complex monodromy group, we study monodromy action based on the behavior of tiered collections of real solutions. To provide a practical example, this talk focuses on computing the real monodromy action of the kinematic 3RPR planar mechanism. We study the robot’s solutions and how the monodromy structure changes as new physical constraints are imposed. This is a joint work with Jonathan Hauenstein, Margaret Regan, and Charles Wampler.", "id": "Paper/65836", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65836"}, {"title": " A Theory for the Emergence of Coordinated Pumping in Cervical Lymphatic Vessels ", "webprogram_exclude": "0", "session_ids": ["Session/17972"], "source_sha256": "c6f1c2faa63a8be98ba725afb78cf34a096a5506da9bf732bbca9037550e1a40", "withdrawn": "", "abstract": "Metabolic waste drains from the brain via cerebrospinal fluid (CSF), much of which reaches cervical lymphatic vessels (CLVs), which return the fluid to venous circulation via the thoracic duct. CSF is transported through CLVs by the coordinated, spontaneous contraction of lymphangions that are the sub-chambers of CLVs organized in serial, separated by one-way valves. The contractile units are lymphatic smooth muscle cells (LSMCs), governed by mechanosensing of stretch and wall shear stress. These mechanisms together produce a propagating antegrade contraction wave to transport CSF across an adverse pressure gradient from the intracranial space to the central venous system. There are very few published models of CLVs, and existing simulations impose this wave by a prescribed contraction frequency and phase lag between neighboring lymphangions. Although more detailed models of other lymphatic vessels incorporate electrophysiology, valve mechanics, and fluid flow, the spontaneous emergence of the propagating contraction wave has not been explained from first principles. Here, we build a model of coupled lymphangions as excitable oscillators, with LSMC electrophysiology governed by the FitzHugh-Nagumo model, and mechanical coupling via fluid flow and one-way valves. We show that this system spontaneously synchronizes into an coordinated antegrade contraction wave that pumps CSF across an adverse pressure gradient. Furthermore, we derive analytical predictions for the resulting contraction frequency and amplitude as functions of the boundary conditions. We use this theory to give a physical grounding to the sensitivity of various parameters on the system and identify the driving forces behind coordinated lymphatic pumping. Finally, we use this model to identify mechanisms by which impaired CLV pumping occurs as a result of traumatic brain injury and aging, consistent with experimental observations in mice.", "id": "Paper/65839", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65839"}, {"title": " Recent developments on singular stochastic partial differential equations ", "webprogram_exclude": "0", "session_ids": ["Session/18445"], "source_sha256": "ee0d82ea33c600c175d1a976c10b839da499b3394628817e82af4529f57a26b5", "withdrawn": "", "abstract": "Stochastic partial differential equations are PDEs forced by random noise. A typical example is the space-time white noise, when its covariance is a product of Dirac delta in space and that in time. Mathematically, this force is so rough that the solution becomes a distribution and consequently the product within the nonlinear term becomes ill-defined, and hence the name ``singular'' stochastic PDEs. I will describe the solution theory of singular SPDEs with a focus on the global-in-time direction, in which multiple problems remain open. The equations of focus include, but are not limited to, Navier-Stokes equations, Phi4 model, and Cahn-Hilliard equation.", "id": "Paper/65840", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65840"}, {"title": " How Far Down? A Look at the Effects of Collapsing Curves on Critical Behavior ", "webprogram_exclude": "0", "session_ids": ["Session/18240"], "source_sha256": "4297ff7a22e7cff35e4cbb3463e6cf2b826247f33e4589925a75f2e9858c0bef", "withdrawn": "", "abstract": "Post-Critically Finite (PCF) maps are the backbone of families of rational maps in discrete complex dynamics. In one variable, these are maps for which the iterated critical set---an invariant set called the post-critical set---is a finite set of points.  A rational map of two complex variables is PCF if its post-critical set is a finite collection of lower-dimensional objects. When this is the case, we can also ask whether the restriction of the rational map to its post-critical set is also PCF; in this situation, it is called PCF all the way down (PCFAWD). Sometimes, maps of two complex variables map a point $\\mathbf x$ to the point $(\\frac{0}{0},\\frac{0}{0})$, when this is the case we call the point indeterminate. Once more, some maps of two complex variables map map a curve $C$ to a point, in this case we call $C$ a collapsing curve. In 2020, Astorg showed that almost all PCF maps without indeterminate points are PCFAWD. Based on 2025 work from Gauthier, Hurtz, and Kaschner, maps with indeterminate points have been constructed that are PCF but not PCFAWD. We have shown that indeterminate points are a consequence of collapsing curves and isolated ways in which these so-called collapsing curves are the cause of a PCF map's failure to be PCFAWD.", "id": "Paper/65842", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65842"}, {"title": " Domination Number and Total Domination Number of Zero Divisor Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17882"], "source_sha256": "a2980c576dbe3bfc2f8c2ab7f26da80d513f69a2156d238790863187fc46a5c4", "withdrawn": "", "abstract": "The idea of graphs associated with the zero divisors of a commutative ring was first introduced by Beck in the context of coloring rings. Since then, zero divisor graphs have been extensively studied. The vertices of a zero divisor graph are the nonzero zero divisors of a ring, and two vertices are adjacent whenever their product is zero. In this talk, we will focus on the relationship between the domination number and the total domination number of zero-divisor graphs. We will show that, for a commutative ring, these two numbers are equal unless the ring is isomorphic to $\\mathbb{Z}_2 \\times D$ where $D$ is a domain.", "id": "Paper/65845", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65845"}, {"title": " Infinite series, ", "webprogram_exclude": "0", "session_ids": ["Session/19363"], "source_sha256": "06c6e781e5d4859f0b0ae79c54215e279de34701ce8268d4757b37d4ca03fee3", "withdrawn": "", "abstract": "In this talk we look at connections between \\beta \\ \\ expansions, infinite series and iterated function systems. We generalize some of the results of Erdos, Parry and Sidorov. Applications to iterated function systems will be explored.", "id": "Paper/65846", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65846"}, {"title": " On the Fourier decay of fractal measures supported on the parabola ", "webprogram_exclude": "0", "session_ids": ["Session/18279"], "source_sha256": "12b716f8c308e02d993af3e84e040fcfa556ca8438e72ea1a601b7adb2037cdd", "withdrawn": "", "abstract": "I will discuss progress on both discrete and delta-discretized energy problems for the parabola.", "id": "Paper/65848", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65848"}, {"title": " Pig glands, scallop shells, and statistical methods for biologists ", "webprogram_exclude": "0", "session_ids": ["Session/18374"], "source_sha256": "6d01e0b42f582b670e4ffcfd6eec1ee22178ec054be22a885b617f9d9bff0b8c", "withdrawn": "", "abstract": "Writing to the British statistician Karl Pearson in 1904, the American Charles Davenport complained: \"You cannot realize as I do, who am no mathematician and yet have more mathematical training than most biologists, how impossible it is to get biologists to follow a mathematical demonstration or even to pick up the end result so that they can use it.\" Today Charles Davenport is infamous for his direction of the Eugenics Records Office at Cold Spring Harbor, but a decade before founding the ERO he energetically promoted quantitative biological research. This talk exhibits Davenport's wide-ranging efforts to introduce biologists to new statistical tools at the turn of the twentieth century. Through lectures, popular articles, textbooks, laboratories, letters, and a series of collaborative studies, he endeavored to show the value of statistics for understanding biological variation as well as the processes of basic computational techniques. Despite his epistolary pessimism, Davenport laid a rudimentary foundation for biostatistical research in the United States.", "id": "Paper/65853", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65853"}, {"title": " Domination in Zero-Divisor Graphs of Commutative Rings ", "webprogram_exclude": "0", "session_ids": ["Session/17882"], "source_sha256": "1039df50a0c1db61474d727e78d5e66f1c63a4b54e260dc490a02c77b93b6fc9", "withdrawn": "", "abstract": "Since the seminal paper of D.F. Anderson and P. Livingston in 1999, zero-divisor graphs and other graphs associated with algebraic structure have been well represented in the literature.  After a brief survey, which will include work done by undergraduates, we will present several results about dominating sets and domination numbers in zero-divisor graphs, including those concerning direct products of commutative rings as well as Artinian rings.", "id": "Paper/65855", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65855"}, {"title": " An Adaptive Low-Memory Method for Risk-Averse Dynamic PDE-Constrained Optimization ", "webprogram_exclude": "0", "session_ids": ["Session/18245"], "source_sha256": "a838b9f016964db44e065797026d49559808cb260cd282b444475d9d25418e59", "withdrawn": "", "abstract": "We introduce a novel low-memory method to solve risk-averse dynamic PDE-constrained optimization problems. The memory requirements for these problems often present a major obstacle that we overcome using randomized tensor approximation to compress the PDE solution as it is generated. The compressed state is then used to compute approximate gradients and to apply the Hessian to vectors. The approximation error in these quantities is controlled by the target rank of the compressed state. Using this approximate first- and second-order information, we develop an efficient algorithm that adaptively learns the target rank using a posteriori error information, while provably converging to a stationary point of the optimization problem.", "id": "Paper/65860", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65860"}, {"title": " Expected Values of Diagonal Sums for Young Tableaux ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "42f1395e7d4f34295604fea26f2a3363980eb2f95d1b76fc680c462057931951", "withdrawn": "", "abstract": "A \\textit{Young diagram} is a left-justified section of a square grid with a weakly decreasing number of boxes in each row. For a Young diagram with $n$ boxes, a \\textit{Young tableau} is a filling of this figure with integers $\\{1,...,n\\}$ so that each row and each column is an increasing sequence. We compute the expected sum of the boxes along arbitrary diagonals of a uniformly random standard Young tableaux of shape $\\lambda$. Our formula is expressed in terms of the numbers of Young tableaux of shapes obtained by adding a box to the diagonal endpoints of $\\lambda$. As a function of the diagonal index, the expected diagonal sum is piecewise linear, with slope changes only at the boundary corners of $\\lambda$.", "id": "Paper/65863", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65863"}, {"title": " Expected Values of Diagonal Sums in Skew Standard Young Tableaux ", "webprogram_exclude": "0", "session_ids": ["Session/19366"], "source_sha256": "c3e06754329e058f024cf5fb20f71c035040cad84045d44e8f08804ef08b1b36", "withdrawn": "", "abstract": "We compute the expected sum of the boxes along arbitrary diagonals of a uniformly random standard Young tableaux of connected skew shape $\\sigma$ with $n$ boxes. Our formula is expressed in terms of the numbers of Young tableaux of shapes obtained by adding a box to the diagonal endpoints of $\\sigma$. As a function of the diagonal index, the expected diagonal sum is piecewise linear, with slope changes only at the boundary corners of $\\sigma$. Our proof uses the Brill-Noether distribution on staircase paths of Chan-L\\'opez-Pflueger-Teixidor: the expected value of a box becomes $(n+1)$ times the probability of a random path passing above it, which can be calculated using the toggle symmetry of this distribution.", "id": "Paper/65864", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65864"}, {"title": " A Littlewood-Richardson Rule for 2-Grassmannian Permutations ", "webprogram_exclude": "0", "session_ids": ["Session/18308"], "source_sha256": "dcc7c50f6dd4ff43fc9277b78febedf7f4854c1425ecff00e60fc9a2a951fe3f", "withdrawn": "", "abstract": "We give  formulas, in  both ordinary and  equivariant cohomology  of a flag  manifold, for  the coefficients  that arise  when multiplying  a Schubert class  by one  pulled back from  a Grassmannian  of 2-planes. This  uses geometric  constructions including  a novel  description of certain  positroid varieties.   The cohomological  formula identifies each coefficient as particular  Littlewood-Richardson coefficient on a Grassmannian of $k$-planes, for some $k$, not necessarily equal to 2.\n\nThis is joint work with Changzheng Li and Mingzhi Yang.", "id": "Paper/65867", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65867"}, {"title": " Alternating monodromy from an involution ", "webprogram_exclude": "0", "session_ids": ["Session/18356"], "source_sha256": "51e26f8aa6e3eefdde54b04c62a668f8913ee71f9e004250c2326fe02789f5b1", "withdrawn": "", "abstract": "We give a simple geometric  condition on an involution which\nimplies  that a  corresponding imprimitive  Galois/monodromy\ngroup is alternating. We use this to determine the monodromy\ngroup  of an  unmixed system  of reciprocal  polynomials and\nshow how  it explains examples from the  applied mathematics\nliterature with alternating monodromy.   This is joint work\nwith Timothy Duff and Josef Schicho.", "id": "Paper/65868", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65868"}, {"title": " Possible Natural Kinds in Ancient Greek Mathematics ", "webprogram_exclude": "0", "session_ids": ["Session/17713"], "source_sha256": "6d52727363a68fa6ee3b5ac6272d156ad242f8f61e09fee1b6e06bc4037383d8", "withdrawn": "i", "abstract": "Some “natural kinds” are what Plato is seeking when he “divides nature at the joints” (a craft analogy from butchery).  Oft-cited examples notably include Lavoisieran stuffs, such as the elements gold, lead, mercury, sulfur, or carbon.  Examples also include Lavoisieran compound stuffs like water and “heavy water”: respectively, $H_2O$, hydrogen oxide and $D_2O$, deuterium oxide.  The intent is that a natural kind would exist in any possible world that comprehends the definition of the kind.  However, the natural kinds, which a given theory picks out of the disorder of things, are not always absolutely distinct.  Instead they are conditionally distinct: compare in particular the two isotopes of Lithium, namely $^{6}Li$ and $^{7}Li$.\n\nPhilosophers dispute the existence of natural kinds. I believe we can make some progress in this puzzle by examining the definition of the elements introduced by Plato in the \\textit{Timaeus}.  Plato’s mathematics in \\textit{Timaeus} 54ab construct, from “atomic triangles,” the four natural kinds that (for Plato and his co-evals) explain the physical cosmos, namely Fire, Air, Water, and Earth.  However, it is what Plato says about the atomic triangles that interests me here.  I argue that the five regular polyhedra (“Platonic solids”) constitute a closed set of natural kinds.  Moreover, the 14 Archimedean solids described by Pappos also constitute such a set.  The cube for example defines a unique entity in Euclidean 3-space, and every cube is geometrically similar to any cube; likewise for every 4-hedron, every 8-hedron, every 12-hedron, and every 20-hedron.  \n\nHowever, there is a puzzle in the Greek of \\textit{Timaeus} 54a.  “Now of the two triangles, the isosceles (ἰσοσκελὲς) possesses one single nature, but the scalene (πρόμηκες) an infinite number.”  Does Plato here use ἰσοσκελὲς to refer to the ἰσόπλευρος (“equilateral”) triangle?  The equilateral triangle does indeed have a single nature, i.e., every equilateral triangle is geometrically similar to any equilateral triangle.  The isosceles (ἰσοσκελὲς) triangles are indeed infinite in one way.  Upon the same side of a common segment ΑΒ, erect triangles whose sides are in proportion N::N::1 (where the length “1” is the length of the segment ΑΒ).  These will be infinite in number, and look rather similar — but they are not geometrically similar.", "id": "Paper/65869", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65869"}, {"title": " Multiscale modeling of coupled heat and flow in soil and snow with phase change ", "webprogram_exclude": "0", "session_ids": ["Session/18444"], "source_sha256": "d2bddfff815149c17d4dd84a157ad19a2f05e336aee268313c16cecfc6591972", "withdrawn": "", "abstract": "We consider modeling processes of heat conduction with phase change coupled to the water flow in soil and in snow domains, both considered as porous media at the micro-scale (pore-scale) and macro-scale (Darcy scale).  The heat transport model in soil is a nonlinear partial differential equation with a free boundary which extends the Stefan model appropriate at the pore-scale to the case of a distributed set of freezing temperatures; after upscaling we obtain a Darcy scale model with solutions smoother than those to the Stefan problem. The corresponding model in snow accounts for ice to liquid phase transition similarly as in Stefan problem, but the dominant and most interesting part of the model describes the sublimation/deposition of water vapor/ice crystals. The additional challenge for the flow model is that the ice fraction evolves which changes the properties of the soil and of snow as the porosity and permeability change. We present our upscaling approach, the challenges to the discretization and nonlinear solvers, and numerical simulations. \n\nThis is joint work with Praveeni Mathangadeera, Madison Phelps, Stefanie Fazekas, Naren Vohra, Lisa Bigler, and Zachary Hilliard.", "id": "Paper/65870", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65870"}, {"title": " Taft Actions on Gentle Algebras ", "webprogram_exclude": "0", "session_ids": ["Session/17907"], "source_sha256": "545639e0d47f10c001410bf5c0310b6b21b6d0e0b3cc9ecffe29adba5f5d1164", "withdrawn": "", "abstract": "Quantum symmetries of an algebra are given by actions of quantum groups, such as generalized Taft algebras $T_q(r,m)$. In 2021, Kinser and Oswald gave a parametrization of the Hopf actions of $T_q(r,m)$ on path algebras. We apply their classification to describe the Taft algebra actions on gentle algebras, which are tame bound quiver algebras that arise in many representation theoretic contexts. In particular, we describe the conditions on the quiver under which there is a filtered, inner-faithful action of $T_q(r,m)$ on a gentle algebra.", "id": "Paper/65871", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65871"}, {"title": " When Drops Crack Up: Fracture and Out-of-Plane Deformation in Drying Colloidal Suspensions ", "webprogram_exclude": "0", "session_ids": ["Session/17370"], "source_sha256": "c802e08c0d600075922e80a09f37793e61c58ec3fdcfd4e2f1d29cc1e49fe0bf", "withdrawn": "", "abstract": "As water evaporates from a freshly deposited drop of colloidal suspension, a thin close-packed particle deposit forms at the edge of the drop and grows inward. Water evaporation from this particle deposit combined with adhesion of the deposit to the substrate causes tensile stresses leading to the formation of regular radial cracks. Depending on whether the deposit then remains attached to the substrate or delaminates, the remaining stresses in the deposit get released in different ways: If the deposit remains attached, stresses are released by the formation of orthoradial cracks that bridge the radial cracks, creating a complex crack pattern. Conversely, no additional cracks form if the deposit delaminates. Instead, the deposit curves and deforms out of plane to relieve drying stresses, creating shapes that resemble blooming flowers. We show how the combination of poroelasticity with fracture mechanics and non-Euclidian plate mechanics captures both the complex crack pattern formation and the out-of-plane deformation as distinct responses to a similar drying stress.", "id": "Paper/65872", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65872"}, {"title": " Crowdsourcing Mathematical Databases ", "webprogram_exclude": "0", "session_ids": ["Session/18329"], "source_sha256": "8286500278ff6709a87745782735b6bf1addaba1ed02c696590b1fb54f890f85", "withdrawn": "", "abstract": "The L-functions and Modular Forms Database (LMFDB) is one of the largest online repositories of mathematical research data. It contains comprehensive catalogs of mathematical objects that arise in the context of the Langlands program, including number fields, elliptic curves, modular forms, and higher-dimensional analogs of these objects.  While primarily aimed at researchers, it has become an important resource for learners.\n\nIn cooperation with the Foundation for Science and AI Research (SAIR), we recently ran an open competition aimed at solving the inverse Galois problem over $\\mathbb Q$ in degree 24 (IGP24). This goal was achieved by collecting more than 50 million candidate number fields submitted by more than 100 teams, including examples that realize all 25,000 transitive permutation groups of degree 24 as Galois groups. AI tools and computer algebra systems played a central role in this project, both in building the infrastructure to run the contest and in enhancing the capabilities of participants.", "id": "Paper/65874", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65874"}, {"title": " Optimization by Decoded Quantum Interferometry ", "webprogram_exclude": "0", "session_ids": ["Session/18113"], "source_sha256": "ba62cddf31c7e9ec2e57f525d4d8d340bb329a125e38371c950fc6df20cc44fa", "withdrawn": "", "abstract": "Achieving superpolynomial speedups for optimization has long been a central goal for quantum algorithms. I will discuss Decoded Quantum Interferometry (DQI), a quantum algorithm descended from Regev's reduction, that uses the quantum Fourier transform to reduce optimization problems to decoding problems. For approximating optimal polynomial fits over finite fields, DQI achieves a superpolynomial speedup over known classical algorithms. The speedup arises because the problem’s algebraic structure is reflected in the decoding problem, which can be solved efficiently. Whether DQI can also attain quantum advantage for algebraically unstructured optimization problems such as max-k-XORSAT remains an open question. One reason for optimism is that the sparsity of the clause structure in max-k-XORSAT is reflected in the dual decoding problem, which is for LDPC codes. I will describe some ongoing research into this open question, which has uncovered surprising connections between quantum decoding algorithms and classical phase transitions. This talk will target a broad audience without assuming deep background in quantum algorithms.", "id": "Paper/65875", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65875"}, {"title": " Statistics and eugenics in the 20th century: A corpus analysis ", "webprogram_exclude": "0", "session_ids": ["Session/18374"], "source_sha256": "e3ff6850628a38c6345ce2322a199e7b5257101b7b264015f0caf0a87c7ff51d", "withdrawn": "", "abstract": "The confluence of eugenics and statistics in late 19th and early 20th century England has been well-documented by historians of science and mathematics, particularly in the works of Sir Francis Galton (1822-1911), Karl Pearson (1857-1936), and Sir Ronald Aylmer Fisher (1890-1962). The main question of study regarding these practitioners has been how deeply their eugenic convictions impacted their statistical developments. However, little work has been done to extend this question to the broader populace of statisticians in the English-speaking world. Utilizing public domain statistics textbooks published between 1880 and 1970 as a corpus for quantitative analysis, this talk will present a preliminary study into the co-existence of eugenics within statistics across the 20th century. It will also present more in-depth analyses of notable statistics textbooks within the corpus. On the whole, the aim of this talk is to bridge the understanding of eugenics within select figures' work with the practice of statistics writ large in the 20th century.", "id": "Paper/65877", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65877"}, {"title": " Ratios of Graph Gonalities ", "webprogram_exclude": "0", "session_ids": ["Session/19366"], "source_sha256": "0ddde7c9b5d7cd482bd356408f290ff67c255882a95ce32315ede8eb5a24396f", "withdrawn": "", "abstract": "Given positive integers $r>s$, let $\\mathcal{A}_{r,s}$ be the set of ratios $\\frac{\\mathrm{gon}_r(G)}{\\mathrm{gon}_s(G)}$ as $G$ ranges over all graphs, where $\\mathrm{gon}_r(G)$ is the $r^{\\text{th}}$ divisorial graph gonality of $G$. We prove that $\\mathcal{A}_{r,s}=(1,r/s]\\cap\\mathbb{Q}$ when $s$ divides $r$ and that $(1,r/s]\\cap\\mathbb{Q}\\subseteq\\mathcal{A}_{r,s}\\subseteq(1,\\lceil r/s\\rceil)\\cap\\mathbb{Q}$ when $s$ does not divide $r$.", "id": "Paper/65878", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65878"}, {"title": " Why Stand on the Shoulders of Giants? ", "webprogram_exclude": "0", "session_ids": ["Session/17853"], "source_sha256": "f824895cba2b3be02d0c9e3dff0e72999a4c6fa6885e09e8f714d0e1c5e00b43", "withdrawn": "", "abstract": "As we enter the 300th anniversary of the death of Isaac Newton, we know a good deal about his interests besides mathematics.   He spent much of his time on alchemy and biblical chronology.   One may wonder how he ever found time for doing mathematics.   It is certainly legitimate to ask why he thought it worth spending time on mathematics if it was not the most important part of his interests.  By looking at his religious writings, it is possible to establish the source of his readiness to do mathematics and to stand on the shoulders of giants.   His religious views are known to be far removed from the mainstream Christianity of his time.   Does that help to explain his readiness to pursue ideas in mathematics that also were not exactly part of the mainstream?   Details about Newton's religious ideas are taken from Rob Iliffe's 'Priest of Nature' (Oxford, 2017).   No knowledge of calculus will be presumed.", "id": "Paper/65889", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65889"}, {"title": " The matrix exponential gives coherence to a first course in systems of ODEs. ", "webprogram_exclude": "0", "session_ids": ["Session/18271"], "source_sha256": "abb342eac7f0844bf1ee5f4dddfca94f13da03ea94984c07fbbe1619e0457315", "withdrawn": "", "abstract": "We propose and outline here a restructuring of the traditional undergraduate first course in Differential Equations. With engineering students as its target audience, we place early and targeted emphasis on linear algebra concepts in context and in service of a systems-first approach. Unlike traditional treatments, here all higher-order ordinary differential equations are systematically reduced to first-order systems, enabling students to approach problems uniformly,\nregardless of order. Linear algebra—including eigenvalues, eigenvectors, fundamental sets, diagonalization, and matrix exponentiation—is introduced and used repeatedly as an essential\nanalytical tool for solving constant coefficient linear systems, which typically account for at least two-thirds of the course content. Unifying our treatment of linear constant coefficient systems is\nthe fundamental matrix $e^{\\mathbf{A}t}$ . In addition to not requiring that the coefficient matrix be diagonalizable, $e^{\\mathbf{A}t}$ links integrating factor, variation of parameters, and convolution in ways that are meaningful to engineering applications. Nonlinearity is shown to be sometimes treatable with\nCalculus, but in general requires linearization techniques to return to the ability to apply linear algebraic tools. This integrated approach enhances students’ ability to analyze coupled systems,\nassess stability, and apply techniques to mechanical vibrations, electrical circuits, and emerging applications in data-driven engineering. Early assessment indicates improved conceptual\nunderstanding, stronger connections between mathematical theory and engineering practice, and greater confidence in applying linear algebra in dynamic system analysis. This work contributes\nnew practices to the field of engineering education by demonstrating that a unified, systems-oriented approach provides a more coherent and application-ready foundation for engineering undergraduates.\nThe central claim of this work is that the matrix exponential $e^{\\mathbf{A}t}$ provides a unifying analytical framework that can replace the traditional “method-per-topic” structure of introductory\ndifferential equations.", "id": "Paper/65896", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65896"}, {"title": " On the Regularity of Integral Closures of Homogeneous Ideals ", "webprogram_exclude": "0", "session_ids": ["Session/17373"], "source_sha256": "8559eb687be56c67148e8514d70a4c1f4941dacbe89f75186c13e1e55043e021", "withdrawn": "", "abstract": "Let $S=K[x_1,\\ldots,x_n]$ be a standard graded polynomial ring and let $J\\subseteq S$ be a nonzero homogeneous ideal. We study how Castelnuovo--Mumford regularity behaves under integral closure. In particular, we ask whether\n$ \\operatorname{reg}(\\overline{J})\\leq \\operatorname{reg}(J) $\nalways holds. We show that this fails in general by constructing an equigenerated ideal in four variables with $\\operatorname{reg}(J)=3$ and $\\operatorname{reg}(\\overline{J})=4$. On the positive side, if $I=(\\overline{J})^{\\mathrm{sat}}\\neq S$ and $S/I$ is Cohen--Macaulay, then $\\operatorname{reg}(\\overline{J})\\leq \\operatorname{reg}(J)$. The proof uses saturation, high-degree agreement, and regularity properties of Cohen--Macaulay quotients.", "id": "Paper/65898", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65898"}, {"title": " Binomial Edge Ideals and Lefschetz Properties ", "webprogram_exclude": "0", "session_ids": ["Session/18370"], "source_sha256": "c7e1099b4658623e77a060d29910e36a756b6502f25e30fca560a53c387ba906", "withdrawn": "", "abstract": "Let G be a graph with n vertices and K be a field. Its binomial edge ideal $J_G\\subseteq K[x_1,\\ldots,x_n,y_1,\\ldots,y_n]$ is generated by the binomials $x_i y_j-x_j y_i$ corresponding to the edges $\\{i,j\\}$ of G. We study its Lefschetz properties through Artinian reductions by linear systems of parameters. In particular, we use ideas from algebra and combinatorics to construct explicit linear systems of parameters and analyze the algebraic\n properties of the resulting Artinian reduction. We prove in characteristic zero that all path graphs, all cycle graphs, and a family of graphs with Cohen–Macaulay binomial edge ideals have the strong Lefschetz property.", "id": "Paper/65899", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65899"}, {"title": " Reducibilities and algorithms ", "webprogram_exclude": "0", "session_ids": ["Session/18560"], "source_sha256": "ecbf8e93b7fb786d414d24820c63f57c7b531ffef9115155b226f84de0614d45", "withdrawn": "", "abstract": "The notion of relative computational strength lies at the heart of computability theory, and is most commonly captured by Turing reducibility. However, depending on the setting, other notions of reduction may be more appropriate — for instance when the resources available to a reduction are restricted, when reductions are required to\nbehave uniformly, or when the objects being compared are not total. We will discuss several such reducibilities and survey some recent results about the degree structures they induce.", "id": "Paper/65912", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65912"}, {"title": " Enumerating special <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.355ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 583.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\lambda</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-3BB\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-structures on the Burnside ring ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "a34ea2144e833093af152a06fa6d87de62b013367ee234519b2b9b944c094b0f", "withdrawn": "", "abstract": "We study the possible $\\lambda$-structures on the Burnside ring $\\Omega(G)$ of a finite group $G$. Here $\\Omega(G)$ encodes the algebra of finite $G$-sets under disjoint union and Cartesian product, and $\\lambda$-structures are families of operators $\\lambda^k$ satisfying rules similar to binomial coefficients. By a result of Wilkerson, we can study $\\lambda$-structures on $\\Omega(G)$ via their associated Adams operations $\\psi^p$, $p$ prime.\n\nWe reduce the problem of finding $\\lambda$-structures to nilpotent groups by showing that groups admitting a $\\psi^p$ are necessarily $p$-nilpotent. The converse is false, but holds for groups of order dividing $p^{p+1}$ and groups that are almost Dedekind in a particular sense. We also enumerate the Adams operations on certain families of abelian groups. Lastly, we explain some algorithms for enumerating Adams operations.", "id": "Paper/65913", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65913"}, {"title": " Strong and Linear Convergence for Monotone Inclusion Problems ", "webprogram_exclude": "0", "session_ids": ["Session/18363"], "source_sha256": "395478fb168af59c4e804486348df62d27bdba6f39322090475955745e5e9b4c", "withdrawn": "", "abstract": "\\documentclass[a4paper]{amsart}\n\\usepackage{amssymb}\n\\usepackage{hyperref}\n\\pagestyle{empty}\n\\date{}\n\n\\begin{document}\n\n\\title{Strong and Linear Convergence for Monotone Inclusion Problems}\n\\author{Oluwatosin T. Mewomo} %Presenting author only\n\\address{Department of Mathematics, Tarleton State University, Stephenville, United States} % Affiliation of presenting author\n\\email{omewomo@tarleton.edu} % Email address of presenting author only\n\n\\maketitle\n\n% The abstract  ***no more than one page***\n\n\\noindent In this talk, we present a relaxed two-step inertial forward-backward-forward algorithm for solving monotone inclusion problems in real Hilbert spaces. We establish strong and $R$-linear convergence of the proposed algorithm under suitable assumptions. Numerical experiments illustrate the efficiency and performance of the proposed method in comparison with existing algorithms.\n\n\\begin{thebibliography}{1}\n\n\\bibitem{BoCs1}  Bot, R. I., Csetnek, E. R.\n\\newblock Second order forward-backward dynamical systems for monotone inclusion problems.\n\\newblock {\\em SIAM J. Control Optim.} \\textbf{54}(3), 1423-1443 (2016).\n\t\n\n  \\bibitem{Malit2} Malitsky, Y., Tam, M.K.\n \\newblock  A forward–backward splitting method for monotone inclusions without cocoercivity.\n \\newblock  {\\em SIAM J. Optim.} \\textbf{30}, 1451–1472 (2020).\n \n\\bibitem{MOG}  Mewomo, O. T., Uzor, V.A., Gibali, A.\n\\newblock  An alternated inertial projection and contraction algorithm for solving quasimonotone bilevel variational inequalities with application to optimal control problems.\n\\newblock {\\em Acta Appl. Math.} \\textbf{193} (1), (2024).\n\n\\bibitem{Roc2}  Rockafellar, R., T.\n\\newblock  On the maximality of sums of nonlinear monotone operators.\n\\newblock {\\em Trans. Amer. Math. Soc.} {\\bf 149}, 75-88 (1960).\n\t\n\\bibitem{TaXu} Tan, K. K. Xu, H. K.\n\\newblock Approximating Fixed Points of Nonexpansive Mappings by the Ishikawa Iteration Process.\n\\newblock {\\em J. Math. Anal. Appl.} \\textbf{178}, 301-308 (1993).\n    \n\\bibitem{uzor8}  Uzor, V.A., Mewomo, O.T.\n\\newblock R-linear and strong convergence of Tseng methods for solving certain split and non-split problems.\n\\newblock {\\em Optimization}, {\\bf 74} (10), 2425-2456 (2025).\n    \n\t\n\n\n\n\t\n\n\n\n\n\n\t\t\t\t\t\n\t\n\\end{thebibliography}\n\n\\end{document}", "id": "Paper/65914", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65914"}, {"title": " Circuit Filling with Long-Span Girih Connectors ", "webprogram_exclude": "0", "session_ids": ["Session/18234"], "source_sha256": "fe111a896224b185845712ac112046083e61efaada3022ea1444ecb6f0d72f75", "withdrawn": "", "abstract": "Girih tiles are equilateral polygons used to create patterns in Islamic art and architecture. Robert E. Dewar conjectured that any region enclosed by a closed circuit of decagons connected by bowtie tiles can be completely tiled using only bowties and elongated hexagons, with no gaps left over. Motivated by this conjecture, we study a related model using a longer bowtie connection between neighboring decagons. We ask whether the analogous filling property continues to hold: can every void enclosed by such a circuit be tiled using only bowties and elongated hexagons?\nExact arithmetic in the ring generated by the golden ratio determines the required number of each tile. An exhaustive computational search finds verified tilings for all 1,037 valid circuits containing at most eleven decagons, as well as additional cases containing twelve decagons. An accompanying online gallery presents the circuits and their verified tilings.", "id": "Paper/65917", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65917"}, {"title": " Web Duality for the Grassmannian <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"9.067ex\" height=\"3.509ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -1150.1 3903.7 1510.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\widehat {\\operatorname {Gr}}(4,16)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-47\" d=\"M56 342Q56 428 89 500T174 615T283 681T391 705Q394 705 400 705T408 704Q499 704 569 636L582 624L612 663Q639 700 643 704Q644 704 647 704T653 705H657Q660 705 666 699V419L660 413H626Q620 419 619 430Q610 512 571 572T476 651Q457 658 426 658Q401 658 376 654T316 633T254 592T205 519T177 411Q173 369 173 335Q173 259 192 201T238 111T302 58T370 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xlink:href=\"#E1-MJMAIN-31\"></use>\n <use xlink:href=\"#E1-MJMAIN-36\" x=\"500\" y=\"0\"></use>\n</g>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"3514\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18240"], "source_sha256": "6e6783e5c738be008b8ebbc8254b34033f4d49e50f6d655f9438ee8b54d73efa", "withdrawn": "", "abstract": "We study web duality, the correspondence between $SL_r$ and $SL_k$ tensor invariants introduced by Fraser--Lam--Le, in the self-dual case $r = k = 4$, $n = 16$. Using the hourglass plabic graphs of Gaetz--Pechenik--Pfannerer--Striker--Swanson, we construct all $24{,}024$ rank-4 webs indexed by $4 \\times 4$ standard Young tableaux via the GPPSS growth algorithm, and verify computationally that each web's trip permutations $\\mathrm{trip}_\\bullet(G)$ agree with the promotion permutations $\\mathrm{prom}_\\bullet(T)$ of its source tableau $T$. We prove several vanishing lemmas that generalize fork-vanishing and coloring-obstruction results to the $SL_4$ and mixed $SL_r \\times SL_k$ settings. These vanishing lemmas eliminate all but $22{,}137$ of the roughly $36.5$ million candidate pairings $\\langle W, X \\rangle$ before any skein expansion is needed. For the survivors, we describe a computational procedure that expands $X$ via wrench, square, and double-trident moves and evaluates the resulting Pl\\\"ucker monomials by coloring. The data support a transpose-duality conjecture for benzene-free webs, with a small number of exceptions, and motivate new conjectures describing the pairing behavior of webs containing benzene configurations, including those arising from benzene chain reactions.", "id": "Paper/65918", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65918"}, {"title": " Profinite iterated monodromy groups for some classes of rational maps ", "webprogram_exclude": "0", "session_ids": ["Session/18259"], "source_sha256": "0affcaca1b3caee256b3ecfb1a66184c4ee4a665977e86b2c63b328bd3c93274", "withdrawn": "", "abstract": "We will discuss some recent results about the properties of profinite iterated monodromy groups associated to certain classes of cubic polynomials, and of rational maps. Based on joint works with Hlushchanka, Wardell and Nozawa.", "id": "Paper/65920", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65920"}, {"title": " Smooth connectivity in real algebraic varieties ", "webprogram_exclude": "0", "session_ids": ["Session/18042"], "source_sha256": "45285bbb08057cddf5e525780bd5414a0559982e0e6b22f79cec567dd3ce72a7", "withdrawn": "", "abstract": "A standard question in real algebraic geometry is to compute the number of connected components of a real algebraic variety in affine space. In this talk, we will provide algorithms for computing the number of connected components, the Euler characteristic, and deciding the connectivity between two points for a smooth manifold arising as the complement of a real hypersurface of a real algebraic variety. When considering the complement of the set of singular points of a real algebraic variety, this yields an approach for determining smooth connectivity in a real algebraic variety. The method is based upon gradient ascent/descent paths on the real algebraic variety inspired by a method proposed by Hong, Rohal, Safey El Din, and Schost for complements of real hypersurfaces. Several examples will be included to demonstrate the approach.", "id": "Paper/65922", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65922"}, {"title": " The real Brown-Peterson homology of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"7.465ex\" height=\"2.509ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -934.9 3213.9 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\Omega ^\\rho S^{\\rho + 1}</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-3A9\" d=\"M55 454Q55 503 75 546T127 617T197 665T272 695T337 704H352Q396 704 404 703Q527 687 596 615T666 454Q666 392 635 330T559 200T499 83V80H543Q589 81 600 83T617 93Q622 102 629 135T636 172L637 177H677V175L660 89Q645 3 644 2V0H552H488Q461 0 456 3T451 20Q451 89 499 235T548 455Q548 512 530 555T483 622T424 656T361 668Q332 668 303 658T243 626T193 560T174 456Q174 380 222 233T270 20Q270 7 263 0H77V2Q76 3 61 89L44 175V177H84L85 172Q85 171 88 155T96 119T104 93Q109 86 120 84T178 80H222V83Q206 132 162 199T87 329T55 454Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-3C1\" d=\"M58 -216Q25 -216 23 -186Q23 -176 73 26T127 234Q143 289 182 341Q252 427 341 441Q343 441 349 441T359 442Q432 442 471 394T510 276Q510 219 486 165T425 74T345 13T266 -10H255H248Q197 -10 165 35L160 41L133 -71Q108 -168 104 -181T92 -202Q76 -216 58 -216ZM424 322Q424 359 407 382T357 405Q322 405 287 376T231 300Q217 269 193 170L176 102Q193 26 260 26Q298 26 334 62Q367 92 389 158T418 266T424 322Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-53\" d=\"M308 24Q367 24 416 76T466 197Q466 260 414 284Q308 311 278 321T236 341Q176 383 176 462Q176 523 208 573T273 648Q302 673 343 688T407 704H418H425Q521 704 564 640Q565 640 577 653T603 682T623 704Q624 704 627 704T632 705Q645 705 645 698T617 577T585 459T569 456Q549 456 549 465Q549 471 550 475Q550 478 551 494T553 520Q553 554 544 579T526 616T501 641Q465 662 419 662Q362 662 313 616T263 510Q263 480 278 458T319 427Q323 425 389 408T456 390Q490 379 522 342T554 242Q554 216 546 186Q541 164 528 137T492 78T426 18T332 -20Q320 -22 298 -22Q199 -22 144 33L134 44L106 13Q83 -14 78 -18T65 -22Q52 -22 52 -14Q52 -11 110 221Q112 227 130 227H143Q149 221 149 216Q149 214 148 207T144 186T142 153Q144 114 160 87T203 47T255 29T308 24Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-3A9\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-3C1\" x=\"1021\" y=\"513\"></use>\n<g transform=\"translate(1188,0)\">\n <use xlink:href=\"#E1-MJMATHI-53\" x=\"0\" y=\"0\"></use>\n<g transform=\"translate(655,362)\">\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-3C1\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-2B\" x=\"517\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-31\" x=\"1296\" y=\"0\"></use>\n</g>\n</g>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18217"], "source_sha256": "8edeafbd124616a560605f8967da911a7b2be1902a615d434471f25b3b04139e", "withdrawn": "", "abstract": "This talk focuses on a computation of the $RO(C_2)$-graded real Brown--Peterson homology of the representation-loop space $\\Omega^\\rho S^{\\rho + 1}$, where $\\rho$ is the regular representation of the cyclic group of order two, meant to inform the development of an equivariant Dieudonn\\'{e} theory. Along the way, we encounter a number of complications arising from the complexity of $C_2$-equivariant homotopy theory. For instance, determining the comodule Nishida relations for (finite) $\\rho$-loop spaces is more intricate and subtle. Throughout, we compare our techniques with the classical computation of the Brown--Peterson homology of the double loop space $\\Omega^2 S^3$ due to Ravenel.", "id": "Paper/65925", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65925"}, {"title": " On a blended Anderson / NGMRES acceleration for the Navier-Stokes Picard iteration: convergence analysis and adaptive depth selection ", "webprogram_exclude": "0", "session_ids": ["Session/18444"], "source_sha256": "30c57c41f0f9d0c50cc0fb6792834e899c6db5b5ca6d73cc72c3b650edcb47bd", "withdrawn": "", "abstract": "Anderson acceleration (AA) and nonlinear GMRES (NGMRES) have been successfully applied to improve the efficiency and robustness of many nonlinear solvers, with each being shown to have certain advantages over the other.  There are two differences between the AA and NGMRES algorithms: the extrapolations are different, and AA uses fixed point residuals in the optimization problem while NGMRES uses true nonlinear residuals.  Motivated by recent AA and NGMRES analyses and numerical testing, we consider a blend of AA and NGMRES that uses the AA extrapolation and the true nonlinear residuals for the optimization problem.  To focus our study, we consider the blended method applied to the Picard iteration for the Navier-Stokes equations, but many of the ideas developed herein are extendable to a wide variety of  nonlinear systems and solvers.  We provide a convergence analysis and proof of acceleration of the blended method, provide a detailed numerical comparison of AA, NMGRES and the blended method for several benchmark tests, and develop an effective adaptive depth strategy.", "id": "Paper/65930", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65930"}, {"title": " Inviting Students As Partners To Design And Enact Alternative Grading In A Coordinated Introductory Course ", "webprogram_exclude": "0", "session_ids": ["Session/18250"], "source_sha256": "4d3615f8dd019170c1cfcaae3136aae2cbd7971aebde93401d8cbfa5cac8f627", "withdrawn": "", "abstract": "We discuss the implementation of a new mastery-based assessment structure in a multi-section introductory linear algebra course. In a large coordinated course, mastery-based grading presents a particular challenge, as instructors must develop shared standards for what constitutes sufficient evidence of student understanding. Without meaningful agreement about these standards, students may encounter substantially different expectations for demonstrating mastery. We will share the collaborative process through which our teaching team addressed this challenge, including how junior colleagues participated as partners in decisions about curriculum and assessment design, and how we balanced consistency across sections with instructor autonomy and academic integrity. Our approach is inspired by recent work on course coordinator orientations. In particular, we draw on the Humanistic-Growth orientation to frame coordination as an opportunity for professional growth and community building. We argue that instructor partnership in course development can produce a more equitable student experience without requiring uniformity in teaching.", "id": "Paper/65932", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65932"}, {"title": " A Banach Space Formulation for the Navier-Stokes-Biot Coupled Problem ", "webprogram_exclude": "0", "session_ids": ["Session/17782"], "source_sha256": "890828d6c56abababc22116551bac013d47c8742d5bc0685b5a1a5529a55100f", "withdrawn": "", "abstract": "We introduce and analyze a mixed formulation for the coupled problem arising in the interaction\nbetween a free fluid and a poroelastic medium. The flows in the free fluid and poroelastic regions\nare governed by the Navier–Stokes and Biot equations, respectively, and the transmission conditions\nare given by mass conservation, balance of stresses, and the Beavers–Joseph–Saffman law. We apply\ndual-mixed formulations for both the Navier–Stokes and Darcy equations and a displacement-based\nformulation for the elasticity equation. We develop a weak formulation in Banach space framework\nwhere the symmetry of the Navier–Stokes pseudostress tensor is imposed in a weak sense using a\nvorticity Lagrange multiplier. In turn, the transmission conditions are imposed weakly by introducing\nthe traces of the fluid velocity and the poroelastic pressure on the interface as Lagrange multipliers.\nExistence and uniqueness of a weak solution are established using classical results for nonlinear monotone operators, complemented by a regularization technique and the Banach fixed-point theory, under\na small data assumption. We then present a semidiscrete continuous-in-time numerical approximation\nbased on conforming finite element spaces, allowing for nonmatching grids along the interface. We\nestablish well posedness of the numerical scheme and present error analysis with corresponding rates\nof convergence within the Banach space framework. Numerical experiments are presented to verify the\ntheoretical rates of convergence and to illustrate the method’s performance in an application involving\nflow through a filter.", "id": "Paper/65933", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65933"}, {"title": " CANCELLED Beyond Pointwise Dominance in the Stabilization of Damped Wave Equations with Delay \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/19357"], "source_sha256": "9a4bf2441b35acd4708a7117d68577db1f563f0545fe61ddc9a7cb65797645f4", "withdrawn": "", "abstract": "Time delays may destroy the stability of an otherwise dissipative wave equation, and classical stabilization results for delayed wave equations typically require the instantaneous damping to dominate the delayed feedback at every time. In this talk, we present several approaches that relax this pointwise dominance requirement.\n\nWe first consider damped wave equations with discrete delay. A transformation of the delayed term into the time derivative of an integral quantity leads to a modified energy and reveals additional dissipative structure, allowing stability under conditions less restrictive than the classical pointwise dominance condition. We then extend this transformation technique to wave equations with distributed delay through an integrated delay kernel.\n\nA second direction replaces pointwise dominance by average-in-time dissipativity. For wave equations with time-dependent damping and discrete delay, suitable energy estimates lead to a Halanay-type differential inequality, from which exponential decay follows under an average dominance condition, even when instantaneous dominance fails on short time intervals. We finally discuss the extension of this average-based approach to Halanay inequalities with distributed delay. Together, these results provide a progression from classical pointwise stability conditions toward more flexible structural and average-in-time criteria for the stabilization of damped wave equations with delay.", "id": "Paper/65935", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65935"}, {"title": " Convex integration for the Monge-Ampère system and the system of isometric immersions ", "webprogram_exclude": "0", "session_ids": ["Session/17952"], "source_sha256": "7a3da05712102e6899c2feb73f7aeb0163864cfb2bdb6a35abebe7813905dd5c", "withdrawn": "", "abstract": "In this talk, we will present recent results on flexibility for the Monge–Ampère system and the system of isometric immersions in a unified framework. We will clarify  how that the convex integration algorithm developed for one of these systems can be used to obtain the corresponding result for the other system, with the same regularity exponent.", "id": "Paper/65938", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65938"}, {"title": " Quantification of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.852ex\" height=\"2.509ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -934.9 1228 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">C^0</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-43\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-43\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-30\" x=\"1094\" y=\"513\"></use>\n</g>\n</svg> convergence in dimension <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.162ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 500.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">3</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-33\" x=\"0\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18284"], "source_sha256": "f27b65ed4f42370de87c95a97da79f31f64a71cac5ac7bd4527ff20e27c2371e", "withdrawn": "", "abstract": "We address Gromov's Quantification of $C^0$ Convergence Conjecture in dimension three, this is a joint work with Liam Mazurowski.  Let $B$ be the unit ball in $\\mathbb R^3$.  Let $g$ and $g_0$ be smooth metrics on $B$. We prove there are constants $C$ and $\\epsilon_0$ depending only on $g_0$ so that \n\\[\ninf_{x \\in B} R_g(x) < R_{g_0}(0) + C \\|g-g_0\\|_{C^0}^{1/2}\n\\] \nprovided $|g-g_0|_{C^0}\\ < \\epsilon_0$.  We also construct examples to show that the exponent 1/2 is sharp.  This explicitly quantifies the fact that scalar curvature lower bounds are preserved under $C^0$ convergence of metrics.  The proof is based on an analysis of harmonic functions.  We will also briefly discuss some further applications of this method to other problems.", "id": "Paper/65949", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65949"}, {"title": " Quadratic and Koszul Licci Ideals ", "webprogram_exclude": "0", "session_ids": ["Session/18285"], "source_sha256": "4d8f28a37adb09ed1f6994c959285a7a77435d5254af600133ab4398c1a61fd5", "withdrawn": "", "abstract": "We give a complete classification of all Koszul licci ideals, including a complete description of the defining equations and graded Betti tables for these ideals, showing that they exactly correspond to quadratic licci ideals that are at most two links away from a complete intersection.  \n    More generally, we show how to uniquely associate the Hilbert function of a quadratic licci ideal to a partition of its codimension, and use it to  \n    prove that the Hilbert function of a quadratic ideal determines whether or not it is licci. This provides a strong affirmative answer in the quadratic case to a question of Huneke, Polini, and Ulrich asking whether graded Betti tables determine the licci property of graded ideals.", "id": "Paper/65950", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65950"}, {"title": " Partitioning a Graph into Generalized Isolating Sets ", "webprogram_exclude": "0", "session_ids": ["Session/18317"], "source_sha256": "4a1fbecb87562f19a434ae29d01c89c4354fbe74b00d95d1eab42574a72c05dd", "withdrawn": "", "abstract": "An isolating set $S$ of a graph is a set of vertices such that, if we remove $S$ and its neighborhood, only isolated vertices remain. The minimum size of such set is the isolation number. While bounds on this parameter are known for many cases, we explore results attained by partitioning the vertex set using colorings for several families of graphs. We also explore a generalization of the isolation parameter for arbitrary excluded sets.", "id": "Paper/65951", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65951"}, {"title": " Representation categories of the super singlet vertex operator algebra ", "webprogram_exclude": "0", "session_ids": ["Session/18270"], "source_sha256": "5907951180ecd40277fd4804046cb667ca9c158e4a71af5cdd5fa0e26cbcfd9d", "withdrawn": "", "abstract": "The super singlet vertex operator algebra $\\mathcal{SM}(p)$ for $p\\geq2$ was introduced by Adamovi\\'c and Milas in 2009 and is a rich source of examples in logarithmic conformal field theory. In this talk, we will discuss our recent progress in the construction of vertex tensor categories of $\\mathcal{SM}(p)$-modules, including the classification of irreducible modules, the structure of projective modules, and some fusion rules. Based on joint work in progress with T. Creutzig, F. Orosz Hunziker, Y. Wang and J. Yang.", "id": "Paper/65957", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65957"}, {"title": " Proof Verification with Lurch Plus ", "webprogram_exclude": "0", "session_ids": ["Session/18208"], "source_sha256": "d5fdac92dbe2bd56a0b70d2c72218c84a198cf204c8cf4921f13edb75affc4c8", "withdrawn": "", "abstract": "Would your students benefit from an easy-to-use, open-source, web-based word processor that checks their mathematical proofs in real time? Lurch Plus (lurch.plus) is a proof assistant designed to verify proofs written in standard mathematical notation, without requiring students to learn a specialized formal language. We will demonstrate the software and explain how our custom validation algorithm and its underlying mathematical foundation make this possible.", "id": "Paper/65959", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65959"}, {"title": " Higher K-theory of semi-algebraic sets ", "webprogram_exclude": "0", "session_ids": ["Session/18217"], "source_sha256": "879b8dd62a008a23e63c0a39682ded7320e263457e70bf3a7e19957c4b0eced9", "withdrawn": "", "abstract": "The Euler characteristic is an invariant for semialgebraic sets (or more generally, definable sets in an o-minimal structure) which completely determines their Grothendieck group. Higher algebraic K-theory generalizes this group. I will present a lift of the Euler characteristic to a map of K-theory spectra, using the framework of squares K-theory rather than assembler K-theory.", "id": "Paper/65960", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65960"}, {"title": " On the scalar curvature lower bound under weak convergence ", "webprogram_exclude": "0", "session_ids": ["Session/17803"], "source_sha256": "e55bdb03d1865846b404ec0f6c735013934a771b3e14e71313d2c420adb15630", "withdrawn": "", "abstract": "In this talk, we introduce some recent works, joint with Liam Mazurowski, on the scalar curvature lower bound under weak convergence. We will discuss the history, conjectures on this topic and our main results.", "id": "Paper/65961", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65961"}, {"title": " Identifying the Primary Drivers of Life Satisfaction in Maryland: A 2024 Cross-Sectional BRFSS Analysis ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "cdfa0e38cc2153b5b5f4622097021687927ce5cd2f44159ed11b5486b6fefbbc", "withdrawn": "", "abstract": "Aims: Life satisfaction is commonly used as a measure of someone’s well-being, which is influenced by demographic, socioeconomic, and health variables. This study investigates the correlation between those key factors and self-reported life satisfaction among adults. \n\nMethod: We performed a cross-sectional analysis of the 2024 Behavioral Risk Factor Surveillance System (BRFSS) for Maryland. Self-reported life satisfaction responses were dichotomized into two categories: satisfied (satisfied/very satisfied) or dissatisfied (dissatisfied/very dissatisfied). Then descriptive statistics and Rao-Scott chi-square tests were used. We then used survey-weighted multivariate logistic regression to estimate adjusted odds ratios (aOR) with 95\\% confidence interval (CI). Complementary multi-strategy machine learning models for predictive analysis and for handling class imbalances were performed.    \n\nResults: From the 12,197 respondents, 94.93\\% reported being satisfied compared to 5.07\\% dissatisfied. Prolonged psychological distress (≥14 days of poor mental health) was the strongest predictor of life dissatisfaction (aOR = 12.678; 95\\% CI [8.404, 19.126]), with 23.37\\% dissatisfaction rate versus 1.36\\% for those with zero days. Low socioeconomic status was the second critical determinant; respondents with annual household incomes below 25,000 USD reported a 13.34\\% dissatisfaction rate, compared to 1.50\\% for those earning 200,000 USD or more. Ages 40–64 and a marital status of separated significantly predicted diminished life satisfaction. Finally, our machine learning demonstrated that the WeightedEnsemble\\_L2 classifier performed best, yielding an accuracy of 0.8661, precision of 0.8799, recall of 0.848, and an F1-score of 0.8637.  \n\nConclusion: In Maryland, adult life satisfaction is closely tied to mental health, income, marital status, and age. Decision-makers should focus on promoting mental health screenings for vulnerable groups, specifically low-income, middle-aged residents.", "id": "Paper/65964", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65964"}, {"title": " Operator Formulation of Metric Learning ", "webprogram_exclude": "0", "session_ids": ["Session/19368"], "source_sha256": "e258288dac4c9439428e36fcb7c1f2792c8cad1a9af5407e87eae68ac520a2dc", "withdrawn": "", "abstract": "Metric learning seeks to construct notions of distance that reflect the\ngeometry of data rather than relying on a fixed, predetermined metric.\nIn this talk, we introduce an operator formulation of metric\nlearning in which distances are induced by mappings between normed\nspaces. Given an operator $T:X\\to Y,$ we consider the associated distance $d_T(x,y)=\\|T(x)-T(y)\\|_Y.$ This formulation provides a natural connection between metric learning\nand operator theory.\n\nWe investigate conditions under which $d_T$ defines a metric or a\npseudometric and examine how analytical properties of $T$ determine\nthe resulting geometry. In particular, properties such as injectivity,\ncontinuity, and stability of the operator are related to separation of\npoints, topological properties, and robustness of the induced distance.\nDifferent classes of distance operators, including linear and nonlinear\noperators, lead to distinct families of induced geometries.\n\nThe operator viewpoint also provides a framework for studying the\napproximation and learning of metrics in infinite-dimensional settings.\nRather than learning pairwise distances directly, the problem is\nreformulated as learning an operator whose action induces the desired\ngeometry. This perspective connects metric learning with functional\nanalysis, operator theory, and operator approximation, and provides a\nmathematical framework for investigating the representation, stability,\nand approximation of learned distances.", "id": "Paper/65992", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65992"}, {"title": " Boost Like a (Var)Pro: Trust-Region Gradient Boosting via Variable Projection ", "webprogram_exclude": "0", "session_ids": ["Session/17908"], "source_sha256": "35a80da3f1eafbbf91f9af88ff6fea9378d7117b04f00af576742a53fb2be607", "withdrawn": "", "abstract": "Training machine learning models is computationally challenging; one has to solve a high-dimensional, nonconvex optimization problem repeatedly to appropriately calibrate hyperparameters.  Our goal is to reduce the training burden by strategic model design paired with structure-exploiting optimization.  To this end,  we introduce VPBoost (Variable Projection Boosting), a gradient boosting algorithm for separable smooth approximators, i.e., models with a smooth nonlinear featurizer followed by a final linear mapping.   VPBoost fuses variable projection, a training paradigm for separable models that enforces optimality of the linear weights, with a second-order weak learning strategy.  The combination of second-order boosting, separable models, and variable projection give rise to a natural interpretation of VPBoost as a functional trust-region method. We leverage trust-region theory to prove VPBoost converges under mild regularity conditions. Through numerical experiments on synthetic data, image classification, and scientific machine learning, we demonstrate that VPBoost outperforms gradient-descent-based boosting and attains competitive performance relative to an industry-standard decision tree boosting algorithm.", "id": "Paper/65994", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65994"}, {"title": " Supercharacter Theories of the Special Linear and Orthogonal Groups ", "webprogram_exclude": "0", "session_ids": ["Session/18264"], "source_sha256": "1d23f48b0b983c44a488875aafe3b8270ec73ebc6501f15b3fc2aa1b1d8755b0", "withdrawn": "", "abstract": "This talk will begin with an introduction to the supercharacter theory of finite groups as defined by P. Diaconis and I.M. Isaacs (Trans. Amer. Math. Soc., 2008).  In this theory, the concepts of irreducible characters and conjugacy classes are generalized to supercharacters and superclasses, while still maintaining important information about the group.  We will then demonstrate and compare properties of specific supercharacter theories that occur for the special linear groups $SL(2, q)$ and for the orthogonal groups $O(3, q)$, for $q$ a power of a prime.", "id": "Paper/65995", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65995"}, {"title": " Growth in Matrix Products ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "bc6dd7f9b3ef7994372978608531ffd2e9f4f06d08050659aab95f624cd7fbdd", "withdrawn": "", "abstract": "Given two integer matrices $A$ and $B$, we study which words of a fixed length produce the largest absolute value of a matrix entry. We show that alternating words achieve maximal entry growth for a large family of matrix pairs. Our result gives rise to a new elementary proof of the Lagarias-Wang finiteness conjecture for this family by showing that the maximum growth rate is always achieved by a periodic product. We also discuss an application to Cayley hash functions, connecting the growth rate to the length of cycles in relevant Cayley graphs.", "id": "Paper/65996", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65996"}, {"title": " Bifurcation of rotating wave solutions in reaction-diffusion-advection systems with nonlocal reaction on a circle ", "webprogram_exclude": "0", "session_ids": ["Session/18009"], "source_sha256": "81e1d73398ef7b54cf4d952064c061de081fada8f4ae1261642b2e8bfa4df5f3", "withdrawn": "", "abstract": "We investigate the existence and stability of rotating wave solutions for a general class of reaction-diffusion-advection systems with nonlocal reaction terms on a circle. By applying an abstract Hopf bifurcation theorem, we rigorously establish the existence of small-amplitude rotating waves bifurcating from spatially homogeneous steady states and identify their critical wave speeds. The stability of the bifurcating rotating waves is further characterized using center manifold and normal form theory. We then apply the general theoretical framework to two biological models: the Klausmeier model for water-plant interactions and a Keller-Segel-type chemotaxis system. In both cases, we demonstrate how the general theory can be used to characterize the emergence and stability of rotating waves, and numerical simulations are provided to illustrate and validate the analytical results.", "id": "Paper/65999", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/65999"}, {"title": " On Quotients of Calabi–Yau Generalized Fermat Manifolds and Log–Enriques Varieties ", "webprogram_exclude": "0", "session_ids": ["Session/17996"], "source_sha256": "426734740726614cacffeef02244139fa406f667fb69e90f608209d721e0edae", "withdrawn": "", "abstract": "Let $M$ be a Calabi--Yau generalized Fermat manifold of dimension $d$ and degree $k$ in $\\mathbb{P}^n$, and let $\\varphi\\in\\operatorname{Aut}(M)$ be an automorphism acting freely. We show that the quotient $M/\\langle\\varphi\\rangle$ is determined by the parity of $d$: when $d$ is even, $M/\\langle\\varphi\\rangle$ is a log-Enriques variety of Calabi--Yau type and index two, whereas when $d$ is odd, it is a Calabi--Yau variety. Moreover, using the Reid--Tai criterion, we classify its quotient singularities and prove that they are terminal except in the boundary case $(d,k)=(2,4)$, where the singularities are canonical.", "id": "Paper/66000", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66000"}, {"title": " Generalized Laguerre Spectral Methods for Volterra Integral Equations on the Half-Line ", "webprogram_exclude": "0", "session_ids": ["Session/19344"], "source_sha256": "b4a69db4a31f0395bfabc28f0a5d23b431aea4c54f85b20e21b070b930e1c54e", "withdrawn": "", "abstract": "Volterra integral equations on the half-line arise in several applications, including control engineering,\ndiffusion, viscoelasticity, and mathematical biology. Their numerical treatment is challenging due to the\nunbounded domain and the possible growth of solutions at infinity. In this talk, we present a generalized\nLaguerre spectral Galerkin method for second-kind Volterra integral equations on [0, ∞). We first\nintroduce a suitable weight transformation to obtain a bounded reformulated problem, then use generalized\nLaguerre functions as basis functions for the Galerkin approximation. We establish convergence estimates\nin a weighted $", "id": "Paper/66001", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66001"}, {"title": " Some results on point configurations in thin subsets of Euclidean space ", "webprogram_exclude": "0", "session_ids": ["Session/17815"], "source_sha256": "9c7ca1ee4e0d2487c65631242e394da2b9ad32f8d7b0afbc15e207d9ddde419f", "withdrawn": "", "abstract": "In 1946, Paul Erd\\\"os posed a question: what configuration of $n$ distinct points in the Euclidean plane can minimize the number of distinct distances between pairs of these points? More recently, Kenneth Falconer posed a \"continuous\" analog of Erd\\\"os's problem: if a subset $E\\subset\\mathbb{R}^d$ is large enough (in terms of its dimension), can we guarantee that many pairwise distances are achieved between points in $E$? I'll discuss some recent results regarding certain Falconer-type questions, especially those corresponding to more complicated point configurations than the two point configurations from which distances arise. This is based on joint work with Tainara Borges, Alex Iosevich, Yumeng Ou, Eyvi Palsson, and Francisco Romero Acosta.", "id": "Paper/66006", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66006"}, {"title": " Is the generic nonsingular action of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.453ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 625.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\Gamma</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-393\" d=\"M128 619Q121 626 117 628T101 631T58 634H25V680H554V676Q556 670 568 560T582 444V440H542V444Q542 445 538 478T523 545T492 598Q454 634 349 634H334Q264 634 249 633T233 621Q232 618 232 339L233 61Q240 54 245 52T270 48T333 46H360V0H348Q324 3 182 3Q51 3 36 0H25V46H58Q100 47 109 49T128 61V619Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-393\" x=\"0\" y=\"0\"></use>\n</g>\n</svg> weakly mixing? ", "webprogram_exclude": "0", "session_ids": ["Session/18213"], "source_sha256": "a0b0f0d4c8c413b19e31112ca13700c32e9a3f6d295d1ecbda9aa4329b3c2c66", "withdrawn": "", "abstract": "Consider the space of all nonsingular (measure-class preserving) Borel actions of a fixed countable group $\\Gamma$ on a standard probability space $(X, \\mu)$.\nWe are interested in which properties of the action (e.g., weak mixing, or ergodicity of the cartesian square) are generic in the sense of Baire category.\nWhen $\\Gamma = \\mathbb{Z}$ or the space is of \\textit{measure preserving} actions the situation is well understood, but much less is known in our more general context.\nThis is joint work with Garrett Ervin, Bogl\\'arka Geh\\'er, Anett Kocsis, and M\\'at\\'e Palfy.", "id": "Paper/66008", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66008"}, {"title": " Towards combinatorial derivations of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.066ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 889.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">K</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-4B\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-polynomials for determinantal varieties ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "6ebda629b8ed5ed1d425823bdca8faeed9eec49210da61e94ee21d83421b957f", "withdrawn": "", "abstract": "Let $\\mathfrak{X}_k\\subseteq{\\sf Mat}_{m, n}$ denote the variety of $m\\times n$ complex matrices with rank at most $k$. \nThe power series and rational expressions for the Hilbert series of $\\mathfrak{X}_k$ are known by geometric arguments, and equating these expressions yields a family of formulas generalizing the classical Cauchy and dual Cauchy identities.\nWe pose the problem of giving a direct combinatorial proof of these formulas for $0 < k < \\min\\{m, n\\}$. When $k=1$ or $k=\\min\\{m, n\\}-1$, we give such a proof via an explicit sign-reversing involution on certain sets of Littlewood--Richardson tableaux.", "id": "Paper/66011", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66011"}, {"title": " Structural Approaches to Star-Critical Ramsey Numbers ", "webprogram_exclude": "0", "session_ids": ["Session/18106"], "source_sha256": "3e29d1eddb02cc27d5954dfd2d98426e353c8814f558bc99dcbe7d3711e29a7a", "withdrawn": "", "abstract": "The star-critical Ramsey number $r_*(G,H)$ is the smallest integer $k$ such that every red-blue edge-coloring of $K_r - K_{1,r-1-k}$ contains either a red copy of $G$ or a blue copy of $H$, where $r=r(G,H)$ is the graph Ramsey number. A $(G,H)$-critical graph is a red-blue edge coloring of $K_{r-1}$ that avoids both a red copy of $G$ and a blue copy of $H$, demonstrating that $r-1$ vertices are insufficient to force the Ramsey property. Determining $r_*(G,H)$ is an optimization problem: how many edges incident to an added vertex are necessary to guarantee the Ramsey property? Establishing this threshold typically requires extremal constructions and a structural analysis of critical graphs. This talk will discuss advances in star-critical Ramsey numbers with particular attention to results for paths versus cycles.", "id": "Paper/66019", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66019"}, {"title": " EDGE Networking Session ", "webprogram_exclude": "0", "session_ids": ["Session/18368"], "source_sha256": "f19bad9a1f2e2e803fb61667fb9f23cd974d72d9860aa0456803356e30bced8b", "withdrawn": "", "abstract": "This session will feature structured time for interaction and networking between early-career mathematicians and more senior mathematicians, with emphasis on women and gender minorities. A group photo for EDGE-affiliated individuals will be taken at the start of this session. The event is open to everyone and we encourage anyone to attend.", "id": "Paper/66020", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66020"}, {"title": " Grassmannian Methods for Spatial Transcriptomics Analysis ", "webprogram_exclude": "0", "session_ids": ["Session/18229"], "source_sha256": "c02e1cda9d7db3515b7f0da503d8fe7bf6f83327bc498a92dc01b4ec4367cf98", "withdrawn": "", "abstract": "Spatial transcriptomics measures gene expression together with spatial coordinates, but many existing methods represent each spot primarily as a single feature vector. We present GrassST, a subspace method that represents each spot by a low-dimensional subspace fitted to the embedded expression profiles in its spatial neighborhood. These subspaces form points on a Grassmannian and are compared using distances between subspaces. The neighborhood size and subspace rank are selected from the spectral energy of each dataset. Experiments on four spatial transcriptomics datasets show competitive performance in clustering and cross-slice integration.", "id": "Paper/66021", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66021"}, {"title": " Stable localized orthogonal decomposition in Raviart-Thomas spaces ", "webprogram_exclude": "0", "session_ids": ["Session/17850"], "source_sha256": "c279f824637b995ac6b7c1360775767bda155f760375288327684996b25b39c4", "withdrawn": "", "abstract": "This work proposes a computational multiscale method for the mixed formulation of a second-order linear elliptic equation subject to a homogeneous Neumann boundary condition, based on a stable localized\northogonal decomposition (LOD) in Raviart–Thomas finite element spaces. In the spirit of numerical\nhomogenization, the construction provides low-dimensional coarse approximation spaces that incorporate fine-scale information from the heterogeneous coefficients by solving local patch problems on a fine\nmesh. The resulting numerical scheme is accompanied by a rigorous error analysis, and it is applicable\nbeyond periodicity and scale-separation in spatial dimensions two and three. In particular, this novel realization circumvents the presence of pollution terms observed in a previous LOD construction for elliptic problems in mixed formulation. Finally, various numerical experiments are provided that demonstrate the performance of the method.", "id": "Paper/66024", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66024"}, {"title": " Optimal Control in Poroelastic Systems Via E-Radiality Theory ", "webprogram_exclude": "0", "session_ids": ["Session/18351"], "source_sha256": "c3b2e7373786c76f2fc00229d0a85958b6d65cf3d372a4843ff057e512c5cbef", "withdrawn": "", "abstract": "Fluid flows through deformable, porous media arise in numerous applications, ranging from geomechanics to biomechanics. These processes are governed by coupled systems of partial differential equations (PDEs) that describe the interaction between fluid transport and mechanical deformation. A widely adopted framework for such systems is Biot's theory of poroelasticity, which leads, under quasi-static assumptions, to a system of coupled parabolic-elliptic PDEs, falling under the umbrella of implicit, degenerate evolution equations. While the existence and regularity theory for such systems is well established, optimal control problems constrained by poroelastic dynamics, especially relevant in biomedical contexts where internal pressure and displacement must be regulated, have only recently been considered. These control problems are challenging due to the degeneracy of the equations, the implicit nature of the coupling, and the structure of the control-to-state map. In this work, we reinterpret the coupled flow-deformation problem as an implicit dynamical system on Hilbert spaces and analyze it using E-radiality theory - a generalization of the classical Hille-Yosida framework for non-explicit evolution equations. This abstract formulation yields new insights into well-posedness theory and enables a unified treatment of linear control problems constrained by degenerate evolution dynamics.", "id": "Paper/66025", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66025"}, {"title": " Hypergraph Decomposition ", "webprogram_exclude": "0", "session_ids": ["Session/18106"], "source_sha256": "3e62e14d75eb77ddb6beb5a3deefb88900347082bdc123e9387df0ce43ab18b9", "withdrawn": "", "abstract": "The study of combinatorial designs includes some of the oldest questions at the heart of combinatorics. In a breakthrough result of 2014, Keevash proved the longstanding Existence Conjecture by showing the existence of $(n,q,r)$-Steiner systems (equivalently $K_q^r$-decompositions of $K_n^r$) for all large enough $n$ satisfying the necessary divisibility conditions. Additionally, in a milestone result of 2026, Delcourt and Postle proved the celebrated Nash-Williams' Conjecture, showing that every large enough, triangle-divisible graph on $n$ vertices with minimum degree at least $3n/4$ admits a triangle decomposition. In 2021, Glock, K\\\"uhn, and Osthus proposed a generalization of these results by conjecturing a hypergraph version of the Nash-Williams' Conjecture, where their proposed minimum degree $K_q^r$-decomposition threshold is motivated by hypergraph Tur\\'an theory. By using the recently developed method of refined absorption and establishing a non-uniform Tur\\'an theory, we tie the $K_q^r$-decomposition threshold to its fractional relaxation. Combined with the best-known fractional decomposition threshold from Delcourt, Lesgourgues, and Postle, this dramatically closes the gap between what was known and the above conjecture. This talk is based on joint work with Luke Postle.", "id": "Paper/66027", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66027"}, {"title": " The Equivariant Allen–Cahn Equation and the Existence of Cohomogeneity 2 Minimal Hypersurfaces ", "webprogram_exclude": "0", "session_ids": ["Session/18284"], "source_sha256": "7806513896ab117887a12891ef3efe8b8bfc1cce2742175e49758b592c9dafa6", "withdrawn": "", "abstract": "We develop a regularity theory for equivariant Allen--Cahn solutions on closed Riemannian manifolds with a Lie group acting isometrically. When the cohomogeneity of the action is between 3 and 7, we show that a sequence of equivariant Allen--Cahn solutions with uniformly bounded energy and equivariant index converge to embedded equivariant minimal hypersurfaces with optimal regularity, meaning that the singular set is at least codimension 7 and lies in the union of all non-principal orbits. When the cohomogeneity is 2 and the action has no exceptional orbits, we show the same result but the minimal hypersurfaces may be immersed. As a result, any closed Riemmanian manifold with cohomogeneity 2 Lie group action and no exceptional orbits admits a minimal hypersurface with optimal regularity. A key tool is the regularity theory of Chodosh--Mantoulidis, building on the work of Wang--Wei. However, we adapt their arguments to a modified Allen--Cahn equation with a drift Laplacian. We also show appropriate index bounds and extend certain Allen--Cahn min-max invariants to the equivariant setting, making a comparison to their Almgren--Pitts versions.", "id": "Paper/66030", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66030"}, {"title": " Understanding Spherical Data through Sensitivity Analysis ", "webprogram_exclude": "0", "session_ids": ["Session/17718"], "source_sha256": "db4335d01fbcf5ff304b2aea4986951a42a0cd4e4616bd8bbc6b12d6af40eb39", "withdrawn": "", "abstract": "In this talk, we establish sensitivity analysis on the $d$-dimensional sphere by decomposing a function on the sphere into a sum of lower dimensional functions. We develop a spherical analysis of variance (ANOVA) decomposition that allows us to split the total variance of the function into contributions of specific groups of variables. In contrast to the classical ANOVA decomposition, we additionally use the decomposition of a function into functions with different parity. The geometry on the sphere naturally leads to dependencies between the input variables. Using certain orthogonal basis functions for the function approximation, we are able to model high-dimensional functions on the sphere with low-dimensional variable interactions.", "id": "Paper/66034", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66034"}, {"title": " Detecting Symmetries of Spherical CR Space Forms ", "webprogram_exclude": "0", "session_ids": ["Session/18295"], "source_sha256": "637dc4cb98a0662f39d2673803a85614de5fc171c011c3bf574dc04d79f247f7", "withdrawn": "", "abstract": "A spherical CR space form is a quotient of the unit sphere $S^{2n - 1}$, $n \\geq 2$ by a finite, fixed-point-free subgroup $\\Gamma < U(n)$ of the unitary group, inheriting a CR structure from the sphere. We consider several invariants associated to these manifolds and investigate what information each invariant retains about the CR automorphism group of the underlying spherical space form. In particular, we discuss automorphism information determined by the spectrum of the Kohn Laplacian $\\Box_b^{\\Gamma}$.", "id": "Paper/66048", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66048"}, {"title": " Ducks and Robbers ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "8d945bb6288e5607022240449248385e25a1def3322338e0732a3f19da397c66", "withdrawn": "", "abstract": "We combine the game of \\emph{Cops and Robbers} with the chess variant \\emph{Duck Chess} to create \\emph{Ducks and Robbers}. In this pursuit-evasion game, the cops and robbers may place an impenetrable ``duck'' after their moves to obstruct their opponents mobility. We also introduce \\emph{duck graphs} as an extension of regular graphs which record the movement routes taken by the players and how the duck blocks them. The duck cop number is the fewest cops needed to guarantee capture in this game.\n\nOur results include duck cop numbers for several familiar graph families, including trees, cycles, and hypercubes, as well as exact values or bounds for chess graphs. We also prove that the duck cop number is additive over connected components and characterize the graphs on which $k$ cops can guarantee capture. Finally, we prove that for any positive integers $p$ and $k$, there exists a graph with cop number $k$ and duck cop number $p$.", "id": "Paper/66061", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66061"}, {"title": " District Size Matters: How Seats Per District Shapes Proportionality Under STV ", "webprogram_exclude": "0", "session_ids": ["Session/18097"], "source_sha256": "0392f065b38549b19c9135623858fa2a45ee34794ea4e78ef25a86cb0c96dffb", "withdrawn": "", "abstract": "Multimember districts using ranked-choice ballots and Single Transferable Vote (STV) are often proposed as a remedy for partisan gerrymandering, since they tend to produce more proportional outcomes than single-member districts. We study how robust this benefit is to the choice of district magnitude. Using ensemble methods (built both from precincts and by merging existing districts) on the state senates of Illinois, New Hampshire, and New Mexico, we generate ranked-choice ballots under two complementary models and run STV elections across thousands of simulated maps. While multimember districts consistently move outcomes closer to proportionality, we find that the specific choice of 2-, 3-, or 4-member districts can meaningfully skew results toward one party, in a direction shaped by the state's underlying political geography. We confirm, in a 41-state analysis, that multimember STV narrows the range of possible gerrymanders, while district size itself remains a lever a mapmaker could exploit.", "id": "Paper/66063", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66063"}, {"title": " Lattice characterization of cyclic interval hypergraphic posets ", "webprogram_exclude": "0", "session_ids": ["Session/18334"], "source_sha256": "83159cd4df104e182344dc58d734908fc602f707d8c366f800f624e9962e3562", "withdrawn": "", "abstract": "Hypergraphic polytopes $\\Delta_\\mathbb{H}$ arise as Minkowski sums of simplices indexed by the hyperedges of a hypergraph $\\mathbb{H}$. Orienting the $1$-skeleton of such a polytope by a certain generic linear functional gives rise to the associated hypergraphic poset $P_\\mathbb{H}$. Hypergraphic posets include the weak order for the permutahedron and the Tamari lattice for the associahedron. This motivates the problem of determining when $P_\\mathbb{H}$ is a lattice. This talk gives an overview of hypergraphic polytopes and posets, and presents a lattice characterization for cyclic interval hypergraphs. This characterization extends the result of Bergeron and Pilaud for interval hypergraphs, and the result of Adenbaum et al. for the complete cyclic interval hypergraph.", "id": "Paper/66065", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66065"}, {"title": " Beyond Crystals: Colored Lattice Models and Dualities in Schubert Calculus ", "webprogram_exclude": "0", "session_ids": ["Session/18067"], "source_sha256": "1c3b6729d5c29c3deed5ccb8b906532f9cde3fbc6b00a9075df335516f02a084", "withdrawn": "", "abstract": "Schubert calculus and $p$-adic representation theory share deep geometric foundations, rooted in the geometry of the flag variety $G/B$ and double coset decompositions. Across both realms, interesting dualities arise between \"left-going\" and \"right-going\" paths in \\emph{lattice models}. While these dual models evaluate to the same special functions, finding an explicit, weight-preserving bijection between them is difficult. These dualities manifest as Knutson and Zinn-Justin's generic pipe dreams in the former, and as the multiple Dirichlet series models of Brubaker, Bump, and Friedberg in the latter.\n\nIn the example of Brubaker-Bump-Friedberg, lattice models allow us to go beyond crystals and expose the hidden weight-preserving bijections with the introduction of colors. In this talk, we present a direct bijective proof of the duality in Brubaker-Bump-Friedberg, bypassing standard Yang-Baxter equation arguments. We then extend this phenomenon to symmetric function theory, establishing an analogous duality for permuted basement Demazure atoms. Our results presented are joint work on two projects in collaboration with Ben Brubaker, Andy Hardt, and Karlee Westrem.", "id": "Paper/66067", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66067"}, {"title": " Graphs and Pick functions in two variables ", "webprogram_exclude": "0", "session_ids": ["Session/17442"], "source_sha256": "af1568918362b92cfd788a5b29f3c3a2e476c52415f3ba83e410d2d37c7cf8dd", "withdrawn": "", "abstract": "Given a self-adjoint matrix $A$ and a vector $\\alpha$, the map \n\\[\nf(z) = \\langle (A - z I)^{-1}\\alpha,\\alpha \\rangle,\n\\]\nis an example of a so-called Nevanlinna representation or Cauchy transform. The rational functions that result from this transformation are part of a class called Pick functions, and map the complex upper halfplane to itself. With a team of undergraduates, we looked at a version of this transformation in two complex variables. One interesting class of self-adjoint matrices that can be used to produce two-variable Pick functions with this representation is adjacency matrices of simple undirected graphs.  Given a simple undirected graph $G$ with adjacency matrix $A$, one can view the matrix $A - z I$ as the adjacency matrix of a graph that puts self-loops of weight $z$ onto the existing structure of the graph $G$. In this case, certain choices of the vector $\\alpha$ result produce a rational inner function in the Pick class. We will discuss the origins of this work as an undergraduate research project (inspired by an undergraduate honors thesis), the process of discovery using elementary graph theory and linear algebra, and some of the key results in the subsequent paper, which concern the regularity of functions at boundary singularities.", "id": "Paper/66068", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66068"}, {"title": " Math from Hel: What archival research on mathematician Hel Braun taught me about the costs of stripping mathematical knowledge of its messy origin stories ", "webprogram_exclude": "0", "session_ids": ["Session/18374"], "source_sha256": "c1a58b721f2fead302c7de5be2ea88906f70738cca6131bd7b8faa7d1bbed271", "withdrawn": "", "abstract": "Does it matter that mathematical knowledge is often passed along stripped of its complicated origin stories?  That approach is arguably easier than alternatives, but what are the costs?  A serendipitous trip to an archive, which ballooned into a multi-year research project involving ten archives, forced me to reckon with what this approach has cost me in my research, my subfield in number theory, and mathematics more broadly.  In this talk, I will present some of what I learned through my research on Hel Braun, an extraordinary twentieth-century mathematician whose research trajectory is a microcosm of the development of a line of thought stretching from the ancient Greeks to recent Fields medalists.  Braun’s mathematical focus over nearly a half-century progressed from accessible-sounding number theory problems to sophisticated machinery in algebra.  She developed mathematical foundations on which I built my career, although I didn't know it until a few years before that fateful trip to an archive.  I will describe some seemingly extraneous factors that shaped the evolution of her mathematical contributions.  Themes will include politics, gender, immigration, and unrequited love (and Hel Braun's math, of course!).   The talk is related to my recent paper {\\em Introduction to The Mathematical Legacy of Hel Braun}, freely available at \\url{https://www.degruyterbrill.com/document/doi/10.1515/dmvm-2025-0077/html}.  The target audience is historians of mathematics and mathematicians from all fields of mathematics.", "id": "Paper/66069", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66069"}, {"title": " Information Reconstruction in Asymmetric Evolutionary Models on Galton–Watson Trees ", "webprogram_exclude": "0", "session_ids": ["Session/17953"], "source_sha256": "9b9b7635489a88f72d83ea87773e536b8473caead82b51825bcd37f3c7f29b6f", "withdrawn": "", "abstract": "Reconstructing ancestral information from observations at the leaves of a tree is a fundamental problem in phylogenetics, evolutionary modeling, and information theory. In this talk, I will discuss reconstruction for asymmetric two-state evolutionary channels on Poisson Galton–Watson trees, where the random branching structure provides a natural probabilistic model for heterogeneous genealogies and evolutionary histories.\n\nWe study how information about the ancestral state propagates through the tree and characterize the reconstruction transition in terms of the channel asymmetry and the average branching degree. Using recursive posterior equations and a small-signal expansion of the reconstruction order parameter, we identify a nonlinear correction that distinguishes the asymmetric model from the classical symmetric setting. In particular, sufficiently strong asymmetry can permit reconstruction below the classical Kesten–Stigum threshold, while in a complementary regime the Kesten–Stigum bound becomes asymptotically sharp as the average degree grows.\n\nThese results demonstrate that bias in an evolutionary channel can fundamentally alter the recoverability of ancestral information. The analysis also provides a probabilistic framework for studying more general models of sequence evolution and phylogenetic inference on randomly branching trees.", "id": "Paper/66070", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66070"}, {"title": " Solving Stochastic Biochemical Models: Classical, Numerical, and Machine Learning Approaches ", "webprogram_exclude": "0", "session_ids": ["Session/17841"], "source_sha256": "bc6d42e3e99f245312d8e98b85dbd360cbc3a8c26a61bc8e1ed5a9280cef1a6a", "withdrawn": "", "abstract": "Accurately modeling the stochastic dynamics of chemical reaction networks is essential for understanding and predicting the behavior of complex biochemical systems. A fundamental framework for such modeling is the Chemical Master Equation (CME), which describes the time evolution of the probability distribution of molecular populations. However, solving the CME remains a significant computational challenge due to the \\textit{curse of dimensionality}, whereby the state space grows exponentially with the number of chemical species, making direct numerical solutions infeasible for all but the simplest systems.\n\nIn this talk, I will present an overview of several approaches for analyzing and approximating the CME. These include stochastic simulation methods such as Gillespie’s algorithm, continuum approximations based on the Chemical Langevin Equation, and moment-based techniques for estimating key statistical properties of the system. I will also discuss more recent advances, including tensor-train decompositions and machine learning-based surrogate models, which offer scalable alternatives for studying high-dimensional stochastic systems. Together, these methods provide powerful tools for investigating the dynamics of complex chemical and biological networks while mitigating the computational challenges associated with large state spaces.", "id": "Paper/66077", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66077"}, {"title": " Onsager type conjecture for fluid equations ", "webprogram_exclude": "0", "session_ids": ["Session/17952"], "source_sha256": "87503cfa9ecc43fc40182e4311189c01502f291e66ecfea24654ae47e68215b7", "withdrawn": "", "abstract": "It is known that smooth solutions of fluid equations often preserve invariant quantities. We will discuss constructions that produce solutions for some fluid systems with regularity below certain threshold and such solutions violate the conservation laws.", "id": "Paper/66083", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66083"}, {"title": " Non-uniqueness of mild solutions and stationary singular solutions to the Navier-Stokes equations ", "webprogram_exclude": "0", "session_ids": ["Session/18306"], "source_sha256": "cbbbe11f59f23cbffca3ccbb077fc50936720012e2d46f163c745005050b4a0f", "withdrawn": "", "abstract": "In this talk, I will present that the unconditional uniqueness of mild solutions to the Navier-Stokes equations fails in all the Besov spaces with negative regularity index, by constructing non-trivial stationary singular solutions via convex integration. To the best of our knowledge, this is the first non-uniqueness result in subcritical solution classes. Similar results also hold for the fractional Navier-Stokes equations with arbitrarily large power of the Laplacian, even in certain subcritical Lebesgue spaces. This talk is based on a joint work with Alexey Cheskidov.", "id": "Paper/66117", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66117"}, {"title": " The Influence Maximization of Social Media in STEM Education ", "webprogram_exclude": "0", "session_ids": ["Session/18144"], "source_sha256": "92d3679126cbc5b96ca8f6f0f6a2d9ccc1ae44a0308da75193bb84391bb1e4d3", "withdrawn": "", "abstract": "Social media has become an increasingly important tool for communicating and promoting STEM education. This research investigates how optimization methods can maximize the effectiveness of STEM-related social media content by using graph theory to model social networks, where users are represented by vertices and the flow of content is represented by directed edges. We focus on two key performance indicators: total impressions and organic reach, which measure how widely educational content is viewed and forwarded. Using Instagram analytics from the Engineer Factory, we will analyze patterns in content performance and assign probabilities to edges to model the likelihood of content reaching different users. A mathematical optimization model will then determine strategies for maximizing total impressions and organic reach while considering factors such as posting frequency, content type, and engagement. This research aims to provide a data-driven framework for improving STEM outreach through digital platforms.", "id": "Paper/66118", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66118"}, {"title": " On Choosing Parameters for Kronecker Sequences ", "webprogram_exclude": "0", "session_ids": ["Session/17807"], "source_sha256": "29b7aba987f34c70d530cee202da11337bb0d0515eac546ec3c98806ea5408ba", "withdrawn": "", "abstract": "A point in the Kronecker sequence is built by multiplying a well-chosen d-dimensional vector contained in the unit hypercube by the point index (modulo 1). Much effort is usually expended in the generation of ‘good’ generating vectors, for example, the component-by-component construction. In recent years, the median-of-means trick has been implemented as a construction-free quasi-Monte Carlo integration method for rank-1 lattices sampling many random generating vectors and taking the median estimator among these. We extend ’the median trick’ and component-by-component constructions to use with Kronecker sequences, present theoretical results and empirically compare how these approaches perform.", "id": "Paper/66121", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66121"}, {"title": " Decoupling on the fractal sets of the Parabola ", "webprogram_exclude": "0", "session_ids": ["Session/18279"], "source_sha256": "c7547e6b37231c0b090e94625a67b5116ea24dff491e7b4e0fa91599eae941bc", "withdrawn": "", "abstract": "Let $\\mu $   be a Frostman measure on an s-dimensional subset of the parabola, where $s\\leq 1/2$. Demeter-Wang showed that $||\\hat{\\mu}||_{L^{6}{(B_{R})}}^{6} \\lesssim R^{2-2s-s/4}$. We show that there exists $\\sigma(s)$ such that $||\\hat{\\mu}||_{L^{6}{(B_{R})}}^{6} \\lesssim R^{2-2s-s/4-\\sigma(s)}$.", "id": "Paper/66122", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66122"}, {"title": " Speed Limits in Electric Quantum Walks ", "webprogram_exclude": "0", "session_ids": ["Session/18296"], "source_sha256": "d6810bcb53c70ae4761969459b8693be561f9291b851cf65a80c4d2f5067b30b", "withdrawn": "", "abstract": "We consider quantum walks, both shift-coin and split-step, in homogeneous and rational electric fields. Lieb-Robinson type bounds will be presnted which show that such walks can be absolutely continuous, while exhibiting arbitrarily small propagation velocity and thus have localization features. The main tool is analytic dilation of the dispersion relation of the propagator. This uses prior results frm [Cedzich, Rybar, A.H.Werner, Alberti, Genske, R.F.Werner 2013] and [Abdul-Rahman, Cedzich, Stolz, A.H.Werner 2015].\n\nIf time permits and sufficient progress has been made, we will also introduce two models of quantum many-body walks (i.e.\\ particle number preserving quantum cellular automata), and discuss some of their properties. \n\nThis is joint work with Houssam Abdul-Rahman, Christopher Cedzich and Christoph Fischbacher.", "id": "Paper/66123", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66123"}, {"title": " Stochastic PK/PD-Based Bacterial Model of Antibiotic Resistance During Treatment with Distinct Drug and Mutation Modes ", "webprogram_exclude": "0", "session_ids": ["Session/18303"], "source_sha256": "cfe496a5c4484d9f564eb67b68bd8f1802aaff26880fd63b63f8bffd570f0cf6", "withdrawn": "", "abstract": "Mathematical models, e.g. differential equations and stochastic processes,\nhave gained considerable attention for understanding evolution of\nantibiotic resistance. However, most existing models assume standing\ngenetic variation and do not consider the possibility of random or druginduced\nmutation of reference bacterial strains. Therefore, we propose\na pharmacokinetics/pharmacodynamics (PK/PD)-based continuous-time\nMarkov chain considering the competition and mutation between sensitive\nand resistant bacterial within an infected host during treatment. The proposed\nmodel is approximated as a generalized birth–death process with\nimmigration, allowing for explicit derivation of the probability resistant\npopulation establishes during treatment. This framework is validated via\ncomparison with experimental data on establishment probability. Besides\ncapturing the stochasticity of a nascent resistant bacterial strain, we\nexplore the effects of different antibiotic modes of action, horizontal gene\ntransfer, nutrient availability, and drug pharmacokinetics on antibiotic resistance.\nWe find that replication-targeting (biostatic) drugs suppress resistance\nmore than death-targeting (biocidal) drugs. Like prior works, we\nobtain maximized resistance at intermediate drug concentrations, however\nthe consideration of mutation magnifies the superiority of higher doses in\npreventing resistance emergence. Our general approach allows for numerically\ncalculating resistant density distributions and first passage times,\nwhich can provide further advances in quantifying likelihood of multi-drug\nresistance emergence.", "id": "Paper/66124", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66124"}, {"title": " Coarse Balanced Separators in Biclique-Induced-Minor-Free Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/19360"], "source_sha256": "9a52222fc7d73bbed227a05947a982a3851b719f60aa68ae43f15ccef5e43c51", "withdrawn": "", "abstract": "It is a classical theorem of Robertson and Seymour (1986) that the treewidth of a graph is linearly related to its separation number: the smallest integer $k$ such that, for every weight function on the vertices, the graph admits a balanced separator of size at most $k$. Motivated by recent progress on coarse treewidth, Abrishami, Czy\\.zewska, Kluk, Pilipczuk, Pilipczuk, and Rza\\.zewski (2025) conjectured the following coarse analogue: for every $r\\in \\mathbb{N}$ there exists an $r'\\in \\mathbb{N}$ such that every graph that admits balanced separators that can be covered by a bounded number of balls of bounded radius $r$  \nadmits a tree decomposition where every bag can be covered by a bounded number of balls of radius $r'$. \nWe verify a stronger variant of this conjecture for all $r \\in \\mathbb{N}$ for the hereditary class of $K_{t,t}$-induced-minor-free graphs of bounded clique number.\nA key step in the proof is the following result, which we expect to be of independent interest. In $K_{t,t}$-induced-minor-free graphs with clique number bounded by $s$, given a large subset of vertices $Y \\subseteq V(G)$, there is a set $Z$ whose size is bounded by a function polynomial in $s$, such that no ball of radius $r$ in $G- Z$ covers a large proportion of $Y$.", "id": "Paper/66127", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66127"}, {"title": " Ill-Conditioning in Data-Driven, Dictionary-Based Equation Discovery: A Systems Biology Case Study ", "webprogram_exclude": "0", "session_ids": ["Session/17811"], "source_sha256": "c0508bcd97e35f3280f23d56b8e43dd62b5d73d95ee334068813fa757fa77633", "withdrawn": "", "abstract": "Data-driven discovery of governing equations offers a promising approach for identifying dynamics in complex biological systems. However, dictionary-based methods can become severely ill-conditioned when candidate functions are strongly correlated, making the recovered models highly sensitive to measurement noise and data sampling. We investigate the impact of ill-conditioning on sparse equation discovery using benchmark models from systems biology. We show that strong multicollinearity can arise even among small subsets of candidate functions and that orthogonal polynomial bases do not necessarily resolve the problem. Their effectiveness depends critically on the distribution of the sampled data. When sampling is aligned with the weight function associated with the orthogonal basis, conditioning and model recovery can improve substantially.", "id": "Paper/66128", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66128"}, {"title": " Data assimilation with Sparse Observations ", "webprogram_exclude": "0", "session_ids": ["Session/17872"], "source_sha256": "b85c96947ebc77c2ddc5bcebd61454a71a19473ee48bea9cf98e11efd9814396", "withdrawn": "", "abstract": "Data assimilation is the process of incorporating imperfect observational data into a physical model to produce more accurate predictions of flow statistics. It has numerous scientific applications, including weather forecasting, blood flow modeling, ocean modeling, and many others. One implementation technique for data assimilation is nudging, also known as continuous data assimilation (CDA). One of the main challenges of this method is determining the nudging parameter efficiently. It has been proved that, with sufficiently dense observations and a large enough nudging parameter, the error in the CDA approximation decays exponentially fast. In other words, the predictability horizon for such flows is infinite. Unfortunately, these theoretical conditions are often not physically realistic and are computationally expensive.\n\nIn this work, we consider the complementary case of sparse and infrequent observations with moderate nudging parameters. We prove that assimilation with any instance of data and any (positive) parameter decreases errors and strictly increases the (now finite) predictability horizon. For this result, we assume that the observation operator satisfies a positive semidefinite condition with respect to the inner product. We provide a rigorous analysis of this result for a semi-implicit, discrete-time realization of standard nudging. Numerical experiments are also conducted to investigate the effect of nudging with sparse and infrequent observations.", "id": "Paper/66135", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66135"}, {"title": " Intersection of two quadrics in \\mathbb{P}^{4} over global function fields without quadratic points ", "webprogram_exclude": "0", "session_ids": ["Session/18076"], "source_sha256": "942d30e895120d2681f672d8dd51aef6976a279c2b9fe56ddfae4e3c7865bde3", "withdrawn": "", "abstract": "A quartic del Pezzo surface is given by the intersection of two quadrics in \\mathbb{P}^4. We construct an infinite family of quartic del Pezzo surfaces over $\\mathbb{F}_p(t)$ with no quadratic points, for all primes $p\\neq 2$. This answers a question of Colliot--Th\\'el\\`ene, Creutz and Viray in the negative, which asks whether every quartic del Pezzo surface has quadratic points over $C_2$ fields. We exhibit a Brauer--Manin obstruction on the variety parametrising lines associated to the quartic del Pezzo surface.", "id": "Paper/66136", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66136"}, {"title": " Challenges in Quantization ", "webprogram_exclude": "0", "session_ids": ["Session/18273"], "source_sha256": "4d9a4958408f2a0cb3420d61235392556f958824d6795a9209187dafa2a4a3eb", "withdrawn": "", "abstract": "Quantization is a fundamental tool for reducing the complexity of data representations, but it introduces several mathematical challenges. In this talk, we discuss some of these challenges and recent approaches to designing and analysing quantization schemes with rigorous guarantees.", "id": "Paper/66137", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66137"}, {"title": " Two pictures are worth astounding worlds ", "webprogram_exclude": "0", "session_ids": ["Session/18234"], "source_sha256": "11b6bf401df051655819e27471e38baa9aef3aeaea7144813b45a6f507c29f37", "withdrawn": "", "abstract": "Stereoscopy and shadows are both methods that allow us to get two perspective pictures in one; understanding how these images coalesce into a 3D interpretation thereby makes even more sense of (or possibly allows us to be more amazed by) the world.  This talk will describe the geometry of how pictures assist us or thwart us in perceiving depth in various kinds of two-images-in-one techniques.  We'll look at shadows, double-vision, stereoscopic photos and drawings, and Magic Eye drawings; in each of these, we'll describe how these give us (or sometimes destroy) the illusion of depth.", "id": "Paper/66138", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66138"}, {"title": " The metric geometry of valuations ", "webprogram_exclude": "0", "session_ids": ["Session/19352"], "source_sha256": "6196e9968c74479337ea45c2e0df5a9143d0711afb1bf3baf57df6d02e182b4e", "withdrawn": "", "abstract": "It is well known that one may produce metrics on the space of convex bodies by assigning two convex bodies a distance commensurate with how much they differ in a certain kind of geometric data: the seminal example is the symmetric difference metric $\\Delta_{\\text{vol}}(K,L) = \\text{vol}(K \\, \\triangle \\, L) = \\text{vol}(K) + \\text{vol}(L) - 2\\text{vol}(K \\cap L)$, which admits a lesser-known dual in the form of the mean width metric $\\rho_w(K,L) = 2w(\\text{conv}(K \\cup L)) - w(K) - w(L)$. A consequence of the classical Steiner formula in $\\mathbb{R}^n$ is that there are $n$ ``nice'' candidates for functionals capturing such geometric data, known as the intrinsic volumes $\\{\\text{V}_j\\}_{j = 1}^n$. Indeed, $\\text{V}_n(K) = \\text{vol}(K)$, $\\text{V}_{n-1}(K) = \\frac{1}{2} \\mathcal{H}^{n-1}(\\partial K)$, and $\\text{V}_1(K) \\propto w(K)$. Accordingly, there have been sustained efforts in the convex geometry literature to determine what metrics these valuations induce, with limited success.\n\nIn this talk, we resolve this search, giving a general construction that assigns an intrinsic metric to each $\\text{V}_j$. We moreover show that each such metric yields the topology of the Hausdorff distance, something that was true of the prototypes $\\Delta_{\\text{vol}}$ and $\\rho_w$. Lastly, we take a distinctly metric-geometric approach by replacing the role of $\\text{V}_j$ with an arbitrary valuation, thereafter identifying a sufficient measure-theoretic condition for the associated metric to be geodesic. This allows us to apply our study to the metric geometry of singularity types as developed by Darvas, Di Nezza and Lu: we describe a geodesic metric on the space of singularity types of $(S^1)^n$-invariant model potentials in $\\text{PSH}(\\mathbb{CP}^n, \\omega_{FS})$, and show that it is bilipschitz to the well-studied $d_\\mathcal{S}$ metric.", "id": "Paper/66139", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66139"}, {"title": " Cutting pancakes: from teaching to research ", "webprogram_exclude": "0", "session_ids": ["Session/18062"], "source_sha256": "2d950336d0c77031181b70ca67af7223d753dcc64cb717651f83316fd9213689", "withdrawn": "", "abstract": "The classic ``lazy caterer's problem'', which asks the maximum number of pieces $p(n)$ into which a caterer might divide a pancake given $n$ straight knife cuts, is a popular example in introductory combinatorics courses. This popularity is attributable to two traits which, in the classroom, can feel all but mutually exclusive: \\textit{concreteness}, i.e. explicitness, accessibility, even physicality, and \\textit{richness}, the sense that the problem not only utilizes mathematics, but can also be used to motivate the mathematics itself. This latter sense of the problem is recorded in countless lesson plans which utilize the lazy caterer as a means by which to introduce recurrence relations or the Euler characteristic, while the former is well documented in the classic \\textit{Concrete Mathematics} of Graham, Knuth and Patashnik, wherein the problem is generalized by replacing the role of a straight knife with bent $V$ and $Z$ shapes.\n\nFollowing in the footsteps of this text, the present author, together with collaborators Neil J.A. Sloane and Jonas Karlsson, recently considered many additional generalizations of the lazy caterer's problem in the manuscript \\textit{Cutting a Pancake with an Exotic Knife}, subsequently popularized by features in \\textit{The New York Times} and \\textit{Numberphile}. Both the manuscript and the resulting public response have highlighted new ways in which such ``lazy-caterer-type'' problems may be thought of as pedagogical tools (in understanding, say, certain ideas in graph theory) and as the basis for serious research. In this talk, then, we will discuss both aspects of such problems, as well as their confluence, i.e., how they may be considered from the perspectives of teaching, research, and the teaching of research. We will consider some particular examples and show that the line between tractable and research-grade variants of these problems is subtle: we present some examples that are easily integrated into lectures, and others that are more difficult and perhaps even open.", "id": "Paper/66141", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66141"}, {"title": " Constructing Lagrangians from multi-grid diagrams ", "webprogram_exclude": "0", "session_ids": ["Session/18087"], "source_sha256": "8d88a1298c773160a363bc50003a1b0b5549db4e868a2dfccdbe66c3d5170099", "withdrawn": "", "abstract": "We present a new diagrammatic construction of Lagrangian surfaces in any closed toric 4-manifold. This construction generalizes earlier work by Blackwell, Gay, and Lambert-Cole, where they introduced diagrams for Lagrangians in $\\mathbb{CP}^2$. Our diagrams represent Lagrangians in bridge position in what we call \\emph{toric decompositions}.", "id": "Paper/66142", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66142"}, {"title": " From Low Floor Area Preservation to High Ceiling Scissors Congruence: Activities, Lesson Plans, and Research ", "webprogram_exclude": "0", "session_ids": ["Session/17961"], "source_sha256": "742b130d0419d16668ee1f0a6c924008078cf4aa1f6e8874d36f5a9bb03176f1", "withdrawn": "", "abstract": "Starting with activities and games that familiarize students with the intuitive properties of area, we present a sequence of increasingly challenging area-preservation tasks. These tasks prompt students to reflect on the core foundational concepts of scissors congruence: area/space, cut/decomposition, piece/subset, invariants/measures, and transformations. These challenges serve as the departure point for alternative lesson plans that track the evolution of emerging concepts and form the basis for group work where students consider potential generalizations. A dedicated discussion forum allows for the collaborative analysis of alternative conjectures and counterexamples.\nDepending on each group’s initiatives, alternative routes are explored, leading to analogies, generalizations, and proof-generated concepts in scenarios beyond Euclidean plane geometry. The central goal is to understand these heuristic moves and the critical role of counterexamples (à la Lakatos). These investigations may lead to subsequent Math Circle sessions, where we can discuss the results of student-led group research or individual, AI-assisted, explorations carried out between the meetings. \nWe showcase the efficacy of this instructional model through our own experiences conducting Math Circle sessions at Stanford University and California State University, Fresno. We conclude by presenting a comprehensive knowledge graph of scissors congruence topics and results, designed to assist instructors in scaffolding assignments that trace historical concept development and inspire independent research for talented students.", "id": "Paper/66147", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66147"}, {"title": " Traveling Waves and Spatial Spreading Dynamics in a Nonmonotone System of Reaction-Diffusion Equations ", "webprogram_exclude": "0", "session_ids": ["Session/18289"], "source_sha256": "b1a1b1d78e43dfd1a46cc2c6c29accda24741826f9d7fcefa36c9b45450713ee", "withdrawn": "", "abstract": "We present our recent work on the spatial spreading dynamics in traveling waves of a noncooperative system of reaction-diffusion equations. First, we establish the existence of a critical number such that the system admits a traveling wave solution if and only if its speed is greater or equal to this number. We also identify the basin of attraction of the supercritical traveling waves. In particular, we show that the minimum wave speed coincides with the spreading speed of solutions with compactly supported initials.", "id": "Paper/66148", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66148"}, {"title": " Model Selection and Modeling Decisions for the Classification of Heart Failure Phenotypes ", "webprogram_exclude": "0", "session_ids": ["Session/18122"], "source_sha256": "cfe3ec36b9104084b98e47e5e7992bf1b062e1bdac81c5defafdc7a77df4cdb6", "withdrawn": "", "abstract": "", "id": "Paper/66150", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66150"}, {"title": " Effects of Proportional Representation Reforms for the U.S. Congress on Minority Voting Power ", "webprogram_exclude": "0", "session_ids": ["Session/18097"], "source_sha256": "9e49990d16bcac6c7d0bac11681d292acd430dc7510797e2a07d74b41ce28964", "withdrawn": "", "abstract": "This project develops a framework for evaluating the effects of possible proportional representation (PR) reforms to congressional elections in the United States on minority voting power. Drawing on historical election returns and recent advances in ecological inference methods and sampling algorithms for districting, we develop a probabilistic model for congressional ballots at the race-party level. Applying this model to many alternative electoral systems, we measure each system on two representation criteria: proportionality and responsiveness.  We also quantify the extent to which partisan actors can gerrymander or influence aspects of each electoral system. Our results inform ongoing debates over gerrymandering reform and the potential consequences of moving beyond single-member districts.", "id": "Paper/66152", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66152"}, {"title": " Tangible Outcomes of Diversity Initiatives in Mathematics ", "webprogram_exclude": "0", "session_ids": ["Session/18144"], "source_sha256": "cbcc59cbc4f639eb4c098adc6231834e180d06fadfbff5ea0e732acbfa53411c", "withdrawn": "", "abstract": "The pathway to a successful career in mathematics is often fraught with systemic and financial barriers, particularly for women and underrepresented scholars. In this talk, I will share my personal journey to highlight the life-changing impact of diversity and inclusion initiatives in STEM. These targeted support systems shaped my academic career, and without them, pursuing higher education would have been financially unattainable.\n\nI will trace my mathematical trajectory through the pivotal opportunities that made it possible. I found early empowerment via the Women's Technology Program at MIT and the Smithsonian Latino Center’s Young Ambassadors program, and secured college affordability as a National Hispanic Scholar with a full-ride scholarship to Pacific Union College. I will also discuss how critical transition points in graduate education were bridged by specialized initiatives, including the Causeway Program at Northwestern, the EDGE summer program for women in mathematics, and the Carson Carr Diversity Fellowship at SUNY Albany.\n\nBy sharing my narrative, I hope to demonstrate the necessity of these programs. I will share how the support I received directly informs my approach to teaching mathematics and shaping the culture of my department. It is because of these experiences that I am able to cultivate environments where my students and peers feel empowered to ask questions and engage authentically. This talk illustrates the outcomes of diversity initiatives and demonstrates how investing in underrepresented students both changes individual trajectories and fundamentally enriches the broader mathematical community.", "id": "Paper/66155", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66155"}, {"title": " Dimension Reduction for High-Dimensional Binary Classification ", "webprogram_exclude": "0", "session_ids": ["Session/19364"], "source_sha256": "0dd0893392cb3d5064216a874568ee634240f7ae290daf2eb1bd52d92f592e81", "withdrawn": "", "abstract": "High-dimensional classification problems arise when the number of predictors is large relative to the sample size, making standard classification methods difficult to apply directly. Dimension reduction provides a way to replace the original predictor vector with a smaller set of informative linear combinations before classification. In this work, we investigate how such transformations interact with commonly used classification rules, focusing on conditions under which the relevant classification structure is preserved. Theoretical results establish equivalence between classification rules based on the original and transformed predictors under appropriate conditions. In particular, the results establish equivalence for linear discriminant analysis and, under orthonormal transformations, for quadratic discriminant analysis and k-nearest neighbor (k-NN) classification. These results clarify the interaction between dimension reduction and classification and identify conditions under which classification structure is preserved after transformation.", "id": "Paper/66156", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66156"}, {"title": " Marked length spectrum rigidity for Anosov magnetic surfaces ", "webprogram_exclude": "0", "session_ids": ["Session/18316"], "source_sha256": "a015023949c8c2c576238b2a9db588ce54789a6625dc13fa63d4903bc745debf", "withdrawn": "", "abstract": "The \\emph{marked length spectrum conjecture} states that if two Anosov metrics on a closed manifold have the same marked length spectrum, then the metrics are isometric. This conjecture is in general open, but it has been established for surfaces by Guillarmou, Lefeuvre, and Paternain in 2023.\n\nThe problem also makes sense if the Anosov metrics in question get replaced with Anosov magnetic systems instead. Namely, the magnetic marked length spectrum is then defined by assigning to a nontrivial free homotopy class the length of its unique closed magnetic geodesic representative. Must two magnetic systems on a smooth manifold having the same magnetic marked length spectrum be equivalent?\n\nGeneralizing the work of Guillarmou, Lefeuvre, and Paternain mentioned above, we provide an affirmative answer in the case of surfaces. More precisely, we show that two Anosov magnetic systems on a closed surface are conjugate by a volume-preserving conjugacy isotopic to the identity, with the magnetic $2$-forms in the same cohomology class, then the magnetic systems are equivalent; we also show by examples that the cohomology assumption cannot be dropped.\n\nThis is joint work with Valerio Assenza, Jacopo De Simoi, and James Marshall Reber.", "id": "Paper/66158", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66158"}, {"title": " Chemotaxis-Driven Pattern Formation in a Keller–Segel Model on Metapopulation Graphs and Graphons ", "webprogram_exclude": "0", "session_ids": ["Session/18303"], "source_sha256": "fdd06e90a0f52d882277f09b47a6cce157ff67c920445be8acb5c9ae68e09962", "withdrawn": "", "abstract": "We introduce and analyze a Keller–Segel-type model for chemotaxis on metapopulation networks. In our model, directed movement along network edges is modeled by a biased random walk towards higher chemoattractant concentrations, yielding a nonlinear graph dynamical system for population density and signal concentration.\n For dense graph sequences, we derive a nonlocal graphon equation and prove finite-time convergence of the discrete dynamics for deterministic weighted graphs and independent-edge dense graphs sampled on a fixed partition; we also obtain a relabeling-invariant limit in cut distance.\n By linearizing around the homogeneous equilibrium, we decouple the stability problem into a family of two-dimensional systems indexed by the graph Laplacian eigenvalues. This framework provides explicit chemotactic instability thresholds and identifies the dominant mode at the onset of pattern formation.\n For translation-invariant ring graphons, Fourier and weakly nonlinear analyses yield a cubic amplitude equation that distinguishes between supercritical and subcritical pattern-forming regimes. Finally, numerical simulations validate our theoretical predictions, illustrating how network structure drives the emerging spatial aggregation.", "id": "Paper/66159", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66159"}, {"title": " Optimal Nutrient Control of Harmful Algal Blooms in Lake Erie Using a Data-Calibrated Compartmental Model ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "f4c08b3459827d31ad3b1963da59d639e20d79f7a05e3435e3fa09a6d1daeded", "withdrawn": "", "abstract": "Harmful algal blooms (HABs) are an urgent and ongoing public health concern that threatens water quality, aquatic ecosystems, and public health. In Western Lake Erie, recurring blooms are driven largely by excess nutrient loading, making effective nutrient management an important environmental challenge. This study develops a five-compartment nutrient-bloom model, calibrated using 2015 field data, to track water and nutrient dynamics across pre-bloom, active-bloom, and recovery phases. We tested whether seasonal or rainfall-driven loading improved the model’s ability to reproduce the observations, but retained the constant-loading model because the improvements did not justify the added complexity. Identifiability analysis showed that the bloom-progression rate and initial developing-bloom level had essentially identical effects on the model output. Because the bloom-progression rate could not be estimated independently, it was fixed at a literature-supported value before further analyses. Finally, an optimal-control framework was used to determine how nutrient removal could reduce active blooms while limiting intervention effort. Optimal control substantially reduced bloom burden during the management period, but simulations beyond this period indicated that the bloom could rebound after control ended. This suggests that longer or sustained nutrient-control interventions may be necessary to produce lasting reductions.", "id": "Paper/66160", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66160"}, {"title": " A positive combinatorial formula for the double Edelman–Greene coefficients ", "webprogram_exclude": "0", "session_ids": ["Session/18067"], "source_sha256": "77faea5820b3252d7f0838e9afad178bb9ebb5fe84de9b92f09b73f0e1c5fade", "withdrawn": "", "abstract": "Lam, Lee, and Shimozono introduced the double Stanley symmetric functions in their study of the equivariant geometry of the affine Grassmannian. They proved that the associated double Edelman--Greene coefficients, the double Schur expansion coefficients of these functions, are positive, a result later refined by Anderson. They further asked for a combinatorial proof of this positivity. In this paper, we provide the first such proof, together with a combinatorial formula that manifests the finer positivity established by Anderson. Our formula is built from two combinatorial models: bumpless pipedreams and increasing chains in the Bruhat order. The proof relies on three key ingredients: a correspondence between these two models, a natural subdivision of bumpless pipedreams, and a symmetry property of increasing chains.", "id": "Paper/66161", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66161"}, {"title": " Pacemakers in excitable and oscillatory media - a case study of the <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.09ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 469.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\theta</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-3B8\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-model ", "webprogram_exclude": "0", "session_ids": ["Session/18244"], "source_sha256": "7ea76158b4c74fa3c17e49357cf8c53530d60c73451e58d72f7c1baaf449404a", "withdrawn": "", "abstract": "We present results on the existence of pacemakers in the $\\theta$-model, a biological neuron model, $u_t=\\Delta_x u + A(x) + \\mu\\cos(u)$, $u \\in \\mathbb{R}/2\\pi\\mathbb{Z}$ where $x \\in \\mathbb{R}$ and $A(x) = 1 + \\delta \\chi_{x<0}$.\n\nWe show existence when $|\\mu|<1$ (oscillatory regime), identify existence boundary when $|\\mu|>1$ (excitable regime), and present a novel numerical continuation tool based on far-field core decomposition. We also point to a related work for spiral pacemakers when $x \\in \\{|x|>R\\} \\in \\mathbb{R}^2$.", "id": "Paper/66163", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66163"}, {"title": " Smooth Selections and the Schur–Horn Theorem ", "webprogram_exclude": "0", "session_ids": ["Session/18229"], "source_sha256": "8aa7d3ace7b2d678b21ca5e6944e2b61245bbccfecef4eef310b9348874f0b8e", "withdrawn": "", "abstract": "The classical Schur--Horn theorem describes which vectors can occur as\nthe diagonal of a Hermitian matrix with prescribed eigenvalues. In this\ntalk, we revisit this result from a differential-geometric point of view.\nFor an $n\\times n$ Hermitian matrix $A$ with simple spectrum, consider\nthe map\n\\[\n\\mu:\\mathrm{U}(n)\\to\\mathbb{R}^n,\\qquad\n\\mu(U)=\\operatorname{diag}(UAU^{-1}),\n\\]\nwhose image is the Schur--Horn polytope.\n\nWe show that, over the relative interior of this polytope, $\\mu$ is a\nproper submersion. This differential-geometric property has a useful\nconsequence: a path of diagonal vectors in the relative interior can be\nlifted to a smooth path of unitary matrices. In particular, for any line\nsegment in the relative interior, the corresponding unitary matrices can\nbe chosen smoothly along the entire segment. Thus, beyond describing\nwhich diagonals are possible, the Schur--Horn theorem admits a smooth\nselection along such paths.\n\nWe then explain how these ideas extend from Hermitian matrices to the\nQR decomposition of invertible complex matrices. The connection is\nprovided by the Iwasawa decomposition of $\\mathrm{GL}(n,\\mathbb{C})$\nand a theorem of Duistermaat relating the two settings. This allows the\nsmooth selection and convexity results for the Schur--Horn theorem to\nbe transferred to the QR setting, leading to a nonlinear analogue of\nthe Schur--Horn theorem.", "id": "Paper/66165", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66165"}, {"title": " Turnpike properties in linear quadratic Gaussian <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.064ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 888.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">N</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4E\" d=\"M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-4E\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-player differential games ", "webprogram_exclude": "0", "session_ids": ["Session/17781"], "source_sha256": "4e34c3adbb8aff318d6dcb46c3488185e8b24896fba7fd887f9255827e360564", "withdrawn": "", "abstract": "We consider the long-time behavior of equilibrium\nstrategies and state trajectories in a linear quadratic $N$-player game with Gaussian initial data. By comparing the finite-horizon game with its ergodic counterpart, we establish exponential convergence estimates between the solutions of the finite-horizon generalized Riccati system and the associated algebraic system arising in the ergodic setting. Building on these results, we prove the convergence of the time-averaged value function and derive a turnpike property for the equilibrium pairs of each player. Importantly, our approach avoids reliance on the mean field game limiting model, allowing for a fully uniform analysis with respect to the number of players $N$. As a result, we further establish a uniform turnpike property for the equilibrium pairs between the finite-horizon and ergodic games with $N$ players. Numerical experiments are also provided to illustrate and support the theoretical results.", "id": "Paper/66174", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66174"}, {"title": " Target Pebbling in Trees ", "webprogram_exclude": "0", "session_ids": ["Session/18106"], "source_sha256": "313120baab833b9ad38847d3f0162f66e7685307f6a8d3217a51685cb89b82f8", "withdrawn": "", "abstract": "Graph pebbling is a game played on graphs with pebbles on their vertices. \nA pebbling move removes two pebbles from one vertex and places one pebble on an adjacent vertex. \nA configuration $C$ is a supply of pebbles at various vertices of a graph $G$, and a distribution $D$ is a demand of pebbles at various vertices of $G$.\nThe $D$-pebbling number, $\\pi(G, D)$, of a graph $G$ is defined to be the minimum number $m$ such that every configuration of $m$ pebbles can satisfy the demand $D$ via pebbling moves.\nThe special case in which $t$ pebbles are demanded on vertex $v$ is denoted $D=v^t$, and the \\textit{$t$-fold pebbling number}, $\\pi_{t}(G)$, equals  $\\max_{v\\in G}\\pi(G,v^t)$.\n\nThree prominent conjectures in the subject are that the pebbling numbers of chordal graphs forbidding an induced pyramid can be calculated in polynomial time, that every graph $G$ satisfies $\\pi(G,D)\\le \\pi_t(G)-s+1$ for all $D$ (where $t$ is the number of demands of $D$ and $s$ is the number of vertices having a demand of $D$), and that, for chordal graphs, maximum-size configurations that do not satisfy $D$ have a particularly nice structure.\nIn this paper, we prove that trees satisfy all three conjectures.", "id": "Paper/66175", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66175"}, {"title": " A New Galois-Theoretic Approach to Singmaster’s Conjecture ", "webprogram_exclude": "0", "session_ids": ["Session/19355"], "source_sha256": "6ef89a53809d4039c35918a74fc087780876d26ac0be78994fe10c61c8675327", "withdrawn": "", "abstract": "Singmaster's conjecture asserts that the number of solutions $(n, k)$ to the Diophantine equation ${n \\choose k} = t$, for a given $t \\in \\mathbb Z^+$, is bounded by a universal constant. Standard methods have mainly been analytic, using the Gamma function to create a continuous curve and bounding the number of integral points on it. In contrast, our method is Galois-theoretic. We construct a family of polynomials $P_k$ of degree $k$ that encodes binomial collisions and study the resulting orbit sizes in $\\text{Gal}(P_k/\\mathbb Q)$ using the local properties of $P_k$. Through the use of Newton polygons, finite fields, and local inertia and decomposition groups, we determine structural properties of the Galois group for each $P_k$. Finally, we discuss how combining these methods places conditions on the existence of rational roots of $P_k$ (size-one orbits in $\\text{Gal}(P_k/\\mathbb Q)),$ offering a novel method towards bounding the number of solutions to the defining equation.", "id": "Paper/66176", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66176"}, {"title": " Shift-invariant spaces of discrete analytic functions ", "webprogram_exclude": "0", "session_ids": ["Session/19368"], "source_sha256": "923796401b7b472838db7fd7ddaead9b0542dd4f47c5b91270ca582a31958560", "withdrawn": "", "abstract": "The notion of discrete analytic functions on rhombic lattices, originating in the work of J. Ferrand and R. J. Duffin, provides a natural discrete counterpart to classical complex analysis. In this talk, we explore the structure of reproducing kernel Hilbert spaces of discrete analytic functions that remain invariant under suitably defined shift operators. There is a number of important differences with the classical case, including eigenvalues of the backward shift operator. This is joint work with Daniel Alpay and Dan Volok.", "id": "Paper/66177", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66177"}, {"title": " Instantaneous blowup of incompressible flow with passive tracer ", "webprogram_exclude": "0", "session_ids": ["Session/18291"], "source_sha256": "34e22daf0453b4526375de6645b9a2639a0350f3362173dbfc5b03265fe3d5ab", "withdrawn": "", "abstract": "We construct a family of solutions $(u,b)$ of the incompressible flow with a passive tracer for which both $\\|u(t)\\|_{L^\\infty}$ and $\\|b(t)\\|_{L^\\infty}$ blow up at time $T_*$. Away from $T_*$, the solutions remain smooth in both space and time. The argument adapts the inverse cascade mechanism from [CDP25] to the presence of an advected scalar, but the passive component creates a new compatibility constraint: the iteration must propagate the tracer while preserving the same principal velocity profiles from one stage to the next. We resolve it by introducing a simultaneous decomposition lemma for a symmetric tensor and a vector field.\n\nWe also show the existence of an infinitely family of instantaneous blowup solutions to the 2D MHD system, with critical blowup rate for the velocity component according to the scaling of the system. Moreover, the non-uniqueness is sharp in the sense that it occurs in spaces borderline to $L^2_tL_x^\\infty$, the endpoint space of the Ladyzhenskaya--Prodi--Serrin type where uniqueness is known.\n\nJoint work with Mimi Dai (University of Illinois Chicago).", "id": "Paper/66179", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66179"}, {"title": " On the fractional measure and nonlocal curvature of hypersurfaces, curves, and everything in between ", "webprogram_exclude": "0", "session_ids": ["Session/18377"], "source_sha256": "a2661ef286d828b8db8c907f7f52b921f1d106b3e4dfa56de50ae947e3135284", "withdrawn": "", "abstract": "The nonlocal mean curvature can be motivate by considering the first variation of the fractional perimeter, which can be viewed as the Dirichlet energy with the standard gradient replaced by a fractional one acting on characteristic functions. As the name fractional perimeter suggests, the nonlocal mean curvature was initially only defined for hypersurfaces that are the boundary of a set. In this talk I will discuss how to extend this idea to any compact hypersurface by introducing a fractional area functional and computing its first variation. I’ll then go on to explain how the ideas used in formulating the fractional area lead naturally to a fractional notion of length and an associated nonlocal curvature for a curve. Finally, I’ll describe how the same ideas can be used to define a fractional k-dimensional measure and an associated nonlocal mean curvature vector.", "id": "Paper/66181", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66181"}, {"title": " When viscosity fails to select: three non-uniqueness mechanisms for the Navier-Stokes equations ", "webprogram_exclude": "0", "session_ids": ["Session/17952"], "source_sha256": "854feef5567e7ddaaf5260821b5f03cbda54b1ff3d47b06801823c68bde2ef91", "withdrawn": "", "abstract": "Recent work shows that non-uniqueness for fluid equations is not confined to inviscid regimes or rough weak solutions. In this talk, I will discuss three recent non-uniqueness mechanisms that require viscosity and occur for solutions that can enjoy critical or even subcritical regularity. The first produces non-unique dissipative solutions for data that admit a local smooth solution, showing that Lions’ weak-strong uniqueness principle for the Euler equations breaks down in the viscous setting. Second, there exist singular stationary solutions in Besov spaces of arbitrarily negative smoothness, showing that non-uniqueness can occur even in subcritical spaces:  a perturbative mild solution can arise from an initial datum that is itself a stationary solution. Third, for any smooth (or even zero) initial data, there are infinitely many weak solutions belonging to the Koch-Tataru path space and enjoying the same regularity properties as Koch-Tataru solutions. These non-unique solutions are created by a complete energy cascade from infinite wavenumber, leading to instantaneous blow-up. Again, viscosity is essential. The unifying theme is that viscosity not only regularizes, but also opens new mechanisms for non-uniqueness.", "id": "Paper/66182", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66182"}, {"title": " Sharp Ill-Posedness of the Euler Equations in Lorentz Spaces ", "webprogram_exclude": "0", "session_ids": ["Session/17822"], "source_sha256": "8443d193aaba8a5119066b5522d8900a1378d48a81cd7b5e029d138e5c32cea5", "withdrawn": "", "abstract": "We study vortex stretching for the three-dimensional axisymmetric Euler equations without swirl in vorticity formulation.\nDanchin established global existence and uniqueness for bounded vorticity $\\omega_0$ provided $\\omega_0/r$ lies in the endpoint Lorentz space $L^{3,1}(\\mathbb{R}^3)$ (together with a decay assumption on $\\omega_0$).\n\nWe prove that this $L^{3,1}$ endpoint is sharp: for every Lorentz  exponent $q>1$, we construct multi-ring data $\\omega_0 \\in L^\\infty (\\mathbb{R}^3)$ with $\\omega_0/r\\in L^{3,q}(\\mathbb{R}^3)$ that produce $L^\\infty$-norm inflation of the vorticity; moreover, within the same class, we obtain instantaneous blow-up from data with infinitely many rings. This is a joint work with Jeaheang Bang.", "id": "Paper/66183", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66183"}, {"title": " Metric theory of twisted Diophantine approximations ", "webprogram_exclude": "0", "session_ids": ["Session/18261"], "source_sha256": "ce7f58996cb98afab23d6516f03e43b3a492bccf55cb3511746c16a0625ccd27", "withdrawn": "", "abstract": "The topic of this talk is the inhomogeneous Diophantine approximations, that is, approximations of pairs of a matrix and a vector (or, equivalently, approximations of systems of affine forms) from the metric point of view. There are three natural ways to treat this setup: we can just look at all pairs; we can fix the matrix (this is called \"twisted approximations\"),  or we can fix some vector. Until recent years, the majority of metric questions in the twisted case was unsolved.\n\nIn this talk, we will discuss a new method, arising from the parametric geometry of numbers, which allows to answer a lot of the previously open metric question. Namely, we will present a zero-one law for asymptotic twisted approximations, analogous to the classucal Khintchine-Groshev theorem and generalizing the Kurzweil theorem. We will also discuss the exact expressions for Hausdorff dimensions of sets of twisted $\\psi$-Dirichlet vectors and a zero-one law for Hausdorff measures of these sets.\n\nBased on a joint work with Taehyeong Kim.", "id": "Paper/66187", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66187"}, {"title": " Designing an AI Study Bot for Calculus: Can It Reflect the Instructor’s Voice? ", "webprogram_exclude": "0", "session_ids": ["Session/19349"], "source_sha256": "61efaa2a54c1ee7502bd88817ccfbd7e2fff3ca90dbd412f2f7660abce07ae10", "withdrawn": "", "abstract": "At my college, requests for tutors were down across the board last year. At the same time, I observed that AI chatbots frequently answered Calculus I questions using concepts and techniques from later in the course or from subsequent courses. I also hypothesized that students were using AI primarily to ask questions and then did not feel the need to test their knowledge.\n\nIn response, I developed a lightweight, retrieval-augmented AI study bot for Calculus I. Through a guided chat interface, students select the topic, problem, or exam to study. When a student asks a question, the system sends an AI model both the question and relevant material from my course notes and assessments. This not only grounds the answer in the appropriate section of the course but also makes the answer more consistent with how I present and curate the material.\n\nThis grounding only addresses the first challenge. The bot can also generate practice problems based on past homework, quizzes, exams, and the course textbook. By placing the chat box and problem generation within the same interface, I hope students will actively test their understanding.\n\nThe last key feature is full practice-test generation. I expect students may find practicing each topic individually tedious and burdensome. If a student can generate a fresh practice test at the click of a button, I hope they are more likely to engage with the tool. As educators, I think we can design assessments around how students practice. I am considering adding this capability to future versions, although collecting potentially identifying information adds privacy and implementation complexity.\n\nThis presentation describes the working prototype, its pedagogical design, and ongoing efforts to evaluate retrieval quality and improve the student experience through formative feedback.", "id": "Paper/66188", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66188"}, {"title": " Quantitative positivity of transition densities for random perturbations of Hamiltonian systems ", "webprogram_exclude": "0", "session_ids": ["Session/19370"], "source_sha256": "5701597ec80ae4f13a55f02fb8882c9016fc8785709e8b3b49893d72aa6b3ef1", "withdrawn": "", "abstract": "We study a class of hypoelliptic diffusion processes arising from random perturbations of Hamiltonian systems. Our framework includes Langevin dynamics, Galerkin approximations of the 2D stochastic Navier–Stokes equations, and the Lorenz '96 system. Although these models satisfy Hörmander’s condition, the degeneracy of the noise makes it challenging to obtain quantitative minorization estimates. Our main result establishes uniform lower bounds on transition densities over Hamiltonian sublevel sets in the small noise limit. This is joint work with David Herzog and Kyle Liss.", "id": "Paper/66190", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66190"}, {"title": " On the trapping of ray families by mirrors ", "webprogram_exclude": "0", "session_ids": ["Session/19357"], "source_sha256": "afcb8e42a502c16c8e06f7f60b38d3830df4a3a8907011b3970f0e967f0518ae", "withdrawn": "", "abstract": "We settle two questions of Serge Tabachnikov regarding the trapping of light rays by mirrors. We show (i) that the largest dimension of a trapped family of rays in $\\mathbb{R}^n$ is $2n-3$, and (ii) that in $\\mathbb{R}^3$ one can trap a 2-parameter family of rays that is not locally normal to any smooth surface. We first establish that no $2n-2$-parameter family can be trapped by showing that no open subset of $L_n$ (the space of oriented lines in $\\mathbb{R}^n$) can be trapped due to Poincaré's recurrence theorem, yielding an upper bound of $2n-3$. We then show that a system of mirrors traps a $2n-3$ parameter family of rays by noting that a compact subset of the set of states of rays in the central \"waist\" of the trap is a normally hyperbolic invariant manifold, making it amenable to a stable manifold theorem for NHIMs, which implies that the set of rays asymptotic to the waist of the trap has dimension $2n-3$. We then truncate our mirror system, which permits the entrance of rays from arbitrarily far outside of the trap, attaining the upper bound $2n-3$ and resolving the first question. We then show that in $\\mathbb{R}^3$, there exists within the trapped family of rays a 2-parameter subfamily on which the canonical symplectic form on the space of oriented lines is nowhere vanishing, implying that the subfamily is not locally normal to any smooth surface, which settles the second question.", "id": "Paper/66195", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66195"}, {"title": " Short proofs of Cambern’s 1968 theorem and its generalizations applicable to fixed point theory ", "webprogram_exclude": "0", "session_ids": ["Session/18364"], "source_sha256": "08cceaba5808a462913c80c47cc54cfe3dd37919b882ae681e2b7f109e07d896", "withdrawn": "", "abstract": "First we provide short, elementary and self-contained proof of Cambern's 1968 result stating that the Banach--Mazur distance $d(c,c_0)\\geq 3$. Then, we use our new approach to obtain lower bounds for the Banach--Mazur distances between any two $\\ell_1$-preduals $X$ and $Y$. Our estimate depends only on the smallest radiuses $r^*(X)$ and $r^*(Y)$ of the closed balls in $\\ell_1$ containing, respectively, all $\\sigma(\\ell_1,X)$-cluster points and all $\\sigma(\\ell_1,Y)$-cluster points of the set of all extreme points of the closed unit ball in $\\ell_1$, and for any values of $r^*(X)$ and $r^*(Y)$ it is sharp. We apply this result to show that for every $\\ell_1$-predual $X$ with $r^*(X)<1$, every $\\ell_1$-predual $Y$ with the distance from $X$ strictly less than $\\frac{3-r^*(X)}{1+r^*(X)}$ induces a~weak$^*$ topology on $\\ell_1$ such that $\\ell_1$ has the $\\sigma(\\ell_1,Y)$-fixed point property for nonexpansive mappings. If we additionally assume that the standard basis in $\\ell_1$ is $\\sigma(\\ell_1,X)$-convergent, then the estimate is precise. It should be emphasized that the value of this constant was known only for the space $c_0$ so far.\n\nMy talk is based on the article:\n{\\sc María Jap\\'on, Marek Malec, {\\L}ukasz Piasecki}, {\\em Short proofs of Cambern’s 1968 theorem and its generalizations applicable to fixed point theory}, Topol. Methods Nonlinear Anal. 67 (2026), no. 1, 87--102.", "id": "Paper/66197", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66197"}, {"title": " On the Euler system of gas dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/17952"], "source_sha256": "6d16ea85d4e1d9eb8599df0f169284deffd84eff32768ff7be29f209ba5ee57c", "withdrawn": "", "abstract": "We discuss some recent results concerning well/ill posedness of the \n(full) Euler system of gas dynamics. In particular, we show the existence \nof weak solutions attaining only a finite number of states. Moreover, we propose a selection criterion to identify a unique solution in a larger class of the so-called dissipative measure-valued solutions.", "id": "Paper/66198", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66198"}, {"title": " Schäffer’s matrix inequality: the exact asymptotic constant ", "webprogram_exclude": "0", "session_ids": ["Session/18229"], "source_sha256": "0d44e2617f889ffdcc6dae100e5690d32eb7c06e8c9f1683ba4b9b9c70b6c9f9", "withdrawn": "", "abstract": "Let $\\mathcal S_n$ denote the smallest constant such that\n\\[\n|\\det T|\\|T^{-1}\\|\n\\leq \\mathcal S_n \\|T\\|^{n-1}\n\\]\nfor every invertible operator $T$ on every $n$-dimensional complex\nBanach space. In Hilbert space the optimal constant is $1$. For\narbitrary Banach spaces, J.~J.~Sch\\\"affer proved in 1970 that\n\\[\n\\mathcal S_n\\leq \\sqrt{en}.\n\\]\nSubsequent work showed that $\\mathcal S_n$ grows like $\\sqrt n$, but the\nsharp asymptotic constant has remained open for more than five decades.\nWe resolve this problem by proving\n\\[\n\\lim_{n\\to\\infty}\\frac{\\mathcal S_n}{\\sqrt n}=\\sqrt e.\n\\]\nThus Sch\\\"affer's upper bound is asymptotically sharp, including its constant.\n\nOur proof is constructive, providing explicit Banach-space norms through duality and explicit matrices through the theory of model operators.\nAt the analytic core of the argument, an extremal formulation of Sch\\\"affer's problem in the Wiener algebra reduces the matching asymptotic lower bound for $\\mathcal S_n$ to uniformly controlling the Taylor coefficients of products $QB_n$, where $B_n$ is a finite Blaschke product of degree $n$ and $Q$ is a polynomial factor. We optimize\nsimultaneously the zero distribution of $B_n$ and the choice of $Q$.\nThe resulting zeros follow a logarithmic asymptotic distribution, and a\nsharp uniform asymptotic analysis of the Taylor coefficients of $QB_n$ yields the\nconstant $\\sqrt e$. The corresponding model operators then yield\nmatrices with these spectra that asymptotically attain Sch\\\"affer's bound.", "id": "Paper/66199", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66199"}, {"title": " Bubbles and blundary layers ", "webprogram_exclude": "0", "session_ids": ["Session/18103"], "source_sha256": "bf23572d8e721f69fd550fb99c8252fc4750d4d84cafeb6264ed52995cf609fc", "withdrawn": "", "abstract": "We discuss functionals on a disk in $\\mathbb R^2$ which present a {\\it double loss of compactness}: formation of bubbles at the origin and boundary layers in the form of gradient blow-up (infinitesimal shocks). The base is an optimal inhomogenous  inequality which improves the Trudinger-Moser inequality. As application we consider an existence theorem for associated elliptic boundary value problems.", "id": "Paper/66200", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66200"}, {"title": " Exact Solutions for Time-Varying Epidemic Models ", "webprogram_exclude": "0", "session_ids": ["Session/19359"], "source_sha256": "bb869a2d4ba56533c1dc170e123ae9119367763ff69bee0a5fdfb929cd2f32dd", "withdrawn": "", "abstract": "Mathematical models of infectious diseases often assume that transmission and recovery rates are constant over time. In reality, these rates can vary due to seasonal changes in behavior, environmental conditions, and other influences. With this in mind, in this talk, we study a generalized Susceptible-Infectious-Susceptible (SIS) model with a time-varying recovery rate. Despite its time-dependent nature, we show that the model has unusually tractable mathematical properties. In particular, for the multi-strain case, we derive explicit expressions for its Floquet exponents and characterize solution persistence and stability. For the single-strain case, we also obtain a closed-form solution that can accommodate a wide range of infectious-period distributions. Finally, we demonstrate the practical value of these results by applying the model to recent U.S. syphilis incidence data.", "id": "Paper/66203", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66203"}, {"title": " Congeniality, Amenability, and simplicity of bases for matrix algebras ", "webprogram_exclude": "0", "session_ids": ["Session/18372"], "source_sha256": "091e20978060b3c02c8397f7a08bebe6b18b59adccbbb3fd2b36751ae1f9b26b", "withdrawn": "", "abstract": "Focusing on the algebras $M_n(A)$ of $n \\times n$ matrices over a commutative infinite-dimensional $F$-algebra $A$ over an arbitrary field $F$, we extend the study of amenability and congeniality of bases in a natural non-commutative direction. We address the abundance of bases for these algebras, with an initial focus on modular bases. In characterizing amenability and congeniality in this context, we discover a new relation, which we call \\textit{amenable congeniality}. This notion proves instrumental in characterizing both the amenability of modular bases and congeniality among modular bases, and is worthy of consideration in its \nown right. Among our main results, we show that for $n \\geq 2$, the algebra \n$M_n(A)$ is neither left nor right duo amenable.\n\nThe existence of simple bases for $M_n(A)$ remains an open question. In \nparticular, it is unclear whether a simple basis would necessarily be modular. We do establish, however, that for a modular basis to be right simple, each of its component bases must itself be right simple. In our search for such bases, we introduce and fully characterize \\textit{modularly simple} (modular) bases.", "id": "Paper/66204", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66204"}, {"title": " Topological Data Analysis of Social and Spatial Systems ", "webprogram_exclude": "0", "session_ids": ["Session/18260"], "source_sha256": "6a9fbe3c30b679ff2904ab2d2332a921b46ff065ecfcd6d3039aa82fd6cafa8e", "withdrawn": "", "abstract": "I will present several examples that use topological data analysis (TDA), which allows one to study the \"shape\" of data, to examine various social and spatial systems. I will discuss a variety of examples, including the availability of resources (such as polling sites, public parks, and bars and pubs), the spread of infectious diseases, and the structure of webs of spiders that are under the influence of various substances.", "id": "Paper/66205", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66205"}, {"title": " An Alternative Proof of an Erdős-Rényi Law for the Longest Consecutive Monotone Block in a Random Permutation ", "webprogram_exclude": "0", "session_ids": ["Session/18386"], "source_sha256": "77b72003e0e966668d0693381fdc5ff72b1ba57e3e2026b1aa7265a142947b9b", "withdrawn": "", "abstract": "The Erd\\H os-R\\'enyi law states that given a sequence $\\{X_j\\}_{j=1}^\\infty$ of i.i.d.~($p$) coin-tosses, the longest run $L_n$ of heads in the first $n$ coin tosses approaches $\\log_{1/p}n$ almost surely.  In this paper we explore a formulation of this result in the case of random permutations and prove an Erd\\H os-R\\'enyi law for the longest consecutive monotone block in a random permutation.  This problem has been studied before by several authors, and we offer a Poisson approximation viewpoint on this issue using the Stein-Chen method.", "id": "Paper/66206", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66206"}, {"title": " Interpreting the Latent Space of Protein Language Models Using Geometric Features of Protein <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.946ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 1268.4 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">C_\\alpha</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-43\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-43\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-3B1\" x=\"1011\" y=\"-213\"></use>\n</g>\n</svg> Backbone. ", "webprogram_exclude": "0", "session_ids": ["Session/18354"], "source_sha256": "f63eacf3940d609494a8d68f1d89064c8a092bcd769ed29c3158aeb0495ef75b", "withdrawn": "", "abstract": "Protein language models (pLMs) encode information about protein sequences which enable downstream tasks such as structure prediction, but their internal representations are not well understood. Sparse autoencoders (SAEs) provide a promising tool to disentangle latent pLM representations into monosemantic features. However, annotating these features with biologically meaningful and human readable labels remains a challenge. Current methods rely on  rely on protein-level annotations derived from database labels and LLM annotations of top activating sequences. These methods fail to capture localized residue level biologically relevant patterns encoded by SAE features. We introduce an automated and scalable method for interpreting SAE features in the ESM-2 pLM by using geometrically inspired features of the protein $C_\\alpha$ backbone. By exploiting geometric structure inherent to protein language enabling residue level annotation of SAE feature activation, we build a geometric bridge between mechanistic interpretability and structural biology.", "id": "Paper/66207", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66207"}, {"title": " Positive sectional curvature and logarithmic torus symmetry ", "webprogram_exclude": "0", "session_ids": ["Session/18290"], "source_sha256": "4c443e4fa70431395c44ce5c11e8c4d50606e0557be04e7e60bbdbf447787404", "withdrawn": "", "abstract": "Early results in the Grove symmetry program in the 1990s and 2000s involving torus actions provide diffeomorphism or homotopy classifications for torus ranks bounded by linear functions of the manifold dimension. Results in the 2010s and 2020s have weaker conclusions but require less symmetry. A notable example is the work of the authors and Nienhaus showing Hopf’s Euler characteristic positivity conjecture for tori of rank at least four. Ongoing work by the authors revisits results of the 2010s where the torus rank is at least a logarithmic function of the manifold dimension. Equipped with stronger tools, they improve Euler characteristic bounds to calculations, refine statements on cohomology in small degrees, and prove a cohomological embedding statement.", "id": "Paper/66208", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66208"}, {"title": " Large-Vocabulary Limit Perspective on an Algorithmic Transformer Task ", "webprogram_exclude": "0", "session_ids": ["Session/18193"], "source_sha256": "818b3903ce96081c9b4b5a7b17e7c95cb5d4e274a3de47b3ab2f09a95a052916", "withdrawn": "", "abstract": "The virtual assistants that have a growing impact on human society are usually based on the transformer model, a specific artificial neural network architecture. These compositional machine learning models are very difficult to interpret in general. As a step towards understanding how these models learn algorithmic tasks, we train small transformers on a grid-based game subtask which we term Any Row Complete (ARC). In ARC, a model is given sequences of input tokens representing moves on a game board, and the expected output is a token-wise classification of whether a token was the first to complete a row. We train single-head attention-only transformers (with beginning-of-sequence tokens, as provably required) on ARC with varying grid dimensions. We give a theoretical characterization of attention and embedding geometry for two-dimensional models solving ARC in the large row-count limit, predicting that model embeddings lie on origin-centered hyperbolas. Experimentally, we find that models with higher embedding dimensions also place embeddings near level surfaces of non-Euclidean quadratic forms, providing evidence that our theoretical characterizations generalize to larger models.", "id": "Paper/66209", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66209"}, {"title": " From Conditional Stability to Adjoint-Free Reconstruction in a Parabolic Inverse Source Problem ", "webprogram_exclude": "0", "session_ids": ["Session/19369"], "source_sha256": "df6fd1b6e02506ae1488253f154fc1a6fd0d52490d30e3f571ed5b159bd66c72", "withdrawn": "", "abstract": "We study an inverse problem for the recovery of a time-dependent source\nin a linear non-autonomous parabolic equation from an integral observation\nof the solution. The corresponding forward operator can be represented as\na Volterra operator in time. This structure provides insight into the\nill-posedness of the inverse problem and leads to a weak-norm stability\nestimate and, under an a priori regularity assumption, a conditional\nH\\\"older stability estimate in $L^2(0,T)$.\n\nWe then use this analytical structure to motivate an adjoint-free integral\nfeedback approach for reconstructing the unknown source. The resulting\niteration is formulated as a fixed-point method and analyzed with respect\nto exact-data convergence and stability under noisy measurements. In\nparticular, a suitable noise-dependent stopping rule yields an iterative\nregularization method. Numerical examples illustrate the reconstruction\nof both smooth and piecewise constant sources and demonstrate the stability\nof the approach in the presence of noise.", "id": "Paper/66212", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66212"}, {"title": " The Minimum Inscribed Number of an <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"5.63ex\" height=\"1.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -576.1 2423.9 721.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">n \\times n</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-6E\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-D7\" x=\"822\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-6E\" x=\"1823\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "8cd10ea7a232425ca1a68ab76b7d5f7b3b5ccec290b13519f33992edcb4ccff2", "withdrawn": "", "abstract": "We study when a convex quadrilateral is guaranteed to possess an inscribed circle\n(incircle), given that certain sub-quadrilaterals in an $n \\times n$ grid division each\nhave an incircle. The central object is the \\textit{minimum inscribed number} $p(n,n)$:\nthe smallest integer $k$ for which there exists a fixed set of $k$ grid positions such\nthat whenever the sub-quadrilaterals at those positions all have incircles, the large\nquadrilateral necessarily has an incircle too --- regardless of the specific convex\nquadrilateral or division chosen.\n\nUsing the Pitot theorem, Monge's theorem, properties of incircles and excircles, and\ncommon tangent length arguments, we prove $p(2,2) = 4$ and $p(3,3) = 5$. We then show\nthat the union of the two main diagonals of the grid is always an inscribe arrangement,\nwhich gives the upper bound $p(n,n)\\le 2n-(n \\bmod 2)$ for every $n$, and we prove the\nlower bound $p(n,n)\\ge n+2$. We conjecture that the upper bound is exact, i.e.\\\n$p(2n,2n)=4n$ and $p(2n+1,2n+1)=4n+1$, and reduce this conjecture to a single\nstructural statement. Finally, for trapezoids divided by lines parallel to the parallel\nsides and lines through the intersection of the other two sides, we determine the minimum\nexactly: it drops from $2n-(n \\bmod 2)$ to $n$, and the certifying arrangements are\ncharacterised combinatorially.", "id": "Paper/66213", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66213"}, {"title": " Operator Splitting Methods with Online Scaling ", "webprogram_exclude": "0", "session_ids": ["Session/18069"], "source_sha256": "14f8307b34766265779db2aa4eb2bc3e692f722efc95bebc968578dae1de8118", "withdrawn": "", "abstract": "This paper develops a principled framework for automatically tuning preconditioners in operator splitting methods, including forward-backward\nsplitting, Douglas-Rachford splitting, and the alternating direction method of multipliers. We interpret these splitting methods as preconditioned gradient descent applied to their corresponding envelope functions and use online learning to adaptively learn the preconditioner during optimization. Our framework achieves asymptotically faster convergence rates and accelerates the solution of important optimization problems, including Lasso, ℓ1-regularized logistic regression, and quadratic programming. Extensive numerical experiments validate our theoretical results and demonstrate the practical effectiveness of the proposed approach.", "id": "Paper/66216", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66216"}, {"title": " Bayesian inference of planted matchings: Local posterior approximation and infinite-volume limit ", "webprogram_exclude": "0", "session_ids": ["Session/18002"], "source_sha256": "8c9828544d3fda771804133686042ae88f532d84fb796613ee64c340f8f4cb7e", "withdrawn": "", "abstract": "We study Bayesian inference of an unknown matching $\\pi^*$\nbetween two correlated random point sets $\\{X_i\\}_{i=1}^n$ and\n$\\{Y_i\\}_{i=1}^n$ in $[0,1]^d$, under a critical scaling\n$\\|X_i-Y_{\\pi^*(i)}\\|_2 \\asymp n^{-1/d}$, in both an\nexact matching model where all points are observed\nand a partial matching model where a fraction of points may be missing.\nIn the simplest setting of $d=1$, we address the\nquestions of (1) whether the posterior distribution over matchings is\napproximable by a local algorithm, and (2) whether marginal statistics of this\nposterior have a well-defined limit as $n \\to \\infty$. We answer both questions\naffirmatively for partial matching, where a decay-of-correlations\narises for large $n$. For exact matching, we show that\nthe posterior is approximable locally only after a global sorting of the points,\nand that defining a large-$n$ limit of marginal statistics requires a\ncareful indexing of points in the Poisson point process limit of the data,\nbased on a notion of flow. We leave as an open question the extensions of such\nresults to dimensions $d \\geq 2$.", "id": "Paper/66220", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66220"}, {"title": " Representation Varieties and the Topology of 3-Manifolds ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "c700dd3ad77eb17a01a213e9198ffacbddbc46a4a0f5b2ecdd6ebe08b219e259", "withdrawn": "", "abstract": "The representation variety of a manifold is a topological space whose fixed-point sets under certain homeomorphisms correspond to particular Chern-Simons invariants, which are of interest to physicists. We are particularly interested in the representation varieties of 3-manifolds, and will cover several illustrative examples of these objects, including mapping tori and circle bundles. We will also discuss some of our findings, which include the homeomorphism type of representation varieties and fixed-point sets for several families of 3-manifolds constructed from our examples.", "id": "Paper/66221", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66221"}, {"title": " Boundary layers and vanishing diffusivity in run-and-tumble models ", "webprogram_exclude": "0", "session_ids": ["Session/17370"], "source_sha256": "ef0135d49bdb206f24121bab3e9cbf2f9621c674a92e48928fbb21f897549f01", "withdrawn": "", "abstract": "A notable feature of confined active matter systems is the tendency for motile particles to accumulate near solid boundaries. In various linear models with no-flux boundary conditions, this accumulation is realized through the development of sharp boundary layers at small particle diffusivity. In this talk, we rigorously investigate nonlinear boundary layers in the context of confined active matter. Specifically, we consider a family of 1D run-and-tumble models with nonlinear advection and tumbling on the half-line, and rigorously prove the vanishing diffusivity limit with quantitative convergence rates. In the limiting system, the boundary mass enters as a new variable which solves a nonlinear ODE, coupled to the PDE through a dynamic boundary condition. Interestingly, the nonlinearity on the boundary in the inviscid system cannot be obtained without reference to the boundary layer analysis at positive diffusivity. Numerically, these models exhibit rich behavior, including phase transition and hysteresis in the boundary layer. This is joint work with Dallas Albritton and Timur Yastrzhembskiy.", "id": "Paper/66224", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66224"}, {"title": " Handel–Miller laminations and short geodesics ", "webprogram_exclude": "0", "session_ids": ["Session/18267"], "source_sha256": "c4806a7c01df9bfc47c344d92d26e23f778b7045ff65ba4bfd9d9044689930ae", "withdrawn": "", "abstract": "Currently, there is a lot of exciting research activity surrounding \\textit{end-periodic homeomorphisms} of \\textit{infinite-type surfaces}. Such homemorphisms admit tame mapping tori, realized as the interior of a compact $3$-manifold with boundary. If the map is additionally assumed to be \\textit{atoroidal}, then with the application of Thurston's hyperbolization program and work of Field--Kim--Leininger--Loving, its mapping torus admits a hyperbolic structure. One may ask: how might topological properties of the map determine geometric data of the hyperbolic manifold?\n\nAs an ``infinite type\" analogue to work of Minsky in the finite-type setting, we show that given a subsurface $Y\\subset S$, the subsurface projections between the ``positive'' and ``negative'' Handel-Miller laminations provide bounds for the geodesic length of the boundary of $Y$ as it resides in $M_f$. In converse, we show that if a curve $\\gamma$ is sufficiently short in $M_f$, then it must appear as a boundary component of a subsurface which witnesses a large subsurface projection distance between the Handel--Miller laminations.\n\nWe'll discuss the motivating theory for finite-type surfaces and their associated closed fibered hyperbolic $3$-manifolds, show how these techniques are used in the infinite-type setting and how our main theorems actually give back to the closed, fibered setting. This represents joint work with J. Huang.", "id": "Paper/66225", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66225"}, {"title": " An exploration of low-dimensional geometric topology ", "webprogram_exclude": "0", "session_ids": ["Session/18144"], "source_sha256": "dd61995e44e0bc8f37879a9ff4f44ee129e6d500fc3b03740786170b222f1344", "withdrawn": "", "abstract": "In this talk, we will survey tools and results within the world of hyperbolic $3$-manifolds and surfaces. How does one use group theory to build a hyperbolic manifold? How do we think of the space of all hyperbolic structures on a $3$-manifold or the space of all curves on a surface? How can combinatorial data of curves on a surface determine geometric information about a hyperbolic $3$-manifold? \n\nThe talk will be suitable for anyone in the audience who is enthused by topology (undergraduates included!). In efforts to humanize mathematics, we will include some storytelling about the author's journey and the programs like EDGE that made their career possible.", "id": "Paper/66228", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66228"}, {"title": " Clustering in Non-symmetric Multilayer Networks with Groupwise Subspace Structure and Variable Dimensions ", "webprogram_exclude": "0", "session_ids": ["Session/17908"], "source_sha256": "8f274f0ea737f60f8bdd70e18244d6b089e0dcfde23ce1282472f5082dea708b", "withdrawn": "", "abstract": "We study a heterogeneous multilayer network in which every layer records interactions between a common set of $n$ row nodes and a layer-specific set of $n_\\ell$ column nodes, following a Generalized Random Dot Product Graph model. The layers are partitioned into $M$ unknown groups: layers in the same group share a common left latent subspace $U^{(m)}$, while otherwise all adjacency matrices may differ, since $A^{(\\ell)} = U^{(m)} Q^{(\\ell)} (V^{(\\ell)})^\\top + E^{(\\ell)}$ with layer-specific $Q^{(\\ell)}$ and $V^{(\\ell)}$. The task is to recover the grouping and estimate the shared subspaces, extending the classical recovery of one invariant subspace across a whole collection of matrices to structure shared only within groups.\n\nBecause layer dimensions vary, some layers are too sparse for their subspace to be identifiable on their own, and any purely layer-wise pipeline fails on them. We propose a two-stage method. Stage one keeps the active layers, those with dimension exponent $\\beta_\\ell = \\log n_\\ell / \\log n$ above the sparsity exponent $\\beta$, represents each by the hollowed Gram operator $\\mathcal{H}(A^{(\\ell)} A^{(\\ell)\\top})$, clusters the vectorized leading projections by approximate $K$-means, and aggregates Gram matrices within each cluster to sharpen the subspace estimates. Stage two classifies every remaining weak layer by the projection energy $\\|(\\widehat{U}^{(m)})^\\top A^{(\\ell)}\\|_F^2$, a single matrix product per layer that parallelizes across layers.\n\nWe give non-asymptotic guarantees: under mild balance and signal conditions, the active layers are clustered exactly with high probability, every $U^{(m)}$ is estimated consistently, and the weak layers are classified correctly. Simulations and an analysis of MovieLens rating data confirm the theory and show robustness to heterogeneous layer sizes and noise levels. Joint work with Dr Marianna Pensky.", "id": "Paper/66232", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66232"}, {"title": " Two-Stage Stochastic Optimization Model for Hydrogen Export Supply Chains Under Disaster Uncertainty ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "39a9ac39f169b3f546c09bf61338ceb41c3f2375a51efe48e8b9c33d2bca2978", "withdrawn": "", "abstract": "As global demand for clean hydrogen grows, the United States has a major opportunity to become a leading exporter. However, many of its production sites sit on the hurricane-prone Gulf Coast, creating uncertainty that supply chain network designers have to account for. Where and how much infrastructure to build must be decided before the uncertainty is revealed. In this project, we model this uncertainty using a two-stage stochastic mixed-integer linear program, where first-stage decisions (which sites to build, how many production units to install, and whether to build overseas storage) are made before the uncertainty is revealed, and second-stage operational decisions (production, shipping, and storage) adapt to each scenario. The model includes modular capacity, a service-level requirement paired with profit maximization, and non-anticipativity constraints across time periods. We build this model in MATLAB and quantify the cost of resilience and decision-making under uncertainty.\n\nSince the two-stage structure is well suited for decomposition, we also implement the Benders/L-shaped method from scratch, deriving optimality and feasibility cuts from LP duality. We also validate the decomposition against the commercial solver across different problem sizes, confirming the agreement of outputs in every case. This project demonstrates how stochastic programming and decomposition methods can be applied to timely questions in energy systems, and it serves as a foundation for ongoing work extending the model and comparing the decomposition performance as we add more scenarios.", "id": "Paper/66234", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66234"}, {"title": " On the Banach-Mazur distance between <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.007ex\" height=\"1.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -576.1 433.5 721.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">c</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-63\" d=\"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-63\" x=\"0\" y=\"0\"></use>\n</g>\n</svg> and its two coordinate hyperplanes ", "webprogram_exclude": "0", "session_ids": ["Session/18364"], "source_sha256": "51a79acf343448d49175f1365e83331194919025bfe8b8c09c39349a6db276ac", "withdrawn": "", "abstract": "We study the Banach--Mazur distance between the space \\(c\\) of convergent\nsequences and the hyperplane\n\\[\nW_{\\left(\\frac{1}{2},\\frac{1}{2}\\right)}\n=\n\\left\\{\nx=(x(i))\\in c :\n\\lim_{i\\to\\infty}x(i)\n=\n\\frac{x(1)+x(2)}{2}\n\\right\\}.\n\\]\nThis space is an \\(\\aleph_0\\)-hyperconvex \\(L_1\\)-predual that is not\nisometrically isomorphic to any \\(C(K)\\) space. Using a new\ntwo-dimensional geometric approach, we improve the lower estimate\npreviously known and prove that\n\\[\n1+\\tau\n\\leq\nd\\left(c,W_{\\left(\\frac{1}{2},\\frac{1}{2}\\right)}\\right)\n\\leq\n1+\\frac{2}{\\sqrt{5}},\n\\]\nwhere \\(\\frac{2}{\\sqrt{5}}-\\tau\\approx 0.04\\) }", "id": "Paper/66236", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66236"}, {"title": " Integral bases for the universal enveloping algebras of twisted multiloop algebras with diagram automorphism actions ", "webprogram_exclude": "0", "session_ids": ["Session/19342"], "source_sha256": "4ab4d7353bc5437e1519cbbe26b9571beae102ae8c6145b63f667d9973ee4254", "withdrawn": "", "abstract": "We construct integral forms for the universal enveloping algebras of twisted multiloop algebras of the simple finite-dimensional complex Lie algebras where the twist is given by a diagram automorphism. We also give explicit integral bases for these integral forms. These integral forms and bases can be used to study the representations of these infinite-dimensional algebras in positive characteristic.", "id": "Paper/66238", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66238"}, {"title": " Parameter Classification for the Existence of Periodic Points of the P-adic Logistic Map ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "42a0af1288c25ed11b4ca283e246d0549d7298d46d102bc0c7c8852273da665e", "withdrawn": "", "abstract": "In classical applications, the logistic map has provided an interesting example of periodic points depending on the given growth parameter. In the context of p-adic dynamics, we have a polynomial mapping on the p-adic integers $f_r: \\mathbb{Q}_p \\rightarrow \\mathbb{Q}_p$ of the form $f_r(x) = rx(1-x)$, where $r$ is a p-adic integer, and we would like to study the existence and periods of its periodic points under iterated composition. We can reformulate the problem of existence as understanding the existence of roots of $f^n(x) - x$ over the p-adic numbers, presenting a challenging problem. We approach this by studying low-period periodic points through the method of explicitly finding the roots and classifying when the nontrivial roots of exact period $n$ exist depending on $r$ and $p$. Using the arithmetic properties of the p-adic numbers for finding square roots, we have produced a full classification of which values of $r$ and $p$ yield a 2-cycle, as well as an explicit formulation of these points. Additionally, we also propose a potential method for studying higher periods using the conjugate maps and Hensel lifting.", "id": "Paper/66239", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66239"}, {"title": " Galois reconstruction of equivariant Artin-Tate <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.678ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 722.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbb {R}</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJAMS-52\" d=\"M17 665Q17 672 28 683H221Q415 681 439 677Q461 673 481 667T516 654T544 639T566 623T584 607T597 592T607 578T614 565T618 554L621 548Q626 530 626 497Q626 447 613 419Q578 348 473 326L455 321Q462 310 473 292T517 226T578 141T637 72T686 35Q705 30 705 16Q705 7 693 -1H510Q503 6 404 159L306 310H268V183Q270 67 271 59Q274 42 291 38Q295 37 319 35Q344 35 353 28Q362 17 353 3L346 -1H28Q16 5 16 16Q16 35 55 35Q96 38 101 52Q106 60 106 341T101 632Q95 645 55 648Q17 648 17 665ZM241 35Q238 42 237 45T235 78T233 163T233 337V621L237 635L244 648H133Q136 641 137 638T139 603T141 517T141 341Q141 131 140 89T134 37Q133 36 133 35H241ZM457 496Q457 540 449 570T425 615T400 634T377 643Q374 643 339 648Q300 648 281 635Q271 628 270 610T268 481V346H284Q327 346 375 352Q421 364 439 392T457 496ZM492 537T492 496T488 427T478 389T469 371T464 361Q464 360 465 360Q469 360 497 370Q593 400 593 495Q593 592 477 630L457 637L461 626Q474 611 488 561Q492 537 492 496ZM464 243Q411 317 410 317Q404 317 401 315Q384 315 370 312H346L526 35H619L606 50Q553 109 464 243Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJAMS-52\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-motivic spectra via Real global homotopy theory ", "webprogram_exclude": "0", "session_ids": ["Session/17701"], "source_sha256": "2bbba2ac1aaaceb62e562f17e6241b802a2f58a2739134e851fb18bd31dab09c", "withdrawn": "", "abstract": "Let $A$ be a finite abelian group, we present work in progress establishing a Galois reconstruction result for $A^\\vee$-equivariant Artin-Tate $\\mathbb{R}$-motivic spectra as a deformation of $(A\\rtimes C_2)$-equivariant spectra, with $C_2$ acting by inversion. This extends results by Allen-Piessevaux on a synthetic reconstruction of equivariant $\\mathbb{C}$-motivic spectra. The key input we use is the Real global homotopy theory of Real bordism $M\\mathbb{R}$ as developed by Carlisle-Wisdom-Yan.", "id": "Paper/66242", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66242"}, {"title": " Vanishing theorems in positive and mixed characteristics. ", "webprogram_exclude": "0", "session_ids": ["Session/17996"], "source_sha256": "6cf9d7bf2ab1d2d82c285665406196464db851621178ec37c8d387c4c93dffbe", "withdrawn": "", "abstract": "In this talk, we discuss Kawamata–Viehweg vanishing for surfaces of del Pezzo type over imperfect fields and its applications to the study of singularities arising in the minimal model program. We also discuss Kovács vanishing for threefolds in positive and mixed characteristics.", "id": "Paper/66243", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66243"}, {"title": " Minimax optimization in Bures–Wasserstein geometry ", "webprogram_exclude": "0", "session_ids": ["Session/18273"], "source_sha256": "203f60ed258652a831d91ce6c6d72d7e200695fa270ed1fef1764afcd41dc7b8", "withdrawn": "", "abstract": "Distributionally robust formulations of statistical risk lead to minimax\nproblems over the product of a Euclidean space and a Riemannian manifold.\nSuch landscapes are nonconvex--nonconcave in general, and no first-order\nmethod is known to converge globally. I will introduce the \\emph{basin\nsaddle point}: a Nash equilibrium defined locally, on the product of a\n$\\delta$-basin around a connected component of the local-minima critical\nset with a geodesic ball on the measure manifold. For a Riemannian\ngradient ascent--multistep descent iteration, I will give a convergence\nframework under a local \\L{}ojasiewicz-type growth condition with exponent\n$\\beta \\in (1,2]$, yielding linear rates when $\\beta = 2$ and polynomial\nrates for $\\beta \\in (1,2)$, with explicit dependence on the sectional\ncurvature of the manifold. The second half instantiates the theory over\nGaussian measures, where the ambiguity set is the product of a Euclidean\nspace with the Bures--Wasserstein manifold of covariance matrices. There,\nHessian estimates for the Lagrangian give existence and local uniqueness\nof the maximizer, and an alternating Riemannian gradient scheme attains\nthe abstract rates with all constants explicit in the data dimension,\nloss moments, and reference covariance.", "id": "Paper/66244", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66244"}, {"title": " K-Slice Knots and Links in Symplectic 4-Manifolds ", "webprogram_exclude": "0", "session_ids": ["Session/18087"], "source_sha256": "569e2e23d6ca98b50976ae0741ee8f377d14012e3398a23507137e0d6b49e766", "withdrawn": "", "abstract": "A knot is k-slice if it bounds a properly-embedded disk with self-intersection -k. We give an obstruction to k-sliceness in symplectic 4-manifolds using the maximal Thurston–Bennequin number. We then study k-sliceness in K3 and construct families of knots that are k-slice, as well as knots that are slice but not k-slice. We also give applications to the sliceness of links. This is joint work with Kai Nakamura.", "id": "Paper/66250", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66250"}, {"title": " A Compression Formula for Non-attacking Fillings ", "webprogram_exclude": "0", "session_ids": ["Session/18376"], "source_sha256": "d2e57725bf7ab7776b184215a566934c537595d2cdca2d11ff52710508b2fc71", "withdrawn": "", "abstract": "Nonsymmetric Macdonald polynomials $E_\\mu$ are a family of polynomials constructed using the framework of the double affine Hecke algebra. In 2008, J. Haglund, M. Haiman and N. Loehr proved a generating function formula for $E_\\mu$ using non-attacking fillings, and, in 2018, S. Corteel, O. Mandelshtam, and L. Williams introduced a new generating function using multiline queues for $E_\\lambda$, where $\\lambda$ is a partition. In this talk, we will present a conjectured compression formula for non-attacking fillings motivated by the multiline queues model and provide a sketch of the proof for a large family of compositions.", "id": "Paper/66251", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66251"}, {"title": " Critical loci of self-maps of projective space ", "webprogram_exclude": "0", "session_ids": ["Session/18259"], "source_sha256": "408e0f257bd1d4cab4f2fa6b079b7e0d624065ba46d60b919e07f3558bd2d491", "withdrawn": "", "abstract": "Let $K$ be an algebraically closed field and let $n,d \\geq 2$. We show that the critical scheme of a general endomorphism of $\\mathbb{P}^n_K$ of degree $d$ is an integral hypersurface. This extends a result of Ingram--Ramadas--Silverman to arbitrary characteristic. We use basic facts about polynomial rings to show that certain carefully chosen examples have absolutely irreducible Jacobian. To handle the wild case where the characteristic of $K$ divides $d$, we introduce a polynomial that imitates the homogeneous Jacobian determinant.", "id": "Paper/66255", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66255"}, {"title": " Geometric information of vanishing Jacobians for maps of fractional order ", "webprogram_exclude": "0", "session_ids": ["Session/17883"], "source_sha256": "54995fa34174e7b8b1e38a525ccdd2053db022c6ac60d731b908594cb24d0e44", "withdrawn": "", "abstract": "It is well known that a H\\\"older function whose derivative vanishes a.e. may not be constant, take for example the  Heaviside function or the devils staircase. If it the derivative vanishes in distributional sense, the function is constant.\nSimilar statements hold true for multidimensional maps, where the Jacobian derivative vanishes a.e. or in distributional sense: a vanishing Jacobian may or may not prevent the map from being an embedding -- depending on the H\\\"older regularity.", "id": "Paper/66256", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66256"}, {"title": " Integrability of Vortex Rings on a Sphere ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "ca2821eb13352a9e697bb60ab9905a544966aec2f13b2bffa821ecdee199e40b", "withdrawn": "", "abstract": "The N-vortex problem is well-studied in mathematical physics and has applications to cyclone modelling, coupled electrons, and other dynamical systems. The most general version of the problem is known to be integrable for N ≤ 3 vortices, but quickly becomes chaotic as more are added. A recent variant of this problem considers N vortices arranged on latitudinal rings. We prove the integrability of this system for an arbitrary number of vortices arranged on two rings. We then study the geometry of the special case where each ring contains two vortices, finding five classes of singular points and analyzing the system’s behavior in these configurations.", "id": "Paper/66257", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66257"}, {"title": " Cayley-Kalai Formula in the context of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"7.445ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 3205.5 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">HP(G)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-48\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 219 683Q260 681 355 681Q389 681 418 681T463 682T483 682Q499 682 499 672Q499 670 497 658Q492 641 487 638H485Q483 638 480 638T473 638T464 637T455 637Q416 636 405 634T387 623Q384 619 355 500Q348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504Q674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660Q586 677 588 679T604 682Q609 682 646 681T740 680Q802 680 835 681T871 682Q888 682 888 672Q888 645 876 638H874Q872 638 869 638T862 638T853 637T844 637Q805 636 794 634T776 623Q773 618 704 340T634 58Q634 51 638 51Q646 48 692 46H723Q729 38 729 37T726 19Q722 6 716 0H701Q664 2 567 2Q533 2 504 2T458 2T437 1Q420 1 420 10Q420 15 423 24Q428 43 433 45Q437 46 448 46H454Q481 46 514 49Q520 50 522 50T528 55T534 64T540 82T547 110T558 153Q565 181 569 198Q602 330 602 331T457 332H312L279 197Q245 63 245 58Q245 51 253 49T303 46H334Q340 38 340 37T337 19Q333 6 327 0H312Q275 2 178 2Q144 2 115 2T69 2T48 1Q31 1 31 10Q31 12 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-50\" d=\"M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-47\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q492 659 471 656T418 643T357 615T294 567T236 496T189 394T158 260Q156 242 156 221Q156 173 170 136T206 79T256 45T308 28T353 24Q407 24 452 47T514 106Q517 114 529 161T541 214Q541 222 528 224T468 227H431Q425 233 425 235T427 254Q431 267 437 273H454Q494 271 594 271Q634 271 659 271T695 272T707 272Q721 272 721 263Q721 261 719 249Q714 230 709 228Q706 227 694 227Q674 227 653 224Q646 221 643 215T629 164Q620 131 614 108Q589 6 586 3Q584 1 581 1Q571 1 553 21T530 52Q530 53 528 52T522 47Q448 -22 322 -22Q201 -22 126 55T50 252Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-48\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-50\" x=\"888\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"1640\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-47\" x=\"2029\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"2816\" y=\"0\"></use>\n</g>\n</svg> homology ", "webprogram_exclude": "0", "session_ids": ["Session/18146"], "source_sha256": "49ea54e14e15ab45949a5b1cfd3ac1cb28c514dd7b184641dad999ab4ce2185d", "withdrawn": "", "abstract": "In this talk we introduce a homology theory $HP(G)$ associated to a graph $G$. We show that $HP(G)$ is a graph invariant but not a topological invariant. The main result is the analog of Cayley-Kalai Formula in this context. More precisely, we show that $\\sum_{G\\in \\mathcal{A}} |HP_0(G)|^2=(n-2)^{n-1}n$, where $\\mathcal{A}$ is the set of all labeled graphs $G$ that have $n$ vertices, $n-1$ edges, and $|HP_1(G)|=0$.", "id": "Paper/66259", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66259"}, {"title": " On decay of the local mean oscillations of the vorticity direction in critical Navier-Stokes flows ", "webprogram_exclude": "0", "session_ids": ["Session/18050"], "source_sha256": "555f781005543e638a359a2f61675a7d93d4b21314ed2a725ac73c06bdd4e948", "withdrawn": "", "abstract": "The purpose of this talk is to present some recent results on the evasion of \\emph{critical spatial point singularities} (the vorticity magnitude scales like $O(|x|^{-2})$, inhabiting the critical Lorentz space $L^{3/2, \\infty}$) in 3D Navier-Stokes (NS) flows. In this setting, the classical regularity criteria are based on smallness of a suitable scaling-invariant quantity. The argument here is set up as a two-part scheme. \n\nIn the first part, we consider the evolution of the magnitude and show that if the direction $\\xi$ belongs to a local, log-weighted space of bounded mean oscillations, $bmo_\\frac{1}{|\\log r|}$, the stretching component of the strain tensor is (locally) logarithmically depleted which eventually forces the local scale of sparseness of the velocity super-level sets below the lower bound on the radius of spatial analyticity, averting the blow-up via the harmonic measure maximum principle. It is worth noting that a field in $bmo_\\frac{1}{|\\log r|}$ fails the Dini test; hence the direction could exhibit wild, discontinuous phase defects and still regularize the magnitude, preventing singularity formation. \n\nIn the second part, we consider the question of whether the NS mechanics can propagate this type of topological regularity. Here, we consider a geometric PDE satisfied by the direction consisting of the Harmonic Map Heat Flow (HMHF) supplemented with the fluid transport, cross-diffusion and the tangential strain (the tangential component of the strain tensor). A key obstacle here is that -- due to the centripetal constraint $|\\nabla \\xi|^2 \\xi$ -- even a pure HMHF into the sphere can exhibit a finite time geometric singularity, e.g., a dipole bubble, which would in this case lock the vorticity direction in unweighted $bmo$. Interestingly, factoring the singular envelope out of the cross-diffusion term generates an outward radial drift working hard to prevent the concentration at the core. One still needs to handle the tangential strain, and the key observation here is that it vanishes precisely when the direction is one of the eigenvectors of the strain tensor, including the one that generates the maximal stretching. This is in sharp contrast to classical geometric regularity criteria which are based on depleting the full vortex-stretching term and inhabit the realm of weak stretching.", "id": "Paper/66261", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66261"}, {"title": " A Gamification Platform and Assessment Tools for a STEM Hub for Innovation in Numeracy Education (SHINE) ", "webprogram_exclude": "0", "session_ids": ["Session/18199"], "source_sha256": "8379caae3d8ba518abe000e023677ef7f8134443f2f048104e030e09627dcd4e", "withdrawn": "", "abstract": "This presentation describes the development of Scalaris, a gamified quantitative reasoning learning environment being created through the Hispanic Serving Institutions STEM Hub for Innovation in Numeracy Education (HSI-SHINE). Scalaris places students in an interactive world where they navigate sectors, complete missions, analyze authentic data, make evidence-based decisions, and build quantitative reasoning skills including percentages, data interpretation, descriptive statistics, and spreadsheet use. Students progress through increasingly challenging experiences while developing a digital identity that reflects their skills and accomplishments.\n\nThe design of Scalaris is informed by a survey of 88 students enrolled in courses taught by HSI-SHINE faculty. Students expressed the strongest preferences for immediate feedback, real-world applications, visible progress, opportunities to retry problems, and short interactive activities. They were less enthusiastic about competition, timers, penalties, repetitive tasks, and reward-driven experiences.\n\nThese findings are shaping Scalaris around mastery rather than competition. The platform incorporates pre- and post-assessments, skill checks, mission-based learning, feedback and retry opportunities, and project-based assessment to examine student growth across multiple forms of quantitative reasoning. The presentation will also describe the assessment tools developed for Scalaris and how they are being embedded within the application. Scalaris will generate learning and engagement data that can help the project team examine how students progress through activities, where they encounter difficulty, and which instructional supports are most useful.\n\nThe presentation will demonstrate how student-informed design, gamification, authentic problem solving, assessment, and learning analytics are being integrated into Scalaris and will describe the next phase of implementation, testing, and evaluation within the HSI-SHINE initiative.", "id": "Paper/66263", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66263"}, {"title": " Log-concavity and log-convexity via distributive lattices ", "webprogram_exclude": "0", "session_ids": ["Session/17943"], "source_sha256": "7a05c0ef7ef812c82bef3371a7e1bc6a5defcc4df7cc67db5d1c446ebc164200", "withdrawn": "", "abstract": "Let $L$ be a distributive lattice. It follows easily from the FKG inequality that, if $I$ and $J$ are lower order ideals in $L$, then $|I|\\cdot|J|\\leq |L|\\cdot|I\\cap J|$  where vertical bars denote cardinality. The inequality is reversed if  is a lower order ideal and  is an upper order ideal. These inequalities can be used to combinatorially prove log-concavity and log-convexity results for various sequences including binomial coefficients, Catalan numbers, Fibonacci numbers, Stirling numbers of the second kind, order polynomials, and more. In the process, we construct several new distributive lattices that provide combinatorial interpretations of these inequalities. This is joint work with Bruce Sagan.", "id": "Paper/66266", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66266"}, {"title": " A Quasisymmetric Analogue of Bruhat Order ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "7c9eae4163ab1b976b3e4a3e48f5fdbf04c6a1c4b6e162d309eefbc7dab537af", "withdrawn": "", "abstract": "We define a quasisymmetric analogue of the classical Bruhat order and\nprove results on its Sperner properties and the structure of its\nprincipal lower intervals. Monk's multiplication rule for Schubert\nclasses encodes the classical order. Forest polynomials, introduced\nby Nadeau and Tewari, satisfy an analogous multiplicity-free rule whose\nsummands we use to define the covers of a graded order on indexed binary\nforests. Its finite\nwindows can have multiple maximal elements, and its principal lower\nintervals need not be Eulerian. It differs from both the classical\nBruhat order and its restriction to algebraic noncrossing partitions,\nwhich appears in the geometry of the quasisymmetric flag variety.\n\nOur first theorem is that every finite window $\\mathcal{P}_n$\nis strongly Sperner. Sperner properties can be difficult even for classical permutation orders: the weak-order\nSperner problem goes back to Bj{\\\"o}rner (1984), and Stanley (2017)\nconjectured a positive answer. Gaetz and Gao proved the strong Sperner\nproperty using a combinatorially defined $\\mathfrak{sl}_2$-action in a\n2018 preprint, published in 2020. For forests, however, a pleasantly direct\ncombinatorial proof partitions $\\mathcal{P}_n$ into saturated chains\nending in the top rank.\n\nOur second theorem characterizes the principal lower intervals\nthat are lattices: they are exactly the Boolean intervals.\nTheir tops are precisely the forests avoiding a bent corner,\na path of three internal vertices that changes direction.\nThis parallels the $321$- and $3412$-avoidance characterization of\nBoolean principal Bruhat ideals.\n\nFinally, we conjecture that every principal lower interval is shellable,\nas in the classical Bruhat order. Recursive coatom orderings prove this\nfor the hook family with top code $(n,1)$. Computational checks have verified shellability for all $188$ binary\ntree shapes with four to six internal vertices.\n\nIn classical Schubert theory, the\nBruhat order connects multiplication of cohomology classes with\ncontainment relations among Schubert varieties. The quasisymmetric\nflag variety offers a setting in which to seek corresponding geometric\nexplanations for the chain partition and Boolean classification,\npotentially elucidating why these Bruhat phenomena persist for forests.", "id": "Paper/66267", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66267"}, {"title": " Optimal Estimation of Quadratic Forms ", "webprogram_exclude": "0", "session_ids": ["Session/17718"], "source_sha256": "4729415f8aa869cf352b6d3a823505f2b33608480431c92f3b43214ae8dac614", "withdrawn": "", "abstract": "This talk showcases the speaker's recent result establishing that, in order for a quadratic form of an unknown object to be estimated optimally (in a worst-case sense) from the {\\em a priori} knowledge that the object belongs to an hyperellipsoid and the {\\em a posteriori} availability of linear observations, a quadratic functional of these observations can be used. The proof of existence of such an optimal quadratic functional relies on slightly refined minimax and convexity theorems. In addition, when the underlying Hilbert space is finite-dimensional, a computational construction of the optimal quadratic functional is uncovered. The results are then extended to take into account some observation errors modeled deterministically.", "id": "Paper/66269", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66269"}, {"title": " Stability of the <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.637ex\" height=\"2.509ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -934.9 1135.4 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">L^2</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4C\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-4C\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-32\" x=\"963\" y=\"513\"></use>\n</g>\n</svg>-Caffarelli-Kohn-Nirenberg inequalities ", "webprogram_exclude": "0", "session_ids": ["Session/18441"], "source_sha256": "c4877906cc6666155bb1b2c83875eb246202924a0e4cbc8d9f7ce0dbb937ff01", "withdrawn": "", "abstract": "The Caffarelli–Kohn–Nirenberg (CKN) inequalities form a two-parameter family unifying the Hardy, Heisenberg, and hydrogen-atom uncertainty inequalities. Their stability — a quantitative bound on the distance to optimizers in terms of the deficit — had previously been known only in restricted parameter ranges. In this talk, I present joint work with A. X. Do, G. Lu, and V. H. Nguyen establishing sharp stability estimates for the $L^2$-CKN inequality over the entire admissible parameter range, with explicit optimal constants. The key tool is a new family of weighted Gaussian-type $L^2$-Poincar\\'e inequalities, proved via Laguerre polynomial expansions, spherical harmonics, and a Kelvin transform. As a byproduct, we obtain the first sharp stability estimate for the Hydrogen Uncertainty Principle.", "id": "Paper/66274", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66274"}, {"title": " A time integration method of approximate fundamental solutions for nonlinear PDEs of elliptic type ", "webprogram_exclude": "0", "session_ids": ["Session/17823"], "source_sha256": "b9cc7365ab393416e0d78214f42be32cd3578f65ca1684d0f0680c254bf3f09e", "withdrawn": "", "abstract": "Nonlinear elliptic PDEs over irregular-shaped domains are solved using a fictitious-time formulation coupled with delta-shaped basis methods of approximate particular solutions and approximate fundamental solutions. The minimal solution of a steady-state blow-up problem is computed through a sequence of time-dependent boundary value problems, with the computational scheme requiring a continuous update of the evolving solution state. Numerical results demonstrate high accuracy while effectively accommodating complex geometries. Critical values of the Frank-Kamenetskii parameter are determined for two-dimensional problems over domains with different geometric boundaries.", "id": "Paper/66275", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66275"}, {"title": " Transition matrices for the permutation character basis of the symmetric group ", "webprogram_exclude": "0", "session_ids": ["Session/18375"], "source_sha256": "d6b897be39be1ff51b2128a23d8cd2764420a1d87918187cedfa5caf14e9f333", "withdrawn": "", "abstract": "We consider inhomogeneous bases of symmetric functions which evaluate to characters of the symmetric group and are closely related to long-standing open problems in combinatorial representation theory such as the Kronecker problem and the restriction problem. We describe combinatorial interpretations for the transition matrices from the basis that evaluates to induced trivial characters (or permutation characters) to other classical bases of symmetric functions. In particular, we use Lyndon words and tableau combinatorics to express the permutation character basis in terms of the homogeneous, monomial, Schur, and elementary bases.", "id": "Paper/66276", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66276"}, {"title": " Fractional Heisenberg Uncertainty Principles and Their Stability ", "webprogram_exclude": "0", "session_ids": ["Session/18265"], "source_sha256": "e4e7bade6cb1d003dc18d242d519e6a6e9e7b2238c65492e756738050616c635", "withdrawn": "", "abstract": "We introduce two one-parameter families of sharp fractional Heisenberg Uncertainty Principles, in which the gradient is replaced by a fractional power of the Laplacian. In one family the classical second moment is retained, while in the other it is replaced by a weighted Dirichlet integral. In both cases we identify the sharp constants, characterize all optimizers, and establish sharp stability estimates; remarkably, the stability constant for the first family equals $1$ for every order and every dimension. The key idea is a Fourier-side correspondence with the first-order $L^2$-Caffarelli–Kohn–Nirenberg inequality, which transports sharp constants, optimizers, and stability estimates, while the Hecke–Bochner formula produces explicit profiles in the physical variable. We also treat negative orders, where the fractional Laplacian becomes a Riesz potential. Finally, we show that the deficit controls an entire chain of successive remainder terms, of which the sharp stability estimate is only the first; for the classical Heisenberg principle this yields three such terms, and for the second-order case, four, measured against explicit confluent hypergeometric profiles.", "id": "Paper/66277", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66277"}, {"title": " Tensor-Train Sketching for Permutation-Structured Function Estimation from Samples ", "webprogram_exclude": "0", "session_ids": ["Session/16950"], "source_sha256": "5c9d72cdec3a2d0e1a11620c2573cae5ef7ef0319ed92db4818f85a9752c2678", "withdrawn": "", "abstract": "We propose a tensor-train (TT) framework for estimating high-dimensional functions with prescribed permutation structure from samples, including symmetric probability densities and antisymmetric fermionic wavefunctions. \nThe key idea is to represent the target functions in a symmetric or antisymmetric basis, so that its coefficient tensor is free of permutation constraints and can be reconstructed using TT sketching. \nNumerical experiments on repulsive particle systems, the $t$-$V$ model, and the Hubbard model demonstrate accurate recovery of physically relevant observables using low TT-ranks and moderate sample sizes.", "id": "Paper/66278", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66278"}, {"title": " Positive curvature and discrete torus actions ", "webprogram_exclude": "0", "session_ids": ["Session/17998"], "source_sha256": "31adcb861670915be6ee3a72190c8f86d7c9cddcd3d9a63b361544ebdac0e253", "withdrawn": "", "abstract": "The classification of Riemannian manifolds with positive sectional curvature is a long-standing problem in Riemannian geometry.  A common tool is to focus on manifolds with symmetry with the goal of gradually relaxing the restrictions of the size of the isometry group.  In this talk I will give an overview of known results and summarize joint work with Catherine Searle on the properties of closed, positively curved Riemannian manifolds admitting an isometric, effective, discrete torus action, that is an action of $(Z_2)^k$, with non-empty fixed-point set.", "id": "Paper/66284", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66284"}, {"title": " The Structure of the Fixed Locus of a Rational Function on the Berkovich Line ", "webprogram_exclude": "0", "session_ids": ["Session/17755"], "source_sha256": "0003d8e9835a05b7cf80b21f5e95ca446ef367b6b3b4b2145e5df9d712aac197", "withdrawn": "", "abstract": "A rational function \\(f(z)\\) of degree \\(d\\) over an algebraically closed field \\(K\\) has exactly \\(d+1\\) \\(K\\)-rational fixed points, when counted with appropriate multiplicity. If \\(K\\) is a nonarchimedean field, and if we interpret \\(f\\) as a self-map of the Berkovich line, then the fixed locus of \\(f\\), denoted \\(\\operatorname{Fix}(f)\\), can have infinitely many fixed points. We classify the connected components of \\(\\operatorname{Fix}(f)\\), describe a number of its structural properties, and give a sharp upper bound for the number of connected components which depends only on \\(d\\) and the residue characteristic of \\(K\\).", "id": "Paper/66288", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66288"}, {"title": " ON REVIEWS AND REVIEWING ", "webprogram_exclude": "0", "session_ids": ["Session/18554"], "source_sha256": "f6c6d29cb5e84767b35a3e7b725e1d0eedc20e0a608e59b98d283c5302eb617f", "withdrawn": "", "abstract": "In this talk, I will share personal observations after contributing over 500 reviews of papers and books for Zentralblatt and Math Reviews, over several decades of reviewing. Why would one donate to the world (sometimes a substantial amount of) time as a reviewer? What subjects should one review? What constitutes an honest-to-goodness (HTG) review? How to ensure that a review is correct, accurate and fair? Reviewing papers written in different languages? Value of published reviews in tenure and promotion process. Interactions of the databases staff with reviewers. What the future holds for reviews and reviewing.", "id": "Paper/66290", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66290"}, {"title": " Highly structured complex orientations are atypically p-typical ", "webprogram_exclude": "0", "session_ids": ["Session/17843"], "source_sha256": "4302095682bde4b87d36ed7975c6cd9158c565eaa0f140e8494fa893a4d08142", "withdrawn": "", "abstract": "Using the Ando-Hopkins-Rezk criterion and the generalized p-adic gamma function, we show that $H_{\\infty}$-orientations are atypically p-typical. This is joint work with Andrew Senger.", "id": "Paper/66292", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66292"}, {"title": " A Discrete Linear Systems Approach to Baumol’s Cost Disease in Performing Arts Organizations ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "ac553beb9a84f343462d12f9d2d986f77834c3f7fdc59209e37972d4805952f3", "withdrawn": "", "abstract": "Classical music organizations face a structural problem first described by William Baumol: musician productivity cannot rise the way it does in manufacturing, since a string quartet still requires four players and the same forty minutes it did two centuries ago, while wages must track the broader economy. Costs therefore grow faster than earned income can, and the gap widens by construction rather than by mismanagement. This project formalizes that gap as a discrete linear system, treating ticket revenue, donations, and musician wages as coupled state variables that evolve year to year through a $3\\times3$ transition matrix. Steady state requires that the state vector satisfy $x^{*} = Ax^{*}$, which reduces to $(A - I)x^* = 0$ and admits a nonzero solution only when the matrix is singular. Under the parameters modeled here, that condition fails: the three eigenvalues are approximately $0.847, 0.800$, and $0.653$, all inside the unit circle. The system is mathematically stable, and it converges to zero. The distinction matters, because stability in the technical sense describes an orchestra that shrinks predictably rather than one that survives, and closing that gap requires changing the matrix itself rather than the starting conditions.", "id": "Paper/66295", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66295"}, {"title": " Random Leja points on <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.385ex\" height=\"2.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -1006.6 1026.7 1152.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbb {S}^d</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJAMS-53\" d=\"M54 238Q72 238 72 212Q72 174 106 121Q113 110 132 90T166 59Q221 23 264 23Q315 23 348 41Q368 50 384 79Q393 102 393 129Q393 181 356 219T221 299Q120 343 74 390T28 501Q28 561 55 610Q98 682 212 699Q214 699 231 700T261 701Q309 698 340 687T408 675Q431 678 445 690T465 702Q474 702 481 690V497L477 490Q464 481 450 490Q446 500 446 501Q446 546 386 606T260 666Q215 666 182 639T148 565Q148 528 186 496T319 428Q352 414 370 405T418 379T468 338T506 284Q528 239 528 191Q528 102 456 46T266 -10Q211 -10 176 2T110 15Q86 9 73 -1T53 -12Q44 -12 37 -1V112V182Q37 214 40 226T54 238ZM446 619Q446 648 444 648Q439 646 435 644Q425 644 415 639H404L417 624Q435 606 439 601L446 592V619ZM124 619L128 635Q126 635 108 617Q64 576 64 502Q64 489 65 479T76 449T102 414T150 376T228 335Q335 291 381 245T427 128Q427 94 419 75L415 61Q421 61 448 88Q490 127 490 190Q490 233 475 264Q456 299 430 321Q402 349 369 367T287 404T204 441Q138 481 119 526Q113 544 113 565Q113 596 124 619ZM75 43Q76 43 90 46T110 50H119L106 64L74 101Q72 101 72 72T75 43Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-64\" d=\"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJAMS-53\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-64\" x=\"787\" y=\"608\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18277"], "source_sha256": "ee6cfd0c4a7b133d1874fb4702734f5c79de578f3ff8b007da164257dea6e7b9", "withdrawn": "", "abstract": "The Lagrange interpolation operator is central in polynomial approximation, and its norm, the Lebesgue constant, measures the stability of interpolation. Understanding its growth for a given sequence of nodes is therefore a basic problem in approximation theory.\n\nA random alternative to classical Leja points, introduced by Pouchol for a compact set \\(K\\subset\\mathbb{C}\\), defines points recursively by\n\n$$\nZ_n\\sim |\\pi_n(z)|=\\prod_{i=0}^{n-1}|z-Z_i|.\n$$\n\nConditionally on \\((Z_0,\\ldots,Z_{n-1})\\), the law of \\(Z_n\\) is absolutely continuous with respect to a Borel measure \\(\\sigma\\) on \\(K\\), with density proportional to \\(|\\pi_n|\\). This construction extends naturally to higher dimensions. We study the growth of the Lebesgue constant for such random configurations on the unit sphere \\(\\mathbb{S}^d\\subset\\mathbb{R}^{d+1}\\) and investigate their separation properties.", "id": "Paper/66299", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66299"}, {"title": " Harmonic Bergman Kernel and Projection on Annular Regions ", "webprogram_exclude": "0", "session_ids": ["Session/17887"], "source_sha256": "f95b9c94964b4cba614c88adee65172c959a72009971357d7755f725f1cb6d4f", "withdrawn": "", "abstract": "Harmonic Bergman spaces are much less studied compared to their holomorphic counterparts. Harmonic Bergman kernel is known only in a handful of cases, such as when the domain is the unit ball, upper half space or exterior of the ball. In this talk, we obtain a previously unknown series representation for the harmonic Bergman kernel on annular regions and we prove a related decomposition theorem. Moreover, we provide a complete characterization of the values of $p$ for which the corresponding harmonic Bergman projection is bounded on $L^p$, including the cases in which the inner radius is zero or the outer radius is $\\infty$. We observe some interesting sharp dimension-dependent behavior.", "id": "Paper/66300", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66300"}, {"title": " Exact Fibers and a Sharp Reconstruction Threshold for the Permutation Tutte Polynomial ", "webprogram_exclude": "0", "session_ids": ["Session/19354"], "source_sha256": "aedfc8e6e71d18546b226274c6968653cc3008bc1f56121acd50656807726a96", "withdrawn": "", "abstract": "Graph polynomials compress combinatorial structure, and a basic inverse problem asks when the polynomial still determines the graph. The permutation Tutte polynomial \\(\\widetilde T_H(x,y)\\), introduced by Beke--Csaji--Csikvari--Pituk, is obtained by averaging internal and external activity over random vertex orders of a bipartite graph. We determine an exact reconstruction threshold for this invariant. The full bivariate polynomial determines every bipartite graph, up to bipartition-preserving isomorphism, whose smaller side has size at most \\(3\\). The bound is sharp: three pairwise nonisomorphic \\(4\\times4\\) bipartite graphs have the same full polynomial. The proof reduces the boundary case to the external marginal \\(F_H(y)=\\widetilde T_H(1,y)\\) on \\(3\\times q\\) graphs and classifies its fibers for all \\(q\\). Every fiber has size at most two, and every nontrivial fiber arises from one explicit midpoint insertion mechanism. Equivalently, all marginal collisions are positive integer multiples of a single primitive neighborhood-histogram direction. Each collision is separated by the first transverse derivative of the full polynomial, and one additional bit is necessary and sufficient to reconstruct from the marginal. I will explain the Cauchy-flow viewpoint behind the classification: the extracted charge is a divergence of six interval flows, and the unique surviving circulation is the midpoint triangle.", "id": "Paper/66303", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66303"}, {"title": " Operator Learning for Smoothing and Forecasting ", "webprogram_exclude": "0", "session_ids": ["Session/18447"], "source_sha256": "bb7595b7fcb282830accd3f3a6125c066af036b3292871cd30d77a6491e86f44", "withdrawn": "", "abstract": "Machine learning has opened new frontiers in purely data-driven algorithms for data assimilation in, and for forecasting of, dynamical systems; the resulting methods are showing some promise. However, in contrast to model-driven algorithms, analysis of these data-driven methods is poorly developed. In this talk we address this issue, developing a theory to underpin data-driven methods to solve smoothing problems arising in data assimilation and forecasting problems. The theoretical framework relies on two key components: (i) establishing the existence of the mapping to be learned; (ii) the properties of the operator learning architecture used to approximate this mapping. By studying these two components in conjunction, we establish novel universal approximation theorems for purely data driven algorithms for both smoothing and forecasting of dynamical systems. We work in the continuous time setting, hence deploying neural operator architectures. The theoretical results are illustrated with experiments studying the Lorenz `63, Lorenz `96 and Kuramoto-Sivashinsky dynamical systems.", "id": "Paper/66305", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66305"}, {"title": " Explicit Symmetric Low-Regularity Integrator for the Nonlinear Schrödinger Equation ", "webprogram_exclude": "0", "session_ids": ["Session/18281"], "source_sha256": "6c2986b8d106cebfb81e9cdae36d10671a05620d2ed98ab623e9e1f682a30e7d", "withdrawn": "", "abstract": "The numerical approximation of low-regularity solutions to the nonlinear Schr\\\"odinger equation (NLSE) is notoriously difficult and even more so if structure-preserving schemes are sought. Recent works have been successful in establishing symmetric low-regularity integrators for NLSE. However, so far, all prior symmetric low-regularity algorithms are fully implicit, and therefore require the solution of a nonlinear equation at each time step, leading to significant numerical cost in the iteration. In this work, we introduce the first fully explicit (multi-step) symmetric low-regularity integrators for NLSE. We demonstrate the construction of an entire class of such schemes which notably can be used to symmetrise (in explicit form) a large amount of existing low-regularity integrators. We provide rigorous convergence analysis of our schemes and numerical examples demonstrating both the favourable structure preservation properties obtained with our novel schemes, and the significant reduction in computational cost over implicit methods.", "id": "Paper/66311", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66311"}, {"title": " Degrees of Tensor Train Varieties via Volumes ", "webprogram_exclude": "0", "session_ids": ["Session/18355"], "source_sha256": "aa42d71fcf2c784d8122d535bfe46fd8faa798edd462119f32de868f248a9800", "withdrawn": "", "abstract": "The degree of an algebraic variety is one of its fundamental algebraic invariants. At first sight, the volume seems instead to be of a rather different nature. In the first part of the talk we show that these two notions coincide when an appropriate metric is chosen. We explain how this result can be used for degree computations and discuss the advantages, challenges and limitations of this approach compared with algebraic and numerical ones. In the second part, we apply this technique to the case of Tensor Train varieties. Via a recursive application of the coarea formula, we obtain a combinatorial expression for their degrees. Finally, we show that our algorithmic implementation of this strategy outperforms existing symbolic and numerical methods.\n\nThis is joint work with Otto T.P. Schmidt (https://arxiv.org/abs/2606.11847).", "id": "Paper/66321", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66321"}, {"title": " Trapping strips of wind-tree tiling billiards ", "webprogram_exclude": "0", "session_ids": ["Session/18269"], "source_sha256": "8775f095c9ec7937d6027ed38d44dde2d94b2924a7743a19da0885f4cf10fe41", "withdrawn": "w", "abstract": "In this talk, I will present the meeting of different dynamical systems: tiling billiards, the wind-tree model and the Eaton lenses. The three of them are motivated by physics.\\\\\n\nIn the beginning of the 2000's, physicists have conceived metamaterials with negative index of refraction. Tilling billiards' trajectories consist of light rays moving in an arrangement of metamaterials with opposite index of refraction. The wind-tree model was introduced by Paul and Tatyana Ehrenfest to study a gaz: a particle is moving in a plane where obstacles are periodically placed, on which the particle bounces. The Eaton lenses are a periodic array of lenses in the plane, in which we consider a light ray that is reflected each time it crosses a lens.\\\\\n\nAfter having introduced these dynamical systems, I will consider a mix of them: an arrangement of rectangles in the plane, like in the wind-tree model, but made of metamaterials, like for tiling billiards. I study the trajectories of light in this plane. They are refracted each time they cross a rectangle.\nUsing dynamics on half-translation surfaces and their moduli space, I show that these trajectories are trapped in a strip, for almost every parameter. This behavior is similar to the one of the Eaton lenses.", "id": "Paper/66325", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66325"}, {"title": " Flexibility of the isometric immersion system in arbitrary dimension and codimension and the energy scaling of prestrained thin films ", "webprogram_exclude": "0", "session_ids": ["Session/18306"], "source_sha256": "cf597f27493eb8b53b397658d7d6a4eb62ad1db275f569a0a02980a62c689ed8", "withdrawn": "", "abstract": "In this talk, I will present our new result on the isometric immersion problem for Riemannian metrics. We consider a $\\mathcal{C}^{r,\\beta}$-regular Riemannian metric defined on a $d$-dimensional domain. Our main theorem states that any short immersion into the Euclidean space $\\mathbb{R}^{d+k}$ can be uniformly approximated by exact isometric immersions of class $\\mathcal{C}^{1,\\alpha}$, for every  \n$\\alpha<\\alpha_0=\\min\\{\\frac{r+\\beta}{2}, \\frac{1}{1+d(d+1)/k}\\}$.\n\nOur theorem recovers several previously known results as special cases. The novelty thereof lies in providing a unified flexibility statement for arbitrary dimensions $d$ and codimensions $k$, while \nalso treating the so far uncharted range $k\\in (1, \\frac{d(d+1)}{2}-d+1)\\setminus \\{d\\}$, where no corresponding general result was previously available. Our threshold flexibility exponent $\\alpha_0$ agrees with the one obtained  for the closely related Monge-Amp\\`ere system.\n\nAs an application, we prove a new estimate in the quantitative immersability of thin prestrained films, showing that the infimum of non-Euclidean energies in presence of an arbitrary prestrain metric scales at most like $h^{\\frac{4\\alpha_0}{\\alpha_0+1}}$, where $h$ represents the vanishing thickness of the film.", "id": "Paper/66326", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66326"}, {"title": " The isoresidual fibration ", "webprogram_exclude": "0", "session_ids": ["Session/18269"], "source_sha256": "c31374004832a39d03be658435d1383e2a2cdc09b4b65b5cabaa00340b66bb30", "withdrawn": "", "abstract": "Let $\\Omega$ be a stratum of meromorphic differentials with $p$ poles, and let $R_p \\subset \\mathbb{C}^p$ be the space of $p$-tuples of total sum zero. There is a {\\em residue map} $\\operatorname{res}: \\Omega \\to R_p$ (recording the residues at the poles). What is the topological structure of this map? I will report on joint work with Guillaume Tahar and Dawei Chen that shows that in genus zero, the residue map is a {\\em stratified fibration}: there is a hyperplane arrangement called the {\\em resonance arrangement} in $R_p$, and $\\operatorname{res}$ is a fibration over each flat in this arrangement. This is a consequence of the existence of a certain nice period mapping for genus-zero differentials, realizing each fiber as a union of convex polyhedra.", "id": "Paper/66327", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66327"}, {"title": " Series-based implementation of wave kernels in the Method of approximate particular solutions ", "webprogram_exclude": "0", "session_ids": ["Session/17823"], "source_sha256": "f28da04c45f6d39a9f90a75d9401de429ec607e78d20821511b48453ac6e8877", "withdrawn": "", "abstract": "In this talk, I will present the the use of wave kernels within the Method of Approximate Particular Solutions (MAPS) by deriving particular solutions in series form with wave kernels as forcing terms. These particular solutions are then incorporated into the MAPS framework for numerical approximation. Several numerical experiments are presented to validate the proposed approach.", "id": "Paper/66329", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66329"}, {"title": " Compact Vaisman and l.c.K. manifolds with nonnegative bisectional curvature ", "webprogram_exclude": "0", "session_ids": ["Session/17947"], "source_sha256": "d347be31759ce304cd8dd52a4944e1c2af88e151b4ba9a5d963be5b53b7568c1", "withdrawn": "", "abstract": "Mok’s uniformization theorem for compact K\\\"{a}hler manifolds with nonnegative holomorphic bisectional curvature is a landmark result in K\\\"{a}hler geometry. A natural question is to what extent this theorem extends to the broader Hermitian setting.\n\nIn this talk, we explore this question for locally conformally K\\\"{a}hler (l.c.K.) manifolds, with particular emphasis on Vaisman manifolds. We present a uniformization theorem for compact Vaisman manifolds with nonnegative Chern bisectional curvature and a structural trichotomy for compact l.c.K. manifolds satisfying the same curvature condition.", "id": "Paper/66333", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66333"}, {"title": " Submanifolds with small normal curvatures ", "webprogram_exclude": "0", "session_ids": ["Session/17691"], "source_sha256": "6e51bd7f0648460315a758d8de3b38aeda288892f514b71cd89d2f4d37ab9957", "withdrawn": "", "abstract": "Recent works by M. Gromov, A. Petrunin, O. Chodosh, and C. Li deals with the question: Given a closed smooth manifold M, minimize the maximum normal curvatures among all immersions of M into (high-dimensional) Euclidean spaces, under the constraint that the image lies in a closed ball of radius one.\n\nReplacing this constraint with the condition that the (extrinsic) diameter is at most two, one arrives at a different, but still natural, question.\n\nThe result I will present is a first step in the exploration of this new question, namely: For any immersed submanifold M with diameter at most two, the maximum normal curvature is at least one, and equality holds if and only if M is diffeomorphic to a sphere or (real/complex/quaternionic/octonionic) projective space, embedded either as an affine sphere, or as a \"Veronese\" variety.", "id": "Paper/66335", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66335"}, {"title": " Combinatorially symmetric nullity of graphs. ", "webprogram_exclude": "0", "session_ids": ["Session/18146"], "source_sha256": "e0e385c5f86ee77ee9838f5f8e87e03933c7d7de4c17500973aefdb4d4d98a71", "withdrawn": "", "abstract": "We study the maximum nullity of combinatorically symmetric matrices, finding a characterization using forts of the graph and matroid representability.", "id": "Paper/66336", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66336"}, {"title": " Why Formalize? ", "webprogram_exclude": "0", "session_ids": ["Session/18101"], "source_sha256": "d30e39c449e79fd56ac55abf4d097867db367d25bab2906b798e88211361e0fa", "withdrawn": "", "abstract": "Consider the following questions:\n\\begin{itemize}\n\\item Should we teach elementary school students to multiply numbers, when calculators can do it?\n\\item Should we teach high school students to factor polynomials, when computer algebra systems can do it?\n\\item Should we teach high school students to solve optimization problems with calculus, when foundation models can do it? \n\\end{itemize}\nIt is reasonable to hold that, even though the need to execute calculations diminishes with the availability of computational tools, the ability to reason about the underlying mathematical structures and principles remains crucial. Recent advances in technology raise additional questions:\n\\begin{itemize}\n\\item Should we teach undergraduates majoring in mathematics to prove theorems, when AI can do it?\n\\item Should we teach mathematicians of all ages to read and write formal proofs, when AI can do that too?\n\\end{itemize}\nThis talk is concerned with the last two questions.\n\nThe most straightforward case for formalization is that it provides a way to verify the correctness of mathematical claims. Historically, however, mathematicians did not find that argument compelling. Formalization began to take root in the mathematics community about a decade ago as practitioners came to appreciate that formalization contributes to other aspects of mathematics, including collaboration, communication, curation, exploration, experimentation, discovery, teaching, and understanding. With the advent of powerful AI theorem provers, the pendulum has swung back toward viewing formalization primarily as a way of ensuring the correctness of AI-generated proofs. This is making the formalization community uneasy.\n\nIn this talk, I will explore the various reasons we formalize mathematics and what is gained and what is lost when we use AI. I will argue that the best strategy is to leverage the benefits of AI to enhance our engagement with formal methods rather than replace it.", "id": "Paper/66337", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66337"}, {"title": " Designing and Implementing Custom AI Tools in Undergraduate Mathematics: A Practical Approach for Instructors ", "webprogram_exclude": "0", "session_ids": ["Session/19349"], "source_sha256": "b429c715ca619e1ed8f84f4e0add082060add7d6055d66ab6c4cb3354663b815", "withdrawn": "", "abstract": "Generative AI platforms provide opportunities for instructors to design customized tools for specific teaching and learning purposes without requiring extensive technical expertise. In this talk, I will share my experience designing and implementing custom AI tools using Gemini Gems and ChatGPT Custom GPTs in undergraduate mathematics courses. These tools support guided learning, practice, and self-assessment; connect mathematical concepts with students’ fields of study; and assist instructors in creating accessible, discipline-specific concept checks. Examples from calculus and differential equations will illustrate how these tools can be incorporated into course learning experiences.", "id": "Paper/66338", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66338"}, {"title": " Some Recent Progress on Weak-Type Inequalities for the Bergman projection ", "webprogram_exclude": "0", "session_ids": ["Session/17887"], "source_sha256": "9ee4d88559274974126051a4dc13bd0af1966e0782a7655c341399c58e948671", "withdrawn": "", "abstract": "In this talk, we will highlight some recent advances in weak-type inequalities for the Bergman projection made in two separate collaborations. First, we discuss quantitative improvements for weak-type $(1,1)$ and $(p,p)$ estimates obtained jointly with Chen, Nieraeth, and Stockdale. These improved estimates hold true on the upper-half plane, the unit ball, and more generally on smoothly bounded, pseudoconvex domains where the Bergman kernel can be estimated effectively. Second, we present recent theorems obtained in collaboration with Green, Stockdale, and Sweeting concerning weak-type $(1,1)$ bounds for the Bergman projection on more general planar domains with substantially less boundary regularity. Such results rely explicitly on a conformal mapping to the unit disk. We will also explain some function-theoretic consequences of this work and time permitting pose some open questions in the same spirit in several complex variables. Both of these projects are connected via the use of common techniques in modern dyadic harmonic analysis.", "id": "Paper/66340", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66340"}, {"title": " From Convex Geometries to Descents and Peaks ", "webprogram_exclude": "0", "session_ids": ["Session/18134"], "source_sha256": "015aa8d0ed45546f42a5f9d716de07e2094590d7387d3f80ef299f67236f7eca", "withdrawn": "", "abstract": "Convex geometries are finite closure systems that generalize partial orders through their lower sets. In this talk, we study convex geometries from the perspective of Hopf monoids and investigate geometric interpretations of the associated combinatorial invariants in the braid arrangement. The order complex associated with a convex geometry determines a subcomplex of the Coxeter complex, and its maximal convex cones correspond to partial orders. We present a characterization of supersolvable convex geometries in terms of this structure: a convex geometry is supersolvable if and only if its maximal convex cones have a common chamber. We then apply this characterization to the associated $ab$- and $cd$-indices in the Hopf monoid framework. We show that, in the supersolvable case, their coefficients admit descriptions in terms of descent and peak statistics of chambers in the braid arrangement.", "id": "Paper/66341", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66341"}, {"title": " Polynomial bounds on torsion points of elliptic curves ", "webprogram_exclude": "0", "session_ids": ["Session/18076"], "source_sha256": "23ade3920ba7e1590f75d18691842a1ca74135c55cc617fd130ee582b1fbe181", "withdrawn": "", "abstract": "An elliptic curve is a curve in projective space whose points can be given the structure of an abelian group. Much of the current research on elliptic curves concerns so-called ``uniformity problems,\" which seek to control arithmetic properties of all elliptic curves in an infinite family. In this talk, I will highlight uniformity problems for torsion points, which are points of finite order under the associated group law. One important example is the problem of finding bounds on the order of a torsion point that are polynomial in the degree of its field of definition. For the special class of elliptic curves with $j$-invariant in $\\mathbb{Q}$, polynomial bounds were first established by Clark and Pollack in 2018. I will discuss recent improvements to these bounds that are essentially optimal, refining prior joint work with Genao.", "id": "Paper/66342", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66342"}, {"title": " Cyclotomic Schur–Weyl duality in orthogonal and sympletic types ", "webprogram_exclude": "0", "session_ids": ["Session/17998"], "source_sha256": "2171f0ae007854f933304236888971bf03fd3a221893c02e045c19e588bbb1d5", "withdrawn": "", "abstract": "Schur--Weyl dualities have played a fundamental role in the study of representations of Lie algebras.  In this talk, we look at a Schur--Weyl duality for the classical cyclotomic Lie algebras of orthogonal and symplectic types.", "id": "Paper/66345", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66345"}, {"title": " Voevodsky’s slice conjectures ", "webprogram_exclude": "0", "session_ids": ["Session/17701"], "source_sha256": "bfed2f5d33cbc378e2f38780188385345d1277b0fef9ee3dc406ffec274bd912", "withdrawn": "", "abstract": "Empirical evidence suggests that there is an interesting class of motivic spectra whose effective motivic slices are indexed by the Adams-Novikov $E_2$-page of their Betti realization. This was originally conjectured by Voevodsky. The class of such spectra contains for example the sphere spectrum, the algebraic cobordism spectrum and the very effective cover of Hermitian $K$-theory. In this talk, we will show that there are more spectra satisfying this property in the $\\mathbb{C}$-motivic, $2$-complete setting. For example, the $\\mathbb{C}$-motivic modular forms spectrum $mmf$. Our approach to this problem will also recompute the slices of the aforementioned spectra.\n\nThe results rely on the filtered spectrum model for $\\mathbb{C}$-motivic (stable, cellular, $2$-complete) homotopy theory due to Gheorghe-Isaksen-Krause-Ricka. We construct filtered spectrum models for the effective filtration and use these to compute the effective slices.", "id": "Paper/66347", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66347"}, {"title": " Weak and strong uniform computable categoricity ", "webprogram_exclude": "0", "session_ids": ["Session/17922"], "source_sha256": "780def1f55bbcd62b282545a885a432d26192d6a0709a386e5e983d0b2996875", "withdrawn": "", "abstract": "A computable structure $\\mathcal{A}$ is \\emph{uniformly computably categorical} if isomorphisms between arbitrary copies of $\\mathcal{A}$ can be computed uniformly in the atomic diagrams of those copies. On the other hand, $\\mathcal{A}$ is \\emph{weakly} uniformly computably categorical if isomorphisms can be computed uniformly in the \\emph{indices} of copies. We will compare the natural relativizations of these two notions with a special focus on computable groups. While uniform computable categoricity is a strictly stronger property than weak uniform computable categoricity, their relativizations have a much more complicated relationship and measure fundamentally different aspects of the complexity of structures. We will present some new results about what weak uniform categoricity spectra exist, and about the surprisingly complex weak uniform categoricity of natural structures such as the additive group of integers.", "id": "Paper/66348", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66348"}, {"title": " BDDC Algorithms for Parabolic Problems ", "webprogram_exclude": "0", "session_ids": ["Session/18367"], "source_sha256": "4f5c0c17d07ade75d245c6d9e8c283453f8f91b9f208dce09a51923724a758a7", "withdrawn": "", "abstract": "To obtain numerical solutions to a parabolic partial differential equation (PDE), we discretize the problem in both space and time, resulting in a sequence of linear systems which are typically solved sequentially at different time steps. Parallel-in-time (PinT) algorithms provide an alternative approach by allowing these systems to be solved in parallel. However, the resulting linear systems are generally nonsymmetric but positive definite, and the number of GMRES iterations required to achieve a prescribed accuracy can vary significantly across different time steps.\n\nIn this talk, we present an application of balancing domain decomposition by constraints (BDDC) methods to the linear systems arising from PinT algorithms. Our analysis shows that, provided the subdomain size is sufficiently small, the number of BDDC-preconditioned GMRES iterations depends only weakly on the subdomain problem size and is independent of other parameters, including the number of subdomains, the time-step size, and the coefficients generated by the PinT algorithm. We confirm our theoretical results with numerical experiments.", "id": "Paper/66349", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66349"}, {"title": " <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.332ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 573.5 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\beta</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-3B2\" d=\"M29 -194Q23 -188 23 -186Q23 -183 102 134T186 465Q208 533 243 584T309 658Q365 705 429 705H431Q493 705 533 667T573 570Q573 465 469 396L482 383Q533 332 533 252Q533 139 448 65T257 -10Q227 -10 203 -2T165 17T143 40T131 59T126 65L62 -188Q60 -194 42 -194H29ZM353 431Q392 431 427 419L432 422Q436 426 439 429T449 439T461 453T472 471T484 495T493 524T501 560Q503 569 503 593Q503 611 502 616Q487 667 426 667Q384 667 347 643T286 582T247 514T224 455Q219 439 186 308T152 168Q151 163 151 147Q151 99 173 68Q204 26 260 26Q302 26 349 51T425 137Q441 171 449 214T457 279Q457 337 422 372Q380 358 347 358H337Q258 358 258 389Q258 396 261 403Q275 431 353 431Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-3B2\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Uniform Convexity and Divisible Domains ", "webprogram_exclude": "0", "session_ids": ["Session/18362"], "source_sha256": "2d4cbb041cff68cc54805b5ae0513fe7ea40b1067171284bd6dded4924764ad7", "withdrawn": "", "abstract": "Divisible convex domains in real projective space have long been objects of interest due to their rich connections to multiple areas of geometry. When a divisible convex domain is an ellipsoid, one recovers the Klein model of hyperbolic space. More generally, strictly convex divisible domains exhibit some nonpositive curvature properties. Yet only the ellipsoid, equipped with its Hilbert metric, is CAT(0). The notion of p-uniform convexity from the theory of Banach spaces has been proposed by Shin-ichi Ohta as a generalization of the Alexandrov-Toponogov comparison theorems to the setting of Finsler manifolds. In this talk, I will give an overview of strictly convex divisible domains and discuss how their boundary regularity implies that their natural Finsler metric is $\\beta$-uniformly convex. I will then discuss how this result led to a local, scale-dependent $\\beta$-uniform convexity result for the associated Hilbert metric, obtained with assistance from ChatGPT 5.5.", "id": "Paper/66350", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66350"}, {"title": " Cohomology of symplectic groups via Steinberg modules ", "webprogram_exclude": "0", "session_ids": ["Session/18297"], "source_sha256": "1bb8cf92e81ddf24755be4783a917dd3cd63a089e8439efbc0a240dc0767b6e3", "withdrawn": "", "abstract": "I will describe how studying the algebraic structure of certain representations of the symplectic group, namely symplectic Steinberg modules, uncovers information on its group cohomology. In particular, I will discuss how one can use these Steinberg modules to get bounds on the Betti numbers of symplectic groups and their principal congruence subgroups. This talk will feature work-in-progress with Jeremy Miller, Peter Patzt, and Sam Payne.", "id": "Paper/66365", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66365"}, {"title": " Teaching to Learn: A First Experience Teaching Discrete-Time Mathematical Modeling ", "webprogram_exclude": "0", "session_ids": ["Session/18271"], "source_sha256": "99e0c22eac268a2f0a56c9e2f3fe1b7d9d96e65ea9b8b7181762d3de718fad14", "withdrawn": "", "abstract": "Teaching discrete-time mathematical modeling for the first time presents both an instructional challenge and an opportunity to rethink how students encounter mathematics. Rather than beginning with mathematical techniques and introducing applications afterward, a modeling-first approach begins with meaningful problems and uses them to motivate the development of mathematical ideas. In this approach, students learn to identify quantities, make assumptions, define variables, construct relationships, develop recurrence equations, analyze model behavior, and interpret results in the context of the original problem.\nThis presentation reflects on my first experience teaching discrete-time mathematics through a modeling-first perspective. I discuss how classroom activities were organized around an iterative modeling process: understanding a problem, formulating a model, exploring it computationally and mathematically, evaluating its assumptions. Examples involving population change, finance, resource management, and other dynamic systems illustrate how relatively simple difference equations can lead students to important mathematical ideas such as equilibrium, stability, long-term behavior, and parameter dependence. Finally, I present some of the projects completed by my math modeling students.", "id": "Paper/66371", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66371"}, {"title": " New topological restrictions for spaces with nonnegative Ricci curvature ", "webprogram_exclude": "0", "session_ids": ["Session/18284"], "source_sha256": "65555bfc7370f4c7c73529ecc1bc04d45e319ad30e625ed1560bb137640350fa", "withdrawn": "", "abstract": "The topology of complete noncompact Riemannian manifolds with nonnegative Ricci curvature has been studied extensively since the earliest developments of Geometric Analysis. In dimension $3$, a complete topological classification was only recently achieved by Gang Liu, with a strategy based on minimal surfaces methods. They proved that a $3$-dimensional Riemannian manifold with nonnegative Ricci curvature either is homeomorphic to $\\mathbb R^3$ or the universal cover splits a line isometrically. In this talk, I present an alternative proof of Liu’s classification, which also works for nonsmooth $\\mathrm{RCD}(0,3)$ spaces. This generalisation of Liu’s theorem yields, as a consequence, the full classification of non-collapsed $\\mathrm{RCD}(0,3)$ spaces without boundary.  Our strategy relies on two main building blocks of independent interest, which provide results that are new also in the smooth setting. In particular, we prove that, given a complete $n$-dimensional Riemannian manifold $(M,\\mathrm g)$ with nonnegative Ricci curvature and first Betti number $b_1(M) \\geq n-2$, the universal cover splits $\\mathbb R^{n-2}$ isometrically. Moreover, we show that every complete oriented $n$-dimensional Riemannian manifold with nonnegative Ricci curvature has vanishing simplicial volume.", "id": "Paper/66377", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66377"}, {"title": " A Space-Time Polynomial Particular Solution Method on Sequential Time Slabs for Variable-Coefficient Parabolic and Hyperbolic PDEs ", "webprogram_exclude": "0", "session_ids": ["Session/17823"], "source_sha256": "5456f34a2b41c4ef90cfeb1c239b6bd7f4a45e15148e2c209df0bde49ff1cfc6", "withdrawn": "", "abstract": "This work presents a sequential time-slab space-time polynomial particular solution method for solving variable-coefficient parabolic and hyperbolic partial differential equations. The method decomposes the space-time domain into temporal slabs, where a space-time polynomial approximation is constructed independently within each slab and the terminal solution is transferred as the initial condition for the next. The proposed meshfree framework accommodates smooth, singular,and space-time dependent coefficients while avoiding conventional time-stepping. Numerical experiments demonstrate high accuracy and stability over long time intervals for a broad class of variable-coefficient problems.", "id": "Paper/66382", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66382"}, {"title": " Polynomial Link Invariants via Decategorification of Subquandle Quiver Filtrations ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "600eb026e4f822cc167eb1e24523170d775aa4bd8211f23f6cbc4db754f282b7", "withdrawn": "", "abstract": "In this paper, we introduce the notion of subquandle filtrations for finite quandles as a foundation to construct algebraic and combinatorial link invariants. A nested sequence of subquandles naturally induces a filtration of the associated quandle coloring quiver by subquivers. By decategorifying these subquivers, we define two new polynomial-valued invariants of links: the disrespectful polynomial and the graded disrespectful polynomial, which measure how a chosen set of quandle endomorphisms respects and disrespects subquandle structure. Finally, we illustrate the distinguishing power of these new tools by comparing them to both classical quandle counting invariants and the quiver in-degree polynomial.", "id": "Paper/66383", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66383"}, {"title": " Lower bounds on face numbers ", "webprogram_exclude": "0", "session_ids": ["Session/18352"], "source_sha256": "7b4c334bccd07a6d027c0aec228622ccc47740625f03f4943ad8a06d32ff9281", "withdrawn": "", "abstract": "In this talk, we discuss several approaches to studying the face numbers of simplicial complexes, with a particular focus on lower bounds. These approaches include classical rigidity theory, Stanley–Reisner rings, and higher-dimensional stress spaces. We also describe a number of classical and recent results on face numbers obtained using these tools.", "id": "Paper/66389", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66389"}, {"title": " Beyond the Poll: Performance Metrics and Predictive Rankings in NCAA Men’s Volleyball ", "webprogram_exclude": "0", "session_ids": ["Session/17756"], "source_sha256": "da5fc1c30a6fe56d9f6550baddaffb31228712255a6ae070ef9bfd7b014d5ed7", "withdrawn": "", "abstract": "This study investigates the presence and extent of home court advantage in NCAA National Collegiate Men’s Volleyball by conducting a comprehensive statistical analysis across 18 game-related performance metrics. Using data from the 2024 and 2025 seasons, we compare home and away game statistics to identify significant differences that may indicate an advantage when playing on home courts. Results reveal statistical significance in several key metrics favoring home teams, suggesting that factors like a familiar environment may enhance performance. Predictive analytics in NCAA National Collegiate Men’s Volleyball are further explored using the Colley ranking method and a focus on incorporating home-court performance into the model design. We extend the Colley model by applying custom weightings to game outcomes based on location. Using the optimal combination of home, away, and neutral weights that minimize error, we compare predicted rankings to actual AVCA Coaches Polls. This work highlights how statistical analysis and a modified Colley algorithm can be combined to generate data-informed assessments of competitive performance in NCAA National Collegiate Men’s Volleyball.", "id": "Paper/66390", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66390"}, {"title": " Fixed Points in Certain Restricted Integer Partitions ", "webprogram_exclude": "0", "session_ids": ["Session/17968"], "source_sha256": "a4885279d8f6dac7f71505b297d6a2a3cd80ae0381078e96ff5d90eeeac32485", "withdrawn": "", "abstract": "In 2022, Blecher and Knopfmacher applied the notion of fixed points to integer partitions and conjectured that, for sufficiently large $n$, there are more partitions of $n$ without a fixed point than with a fixed point.  Soon after, Hopkins and Sellers confirmed the above conjecture by connecting fixed points to other partition statistics such as Dyson's crank.  \n\nHere we initiate the study of fixed points of restricted partitions, considering distinct, odd, simultaneously distinct and odd, and self-conjugate partitions.  We establish generating functions for the counts of partitions with and without fixed points for these four types of partitions.  In all four cases, we believe that the analogues of Blecher and Knopfmacher's conjectured inequality still hold; we will discuss these results at the end of the talk as time permits.  \n\nThis is joint work with Aritram Dhar (Chern Institute of Mathematics, Nankai University, China) and Brian Hopkins (Saint Peter's University).", "id": "Paper/66391", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66391"}, {"title": " Data-Driven Analysis and Modeling of Erosion Networks ", "webprogram_exclude": "0", "session_ids": ["Session/18222"], "source_sha256": "38da667b1ab1d7cb3b091259b91659b27667b32382368f59f753a4894a009599", "withdrawn": "", "abstract": "Channel formation and branching is widely seen in physical systems where movement of fluid though a porous structure causes the erosion of the medium. We introduce a simple model to capture this feedback mechanism in a multiphase model of flow through a frangible porous medium with dynamic permeability. We explore the model through simulations and examine how the channel morphology changes with different parameters. In addition, given a channel network, we develop a data-driven approach to predict the flow characteristics that led to the network formation.", "id": "Paper/66392", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66392"}, {"title": " Bijections with Self-Pseudo-Conjugate Partitions ", "webprogram_exclude": "0", "session_ids": ["Session/17968"], "source_sha256": "2c4e5b435956bd7284fb9015bed0c49d1ea7b6bac588046e2eca2b4fc6311be1", "withdrawn": "", "abstract": "Berkovich and Garvan developed the `pseudo-conjugation' map on partitions which shows the symmetry of the important crank statistic.  Using generating functions, they established the surprising result that the number of self-pseudo-conjugate partitions of $n$ (those fixed under their map) equals the number of self-conjugate partitions of $n$ (those unchanged by reversing the roles of rows and columns in the Ferrers diagram).  We give a bijective proof of this equality.  Also, building on an involution of Huh and Kim, we give a combinatorial proof of the following identity: Among the partitions of $n$, the number of self-conjugate partitions equals the number of even-length crank 0 partitions minus the number of odd-length crank 0 partitions.", "id": "Paper/66393", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66393"}, {"title": " Energy-positive soaring using transient turbulent fluctuations ", "webprogram_exclude": "0", "session_ids": ["Session/18357"], "source_sha256": "2ab49d5e122a39e25cea5b06a2dc9b929d68172222595928336cec613c7a3fed", "withdrawn": "", "abstract": "Soaring birds gain energy from stable ascending currents or shear. However, it remains unclear whether energy loss due to drag can be overcome by extracting work from transient turbulent fluctuations. We designed numerical simulations of gliders navigating in a kinematic model that captures the second-order spatio-temporal correlations of atmospheric turbulence. Energy extraction is enabled by an adaptive algorithm based on Monte Carlo tree search that dynamically filters acquired information about the flow to plan future paths. We show that net energy gain is feasible with lift-to-drag ratios and spatio-temporal correlation scales experienced by soaring birds. Glider paths reflect patterns of foraging, where exploration of the flow is interspersed with bouts of energy extraction through localized spirals.", "id": "Paper/66394", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66394"}, {"title": " K-regularity for quotient singularities ", "webprogram_exclude": "0", "session_ids": ["Session/17996"], "source_sha256": "50f1d8ae1228446afcd9bcb4cd303396c6bbd38a12bb9a34ef11ac613aaa2cc0", "withdrawn": "", "abstract": "We study the homotopy invariance of the algebraic K-groups for varieties with finite quotient singularities, and provide a smoothness criterion for such varieties. This is based on joint work with Matthew Satriano.", "id": "Paper/66396", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66396"}, {"title": " Ricci flow on homogeneous spaces with equivalent isotropy summands ", "webprogram_exclude": "0", "session_ids": ["Session/18266"], "source_sha256": "f47d02739c9c4fae9dd77927713e8f8f342c478fea549291fa0c49ea98526370", "withdrawn": "", "abstract": "Ricci flow is generally governed by a nonlinear PDE whose dynamics are notoriously difficult to study. \nHowever, if we restrict the flow to invariant metrics on a homogeneous space, then the PDE reduces to a system of ODEs, making it possible to analyze the long-time behavior.\n\nIn this talk, I will focus on compact, simply connected homogeneous spaces whose isotropy representation decomposes into two equivalent irreducible subrepresentations.\nI will illustrate that the normalized Ricci flow system can be completely visualized through its phase portrait, allowing us to classify the stability of Einstein metrics and describe the convergence of generic metrics.\nFurthermore, I will show that every invariant metric evolves to one with positive Ricci curvature and that the positivity of Ricci curvature is preserved under the flow.\nThis is joint work with E. Cochran, A. Mingajev, and N. Valiyakath.", "id": "Paper/66397", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66397"}, {"title": " Computads with invertible generators for weak <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.446ex\" height=\"1.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -576.1 622.5 721.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\omega</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-3C9\" d=\"M495 384Q495 406 514 424T555 443Q574 443 589 425T604 364Q604 334 592 278T555 155T483 38T377 -11Q297 -11 267 66Q266 68 260 61Q201 -11 125 -11Q15 -11 15 139Q15 230 56 325T123 434Q135 441 147 436Q160 429 160 418Q160 406 140 379T94 306T62 208Q61 202 61 187Q61 124 85 100T143 76Q201 76 245 129L253 137V156Q258 297 317 297Q348 297 348 261Q348 243 338 213T318 158L308 135Q309 133 310 129T318 115T334 97T358 83T393 76Q456 76 501 148T546 274Q546 305 533 325T508 357T495 384Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-3C9\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-categories ", "webprogram_exclude": "0", "session_ids": ["Session/18000"], "source_sha256": "3b55c06e864719f7c6843a578b5dedec089c223edfb168bc4744221fc23e5fa1", "withdrawn": "", "abstract": "In its original formulation by Grothendieck, the homotopy hypothesis posits an equivalence between homotopy types and \\(\\omega\\)-groupoids, an algebraic structure based on the geometry of globular sets. Modifying Grothendieck’s definition, Batanin and Leinster, and Maltsiniotis have independently given definitions of directed structures conjectured to model \\((\\infty,\\infty)\\)-categories with the appropriate notion of equivalence. In this talk, we will give an inductive description of weak \\(\\omega\\)-categories and computads with invertible generators as generating data for them. This is inspired by the type-theoretic approach to weak \\(\\omega\\)-categories of Finster and Mimram. We will then sketch recent work towards understanding the homotopy theory of \\(\\omega\\)-categories.", "id": "Paper/66401", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66401"}, {"title": " Generalizing a Pair of Diophantine Equations ", "webprogram_exclude": "0", "session_ids": ["Session/17106"], "source_sha256": "c119d3313166f3e92f576933036f3cb232954632d4951cccff8d75c85e314eec", "withdrawn": "", "abstract": "For coprime integers $a$ and $b$, it is known that exactly one of the two Diophantine equations\n$$\nax+by\\ =\\ \\frac{(a-1)(b-1)}{2}\n\\qquad\\text{and}\\qquad\n1+ax+by\\ =\\ \\frac{(a-1)(b-1)}{2}\n$$\nadmits a nonnegative integer solution, and that this solution is unique. We first generalize this result by replacing the right-hand side with an arbitrary integer $m$ and its complement $ab-a-b-m$. This framework enables us to study the existence and uniqueness of nonnegative integer solutions to\n$$\nax+by\\ =\\ \\frac{(a-1)(b-1)}{k}\n\\qquad\\text{and}\\qquad\n1+ax+by\\ =\\ \\frac{(a-1)(b-1)}{k},\n$$\nwhere $k$ is a fixed positive integer. We then obtain explicit results when $a$ and $b$ are consecutive Fibonacci numbers. Finally, we examine the original pair of equations in several particular settings, including when $b\\equiv \\pm1\\mod a$, when $b$ is replaced by a higher power, and when the parameters are squared.", "id": "Paper/66403", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66403"}, {"title": " Extremal constant-sign and nodal solutions of fractional logistic <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.259ex\" height=\"2.009ex\" style=\"vertical-align: -0.671ex; margin-left: -0.089ex;\" viewBox=\"-38.5 -576.1 542 865.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">p</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-70\" d=\"M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-70\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Laplacian equations in <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"9.391ex\" height=\"3.176ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -1006.6 4043.2 1367.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">D^{s,p}(\\mathbb {R}^N)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-44\" d=\"M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-73\" d=\"M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 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transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-73\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-2C\" x=\"469\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-70\" x=\"748\" y=\"0\"></use>\n</g>\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"1813\" y=\"0\"></use>\n<g transform=\"translate(2202,0)\">\n <use xlink:href=\"#E1-MJAMS-52\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-4E\" x=\"1021\" y=\"581\"></use>\n</g>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"3653\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18103"], "source_sha256": "b59381dbd8d7a126bec4af32384275724e5af234a0fd7c4d68c365cc48f0a268", "withdrawn": "", "abstract": "We discuss the existence of extremal constant-sign and nodal solutions of fractional logistic $p$-Laplacian equations in all $\\mathbb{R}^N$ of the form\n%\n$$\nu\\in D^{s,p}(\\mathbb{R}^N): (-\\Delta_p)^s u=\\lambda a(x)|u|^{p-2}u-b(x)g(u) \\quad\\mbox{in }\\mathbb{R}^N,\n$$\n%\nwhere $D^{s,p}(\\mathbb{R}^N)$ is the homogeneous fractional Sobolev space, and $(-\\Delta_p)^s$ is the fractional $p$-Laplacian operator. Unlike similar questions in bounded domains, the treatment of the problem in all $\\mathbb{R}^N$ requires new tools such as some compact embeddings of the relevant function spaces as well as decay estimates and a Hopf-type lemma for solutions of fractional  $p$-Laplacian equations in $\\mathbb{R}^N$.", "id": "Paper/66404", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66404"}, {"title": " Llama-Polya: Instruction Tuning for Large Language Model based on Polya’s Problem-solving ", "webprogram_exclude": "0", "session_ids": ["Session/18346"], "source_sha256": "0860a3e3d5bb5b13dc5d51b58421bb45dc965874d46253249e5792628de9a7fb", "withdrawn": "", "abstract": "This paper introduces Llama-Polya, an instruction-tuned large language model that integrates Polya's four-step problem-solving framework into its dialogue structure to support mathematical reasoning. Mathematical problem-solving is central to students' success, yet many learners struggle to plan, justify, and verify their solutions. Although large language models (LLMs) show promise as intelligent tutors, they often lack structured pedagogical alignment grounded in established learning theories. To address this gap, we operationalize Polya's framework within an instruction-tuned LLM to promote metacognitive engagement and compare pedagogy-aligned fine-tuning with domain-only and general-purpose instruction tuning. Built on Llama-3.1-8B, Llama-Polya was fine-tuned on synthetic math problem-solving data derived from GSM8K, structured according to Polya's four stages. We evaluated multiple variants—general-purpose instruct, math-domain metamath, pedagogy-aligned polya-v2, and sequential metamath+polya-v2—using quantitative accuracy metrics and qualitative pedagogical assessments. Models tuned with Polya's framework and domain-specific data produced more balanced reasoning-stage distributions and fewer premature answers. Expert evaluators also observed improved pedagogical coherence and metacognitive prompting, although limitations in personalization and mathematical rigor remained. These findings suggest that pedagogy-grounded instruction tuning can enhance educational alignment and reasoning transparency in LLM tutors. Llama-Polya was the starting point of our research line on pedagogical alignment, which has since extended from supervised fine-tuning to aligning reasoning traces with pedagogical principles (Pedagogy-R1), rewarding pedagogical thinking via reinforcement learning (PedagogicalRL-Thinking), and evaluating tutor agents over long horizons with simulated learners (EduClaw-Bench). We discuss how these directions build on the alignment explored here.", "id": "Paper/66405", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66405"}, {"title": " An Apollonian Sorting Hat ", "webprogram_exclude": "0", "session_ids": ["Session/18235"], "source_sha256": "69f209d8cadaf3748970d8e22e628f2b3ca4f83d851588b5974abba9c946823e", "withdrawn": "", "abstract": "The {\\em Sorting Hat} in the Harry Potter stories is described as ``a pointed wizard's hat\\ldots patched and frayed\\ldots a thinking hat,\" which sorts students into four distinct houses. We use an algorithm of Apollonius which sorts circles into families with a common index $n$. That is, given distinct planar  points $A$ and $B$ and a positive number $n>1$, the locus of all points $P$ such that $|AP|=n|BP|$ is the circle of Apollonius with index $n$; we call $A$ and $B$, respectively, the outer and inner Apollonian foci of the circle. To create a wizard's hat, we'll choose an index $n$ and stack all the Apollonian circles within the hyperbolic Poincar\\'e unit disk with positive inner Apollonian focus $B$ as $B$ ranges from from least to greatest (so that each stacked circle has artificial third component $B$).  Allowing each circle to be rotated slightly about the $z$-axis, we induce a little twist as the hat rises above its rim.  If $\\mathcal D$ is a circle with hyperbolic center $B$ and Euclidean radius $\\delta>0$, there is a circle $\\mathcal E$ with Euclidean center  $O$, Euclidean radius $\\epsilon>0$, and a hyperbolic translation mapping $\\mathcal E$ to $\\mathcal D$. As it turns out, these parameters are related by the equation $\\delta n B=1.$   We exploit this identity, and  ask for the most appropriate $n$ for which the stack of all circles of that index forms  the ideal wizard hat.", "id": "Paper/66410", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66410"}, {"title": " The Minimal Displacement Problem ", "webprogram_exclude": "0", "session_ids": ["Session/17782"], "source_sha256": "7d29bf69283020a4bfaf7030c17d8f97423fe5e6de0aec66776d4d983967422b", "withdrawn": "", "abstract": "Let $X$ be an infinite-dimensional Banach space. The minimal displacement problem for the closed unit ball $B_X$, posed by Kazimierz Goebel in 1973, asks for the exact values, or at least estimates, of the function\n\\[\n\\Psi_X(k) = \\sup \\Bigl\\{ d(T) \\mid T: B_X \\rightarrow B_X,\\ T \\text{ is } k\\text{-Lipschitz}\\Bigr\\}, \\quad k \\geq 1,\n\\]\nwhere $d(T) = \\inf_{x \\in B_X}\\|x - Tx\\|$ is the minimal displacement of $T$. It is known that $\\Psi_X(1) = 0$ and for every $k > 1$\n\\[\n0 < \\Psi_X(k) \\leq 1 - \\frac{1}{k}.\n\\]\nFor some spaces the above estimate is sharp, that is, for every $k \\geq 1$,\n\\[\n\\Psi_X(k) = 1 - \\frac{1}{k}.\n\\]\nSuch spaces are called extremal with respect to the minimal displacement problem.\n\nIn this talk, we present some recent results on the minimal displacement problem. In particular, we describe a broad class of extremal spaces that encompasses the currently known examples and substantially extends the known collection of extremal spaces. The talk is based on joint work with \\L{}ukasz Piasecki.", "id": "Paper/66411", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66411"}, {"title": " Analyzing the Effects of Alternative Assessment Practices in Mathematics Courses ", "webprogram_exclude": "0", "session_ids": ["Session/18440"], "source_sha256": "63d3da0282c3c9b275dbd83d57bf729ebf9799a54fafd132a8ca1bc5a537960d", "withdrawn": "", "abstract": "Students' beliefs about intelligence and learning can influence both academic performance and confidence. While a fixed mindset views ability as largely unchangeable, a growth mindset emphasizes the potential for improvement through effort and persistence. To support student learning and reduce test anxiety, many mathematics instructors are adopting alternative assessment approaches such as specifications grading and mastery- or standards-based grading. This presentation reports findings from a multi-institutional study examining the relationship between assessment practices, growth mindset, and test anxiety across a variety of mathematics courses. Using pre- and post-semester surveys, we investigate differences among student populations and explore how mindset and test anxiety change over the semester.", "id": "Paper/66412", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66412"}, {"title": " Higher Segal spaces and higher associativity ", "webprogram_exclude": "0", "session_ids": ["Session/17843"], "source_sha256": "79bf23a1fcfe6a31114c01e4b41aec3879b5e2c3f98bfba939b479d1330668da", "withdrawn": "", "abstract": "The theory of Segal spaces is a useful tool for describing structures that behave like categories, but for which objects and morphisms form spaces and composition is only defined up to homotopy.  More recently many mathematical structures have been shown to be 2-Segal spaces, which are somewhat weaker: composition need not exist or be unique, yet is still associative.  While there is a natural generalization to $d$-Segal spaces for higher $d$, their algebraic structure is more difficult to describe.  In this talk, we'll discuss how higher Segal spaces can be understood using the higher associativity conditions used to define homotopy associative spaces.", "id": "Paper/66414", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66414"}, {"title": " Large Time Behavior of Collisionless Plasmas ", "webprogram_exclude": "0", "session_ids": ["Session/19363"], "source_sha256": "3cafd1a29da29ff743eb48252fce9c80fe0c31ed99e4484136dd3a77533a2edf", "withdrawn": "", "abstract": "Collisionless plasmas arise in a variety of physical settings, ranging from magnetically confined plasmas for the generation of thermonuclear energy to space plasmas in planetary magnetospheres and stellar winds. The fundamental models that describe such phenomena are nonlinear systems of PDEs, in particular the Vlasov-Maxwell, Vlasov-Poisson, and Vlasov-Riesz systems. We will briefly review these foundational models of kinetic theory and describe recent results concerning the large-time asymptotic behavior of solutions to such systems, including modified scattering and improved decay properties arising from dispersion and charge cancellation.", "id": "Paper/66417", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66417"}, {"title": " Dynamically Regularized Lagrange Multiplier Method for the Incompressible Magnetohydrodynamic System ", "webprogram_exclude": "0", "session_ids": ["Session/18258"], "source_sha256": "5b1949b943e808019ea79f5ff59eab542d4d995a5b4cf63ca6eaff0acafe824c", "withdrawn": "", "abstract": "We analyze a first order in time, implicitly-explicit (IMEX) finite\nelement method (FEM) for the incompressible magnetohydrodynamics(MHD)\nequations based on the relatively new dynamically regularized Lagrange multiplier\n(DRLM) formulation. we discretize in space with the Scott--Vogelius element $(\\mathbb P_k, \\mathbb P_{k-1}^{\\rm disc})$, $k\\ge d$ to ensure the discrete velocity and magnetic field are pointwise divergence free. We prove the unconditional discrete energy stability of the scheme, the unique solvability via a decoupled solution strategy (four linear generalized Stokes problems plus a scalar quadratic equation for the multiplier $Q^{n+1}$), and derive optimal error estimates. Several Numerical examples will be showcased.", "id": "Paper/66418", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66418"}, {"title": " The sharp constant in the Mashreghi–Ransford inequality ", "webprogram_exclude": "0", "session_ids": ["Session/18277"], "source_sha256": "6cd9da1049ac8c1b8eac27fe240e09a2bf66068744e691728ea6c798d087b2b9", "withdrawn": "", "abstract": "Let $(a_n)_{n\\geq0}$ be a sequence of complex numbers, and define\n\\[\n b_n=\\sum_{k=0}^n \\binom{n}{k}a_k,\n \\qquad\n c_n=\\sum_{k=0}^n  \\binom{n}{k}(-1)^{n-k}a_k.\n\\]\nLet $\\beta>1$, put $\\alpha=\\sqrt{\\beta^2-1}$, and suppose that $b_n,c_n=O(\\beta^n)$. Mashreghi and Ransford proved that\n\\[\n  \\limsup_{n\\to\\infty}\\frac{|a_n|}{\\alpha^n} \\leq \\kappa \\left(\\limsup_{n\\to\\infty}\\frac{|b_n|}{\\beta^n}\\right)^{\\!1/2}\\! \\left(\\limsup_{n\\to\\infty}\\frac{|c_n|}{\\beta^n}\\right)^{\\!1/2}\n\\]\nwith a universal constant satisfying $2/\\sqrt{3} \\leq \\kappa\\leq2$.  We prove that the optimal constant is indeed $\\kappa=2/\\sqrt{3}$. The proof, which uses exponential generating functions, Phragm\\'en--Lindel\\\"of estimates, and Cauchy's formula, is presented and compared to the classical one of Mashreghi and Ransford.", "id": "Paper/66419", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66419"}, {"title": " A Structure-Preserving Newton Approach to Quadratic Optimal Transport ", "webprogram_exclude": "0", "session_ids": ["Session/18258"], "source_sha256": "54760803a893606cb8e38c7bfaf75b58ae7b1428f9a2aa82c9d5f0d90e739f3a", "withdrawn": "", "abstract": "We introduce and develop a novel structure-preserving approach for numerically solving the dynamic formulation of quadratic optimal transport. Thanks to the seminal work of Benamou and Brenier in providing a fluid dynamics interpretation to the classical Monge-Kantorovich problem of optimal transport, one can view the problem as a variational problem constrained to a conservation law. We recast the formulation as a convex optimization problem in a single variable by eliminating the density and derive the forward equation, adjoint equation, and gradients. We propose solving a sequence of projected Newton subproblems that enforce the terminal density and positivity constraints. We compare our algorithm with the splitting algorithm proposed by Benamou and Brenier. Our numerical experiments demonstrate that our Newton method requires fewer iterations to achieve the same qualitative accuracy while also maintaining key physical properties including mass conservation and positivity.", "id": "Paper/66420", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66420"}, {"title": " From Instructor Development to a Shared Student Experience: Coordinating a Multi-Section Course ", "webprogram_exclude": "0", "session_ids": ["Session/19349"], "source_sha256": "979fbf32cfed512000e6e238f4311772a052429555bc8ed065c30bc6e366ef85", "withdrawn": "", "abstract": "Coordinating a large multi-section course usually means coordinating its infrastructure: common assessments, grading policies, schedules, and materials. Shared infrastructure, however, does not necessarily produce a shared in-class experience for students. Our multivariable calculus course enrolls roughly 400 students across 15 sections, many taught by instructors new to the course or new to teaching. Our goal is not only consistency in course materials and expectations, but also coherence in the mathematical story, in the ideas and connections students encounter and in the teaching practices that support their learning. Instructors, like students, do not all think about the same ideas or teach them in the same way, and that variety is a resource rather than a problem to be managed. The goal is not for every classroom to look exactly the same, but for instructors with different styles to work towards a shared vision of what we want students to learn and experience. \nIn this talk, I describe an approach to coordination centered on weekly teaching-team meetings and supported by classroom observation, feedback, and reflection. I will share examples of how we use these meetings and our lesson plans to develop a shared understanding of the mathematical story of the course: why ideas are introduced when they are, what each lesson is building towards, which problems carry its central ideas, and what mathematical understanding we want students to develop through them. I will also discuss how we create space to practice and reflect on teaching, from facilitating group work and responding to student thinking to grading and designing assessments. \nIn this way, working towards coherence in the student experience makes course coordination a space for ongoing professional development as well as course design. The approach offers a framework that instructors and course coordinators can adapt to other large, multi-section courses.", "id": "Paper/66421", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66421"}, {"title": " Local rigidity of some actions of rank-one Lie groups ", "webprogram_exclude": "0", "session_ids": ["Session/18361"], "source_sha256": "d154004793b5b58d07fc0fe3312d83c6836e49590ec82edf77949260d0d9a1e7", "withdrawn": "", "abstract": "An action is \\emph{locally rigid} if it is conjugate to every nearby action. Many actions of higher-rank Lie groups are known to be locally rigid, but actions of rank-one Lie groups have been less studied. I prove local rigidity of a certain family of actions of rank-one Lie groups (namely, standard actions of Borel subgroups of $\\mathrm{PU}(n, 1)$, the isometry group of complex hyperbolic space). This extends Masayuki Asaoka's earlier work for $\\mathrm{SO}^+ (n, 1)$. My main technical result is a periodic Lyapunov spectrum rigidity theorem for ``half-complex-hyperbolic'' Anosov flows, which extends part of Clark Butler's thesis.", "id": "Paper/66422", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66422"}, {"title": " Kuratowski Subgraphs and Crossing Number ", "webprogram_exclude": "0", "session_ids": ["Session/18011"], "source_sha256": "74d5810c146a4bc6a35c25f9724ca40509620684e25ae3845a04e6a191e7e9b8", "withdrawn": "", "abstract": "Graphs may be drawn into the plane by assigning points to vertices and curves to edges, such that the endpoints of an edge-curve are the vertex points for the edge's endvertices. Planar graphs may be drawn such that these edge curves do not intersect each other, but this is not always possible. We call the crossing number of a graph the least number of such intersections needed to draw the graph in the plane. A natural extremal notion is that of the $k$-crossing-critical graphs, which are graphs that have crossing number at least k but all proper subgraphs of which have crossing number less than $k$. Kuratowski's Theorem shows that there are effectively only two $1$-crossing critical graphs, which we call Kuratowski Subgraphs. Unlike the $k=1$ case, Siran showed that there are infintiely many $k$-crossing critical graphs for $k\\geq 2$. This leads us to examining the relationships between a graph's crossing number and the structurs of its Kuratowski Subgraphs. We will discuss some unintuitive examples where edges can belong to every Kuratowski Subgraph of a graph, but not impact its crossing number, and conversely edges that have a large impact on the crossing number of a graph but belong to none of its Kuratowski Subgraphs. Finally, we will discuss a recent result which allows one to bound a graph's crossing number given information only about its Kuratowski Subgraphs. This is joint work with Éva Czabarka and Géza Tóth.", "id": "Paper/66423", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66423"}, {"title": " Structural Identifiability and Learning in Non-Gaussian Graphical Discrete Lyapunov Models ", "webprogram_exclude": "0", "session_ids": ["Session/18115"], "source_sha256": "8c79393ccfc3e23137b1041666cc6286f69f0374c66998bfca898a1bff8e1d23", "withdrawn": "", "abstract": "A vector autoregressive process driven by a Schur-stable matrix A admits a unique stationary distribution. For a graph G, we consider the stationary distributions of processes driven by Schur-stable matrices with the sparsity pattern determined by G. This set of stationary distributions is referred to as the discrete Lyapunov model associated with the graph G.\n\nRecent work of Recke, Lumpp, Kushnerchuk et al. represents these distributions by their cumulant tensors and this approach has proven fruitful in showing parameter identifiability in such models when G is known and the noise is non-Gaussian. The non-Gaussianity of the noise ensures that higher-order Lyapunov equations, which relate stationary cumulant tensors to noise cumulant tensors and A, provide nontrivial information.\n\nIn this talk, I will explore the problem of structural identifiability and learning for these graphical models under non-Gaussianity by leveraging the cumulant tensors of the stationary distributions.", "id": "Paper/66425", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66425"}, {"title": " Dimensions of Second-Order Graphical Model Mixtures ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "f204d708769aeba35818cbe638c46c8435f049a27fc432c73585525b2386e9be", "withdrawn": "", "abstract": "Graphs of discrete random variables can represent complex conditional dependence relations between the variables. The associated graphical model represents the set of probability distributions that satisfy the conditional dependence statements specified by the graph. Given a statistical model, we may also consider its $r$-mixture, the set of convex combinations of $r$ points in the model. Of particular interest is the dimension of a model and its $r$-mixture models. Algebraically, the Zariski closure of an $r$-mixture corresponds to a secant of toric varieties, and tools from algebraic geometry can help find lower bounds for the dimension. If we can find that the dimension is as high as it possibly can be, it is possible to locally identify the continuous parameters that define the model. In this presentation, we focus on 2-mixtures of graphical models. Previous work identified families of graphs whose 2-mixture models have the expected dimension, and families with a lower than expected dimension. Using modified techniques, we will classify the dimension of the 2-mixtures of all graphical models.", "id": "Paper/66426", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66426"}, {"title": " Singular problems with mixed Dirichlet-nonlinear boundary conditions on annular-type domains ", "webprogram_exclude": "0", "session_ids": ["Session/18103"], "source_sha256": "a4abae32fa2fedc542e246edd0603462f87ddee327b91d6e7b6e6c1422d3bcc6", "withdrawn": "", "abstract": "We consider a class of singular elliptic problems in an annular-type domain, subject to zero Dirichlet condition on the interior boundary and a nonlinear boundary condition on the exterior boundary. We establish the existence of positive solutions for both mildly and strongly singular cases when the boundary nonlinearity exhibits certain growth at infinity. To accomplish this, we first discuss  existence results for a more general class of problems with mixed Dirichlet–nonlinear boundary conditions, using the sub- and supersolution method.", "id": "Paper/66427", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66427"}, {"title": " Bifurcation Analysis in a Discrete-Time SIS model with Vaccination ", "webprogram_exclude": "0", "session_ids": ["Session/19359"], "source_sha256": "9831b995ecfb18f20ddc42ede1692650b89456dc6d22115b37ac12045dad9a14", "withdrawn": "", "abstract": "We develop a discrete-time SISV (susceptible-infectious-susceptible-vaccinated) epidemic model in which vaccination reduces, but does not eliminate, the risk of infection. We establish the stability of the disease-free equilibrium and apply a version of the fundamental bifurcation theorem to determine the conditions under which a branch of backward bifurcating endemic equilibria exists. Importantly, we find that both disease recovery and imperfect vaccination efficacy are necessary for a backward bifurcation to occur. We compare our findings to those of a continuous-time counterpart and examine how specific modeling assumptions influence endemic dynamics.", "id": "Paper/66428", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66428"}, {"title": " Polynomial bounds for eigenfunctions and eigenvalues on random hyperbolic surfaces ", "webprogram_exclude": "0", "session_ids": ["Session/17960"], "source_sha256": "f06ebf5c413c3fe31f09e7b276b646d483a9150d0c57e4071479baf57db85d6e", "withdrawn": "", "abstract": "We study random compact hyperbolic surfaces with genus $g \\rightarrow \\infty$. We show that, with high probability, the $L^\\infty$ norm of every Laplace eigenfunction on a random genus $g$ surface with bounded eigenvalue decays polynomially in $g$.   Using similar methods,  we also show that, with high probability, the distribution of eigenvalues of the Laplacian converges to the spectral measure of the hyperbolic plane with polynomially decaying error. Our proof relies on the Selberg pre-trace formula and a variant of the polynomial method.", "id": "Paper/66430", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66430"}, {"title": " Discrete Mixed Quantization for Cat Maps ", "webprogram_exclude": "0", "session_ids": ["Session/18326"], "source_sha256": "4ae124b09c9da47a43381ff5fe185d7dc9e0887bfeccbb6662730574c0250d33", "withdrawn": "", "abstract": "We develop a mixed quantization technique for graph vector bundles that combines semiclassical analysis and quantum cat maps. We prove a Kesten--McKay type eigenvalue density law and a quantum ergodicity result.", "id": "Paper/66438", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66438"}, {"title": " CANCELLED - Cyclic Cayley Tournaments Simultaneously Critical for the Clique and Dichromatic Numbers \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/16805"], "source_sha256": "39e49c6cd7d09efc2bf0b15b6afb223fafc870ce877f7539b754b23dfacfdadb", "withdrawn": "", "abstract": "For a tournament $T$, let $\\omega(T)$ denote the minimum clique number\namong all backedge graphs of $T$, and let $\\chi(T)$ denote its\ndichromatic number. We prove that, for every integer $k\\geq 3$, there\nexists a positive even integer $m_k$ such that, for every integer\n$N>1$ with\n\\(\n    N\\equiv 1 \\pmod{m_k},\n\\)\nthere is a regular, vertex-transitive cyclic Cayley tournament of order\n$N$ that is simultaneously $k$-$\\omega$-critical and\n$k$-$\\chi$-critical. In particular, this proves a conjecture of\nAboulker, Aubian, Charbit, and Lopes asserting the existence of\ninfinitely many pairwise nonisomorphic $k$-$\\omega$-critical\ntournaments for every $k\\geq 3$, and consequently gives a negative\nanswer to their bounded-certificate question under the hypothesis\n$\\omega(T)\\geq k$.\n\nWe also study substitutions into a cyclic triangle. We determine the\nclique number of such a substitution when each of its three blocks\nsatisfies $\\omega=\\chi$, and characterize exactly when the resulting\ntournament is $\\omega$-critical, provided that the blocks are\n$\\chi$-critical and satisfy $\\omega=\\chi$.", "id": "Paper/66439", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66439"}, {"title": " Permutation classes need not have proper growth rates ", "webprogram_exclude": "0", "session_ids": ["Session/17943"], "source_sha256": "8bf7846e65ee4127f1f4a10c3aea139a4f3b6953b043f4d5ad9b3890686d725f", "withdrawn": "", "abstract": "By the Marcus--Tardos Theorem (formerly the Stanley--Wilf Conjecture), every permutation class other than the class of all permutations has a finite upper growth rate, meaning that the $n$th root of the number of permutations of length~$n$ in the class has a finite limit superior. It has long been conjectured that this limit superior is in fact a limit. We disprove this by constructing a permutation class whose upper and lower growth rates differ. The construction uses generalized grid classes and the bipartite adjacency matrices of Haar graphs of finite $2$-groups in which three chosen generators satisfy no short relation. The corresponding hereditary property of ordered graphs also disproves an analogous 2006 conjecture of Balogh, Bollob\\'as, and Morris.", "id": "Paper/66449", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66449"}, {"title": " To <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"7.491ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 3225.2 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">(\\infty ,\\infty )</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-221E\" x=\"389\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2C\" x=\"1390\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-221E\" x=\"1835\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"2835\" y=\"0\"></use>\n</g>\n</svg> and Beyond! A Closer Look at Some Examples ", "webprogram_exclude": "0", "session_ids": ["Session/18209"], "source_sha256": "45e6b6d270b63694520b7326de0119e5f91d4d9ef9be0319e6b9184a7f7ce813", "withdrawn": "", "abstract": "Recently, several frameworks have emerged that provide ambient settings for higher categories extending beyond $(\\infty,n)$-categories for a fixed $n$. For finite $n$, $(\\infty,n)$-categories are characterized by the requirement that all $k$-morphisms for $k>n$ be invertible. Dropping this requirement leads to $(\\infty,\\infty)$-categories. Between these two extremes lie Postnikov-complete $(\\infty,\\infty)$-categories, which can be reconstructed from their finite truncations. In this talk, I will discuss specific examples of $(\\infty,\\infty)$-categories in the form of marked simplicial sets arising from certain strict $\\omega$-categories, and use them to illustrate some of the differences between these larger ambient theories of higher categories. The constructions discussed arise from joint work, in various combinations, with Loubaton, Hadzihasanovic, Ozornova, and Walde.", "id": "Paper/66459", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66459"}, {"title": " Translational Scissors Congruence K-theory Structures ", "webprogram_exclude": "0", "session_ids": ["Session/17701"], "source_sha256": "733ee39df97a5e623af321a74d426123617a2cd0e14fda59e08e9beacd5363a7", "withdrawn": "", "abstract": "The question of when are two polygons invariant under ``cutting and pasting\" has been around since ancient times, the subject of which we call scissors congruence. Hilbert’s Third Problem asks when two polyhedra P and Q in three-dimensional Euclidean space are scissors congruent. This question can be rewritten in terms of Zakharevich’s scissors congruence K-theory. In this talk, we will introduce scissors congruence, and scissors congruence K-theory. We will discuss structures and computations of translational scissors congruence K-theory of two-dimensional Euclidean space.", "id": "Paper/66462", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66462"}, {"title": " Transfer Systems and Composition-closed Premodel Structures on Finite Lattices ", "webprogram_exclude": "0", "session_ids": ["Session/17843"], "source_sha256": "4b8a39cb35dc72739f81f92424d60f4333c52425ac547ba704ef32a047ff84e2", "withdrawn": "", "abstract": "Given a finite lattice $L$, consider the set of transfer systems of $L$, $\\text{Tr}(L)$. There is an ordering on this set, $\\preceq$, that is a refinement of the natural ordering given by containment. Moreover, $(\\text{Tr}(L), \\preceq)$ forms a poset. If transfer systems $T_1$ and $T_2$ satisfy $T_1 \\preceq T_2$, then the pair $(T_1, T_2)$ provides a premodel structure on $L$, i.e. a structure where most notions of homotopy theory make sense. Balchin, MacBrough, and Ormsby study this and show that $(\\text{Tr}(L), \\preceq)$ is a lattice when $L$ is a total order.\n\nIn this talk we attempt a complete answer for when is $(\\text{Tr}(L), \\preceq)$ a lattice.", "id": "Paper/66463", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66463"}, {"title": " Duality of Orthogonal Polynomials with Rational Weights ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "310f9d2e83f465c1c825a8e39740aeb0d1ea6e8e18da772814d37d0863326861", "withdrawn": "", "abstract": "Given a rational function $w(z)$, we consider the space of polynomials with degree at most $n$ under the bilinear form \\[\\langle f,g\\rangle_w=\\int_\\gamma f(z)g(z)w(z)dz\\]\nwhere $\\gamma$ is a smooth curve encircling the zeros and poles of $w(z)$. A dual bilinear form is given by the replacement $w(z) \\mapsto \\frac{1}{w(z)}$. For each bilinear form, conditional on the non-vanishing of certain determinants, one can define two families of orthogonal polynomials $\\{P_n\\}$ and $\\{Q_n\\}$ respectively. Motivated by appearances of this duality in random tiling models, we prove two different formulas for $Q_n$. The first is an explicit description of the coefficients in terms of supersymmetric skew Schur functions (Schur functions in two sets of variables). In this formula, the duality can be thought of as a swap in these sets of variables. The second formula expresses a particular $Q_n(z)$ as the polynomial part (terms with positive powers) of the Laurent expansion of $P_n(z)w(z)$ at $z=\\infty$.", "id": "Paper/66464", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66464"}, {"title": " Time-Step Effects on Epidemic Dynamics and the Basic Reproduction Number ", "webprogram_exclude": "0", "session_ids": ["Session/17446"], "source_sha256": "755954adc72a8796a96abe4bfcaa8d207da9fcb2d3aa7ef87ac3f3c39ae2faae", "withdrawn": "", "abstract": "The choice of time step is an essential component of discrete epidemic modeling and can have a substantial impact on the resulting disease dynamics. To investigate this effect, we develop explicit and implicit discrete epidemic models and examine how their mathematical properties and predictions depend on the underlying time step. We characterize the basic reproduction numbers of the models using a next-generation matrix approach adapted to the discrete setting, providing a systematic way to study disease invasion under both formulations. We further investigate the dynamical behavior of the models through global and exponential stability analysis. In addition to the theoretical development, we perform parameter estimation and global sensitivity analysis based on Swine flu data. The resulting analysis illustrates how the time step enters both the mathematical structure and the epidemiological behavior of the models, providing further insight into the role of discrete-time formulation in epidemic modeling.", "id": "Paper/66467", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66467"}, {"title": " Reich-Wing Mathematics: Nazism, Political Neutrality, and the Destruction of German Scientific Dominance ", "webprogram_exclude": "0", "session_ids": ["Session/18554"], "source_sha256": "2877c986806e173ed8d7b82cbbbe2348b26b87af4846d0d416b8b034493b4d3c", "withdrawn": "", "abstract": "The year is 1933, and Hitler has just come to power. The country is Germany, the mathematical powerhouse of Europe, if not the world. Many of the greatest mathematicians of the age experienced the fall of the Weimar Republic firsthand—and each was faced with the decision of how to respond. From Emil Artin to Ernst Zermelo, this talk will chronicle one of the darkest moments in humanity’s history through the eyes of mathematicians: who fled, who fought, who died, and who stood idly by in the name of apolitical science. In doing so, we will consider what roles mathematicians could (or should) be expected to play during times of political upheaval.", "id": "Paper/66472", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66472"}, {"title": " A spectral Bishop theorem ", "webprogram_exclude": "0", "session_ids": ["Session/17749"], "source_sha256": "b4306bc5391f822e3952f0031e49c78a9d09e0bd68a131208ca95865641ee066", "withdrawn": "", "abstract": "Let $(M^n,g)$ be a closed, connected Riemannian manifold, $n\\geq3$, and let $\\mathrm{Ric}$ denote the (pointwise) smallest eigenvalue of its Ricci tensor. We show that if there exists a smooth positive function $u$ satisfying\n$$\n-\\gamma\\Delta_g u+\\mathrm{Ric}\\cdot u\\geq(n-1)u\n\\qquad\\text{for some }0\\leq\\gamma\\leq\\frac{n-1}{n-2},\n$$\nthen\n$$\n\\operatorname{Vol}_g(M)\\leq\\operatorname{Vol}(\\mathbb S^n),\n$$\nwhere $\\mathbb S^n$ is the unit round sphere. The range of $\\gamma$ is sharp. We will discuss a proof based on a weighted isoperimetric problem, and related questions connecting PDEs, Schroedinger operators, and comparison geometry. This is joint work with Kai Xu.", "id": "Paper/66473", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66473"}, {"title": " Bergman–Toeplitz Operators with Indicator Symbols ", "webprogram_exclude": "0", "session_ids": ["Session/17887"], "source_sha256": "54fd398b3dbcf7c13a0e4434dfc355396cd76614c02582912c209cba6e164af9", "withdrawn": "", "abstract": "For a measurable subset of the unit disc, we consider the Toeplitz operator on the Bergman space with symbol equal to the indicator function of that subset. We study how the spectrum of this operator relates to the geometry of the subset. Schatten $p$-norms of these operators provide spectral quantities that can be expressed using invariants of hyperbolic geometry, connecting operator theory with the intrinsic geometry of the disc.\n\nFor the Schatten $2$-norm, the relevant integral depends only on hyperbolic distance. This allows rearrangement inequalities to be applied and shows that, among measurable subsets of the disc with fixed hyperbolic area, the Schatten $2$-norm is maximized precisely by hyperbolic discs. Thus, a spectral quantity detects a geometric extremal property of the underlying set.\n\nWe will also discuss the analogous results for higher Schatten norms and in higher-dimensional balls.", "id": "Paper/66475", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66475"}, {"title": " CANCELLED-Jacob Bernoulli on the Evolute of the Cycloid and Its Properties \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18554"], "source_sha256": "5030c9efe4c4eb62bcb485c31c59bc74c148b1d784697d756125e48cf4b2b228", "withdrawn": "", "abstract": "In the June 1692 volume of the \\textit{Acta Eruditorum} Jacob Bernoulli wrote: “I had scarcely submitted to the Editors of the \\textit{Acta} my recent speculation on Cycloids and other curves, when on the following day I received a letter from my Brother [Johann Bernoulli] in Paris, in which he communicated some excellent things pertaining to this topic... all of which I could not read without astonishment, when I considered that neither of us knew anything of the other’s speculations concerning these curves. But these things gave me the opportunity to take up again this material, which had already been set aside.” During this period, Johann Bernoulli was working with Guillaume François Antoine, Marquis de l'Hôpital. This talk will consider Jacob Bernoulli’s May and June 1692 \\textit{Acta} papers and the results related to the evolutes and cuastics of cycloids. This will also be connected to some of what L'Hôpital later published about the same topics in \\textit{Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes}.", "id": "Paper/66476", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66476"}, {"title": " Matrix Continued Fractions and Nonlinear Approximation of Resolvents of Difference Operators ", "webprogram_exclude": "0", "session_ids": ["Session/17872"], "source_sha256": "70c6c812de8d59baff4de33d1091a6e1f7a522e98d60e1990dfd840d37e0efaf", "withdrawn": "", "abstract": "We study methods of rational approximation based on matrix continued fractions generated by iterated nonlinear matrix transformations. We develop these methods for matrices of resolvent functions associated with one-sided and two-sided difference operators of arbitrary finite order. We establish connections between these matrix continued fractions and generating functions for weighted lattice paths.\n\nFor one-sided operators, the resolvent entries of finite principal truncations provide rational approximants that interpolate the corresponding resolvent functions at infinity to an order that increases with the truncation size. The approximating resolvent matrices admit finite matrix continued-fraction representations.\nThe construction connects with matrix Pad\\'e approximation, classical Pad\\'e approximation, and type II Hermite--Pad\\'e approximation.\n\nThis is joint work with J. Kim and A. L\\'opez-Garc\\'ia.\n\n\\vspace{0.75em}\n\n\\noindent\n[1] J. Kim, A. L\\'opez-Garc\\'ia, and V. A. Prokhorov, \\emph{Matrix continued fractions associated with lattice paths, resolvents of difference operators, and random polynomials}, \\emph{Constructive Approximation} \\textbf{62} (2025), 185--242.", "id": "Paper/66483", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66483"}, {"title": " Fantasy Needs More Mathematics (and Mathematics Needs More Fantasy) ", "webprogram_exclude": "0", "session_ids": ["Session/18233"], "source_sha256": "f7b42d86d9c74eae613e4ff82e58f477f433c007a93c8cbaecbf47d962f269f0", "withdrawn": "", "abstract": "Mathematics and magic have always shared a curious kinship—one that extends back through literature for hundreds (if not thousands) of years. This talk explores how fantasy authors have drawn directly from mathematics to inform their magic—from Lewis Carroll’s critiques of then-modern mathematics in Alice in Wonderland to the paradoxical analytic magick and hyperbolic Hellscape of R.F. Kuang’s Katabasis. I will also highlight some examples of when fantasy has, in turn, inspired mathematics.", "id": "Paper/66484", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66484"}, {"title": " Counting Independent sets in <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.769ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 1192.1 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbb {Z}_3^n</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJAMS-5A\" d=\"M39 -1Q29 9 29 12Q29 23 60 77T219 337L410 648H364Q261 648 210 628Q168 612 142 588T109 545T97 509T88 490Q85 489 80 489Q72 489 61 503L70 588Q72 607 75 628T79 662T81 675Q84 677 88 681Q90 683 341 683H592Q604 673 604 666Q604 662 412 348L221 37Q221 35 301 35Q406 35 446 48Q504 68 543 111T597 212Q602 239 617 239Q624 239 629 234T635 223Q635 215 621 113T604 8L597 1Q595 -1 317 -1H39ZM148 637L166 648H112V632Q111 629 110 622T108 612Q108 608 110 608T116 612T129 623T148 637ZM552 646Q552 648 504 648Q452 648 450 643Q448 639 266 343T77 37Q77 35 128 35H179L366 339L552 646ZM572 35Q581 89 581 97L561 77Q542 59 526 48L508 37L539 35H572Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJAMS-5A\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-6E\" x=\"943\" y=\"581\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-33\" x=\"943\" y=\"-352\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18315"], "source_sha256": "704a6230dbebcf4a46b441a4a25477dd496779422f8c0c1dd91e2af4d76c0c5c", "withdrawn": "", "abstract": "In the 80's, Sapozhenko developed a container method for asymptotically counting the number of independent sets in the hypercube $\\mathbb{Z}_2^n$, where two $n$-bit strings are adjacent if they differ in exactly one coordinate; equivalently, Sapozhenko determined the typical structure of a binary code of distance $2$. We asymptotically count the number of independent sets in $\\mathbb{Z}_3^n$, or ternary codes of distance $2$. The proof involves a novel isoperimetry statement (proven by AI with Fourier analysis) and a novel container method.", "id": "Paper/66503", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66503"}, {"title": " An Introduction to Quadrature Domains and the X Marks the Spot Problem ", "webprogram_exclude": "0", "session_ids": ["Session/17442"], "source_sha256": "f6bdf772c102dddd012700f5c324aaa834b8834d338bbb37db742e519feff1c7", "withdrawn": "", "abstract": "We define quadrature domains in the complex plane using only integrals and finite sums. We then discuss the X Marks the Spot problem for quadrature domains: Suppose we bury treasure on an island with smooth boundary. It is known that we can encrypt the location of the treasure as a point in a nearby quadrature domain. Can we now decrypt the location of the treasure using properties of quadrature domains? We also expand on the X Marks the Spot problem to study other functions associated with quadrature domains.", "id": "Paper/66504", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66504"}, {"title": " Bounding the interleaving distance on concrete categories: Toward polynomial time algorithms ", "webprogram_exclude": "0", "session_ids": ["Session/18324"], "source_sha256": "122309a8057ea980d63848e78027b6726c5c6d03f82a975faa296d89902eea64", "withdrawn": "", "abstract": "The interleaving distance is a widely used metric in topological data analysis (TDA) with applications to a broad range of data structures, including multiparameter persistence modules, Reeb graphs, and zigzag modules. Despite its theoretical importance, computing the interleaving distance can be NP-hard, limiting its use in practical settings. In this talk, inspired by the work of Chambers et al. on the interleaving distance for mapper graphs, we develop a general framework for bounding the interleaving distance between generalized persistence modules on concrete categories via a loss function. Under appropriate assumptions, we show that this loss function can be computed in polynomial time. In particular, our framework yields a polynomial-time approach to bounding the interleaving distance between n-parameter persistence modules.", "id": "Paper/66505", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66505"}, {"title": " Boundedness of perturbed Nevo–Thangavelu maximal functions on two-step nilpotent Lie groups ", "webprogram_exclude": "0", "session_ids": ["Session/18279"], "source_sha256": "2b7739448a5dbd21c9570a58c14880f0da45bd35bedc617c6414b4caa130bc61", "withdrawn": "", "abstract": "Let $G$ be a two-step nilpotent Lie group, identified via the exponential map with the Lie-algebra $\\mathfrak g=\\mathfrak g_1\\oplus\\mathfrak g_2$, where $[\\mathfrak g,\\mathfrak g]\\subset \\mathfrak g_2$.\nWe study $L^p$-boundedness results for maximal functions associated to spheres in a $d$-dimensional linear subspace $H$, dilated by the natural parabolic dilations. The case where $H=\\mathfrak g_1$ is well understood. In this talk, we consider the case of a tilted plane  $H\\neq \\mathfrak g_1$ which is not invariant under the automorphic dilations. While in the case of M\\'etivier groups it is known that the $L^p$-boundedness results are stable under a small tilt, we show that this is generally not the case for other two-step nilpotent groups. We discuss various positive and negative results depending on the geometry of $H$  in relation to the group law.", "id": "Paper/66508", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66508"}, {"title": " Disorder-promoted stability in collective dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/17383"], "source_sha256": "c28dcdb4b142251dc84bacf92fe8c00e3cd976ef9b20877b397b734b47d4c72b", "withdrawn": "", "abstract": "A longstanding view in network dynamics is that heterogeneity among nodes undermines the stability of consensus, synchronization, and other functionally relevant collective states. This is puzzling given how heterogeneous most natural and engineered networks actually are. In this presentation, I will show that this view arises from model reductions introduced for mathematical tractability and breaks down when nodal dynamics are higher-dimensional, yielding non-Hermitian Jacobians. In such systems, including neural, power-grid, and material networks, nodal heterogeneity can instead enhance stability, even when parameters are randomly disordered. Non-Hermiticity also underlies the stabilizing effects of network heterogeneity, which can arise even in one-dimensional dynamics through nonreciprocal interactions, as shown for ecological networks. Our framework reveals disorder not as a liability but as a general resource for stabilizing complex systems.", "id": "Paper/66510", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66510"}, {"title": " Near-Optimal Sampling for Plug-and Play Compressive Image Recovery ", "webprogram_exclude": "0", "session_ids": ["Session/17718"], "source_sha256": "b4d6ca9074a05450bb043673d7bf15c2460bfc791917e6fff995c0ae61605a08", "withdrawn": "", "abstract": "The prevalence of machine learning models in computational sciences has shifted the field of compressive image reconstruction toward deep learning approaches, especially plug-and-play methods. This talk will focus on a projected gradient descent algorithm that uses neural network denoisers to mimic projections. The setting will be image recovery from sub-sampled Fourier measurements. To justify the superiority of such neural networks, they will be treated as approximations to proximal operators, for which we provide empirical evidence based on work by Joundi, Traonmilin, and Aujol (2025). With such treatment, existing recovery guarantees for proximal operators can be extended to the neural network denoisers. Further, near-optimal sampling distributions have been developed to minimize the number of necessary samples to maintain recovery as shown by Adcock, Cardenas, and Dexter (2026). These distributions have closed-form representations for some proximal operators which can be used with the neural network denoisers that they approximate. This presentation is based on ongoing joint work with Professor Ben Adcock and Professor Mark Iwen.", "id": "Paper/66512", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66512"}, {"title": " Forward-Backward Stochastic Differential Equations with Continuous-State-Dependent Switching ", "webprogram_exclude": "0", "session_ids": ["Session/17800"], "source_sha256": "f52b63d33216013e5577f49f752ae6b62019f1eeaf7278a76eac61cb135de29e", "withdrawn": "", "abstract": "This work develops a general theory of forward-backward stochastic\ndifferential equations with continuous-state-dependent switching.\nAs a preparation for the study, solvability of a class of systems in the sense of classical solutions of semilinear parabolic partial differential equations (PDEs) with continuous-state-dependent switching is established first. The backward equation is\nformulated under the {\\it natural filtration} generated by\nthe realized switching diffusion. In contrast to the state-independent\nswitching diffusions,  one of the main challenges is:\nthe martingale representation is not available\nunder the natural filtration.\nThis work overcomes the difficulties and obtains a martingale\nrepresentation\ntheorem by using certain results from systems of PDEs.\nBased on this result,  the well-posedness of switching\nbackward stochastic differential equations is proved,\nand a nonlinear Feynman--Kac\nformula is obtained, and  {\\it a priori}\nestimates for the backward components\nare then established. Then the paper is devoted to\nmultiscale systems with fast state-dependent switching. An\naveraging principle is proved for the associated semilinear systems, and the\nweak convergence of the corresponding multiscale BSDEs with $Z$-dependent\ndrivers is established. Finally, the averaging result is used to analyze\ntwo-time-scale stochastic control problems and to derive the effective\nHamilton--Jacobi--Bellman\n(HJB)\nequations governing the limiting value function.", "id": "Paper/66513", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66513"}, {"title": " Filling flatly fibered cusps of hyperbolic <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.395ex\" height=\"1.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -576.1 600.5 721.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">n</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-6E\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-manifolds ", "webprogram_exclude": "0", "session_ids": ["Session/18267"], "source_sha256": "0906a27e76fe5a3a4adbbdc0f6c014a866e621a981217f8f9dfa689f5e2653cc", "withdrawn": "", "abstract": "Dehn filling is a classical tool for producing negatively curved manifolds from cusped hyperbolic 3-manifolds, and results of Mosher-Sageev and Fujiwara-Manning extend this idea to higher dimensions when cusp cross sections are tori. In this talk, I will discuss a generalization to hyperbolic manifolds whose cusps can have more complicated cross sections---ones that admit a Riemannian submersion onto a flat base with totally geodesic fiber. Filling along the fibers of such a cusp can still produce a nonpositively (and in some cases negatively) curved space, provided that the fibers have large enough systole. Group theoretically, this filling takes a relatively hyperbolic fundamental group and creates a related hyperbolic one. I'll introduce the Ratcliffe-Tschantz hyperbolic 5-manifold, whose cusps are bundles with Hantzsche-Wendt fiber over the circle, and show how the filling result, coupled with some group theory, gives information about the geometry of its cusps.", "id": "Paper/66514", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66514"}, {"title": " From Math Circles to Advanced Mathematics ", "webprogram_exclude": "0", "session_ids": ["Session/18212"], "source_sha256": "54af8bef1e61212630f10c9a22e3093fb31254fb5c6db876f39b8a396a38d340", "withdrawn": "", "abstract": "The Mobile Math Circle began in 1998 in the Department of Mathematics and Statistics at the University of South Alabama, and the Alabama School of Mathematics and Science (ASMS) Math Circle began in 2004. For more than two decades, the two programs have worked in close collaboration to support mathematical enrichment for middle- and high-school students in the Mobile area.\n\nJoint activities have included the Mobile Math Olympiad, invited lectures, the USA--ASMS Math Festival, the Middle School Math Olympiad, and regular problem-solving sessions. A central part of this talk will focus on the ASMS experience, where Math Circle activities gradually developed into more advanced and structured offerings, including courses and seminars in problem solving, number theory, game theory, combinatorics, and other topics.\n\nWe will present examples of problem-centered sessions that invite students to explore, discuss, and work together, along with materials that can be readily adapted for other Math Circles and classrooms. We will also describe how this long-term collaboration has encouraged students to take upper-level mathematics and strengthened interest in mathematics majors and minors. Practical problems and session materials used in our day-to-day activities will be shared with participants.", "id": "Paper/66517", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66517"}, {"title": " Model Structures on Posets Coming from Equivariant Homotopy Theory ", "webprogram_exclude": "0", "session_ids": ["Session/18082"], "source_sha256": "e72d1dfd48e965874886aa73778bd2fcd8514e2aefef30fc3c355a24702f09b1", "withdrawn": "", "abstract": "A model structure on a poset consists of three classes of maps that are called weak equivalence, fibrations, and cofibrations. Of relevance to us, a model structure can determine a transfer system, an object that describes equivariant homotopic coherent operations.  When we assign the acyclic fibrations of the model structure to the edges of the transfer system, we are begin to compare model structures on lattices, that is, specifically, do two model structures differ by a left/right Bousfield localization. It is known for the total order poset lattice (namely a line) that there exists a path of right/left Bousfield localizations from the trivial model structure to any other model structure. We present results for a general lattice and explore other functors on the total order lattice in terms of operations on binary trees.", "id": "Paper/66518", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66518"}, {"title": " On the existence of nonzero finite-length Gorenstein projective modules ", "webprogram_exclude": "0", "session_ids": ["Session/18025"], "source_sha256": "370d4dbb08edf79d1a03f025081eef13ed6e022da019e6730a85cb9898646424", "withdrawn": "", "abstract": "Homological dimensions like $G$-dimension and $CI$-dimension not only give a generalization of projective dimension, but classify Gorenstein and Complete Intersection rings. We investigate the question of whether there exist nonzero finite-length Gorenstein projective modules over non-Cohen-Macaulay local rings (of depth zero), and discuss related results for modules of finite complete intersection dimension.", "id": "Paper/66521", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66521"}, {"title": " Closing the existence problem for geometric <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"4.258ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 1833.4 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">(n_4)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"0\" y=\"0\"></use>\n<g transform=\"translate(389,0)\">\n <use xlink:href=\"#E1-MJMATHI-6E\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-34\" x=\"849\" y=\"-213\"></use>\n</g>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"1443\" y=\"0\"></use>\n</g>\n</svg> configurations ", "webprogram_exclude": "0", "session_ids": ["Session/19321"], "source_sha256": "18ad87509b57a643b108b263896e6c07b792f37c54dba066016890f67eafcb0a", "withdrawn": "", "abstract": "A geometric $(n_4)$ configuration is a set of $n$ points and $n$ lines in the real projective plane such that every point lies on exactly four of the lines and every line contains exactly four of the points. The question of which $n$ admit such a configuration was posed by Gr\\\"unbaum in 2000, following his 1990 paper with Rigby that gave the first geometric 4-configuration, a $(21_4)$. Successive work of Bokowski--Schewe, Bokowski--Gr\\\"unbaum--Schewe, Bokowski--Pilaud and Cuntz settled every case but one. Cuntz's 2018 paper, which constructed $(22_4)$ and $(26_4)$ configurations, states that only $n=23$ remained open.\n\nWe settle this last case by exhibiting two geometric $(23_4)$ configurations. The first has integer homogeneous coordinates, so verifying it is an exercise in integer arithmetic; the second is self-polar with respect to a conic and is defined over $\\mathbb{Q}(\\sqrt{17})$, but not over $\\mathbb{Q}$. Consequently geometric $(n_4)$ configurations exist if and only if $n \\ge 18$ and $n \\ne 19$.\n\nWe also explain why $n=23$ resisted the symmetric constructions that settled the other values. We prove that the group of projective symmetries of any geometric $(23_4)$ configuration has order at most four. Reducing the case of a Klein four-group of symmetries to a few thousand bilinear polynomial systems in 18 unknowns, and solving all of them exactly with Gr\\\"obner bases and saturation, shows that our two configurations are the only Klein-symmetric ones, over $\\mathbb{R}$ and over $\\mathbb{C}$. The same method classifies the Klein-symmetric $(22_4)$ and $(26_4)$ configurations, giving three new combinatorial types at $n=22$ and 94 at $n=26$.", "id": "Paper/66522", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66522"}, {"title": " The Art of Fractals: Integrating Mathematical Beauty into General Education Courses ", "webprogram_exclude": "0", "session_ids": ["Session/17091"], "source_sha256": "d069fbdb16f0b02b80c990e55f79e8ba73bee8cd501377cf8c8fb6024549623b", "withdrawn": "", "abstract": "Fractal geometry bridges mathematics and the arts in a most distinctive way by fostering creative thinking and revealing the beauty of mathematics in the mathematics classroom. As self-similar fractal patterns emerge from iterative rules, or codes, students can explore the mathematics and artistry of such patterns and create their own, original fractal designs. The unique experience of making fractals can be especially valuable for non-STEM majors who often feel anxious about mathematics, question the relevance of mathematics beyond STEM fields, or are seeking new experiences in mathematics. This presentation will focus on how topics in fractal geometry can be utilized in undergraduate general education mathematics courses to foster creative thinking, increase student engagement, build connections between mathematics and the arts, and inspire artistic expression and imagination in students. The speaker will showcase classroom practices and implementation strategies for incorporating fractal geometry and fractal art projects into general education mathematics courses, including fractal patterns obtained by iterating the eight symmetry transformations of the square. The session will highlight classroom activity ideas and sample student work, drawing on the speaker’s experience teaching fractal geometry in general education settings. The speaker will share how she has been guiding students in creating fractal-inspired designs across many art forms, including digital art, painting, music composition, dance, knitting, creative writing, and more.", "id": "Paper/66524", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66524"}, {"title": " The chase for diversity: how predator-prey taxis stabilizes ecosystems ", "webprogram_exclude": "0", "session_ids": ["Session/17370"], "source_sha256": "d417b8148401560b5c01833fdab46edfad69019db3a6ae5ebf0509b51ca1087b", "withdrawn": "", "abstract": "Active motion in response to external stimuli is a common feature across the tree of life. Here, we study the effect of inter-specific taxis on the organization and diversity of complex ecosystems. We show that random predator-prey taxis can destabilize a homogeneous state and lead to the formation of dynamical patterns even when ecological interactions are weak. For stronger ecological interactions, this self-generated spatial heterogeneity permits the coexistence of a number of species well beyond May’s bound, leading to a persistent dynamical state. In this patterned state, clusters of high density and low diversity, composed of a stable clique of species, form and coalesce.", "id": "Paper/66525", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66525"}, {"title": " Graph Polynomials and Invariants AIM Research Community ", "webprogram_exclude": "0", "session_ids": ["Session/17900"], "source_sha256": "ed7d3d13d1f5f99993df0b58d13840ad18bb87a029b6c0f66b9f098b73c2582c", "withdrawn": "", "abstract": "This presentation will report on research done by various research groups in the Graph Polynomials and Invariants AIM Research Community (ARC). This virtual research community began in 2026 with support from the American Institute of Mathematics and the NSF which focuses on investigating properties of graph polynomials and invariants. The purpose of the AIM ARC program is to support the ongoing research activities of its participants, especially people who lack nearby collaborators or who cannot travel. Opportunities to join this community will be discussed.", "id": "Paper/66527", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66527"}, {"title": " Using Undercut in an Intro to Game Theory course ", "webprogram_exclude": "0", "session_ids": ["Session/18062"], "source_sha256": "b57fd0e70cfeb38ab860be5c4e387cc3d723a1056ed6d3708c7339466271b535", "withdrawn": "", "abstract": "Game theory is an effective and fun topic for engaging students with limited mathematical background. The game of Undercut, developed by Douglas Hofstadter, is a simple two-player game. Like Rock-Paper-Scissors, it has no pure strategy equilibrium. However, unlike Rock-Paper-Scissors, it is much more difficult to use our intuition to guess at the optimal strategy. To find the optimal strategy, students need to bring together ideas of expected value, solving systems of equations, and the theory of equilibrium mixed strategies for zero-sum games. Undercut provides an ideal game for discussing how mathematical solutions can help us understand games, especially when our intuition is not enough.", "id": "Paper/66530", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66530"}, {"title": " Non-triviality of algebraic cycles associated to modular curves via pullback formula ", "webprogram_exclude": "0", "session_ids": ["Session/17450"], "source_sha256": "a92b718f8c0be3296bdc42964ce847a9266a4a9786977972c1bba8f4026714a0", "withdrawn": "", "abstract": "Associated to an algebraic curve $X$, there are two canonically constructed homologically trivial algebraic $1$-cycles, the \\textit{Ceresa cycle} in \n the Jacobian of $X$,  and the \\textit{Gross--Kudla--Schoen modified diagonal cycle} in the triple product $X \\times X \\times X$. According to Shou-Wu Zhang, one is torsion if and only if the other is. We prove that these two cycles associated to a large family of modular curves are non-torsion in the corresponding Chow groups. We obtain the result by relating this problem to the\nstudy of special cycles on orthogonal Shimura varieties. As the main ingredient and a result of independent interest, we develop a pullback formula for special divisors on modular curves embedded in their products via the diagonal map.", "id": "Paper/66531", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66531"}, {"title": " Ramsey numbers in Kneser graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18011"], "source_sha256": "7e1c97d40e0c9983a7b7f3c5f3cfbb452d4dcdc35800e86eecd6b394f76618ff", "withdrawn": "", "abstract": "The Kneser graph $KG(n,r)$ is the graph whose vertices are the $r$-subsets of $[n]$ in which an edge is present between two vertices if their corresponding $r$-sets are disjoint. We introduce the $r$-Kneser Ramsey number $R^{KG}_r(s,t)$ as the minimum integer $n$ such that every red/blue edge-coloring of $KG(n,r)$ contains a red $s$-clique or a blue $t$-clique. In this talk, we will discuss general bounds on the numbers $R^{KG}_r(s,t)$ as well as progress on a related Ramsey-type problem raised by Holmsen, Hrusak, and Roldan-Pensado.", "id": "Paper/66532", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66532"}, {"title": " Quantum Solvers for Nonlinear Matrix Equations in Quantum Chemistry ", "webprogram_exclude": "0", "session_ids": ["Session/18246"], "source_sha256": "54a6efea5406969ebbb407abebb2d25afc3f82078b904816bfc8240092bcf61f", "withdrawn": "", "abstract": "We present a quantum algorithm for solving algebraic Riccati equations, with applications to quantum-chemical random-phase approximation (RPA) and higher-order RPA theories. Our method block-encodes stabilizing Riccati solutions via Riesz projectors onto invariant subspaces of an associated non-normal matrix. Applied to $m$-particle, $m$-hole RPA under localized-orbital sparsity assumptions, our algorithm's end-to-end cost scales linearly with system size and polynomially with excitation rank $m$, suggesting an exponential advantage in $m$ over plausible classical heuristics. More broadly, this work provides a framework for solving nonlinear matrix equations with quantum computers and motivates further developments in quantum algorithms for nonlinear quantum-chemistry methods.\n\nA preprint of this work is available at \\url{https://arxiv.org/abs/2605.16189}.", "id": "Paper/66534", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66534"}, {"title": " Dynamical Storage Analysis: A Computational Approach to Continuous Systems ", "webprogram_exclude": "0", "session_ids": ["Session/19365"], "source_sha256": "71e77272810370c7f0e5b6d5452e7a09f4f1ac3cc1d86b620b9776f3e1194c2d", "withdrawn": "", "abstract": "Ecosystems are often modeled as compartment models where matter or energy flows between compartments. It is useful to know how much matter or energy is eventually stored in compartment $x_j$ resulting from an instantaneous input into compartment $x_i$. One can think of storage as the amount of material that resides in a compartment for a long (perhaps infinite) amount of time. This question has been addressed by partitioning a system of linear ordinary differential equations into subcompartments and constructing a “dynamical storage matrix” $S$ from the steady-state solution. However, this technique can only be applied to models at constant steady state. The case of nonlinear systems have been addressed with agent-based models. In this talk, we introduce a novel method of partitioning a nonlinear ecosystem model so that its dynamical storage matrix can be computed from the solution of nonlinear ordinary differential equations.", "id": "Paper/66537", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66537"}, {"title": " Allee-Effect Bistability and Predator-Induced Neimark–Sacker Bifurcation in a Discrete-Time Predator–Prey Model ", "webprogram_exclude": "0", "session_ids": ["Session/19351"], "source_sha256": "adc68281d665cd9b42465b85c27575e1eea159f159aad7ff516bb83e644270ab", "withdrawn": "", "abstract": "In this study, we incorporate an Allee effect into the discrete-time predator--prey system developed in \\cite{ackleh2019persistence} through the prey growth function. We show that, in the absence of predators, the model exhibits a strong Allee effect, leading to bistability in the prey population, where both the extinction equilibrium and a predator-free equilibrium are stable. Successful predator invasion through an interior equilibrium destabilizes the stable predator-free equilibrium. When this invasion occurs for a prey growth rate below one, the system displays bistability between the extinction and interior equilibria. In addition, the introduction of predators may trigger a Neimark--Sacker bifurcation, resulting in stable quasi-periodic solutions.", "id": "Paper/66542", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66542"}, {"title": " Modeling and Predicting U.S. Population Growth: Comparing Logistic and Richards Models under Different Error Structures and Estimation Methods Using Real and Synthetic Datasets. ", "webprogram_exclude": "0", "session_ids": ["Session/19322"], "source_sha256": "f4a63a92e650ddf6cfd16230dbba2179cb996e18f69e11d7f8b5f3036336ec7a", "withdrawn": "", "abstract": "The U.S. population grew from 180.7 million in 1960 to 340.1 million in 2024. However, this growth did not occur at a constant rate. Between 1995 and 2005, the population increased by about 24 million people. In contrast, from 2014 to 2024, it grew by only about 10 million. Although both periods cover ten years, the amount of growth was very different. In fact, the most recent five-year period shows the smallest increase in the entire dataset, less than 9 million people, even though the population was larger than ever before.\n\nThis type of behavior is common in many real-world situations. New technologies and products often spread rapidly at first and then slow down as they reach more people. Animal populations may recover quickly after a decline, but eventually level off near an environmental limit. In cases like these, two important questions arise: How large will the population eventually become, and how quickly will it approach that limit? Since the available data do not extend far enough to show the population fully leveling off, we must rely on mathematical models to estimate its long-term behavior.\n\nThis study focuses on two models commonly used to describe growth that slows over time: the Logistic and Richards models. The Logistic model assumes that growth is symmetric around its midpoint. In other words, the rate at which growth slows down mirrors the rate at which it sped up earlier. The Richards model relaxes this assumption by introducing an additional parameter that allows the early and late growth stages to behave differently. When this parameter takes a specific value, the Richards model reduces to the Logistic model. Otherwise, it can produce a wider variety of growth patterns.\n\nWe fit both models to 65 years of U.S. population data and to two synthetic datasets containing 31 observations each. For each model fit, we considered two ways to measure the difference between the observed data and the fitted curve: absolute residuals and relative residuals. We also examined two noise structures, one based on fixed-size errors and another based on percentage-size errors. For each noise structure, we tested multiple error bounds to evaluate how sensitive the results were to this choice.", "id": "Paper/66543", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66543"}, {"title": " Semi-Automatic Segmentation of Touching and Dividing Cell Nuclei in Microscopy Images Using a Regularized PDE Model ", "webprogram_exclude": "0", "session_ids": ["Session/18445"], "source_sha256": "31e643a2d6f9bd2d3ed7c2bdca742a8718ce647e07184ff4a524396c3b48b2c5", "withdrawn": "", "abstract": "Touching and dividing cell nuclei often appear as connected structures in 3D and 3D+time microscopy images, making accurate boundary recovery particularly challenging. This talk presents a semi-automatic segmentation method based on a regularized subjective-surface PDE model that combines image-dependent weighted curvature flow with a monotone reaction term incorporating prescribed information from neighboring nucleus candidates. We will present well-posedness results for the model and introduce a semi-implicit finite-volume discretization of the regularized problem.", "id": "Paper/66552", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66552"}, {"title": " Investigating Polygon Dynamics Under a Recurrence Relation ", "webprogram_exclude": "0", "session_ids": ["Session/17106"], "source_sha256": "27fe4e23fe794d9ac645e2952d3a771e7b728106c319e8528d4bcd663ec2a1b9", "withdrawn": "", "abstract": "Studying polygon vertex dynamics under different operations is an integral field of study at the intersection of algebra, geometry and dynamics, with numerous uses in computer graphics and mathematical biology. One famous example of an operation that generates interesting dynamics is the Midpoint Iteration Algorithm, which asymptotically collapses the polygon to its centroid. This joint work examines the limiting behaviors of n-gon vertices under a Midpoint Iteration inspired operation named ‘Snap’. We introduce the definition of Snap and generalize it to n-gons. We show that any n-gon under the Snap operation converges to a point defined by a weighted sum of its initial vertices. We also show that the rate of collapse slows down asymptotically, and that the area of a convex quadrilateral under snap is halved at each iteration.", "id": "Paper/66553", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66553"}, {"title": " Stable bad reduction of genus two curves with complex multiplication ", "webprogram_exclude": "0", "session_ids": ["Session/17903"], "source_sha256": "8eefde73970d923e9928f98ddb2f092c7f4721c4521dcffbf3b86a0f3995866b", "withdrawn": "", "abstract": "This is a joint work with Jan Bruinier and Peng Yu. When a genus two curve $C$ (over a number field) has complex multiplication by a bi-quadratic CM number field, its Jacobian  is isomorphic to product of two CM elliptic curves with CM by imaginary orders $\\mathcal O_{d_1}$ and $\\mathcal d_2$  with $d_1/d_2 =t^2$ being a square of a positive integer $t$.  In this talk, we will explain the following two results among others:\n\n1. The curve $C$ has always stable bad reduction at some primes (a little surprising);\n\n2.  Such (bad) primes are  non-split in $Q(\\sqrt{d_2})$ and less than or equal to $t |d_2|/4$. \n\n Main ideas of the proof include arithmetic intersection on Siegel $3$-fold and small CM value formula for Borcherds product.", "id": "Paper/66554", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66554"}, {"title": " Intersecting families of sets are typically trivial for <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"10.87ex\" height=\"2.343ex\" style=\"vertical-align: -0.505ex;\" viewBox=\"0 -791.3 4680 1008.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">n\\ge 2k+2</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2265\" d=\"M83 616Q83 624 89 630T99 636Q107 636 253 568T543 431T687 361Q694 356 694 346T687 331Q685 329 395 192L107 56H101Q83 58 83 76Q83 77 83 79Q82 86 98 95Q117 105 248 167Q326 204 378 228L626 346L360 472Q291 505 200 548Q112 589 98 597T83 616ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-6E\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2265\" x=\"878\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-32\" x=\"1934\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-6B\" x=\"2435\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2B\" x=\"3178\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-32\" x=\"4179\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18315"], "source_sha256": "85b66bf14c885490cab4e73efc9d1f417570d6af4cee2fdb638cc338e22b2a84", "withdrawn": "", "abstract": "A family of \\(k\\)-element subsets of \\([n]\\) is intersecting if every pair of its members intersects, and it is trivial if all its members contain a common element. Balogh et al. proved that for \\(n\\geq 2k+100\\ln k\\), almost all intersecting families are trivial, and conjectured that this holds for \\(n\\geq 2k+2\\). Very recently, Yang confirmed the conjecture for \\(n\\geq 2k+3\\). We settle the final remaining case, \\(n=2k+2\\). Our proof uses two different forms of the graph container method: a refined Kleitman–Winston-type container algorithm on the Kneser graph and a Sapozhenko-style container argument on a bipartite inclusion graph.", "id": "Paper/66555", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66555"}, {"title": " Inequalities for the <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.07ex\" height=\"2.009ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -576.1 460.5 865.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">q</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-71\" d=\"M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-71\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Numerical Radius and <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.07ex\" height=\"2.009ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -576.1 460.5 865.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">q</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-71\" d=\"M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-71\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Crawford Number ", "webprogram_exclude": "0", "session_ids": ["Session/18229"], "source_sha256": "326c019d9fa9ef700c98f3052ed1dbd8851c8935dbcb2dd19789470ffb3210c1", "withdrawn": "", "abstract": "Let $T$ be a bounded linear operator on a complex Hilbert space and let $q$ belong to the closed unit disk. In this talk, we investigate properties and inequalities associated with the $q$-numerical radius and the $q$-Crawford number of $T$. We establish continuity results for these quantities and obtain new estimates for the $q$-numerical radius. We also study geometric properties of the $q$-numerical range through its relationship with the Crawford number and derive several related inequalities. In addition, we establish a power inequality for the $q$-numerical radius using the Berger--Okubo--Ando power inequality. Several examples will be presented to illustrate the results and compare the new estimates with existing bounds.", "id": "Paper/66558", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66558"}, {"title": " A Heterogeneous FitzHugh-Nagumo Model Exhibiting Local and Regional Dynamics that Mimic Spontaneous Atrial Fibrillation ", "webprogram_exclude": "0", "session_ids": ["Session/18244"], "source_sha256": "c29328bf0954177c2f6dd2a5916a507ec1932877c4b92dfe78a4f396aa5ec12b", "withdrawn": "", "abstract": "We study two-dimensional networks of FitzHugh-Nagumo oscillators in regimes that mimic cardiac tissue. The networks include small layers of cells that have fast-recovery characteristics and adjacent layers of cells that have slow-recovery. Numerical simulations show that the boundary between the fast- and slow-recovery cells can initiate fibrillatory-like behavior when activated by a single, healthy wave in the network. We discuss possible connections between these structures and the onset of atrial fibrillation, with the goal of improving our understanding and treatment of this costly condition. \n\nOur main conclusion is that a single, normal excitation of small areas of heterogeneity embedded in healthy tissue can  initiate arrhythmias and the two dimensional network can then sustain irregular firing patterns in the form of double swirling-back curves and spiral waves. This occurs with a very simple model of excitable cells and we  give a clear mechanistic  description of the arrhythmia. \nThe model illustrates how increasing heterogeneity in heart tissue can progressively cause first intermittent and then persistent arrhythmic behavior. \nAnother conclusion is that the center of problematic firings can drift away from the heterogeneity into healthy tissue, thus presenting phantom targets for treatment.", "id": "Paper/66559", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66559"}, {"title": " Train Neural Networks for Elliptic PDEs with Mirror Mean Field Langevin Dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/17919"], "source_sha256": "bea0ff09992aa6caf527836f5561a75f00931bb7c0e7a637181566311609a3a3", "withdrawn": "", "abstract": "This paper investigates the theoretical foundations of training procedures within the frameworks of the deep Ritz method and the physics-informed neural networks (PINNs) for solving the elliptic equation with Neumann boundary conditions. We analyze the optimization dynamics of the two-layer neural networks trained via the mirror mean-field Langevin algorithm. In this regime, we characterize the sample and computational complexities for the convergence of the mirror mean-field Langevin algorithm.", "id": "Paper/66560", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66560"}, {"title": " Teaching sophisticated mathematical content to 1st and 2nd graders using only addition ", "webprogram_exclude": "0", "session_ids": ["Session/18211"], "source_sha256": "5529e4e51ca336bf7fc532d9b15c39da8d33331f9ed595c39b17c544c1341233", "withdrawn": "", "abstract": "In mathematics education, motivated students are often accelerated to topics without more fully immersing themselves into fundamentals like addition. I have been teaching a 1st and 2nd grade math circle at Stanford University for several years. Using just addition and subtraction, some of the topics students have successfully explored in just one 10-week quarter include:\n\n•\tCounting: we count squares in a grid and squares and rectangles in a chessboard, and explore what is easy, what is difficult, and what is impossible to count.\n•\tEstimating: how can we make good estimates?\n•\tSquare and Rectangular (and Pronic) Numbers: We learn how to easily go from one to the next Square Number and seek an easy way to Square Numbers ending in 5. We consider “skins” and “insides” of Square Numbers.\n•\tCube Numbers: we learn about Cube Numbers and find two ways to easily find a Cube Number if we know the previous Cube Number.\n•\tForward Differences: We use the powerful idea of forward differences to explore sequences. With just addition and subtraction, we used forward differences to find successive Square, Cube, and other Numbers.\n•\tSquare Dissections: We consider the problem of dividing a square into smaller squares and look at Mrs. Perkin’s Quilts where we use specific dissection rules. We then create a variant to the problem called Pizza Quilts and use forward differences to find some powerful patterns in the number of differences needed to get a constant, and in the constants themselves – a discrete case of Taylor Series which students will learn some years later in calculus. We consider non-decreasing series and wonder if the numbers of Mrs. Perkin’s Quilts are non-decreasing as the squares grow.\n•\tMathematical Art and Mondrian Quilts: In the context of Mrs. Perkin’s Quilts, we consider some variants that are inspired by the art of Dutch painter Piet Mondrian.\n•\tMoney: We talk about taxes – why we have taxes, what kinds of public policy can shape the taxes we pay, what kinds of taxes there are, and how we can be fair and consider equity in tax payments. We learn how to estimate how much money you would collect in a year based on how much you might earn in an hour.\n•\tCalendar Math: Why do we have the kind of complicated calendar that we have? We learn John Conway's “Doomsday Rule”.\n\nI will share typical problems and approaches to engage and encourage 1st and 2nd graders.", "id": "Paper/66561", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66561"}, {"title": " An Introduction to Differential Geometry: Curves, Surfaces, and Curvature ", "webprogram_exclude": "0", "session_ids": ["Session/18240"], "source_sha256": "e19a119a0e7dd3decf3f3f6de6d9ddd2b80726ccf4a3ddf6f054476d418b4ffc", "withdrawn": "", "abstract": "Most of us first meet calculus as a tool for flat spaces, things like lines, planes, and functions of a single variable. But calculus can do much more. It can be used to measure and understand curved objects, from the arc of a circle to the surface of a sphere. This talk is meant as an accessible introduction to differential geometry for students who have taken calculus and linear algebra but have not yet studied the subject formally.\n\nWe will start with a simple question: what does it mean for something to be curved, and how can we actually measure that curvature instead of just describing it? Beginning with parametrised curves, we will build up the idea of a tangent vector as a natural extension of the derivative, and see how arc length and curvature arise from concrete, computable formulas. From there we will move from curves to surfaces, looking at how a surface can be described using calculus and what it means for a surface to bend in more than one direction at once.\n\nThroughout the talk, the focus will be on intuition and visualisation rather than heavy machinery. We will work through examples such as circles, helices, and spheres, and include a few elementary computations so the audience can see these ideas being developed rather than simply stated. No background in differential geometry is assumed, only familiarity with calculus and linear algebra.", "id": "Paper/66566", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66566"}, {"title": " CaTherine wheels in different contexts ", "webprogram_exclude": "0", "session_ids": ["Session/17916"], "source_sha256": "df7682e4271987e8249209d7019b5bc08f2e302143d3d26782a03e7274cea67c", "withdrawn": "", "abstract": "A CaTherine wheel is a surjective continuous map $f:S^1 → S^2$ such that for every closed interval $I \\subseteq S^1$ the image $f(I)$ is homeomorphic to a disk, and $f(\\partial I)$ is contained in the boundary of this disk. Even though the definition (and the name) are inspired by the classical Cannon-thurston map and the world of hyperbolic 3-manifolds, it turns out that CaTherine wheels and variations of them arise in several different areas of mathematics. But how can one understand the way such maps behave? In this talk we will introduce several examples and discuss some of their properties. This is joint work with Danny Calegari.", "id": "Paper/66568", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66568"}, {"title": " Zero-shot flow physics from scaling homogeneous isotropic turbulence training ", "webprogram_exclude": "0", "session_ids": ["Session/17703"], "source_sha256": "fe448b141d6b59b376b0c820fd69a3e96d68313f8f8077f8bae21fe994a28811", "withdrawn": "", "abstract": "Learned fluid models usually rely on diverse training data to generalize across flow regimes. Here we show that large-scale training on a single trajectory of homogeneous isotropic turbulence can produce zero-shot transfer to unseen flows. We train a single neural network with a next-snapshot prediction objective until it reaches spectral accuracy and long-horizon stationarity on the training regime. Without retraining, and changing only the initial and boundary conditions, the model captures vortical dynamics, shear instability, and wall-bounded flow. It reproduces vortex leapfrogging and reconnection, instability growth rates, and the law of the wall. This transfer emerges only at sufficient data and training scale. Our results suggest that scaling a single dynamically rich flow regime can be an alternative route toward general-purpose fluid models.", "id": "Paper/66571", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66571"}, {"title": " Toward an optimal Davenport–Heilbronn theorem ", "webprogram_exclude": "0", "session_ids": ["Session/18010"], "source_sha256": "7964904c2bac81e27bcc9d13b3c5eda2b799df4c23e09ae5c2f219b24f61170c", "withdrawn": "", "abstract": "The counting function of cubic field extensions of $\\mathbb{Q}$, ordered by discriminant $X$, was first studied by Davenport and Heilbronn, who proved the existence of a main term of size $X$. More recently, Bhargava--Shankar--Tsimerman and Taniguchi--Thorne independently established the existence of a secondary term of size $X^{5/6}$ in this counting function. An improvement, due to Bhargava--Taniguchi--Thorne, bounds the error term by a constant multiple of $X^{2/3+\\epsilon}$. Numerical computations, performed by Belabas and analyzed by Roberts, indicate that the true size of the error term is possibly as small as $X^{1/2+\\epsilon}$. We survey recent methods used to study this counting function. In particular, we identify obstacles, as well as possible paths, toward a square-root error term.", "id": "Paper/66574", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66574"}, {"title": " Geometry-Induced Hodge Stars on Rips and Dowker–Rips Complexes ", "webprogram_exclude": "0", "session_ids": ["Session/18026"], "source_sha256": "e80e47bef32dbcc61ce4da2bbf94a4f803a779646467d5a0fd7c3a951474b1be", "withdrawn": "", "abstract": "The Vietoris--Rips complex $\\mathrm{VR}_\\epsilon(X)$, the Dowker complex $\\Dow_R(X,Y)$, and its flagified Dowker--Rips variant $\\DR_R(X,Y)=\\Flag(\\Dow_R(X,Y))$ are simplicial complexes constructed from metric data or witness relations. They are useful in topological data analysis because they encode topology through combinatorial data derived from pairwise information, but at a fixed scale they retain little of the underlying geometry. Unlike alpha complexes or mesh-based discretizations, Rips-type complexes carry no canonical primal--dual cell structure, which is the ingredient used by the discrete exterior calculus Hodge star to encode metric information. We address this gap by equipping a Rips-type complex $K$ with diagonal geometry-induced Hodge stars represented by positive simplex weights $W_k=\\operatorname{diag}\\{w_k(\\sigma):\\sigma\\in K_k\\}$, which define weighted inner products on $k$-cochains. The resulting weighted discrete Hodge Laplacian $\\Delta_k^W$ has kernel dimension equal to the $k$th Betti number of the underlying complex, while its nonzero spectrum is governed by the chosen geometric weights. The central issue is therefore not the existence of a weighted Laplacian, since any positive diagonal weights define one, but the design of weights that encode meaningful metric or witness geometry. We focus on two computable choices: simplex-volume weights, based on Euclidean simplex volumes, and soft witness weights, based on a Dowker-style support function $s_t(\\sigma;Y)$ that quantifies higher-order witness support lost under flagification. We prove positivity, weighted self-adjointness, and Betti-number preservation for arbitrary positive diagonal weights, establish an asymptotic decay-rate characterization for soft witness support, and describe spectral descriptors derived from $\\Delta_k^W$ for comparing geometry-aware Hodge spectra on Rips and Dowker--Rips complexes.", "id": "Paper/66575", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66575"}, {"title": " Frölicher-Nijenhuis bracket and derived bracket associated to a nonsymmetric operad with multiplication ", "webprogram_exclude": "0", "session_ids": ["Session/19340"], "source_sha256": "77d5f0466417bfbdd53ba0b22963ee6b85dd3cbdb560e790f800442eb3de48ea", "withdrawn": "", "abstract": "This paper aims to construct two graded Lie algebras associated with a nonsymmetric operad with multiplication. Maurer-Cartan elements of these graded Lie algebras correspond respectively to Nijenhuis elements and Rota-Baxter elements for the given multiplication. Explicit forms of these brackets are given to study Nijenhuis operators and Rota-Baxter operators on some Loday-type algebras.", "id": "Paper/66580", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66580"}, {"title": " The Impact of Generative AI Usage on Student Academic Performance in Introductory University Mathematics Courses ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "a60b717b7882dc309473b415f75ee02121600d3bcfd2839220e3fb2a49b72e61", "withdrawn": "", "abstract": "Generative Artificial Intelligence (GAI) has rapidly became a tool commonly used among college students, raising questions about its impacts on mathematical learning and student performance. In this study, we investigate GAI use among students enrolled in Statistical Methods and College Algebra at Florida Gulf Coast University during the Fall 2026 semester. We survey students regarding the frequency and purpose of their GAI use and compare these self-reported behaviors with performance on course assessments. Using statistical methods in combination with a scientific programming language, we examine relationships between patterns of GAI usage and student mastery of course outcomes. We interpret our findings through philosophical and pedagogical perspectives on learning, with particular attention to how different modes of GAI use may support or hinder student performance. Our results provide insight into how GAI is being used in undergraduate mathematics courses and suggest considerations for incorporating these tools into the university mathematics classroom.", "id": "Paper/66590", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66590"}, {"title": " Spatiotemporal Patterns in Soft-Threshold Integrate-and-Fire Networks ", "webprogram_exclude": "0", "session_ids": ["Session/18320"], "source_sha256": "ca106cfc0f75feb346b61883a273e33b1d2dad16ef0a20da85ee9078abcb26ee", "withdrawn": "", "abstract": "Spatially and temporally organized activity in large neuronal networks underlies many neurobiological phenomena including feature selectivity and working memory. Large network activity is often modeled using neural field equations, which are macroscopic descriptions of the network. The classic neural field equations can model a variety of network activity types, but lack a direct connection to the biophysical description of single cell and synaptic dynamics. Microscopic spiking models, on the other hand, are designed to capture single cell biophysics, and can exhibit spatiotemporal behaviors which the classic neural-field equations fail to capture. Despite their simple single-neuron dynamics, large spiking networks are high-dimensional and complex.\n\nWe study the bifurcations in spatially extended networks of soft-threshold integrate-and-fire (IF) neurons using a deterministic mean-field approximation derived directly from the microscopic model and preserving its fundamental dynamics. In soft-threshold leaky IF (sLIF) networks, this formalism reveals Hopf, Turing, Turing-Hopf, and secondary instabilities and a rich repertoire of activity states. These include bulk oscillations, spatially localized activity, standing and traveling waves, as well as multistability of those patterns. We confirm predictions of the mean-field approximation with simulations of the underlying sLIF network. More broadly, our approach provides a framework for investigating spatiotemporal dynamics in networks of nonlinear IF neurons such as the soft-threshold adaptive exponential (sAdEx) IF model, which provides a good description of spike generation in cortical neurons and can generate all the fundamental types of single-neuron spiking patterns.", "id": "Paper/66595", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66595"}, {"title": " Implicitization in Real Time ", "webprogram_exclude": "0", "session_ids": ["Session/18366"], "source_sha256": "6b49238d42eacf530f90bc3a3926a6c39385e96dbbc1c6b42aca2d284816aa97", "withdrawn": "", "abstract": "A cubic surface can be realized as the projective plane blown up at six points, and the twenty-seven lines on the surface can be deduced from the coordinates of those six points. This relationship is practically begging for a dynamic visualization, allowing a user to drag around the six points and watch the associated cubic surface (and lines) deform. Building this visualization requires finding the implicit equation of a cubic surface in real time (ideally 60 frames per second). This talk will discuss how searching for ways to quickly solve this implicitization problem led us to some interesting facts about Groebner bases which have applications more generally to the implicitization of rational projective hypersurfaces with base points.", "id": "Paper/66598", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66598"}, {"title": " Calabi-Yau varieties as A-hypergeometric motives ", "webprogram_exclude": "0", "session_ids": ["Session/18263"], "source_sha256": "4f13296734929b610496eddde29df8413eb0623c3cbcf287d65f92c3aa0f5dda", "withdrawn": "", "abstract": "The periods of Calabi-Yau varieties realized as hypersurfaces in\nGorenstein Fano toric varieties satisfy GKZ A-hypergeometric\nequations. We show that the same A-hypergeometric data yields\npoint counts on Calabi-Yau varieties over finite fields, using a notion\nof finite field A-hypergeometric sums defined by Adolphson. This talk\ndescribes joint work with Thais Gomes Ribeiro, Tyler Kelly, Adriana\nSalerno, and John Voight.", "id": "Paper/66602", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66602"}, {"title": " Characters for 2-representations ", "webprogram_exclude": "0", "session_ids": ["Session/18217"], "source_sha256": "b84cda01857a5c2e1cd3454bf67bda2495242af8368c712343d1413b0fe11586", "withdrawn": "", "abstract": "Group representations very comfortably admit a higher categorical generalization.  This includes induction and restriction for 2-representations that very directly parallel classical definitions.  \n\nAn appropriate character theory for 2-representations is more opaque but,  drawing from a range of motivations, I will describe an intuitive character theory for 2-representations.  It is built from \n\n- the bicategorical trace developed to describe topological fixed point theory, \n\n- the secondary traces of Ben-Zvi and  Nadler (which connects to  Riemann-Roch and Lefschetz-type theorems in the context of differential graded categories and Fourier-Mukai transforms), \n\n- Lipmans' work on Grothediek duality, and \n\n- Ganter and Kapranov's approach to characters (that was motivated by Hopkins, Kuhn and Ravenel's work on equivariant Morava $E$-theories).\n\nOur characters are compatible with restriction and induction and, in cases that are sufficiently finite, admit a secondary character.", "id": "Paper/66604", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66604"}, {"title": " Keeping it Real(izable): Realizability of Saturated Transfer Systems of Finite Cyclic Groups ", "webprogram_exclude": "0", "session_ids": ["Session/19362"], "source_sha256": "ca56b3bba2b50a8495ec1eed197bb3dee23943ab8a05cb76fc1027a008122df4", "withdrawn": "", "abstract": "Equivariant homotopy theory has families of generalizations of commutative monoids with $G$-actions, where $G$ is a finite group. These generalizations arise from $G$-operads and differ in which symmetric multiplication operations they admit. A $G$-transfer system is a combinatorial object that encodes these generalizations. Complex linear isometries operads can be used to turn a collection of irreducible $G$-representations into a transfer system. However, we are interested in the inverse direction. For which $G$-transfer systems does such a collection, a \"$G$-universe,\" exist? Which transfer systems are \"realizable\"? When $G$ is cyclic, this question reduces to an incidence geometry problem in the subgroup lattice of $G$. We are especially interested in cyclic groups whose order has at most three distinct prime-power factors. To tackle large families of transfer systems for these groups, our method for realizability involves strategically omitting cosets from the complete set of representations.", "id": "Paper/66606", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66606"}, {"title": " Integrable systems on Poisson homogeneous spaces and GSV-birational maps ", "webprogram_exclude": "0", "session_ids": ["Session/18278"], "source_sha256": "3dd1d4359756dedca5e58e4326f5e21fa960f6a25acf566f946879b234c71737", "withdrawn": "", "abstract": "Gekhtman, Shapiro and Vainshtein introduced a family of birational Poisson maps on simple Lie groups $G$ to study exotic cluster structures compatible with non-standard Poisson-Lie structures on $G$. We employ these maps in the context of integrable systems on Poisson homogeneous spaces (based on a construction of Schrader), and investigate the dynamics of integrable systems obtained via pullback from known systems.", "id": "Paper/66608", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66608"}, {"title": " Upper bounds on sizes of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.09ex\" height=\"1.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -576.1 469.5 721.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">s</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-73\" d=\"M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-73\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-distance sets from annihilator polynomials ", "webprogram_exclude": "0", "session_ids": ["Session/19360"], "source_sha256": "2cbe7a65edee2b37291eadd58a67dae6030b01cd8a9ee67a4b49e8763a1c243a", "withdrawn": "", "abstract": "Consider a finite set $\\mathcal{C} = \\{ x_1, x_2, \\dots, x_n \\}$ in a metric space, $X$. It is considered an $s$-distance set if the set of distances between distinct points a set of size $s$, denoted as $(d_1,d_2, \\dots, d_s)$. Nozaki proved a general bound on these sets with Spherical codes and it was expanded by Musin and Barg to compact distance-transitive spaces. The method relies on a family of orthogonal polynomials associated with the compact distance-transitive space and represents the annihilator polynomial $\\prod (d_i - x)$ in its basis. The bound connects these positive coefficients to the size of $C$. The presentation covers cases in which the annihilator polynomial has degree higher than $s$, examples of cases satisfying the bound, and considers various metric spaces.", "id": "Paper/66609", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66609"}, {"title": " Convex cocompact groups with three-dimensional limit sets ", "webprogram_exclude": "0", "session_ids": ["Session/17916"], "source_sha256": "1f438747c1c49fb9e2afbc08d73b48cabfbf87b6a15db1bc2337a0e53a1d648f", "withdrawn": "", "abstract": "Given a discrete group of isometries of a real hyperbolic space, we can look at its limit set, i.e., the set of accumulation points of its orbits on the sphere at infinity. This is a compact metric space on which the group acts, and which enjoys many interesting geometric, topological, and dynamical features. For example, classical Kleinian groups provide many examples with limit sets that are quasicircles, Cantor sets, and Sierpinski carpets.\nIn this talk, I will discuss how to construct examples whose limit sets are various low-dimensional trees of manifolds. In particular, we answer a question of M. Kapovich, by constructing convex cocompact groups of isometries of real hyperbolic spaces, whose limit sets are Čech cohomology 3-spheres not homeomorphic to $S^3$. These groups are right-angled Coxeter groups and our construction is flexible enough to produce infinitely many quasi-isometry classes. This is joint work with S. Douba, G.-S. Lee, and L. Marquis.", "id": "Paper/66610", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66610"}, {"title": " Autocatalysis and Boundary Stability in Biochemical Reaction Networks ", "webprogram_exclude": "0", "session_ids": ["Session/18257"], "source_sha256": "7865fbe6c444c8cff2cbb890f4f3011b641a90ed5418d3491bf717586d2903ed", "withdrawn": "", "abstract": "Recent work has established autocatalysis as a primary driver for complex dynamical behaviors in biochemical reaction systems, including bistability, oscillations, chaos, and robustness. In this talk, we explore the specific role of autocatalysis in establishing the stability and instability of boundary steady states. Determining the stability of these states is crucial, as it identifies the thresholds for species extinction and survival---the tipping point between metabolic processes thriving or shutting down. To quantify these dynamics, we employ the next-generation matrix method, which has only recently been adapted to biochemical reaction networks, to characterize previously incomputable thresholds for the stability of boundary steady states. We focus on pathways with bifunctional enzymes as a model system.", "id": "Paper/66611", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66611"}, {"title": " Very weak solutions to quadratic Hessian equations ", "webprogram_exclude": "0", "session_ids": ["Session/18306"], "source_sha256": "3f3223254133750e72c9b3aca3814879a22aefde11961872dc481ae19c5c16b8", "withdrawn": "", "abstract": "Hessian type equations form a class of non-linear PDEs that arise in modern geometric analysis. Typically, the sought solution lives in a specific subclass of functions, making the PDE elliptic. It turns out, however, that under the additional assumption of quadratic non-linearity the methods of convex integration can be applied to construct very weak solutions. Building on the works of Lewicka-Pakzad, Cao-Szekelyhidi and others we construct very weak solutions for the real and complex $\\sigma_2$ equation - two special instances of Hessian equations. During the talk the optimal regularity of such solutions will be discussed.", "id": "Paper/66613", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66613"}, {"title": " Weak Reduction of Bridge-Trisected Surfaces ", "webprogram_exclude": "0", "session_ids": ["Session/18087"], "source_sha256": "2d05fdc4ee7516b8fdea32da0fc33028c84936e48e6740772af40d668c44ec56", "withdrawn": "", "abstract": "A bridge splitting of a knot is weakly reducible if it has a pair of disjoint shadows, one from above and one from below, in the splitting surface. The process of weak reduction exchanges local minima and maxima in the splitting, untelescoping the splitting and giving a method for detecting essential surfaces in the knot complement. Bridge trisections generalize bridge splittings to the setting of surfaces in 4-manifolds. We define weak reducibility in this context, giving diagrammatic conditions for carrying out a similar operation on bridge splittings and producing a partial classification of 4-bridge trisections of surfaces in $S^4$.", "id": "Paper/66614", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66614"}, {"title": " The Proof is in the Portfolio: Using Revision, Reflection, and Peer Review To Develop Mathematical Proof-Writers ", "webprogram_exclude": "0", "session_ids": ["Session/18341"], "source_sha256": "595e788cc025792a24b346d09a9d86eac60a70bc22a7b3264e984d22698d6b90", "withdrawn": "", "abstract": "Proof-based mathematics courses can be challenging because students must learn not only to construct valid arguments but also to evaluate, refine, and communicate mathematical ideas. To support the development of these interconnected skills, we implemented a semester-long portfolio in undergraduate Introduction to Proofs and Real Analysis courses. The portfolio engaged students in authentic mathematical practices, including proof-writing, peer review, error analysis, mathematical reflection, and professional communication. In this presentation, we describe the portfolio structure, provide examples of assignments, discuss student responses, and offer recommendations for instructors interested in adopting a similar approach.", "id": "Paper/66616", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66616"}, {"title": " Hilbert Bases of Linear Diophantine Equations ", "webprogram_exclude": "0", "session_ids": ["Session/17882"], "source_sha256": "382ae0ddd0edf6ca7f5d08b982b86bc714644a37754a97ec5d6323007602ed4b", "withdrawn": "", "abstract": "Let $A$ be a $d\\times n$ matrix with integer entries. We are interested in the \\textit{special} solutions of $A{\\mathbb x}={\\bf o}$ whose entries are {\\em nonnegative} integers. It is known that there  is a finite set of nonnegative integral solutions ${\\mathcal H}$ (called Hilbert basis) such that any special solution ${\\mathbb x}$ is a nonnegative integral combination of solutions from ${\\mathcal H}$.    In this talk we will discuss  a geometric characterization of ${\\mathcal H}$ via directed graphs.", "id": "Paper/66618", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66618"}, {"title": " Algebraic statistics of tensors with bounded entries ", "webprogram_exclude": "0", "session_ids": ["Session/18294"], "source_sha256": "3268d3fafa92ae0ca97c6c3d04e0fd14bcc26fd80e776cb2bcfdd812bb63cb4d", "withdrawn": "", "abstract": "Statisticians have long viewed relational data as contingency tables, which gives rise to an approach to testing goodness of fit for network models that are linear exponential families. A table on more than two variables is a tensor. Testing model fit requires sampling the set of tensors with the same linear statistics, such as margins, as the observed data. What makes this different from the classical contingency table problem is that graphs and simple hypergraphs are 0/1 tensors, and the moves that connect all nonnegative integer tensors with given statistics need not connect the ones with bounded entries. When the block structure of the network is latent, the same models become tensors of bounded multilinear rank, which is where the open problems lie. This talk will describe the algebraic ingredients of the resulting sampling algorithms, what changes for tensors with bounded entries, and some open problems for tables of higher order.\n\nThis talk is based on joint work with several researchers over the years, including F\\'elix Almendra-Hern\\'andez, Miles Bakenhus, Vishesh Karwa, and Mitsunori Ogawa.", "id": "Paper/66625", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66625"}, {"title": " The Minimal Global Weight of a Graph with Bounded Weights on Subgraphs ", "webprogram_exclude": "0", "session_ids": ["Session/18240"], "source_sha256": "9c7d57cad262d3b9d1df8d67a7ac4506ab6561e784938c284046f3087eb4ef25", "withdrawn": "", "abstract": "Extremal graph theory is a well-studied area, relating global properties of graphs to restrictions on their local structure, yet little work has been done in the case of \\textit{weighted} graphs. Recall the weight of a graph or subgraph is the sum of the weights of its edges. Recently, Bosman \\textit{et al}. asked what is the minimum weight of a graph with $n$ vertices such that every induced subgraph with $k$ vertices has weight at least $w$, proving a formula over $n$ for the specific case of $k=4$ and $w=3$. We resolved this problem for several families of cases, generally by bounding the minimum weight above by some family of concrete examples, and bounding it below by induction (through lemmas about the degrees of vertices of condition-satisfying graphs of a given order, with $n=k$ as the base case), together covering all cases where $k \\leq 4$, and many beyond that. However, we then discovered that previous research by Bondy and Tuza (1997), Kuchenbrod (1997), and F\\\"{u}redi and K\\\"{u}ndgen (2002) had previously investigated a dual problem—determining a graph's \\textit{maximum} weight, with its order-$k$ subgraphs having weights \\textit{at most} a given integer—solving it for all cases where $k \\leq 7$, and most beyond that; the results of this are trivially transferable to our original problem, although we used different methods. Our current goals are to investigate two conjectures left open by F\\\"{u}redi and K\\\"{u}ndgen which, if proven, would fully solve the problem for all $n$, $k$, and $w$, and to explore variations on the problem, such as allowing self-loops.", "id": "Paper/66628", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66628"}, {"title": " <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.066ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 889.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">K</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-4B\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Theory Cooperations in Equivariant and Motivic Homotopy Theory ", "webprogram_exclude": "0", "session_ids": ["Session/17843"], "source_sha256": "cca447fc440fa61e82d022f4d6fe91226ebc3bd8c024734da886411f22bcedae", "withdrawn": "", "abstract": "In the 1980s, Mahowald and Kane used integral Brown-Gitler spectra to construct\nsplittings of the cooperations algebras for $ko$, connective real $K$-theory, and $ku$, connective complex $K$-theory. These splittings helped make it feasible to do computations using the $ko$-and $ku$-based Adams spectral sequences.\n\nThese spectral sequences have proven to be powerful tools for better understanding the structure of the stable homotopy groups of the sphere, with a variety of interesting applications. For example, Mahowald used them to verify the Telescope Conjecture at height one, and Gonzalez later used them to classify stunted lens spaces. In this talk, I will discuss progress towards developing analogues of these tools in the $C_2$-equivariant and motivic settings. This is joint work with Guchuan Li, Jackson Morris, and Sarah Petersen.", "id": "Paper/66629", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66629"}, {"title": " Enumerating List Colorings ", "webprogram_exclude": "0", "session_ids": ["Session/18360"], "source_sha256": "d88b38816981e74d29923b9454bda0a1aec05f167843b76d98ceb88122a113d9", "withdrawn": "", "abstract": "The chromatic polynomial for enumerating graph colorings has a long history. We will examine how to extend these ideas to  a polynomial for enumerating graph list colorings. We will have a polynomial in many variables that depends only on the graph, with evaluation depending on the sizes of intersections of the lists to count the number of list colorings. In particular we will very briefly see how four historical approaches to the classic chromatic polynomial, Birkhoff's original  approach using Cramer's rule and a determinant as well as deletion-contraction, inclusion-exclusion and Mobius inversion can each  be extended to the list coloring setting. Along the way we also get to explore some interesting history related to the classic chromatic polynomial.", "id": "Paper/66630", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66630"}, {"title": " On the rationally complete modules ", "webprogram_exclude": "0", "session_ids": ["Session/18372"], "source_sha256": "28291d72308bc45672ad2d3062402dac1b00b11d122137313a51ef9f090b6d21", "withdrawn": "", "abstract": "Rings of quotients play an important role in ring theory and have been studied by numerous authors, including Jacobson, Johnson, and Stenstr\\\"{o}m. Utumi provided an alternative construction of a ring of quotients for any ring with a zero left annihilator. This construction is now referred to as the maximal right ring of quotients, denoted by \\(Q(R)\\), which serves as a valuable tool for characterizing the ring \\(R\\).\n\n In this talk, we introduce several new characterizations of the maximal right ring of quotients of a ring by investigating minimal rationally complete modules. Additionally, we establish several properties of the rational hull of modules and rationally complete modules. Since a ring embeds into its maximal right ring of quotients, we prove that the endomorphism ring of a module also embeds into the endomorphism ring of its rational hull. Finally, using the property of relative density, we obtain a necessary and sufficient condition for the finite direct sum of the rational hulls of submodules to equal the rational hull of the direct sum of those submodules.", "id": "Paper/66644", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66644"}, {"title": " μpscaling small models: Principled warm starts and hyperparameter transfer ", "webprogram_exclude": "0", "session_ids": ["Session/17705"], "source_sha256": "eca050dc1a4812b5e7bdd0d2586dd2db1567e01b69c9e12898ec834c0db9e02b", "withdrawn": "", "abstract": "Modern large-scale neural networks are often trained and released in multiple sizes to accommodate diverse inference budgets. To improve efficiency, recent work has explored model upscaling: initializing larger models from trained smaller ones to accelerate convergence. However, this method can be sensitive to hyperparameters that need to be tuned at the target upscaled model size, which is prohibitively costly to do directly. It remains unclear whether tuning hyperparameters on smaller models and extrapolating via scaling laws is sound in this setting. We address this with principled approaches to width-based upscaling and efficient hyperparameter tuning in this setting. Motivated by μP and any-dimensional architectures, we introduce a general upscaling method that, like Net2Net, copies and perturbs weights, but uses theoretically grounded, width-dependent scalings for the perturbation noise and optimizer hyperparameters. First, we prove that under zero perturbation, the upscaled model is functionally equivalent to the base model throughout training. Second, we extend the μP theory to enable infinite-width limit analysis and establish hyperparameter transfer for upscaled models, greatly reducing the tuning cost. We empirically demonstrate that this method is effective on realistic datasets and architectures.", "id": "Paper/66647", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66647"}, {"title": " Modeling PSA Dynamics in Intermittent Androgen Deprivation Therapy: From Constant to Varying Time Scales ", "webprogram_exclude": "0", "session_ids": ["Session/18254"], "source_sha256": "7e0ea9b776903263fbadc0421062e8028e1a44abe6879109b22417cb9e2f32ab", "withdrawn": "", "abstract": "Intermittent Androgen Deprivation (IAD) therapy presents a challenge for mathematical modeling because prostate-specific antigen (PSA) dynamics evolve continuously while treatment occurs in cycles of on- and off-treatment periods. Time scales theory provides a unified framework for modeling these dynamics.\n\nOur initial work developed a constant-time-scale model with fixed treatment-cycle lengths, providing a foundation for understanding and reproducing PSA dynamics during treatment and treatment pauses.\nHowever, clinical data suggest that cycle lengths vary throughout therapy.\nWe therefore extend the framework to varying time scales, allowing both on- and off-treatment intervals to change over time. This provides a more flexible representation of IAD therapy while retaining the advantages of the time-scales framework.\n\nWe will use both models to replicate, explain, and predict clinical PSA data and to determine whether variable treatment-cycle lengths improve model accuracy. In this talk, we present both approaches, insights from the initial model, and preliminary progress toward the varying-time-scale framework.", "id": "Paper/66648", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66648"}, {"title": " Exploring a Vast Perturbation Space: Theory and Experiment Reveal Rules of Recurrent Cortical Computation ", "webprogram_exclude": "0", "session_ids": ["Session/18357"], "source_sha256": "afff2b4c1d8e8b0b984610d772f994c4941f3e40d94c47c3cd67fb9c78167a60", "withdrawn": "", "abstract": "Most neocortical synapses are recurrent, yet the logic governing when recurrence promotes cooperation versus competition among neurons remains poorly understood. Multi-photon holographic optogenetics can activate arbitrary ensembles of neurons in mouse primary visual cortex with cellular resolution, isolating recurrent dynamics from external input. The difficulty is dimensionality: ensembles vary in size, spatial arrangement, and the stimulus preferences of their members, and the number of possible ten-cell ensembles is incredibly large. We therefore fixed ensemble size and total added spikes, and varied ensembles along two axes: spatial spread and orientation tuning.\n\nThese perturbations showed that physical space and feature space jointly determine the sign of recurrent modulation. Spatially compact, co-tuned ensembles suppressed the surrounding population while activating only nearby iso-oriented cells; diffuse ensembles of the same tuning instead produced center-surround modulation. We modeled V1 as a two-dimensional neural field whose connection kernels factor into a spatial component and a feature component. Because the perturbations are weak, the steady-state response linearizes and admits a convergent expansion over synaptic pathways, making the competition between monosynaptic excitation and disynaptic inhibition explicit. The model, constrained by anatomical connectivity data, reproduced these effects only when it included a narrow like-to-like excitatory scale and orientation-specific excitatory-to-inhibitory connectivity. Decomposing the response into the two pathways shows that compacting an ensemble recruits both more strongly, with inhibition growing faster, a testable prediction about the wiring of inhibitory neurons in V1.\n\nI will close by asking what geometric and topological descriptions of these response landscapes might capture that mechanistic decompositions do not, and where such tools might help as datasets of this kind grow richer.", "id": "Paper/66649", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66649"}, {"title": " Geometry of harmonic maps with polynomial Hopf differential from the complex to hyperbolic plane ", "webprogram_exclude": "0", "session_ids": ["Session/17283"], "source_sha256": "8853255c02830b8149aeeb813754b4f3c19061f0d8c4e6f1d7b6b995e34c3405", "withdrawn": "", "abstract": "We describe the geometry of harmonic maps (not necessarily diffeomorphisms) from the complex plane to hyperbolic plane with polynomial Hopf differential and prescribed divisor data on the holomorphic energy. This generalizes work of Han, Tam, Treibergs and Wan in the diffeomorphism case. This talk is intended to be accessible, so we will try to introduce all necessary terminology. This is joint work in progress with S. Maloni and N. Sagman.", "id": "Paper/66653", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66653"}, {"title": " The Elliptic Curve Rank Leaderboard ", "webprogram_exclude": "0", "session_ids": ["Session/18208"], "source_sha256": "472fb74aeebc44369938d9c55fe290e73881011543b0988d30a01d030d603bef", "withdrawn": "", "abstract": "I will describe my experiences in creating and maintaining a collaborative website that tracks the smallest known rational elliptic curves of each Mordell-Weil rank. Searching for such curves is a difficult problem in computational number theory. It is currently unknown whether curves with arbitrarily large ranks even exist.\n\nRunning a website like this is an inside-out way of doing math; instead of attacking the problem head-on, we instead cultivate a space that teaches others about the problem and invites them to contribute. The goal is to encourage rapid sharing of results and to build a thriving community. So far it has been a lot of fun. Maybe you too can create a website for your own pet problem!", "id": "Paper/66655", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66655"}, {"title": " Data Science and AI Opportunities Across Campus through Project-Based Teaching and Learning ", "webprogram_exclude": "0", "session_ids": ["Session/18199"], "source_sha256": "5df86f4ae3d4774d066a16aaf84778af67efe7c49e2270e62f366d80ed16b7a5", "withdrawn": "", "abstract": "The All Campus Data Science and AI Project-Based Teaching and Learning (ADAPT) model has been the subject of study for 5 years at NC State University and partner institutions, supported by NSF IUSE and NSF DRK12- . In this model, students from many different topical data science and AI courses from all 10 colleges of a large public R1 university engage in 1-credit project-based courses taught by a variety of instructors from business, government and academia. The model has common learning elements that support conversation among instructors and connection across courses. The 1-credit courses have been incorporated into credentials across the institution, as a mechanism for bringing data science and AI learning options to all students. This talk will include work in collaboration with NC State graduate student Laura Short and colleagues Sunghwan Byun and Daniela Castellanos-Reyes.", "id": "Paper/66656", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66656"}, {"title": " A Gift to Algebra Students from Lennard-Jones. ", "webprogram_exclude": "0", "session_ids": ["Session/19341"], "source_sha256": "f4c0b5f1259c5c67dd00d7b194a2f1b41e856bc002936ebec48f00fd2b239ec9", "withdrawn": "", "abstract": "The Lennard-Jones Potential (LJP) is a real-world mathematical function that is mathematically accessible to students of algebra before they begin calculus.  We present the LJP as an algebraic function, consider questions about the LJP that are appropriate for a pre-calculus algebra course, and then answer those questions.", "id": "Paper/66661", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66661"}, {"title": " A proof of conjectures of Esterle and Ransford on negative powers of contractions ", "webprogram_exclude": "0", "session_ids": ["Session/18277"], "source_sha256": "9a93252867cd99012382e17648f8953f46e49f16abb51596b99c43474fc3594b", "withdrawn": "", "abstract": "Building on work of Ransford, we prove that whenever $E$ is a closed subset of the unit circle of Lebesgue measure zero, there exists a positive sequence $u_n\\to\\infty$ such that if $T$ is a contraction on a Hilbert space with $\\sigma(T)\\subset E$ and $\\|T^{-n}\\|=O(u_n)$, then $T$ is unitary.\nThis confirms conjectures of Esterle and Ransford. Our main new idea is a spikes-in-collars principle for positive subharmonic functions.", "id": "Paper/66663", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66663"}, {"title": " Can an AI Agent Rediscover a Blaschke-Curve Invariant? ", "webprogram_exclude": "0", "session_ids": ["Session/17887"], "source_sha256": "84d379a1ab4aef02af7daacad657e272a8b849bbc07a7ef7bb3dd109ef7eaf40", "withdrawn": "", "abstract": "We propose generalized Blaschke curves as a controlled testbed for AI-assisted mathematical discovery. A degree-four finite Blaschke product maps each parameter $\\lambda$ on the unit circle to four roots. The six lines determined by pairs of roots are tangent to a parameter-independent class-three algebraic curve. We withhold this fact from an agent and provide only normalized line coordinates from 80 parameter values. The agent rejects simpler fixed-point and conic hypotheses, discovers a homogeneous cubic in the dual projective plane, extends it from polygon sides to diagonals, and freezes its equation before evaluation. The experiment illustrates a compact protocol for separating observation, conjecture, held-out validation, and proof in automated mathematical research.", "id": "Paper/66665", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66665"}, {"title": " Towers of Bell–Rogalski algebras ", "webprogram_exclude": "0", "session_ids": ["Session/18278"], "source_sha256": "2216eb2f1b23b9710d2130f3b6304727e086c43d5093659c19d64c2fa15f18cd", "withdrawn": "", "abstract": "Given a two generalized Weyl algebras (GWAs), $A$ and $A'$, over a fixed commutative ring $R$ with a fixed automorphism $\\sigma$, the work of Hartwig and Rosso shows how to construct a weight module for $A \\otimes_R A'$ from weight modules for $A$ and $A'$. Taking the direct sum of Grothendieck groups of the category of weight modules for such GWAs, this tensor product on modules then defines a ring structure on this direct sum. We extend this to the setting of Bell--Rogalski (BR) algebras and connect indecomposable representations of rank 1 BR algebras to certain quiver representations, generalizing the work of Drozd, Guzner, and Ovsienko. This is joint work with Daniele Rosso.", "id": "Paper/66666", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66666"}, {"title": " Equivariant formality, representation theory and K-theoretic indices ", "webprogram_exclude": "0", "session_ids": ["Session/19358"], "source_sha256": "f41ce060d6f700ad364e10bf7dc8d8b0ca488e20599f062e3930405b3d5beb8d", "withdrawn": "", "abstract": "Let $G$ be a compact connected Lie group and $K$ its connected Lie subgroup. Using the $K$-theoretic version of equivariant formality which involves analysis of vector bundles over $G/K$, we find two characterizations of equivariant formality of the isotropy action of $K$ on $G/K$. The first one equates equivariant formality with a ``smoothness\" condition of the restriction map of the representation ring of $G$ to that of $K$ and strengthens a previous result by rendering the condition of torsion-freeness of $\\pi_1(G)$ unnecessary. The second characterization asserts that equivariant formality amounts to the equivariant $K$-theoretic index pairing of two certain special $K$-theory classes being nontrivial in some sense. By applying these characterizations, we give a representation theoretic criterion for equivariant formality of the isotropy action by a circle subgroup, as well as an invariant theory criterion for the case where $K$ is a torus of dimension one less than the rank of $G$, culminating in a complete classification of equivariant formality where $G$ is further assumed to be simple.", "id": "Paper/66670", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66670"}, {"title": " The Lake Wobegon Paradox ", "webprogram_exclude": "0", "session_ids": ["Session/19355"], "source_sha256": "e6fba9bdc213835668001fa3b71574efd4629b5edac3ecdcdf889605060c8c85", "withdrawn": "", "abstract": "The long-running radio program {\\it A Prairie Home Companion} contained a recurring skit called ``News from Lake Wobegon,'' which featured a fictional town in which ``all the children are above average.''  The humor of that line stems from its seeming impossibility, since in any list of numbers the arithmetic mean cannot be less than the minimum value.\nAccordingly, it should be impossible for all of a function's values to be above average.  But in Lake Wobegon \\dots ?", "id": "Paper/66674", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66674"}, {"title": " Dynamics of an Electron in an Inhomogeneous Magnetic Field ", "webprogram_exclude": "0", "session_ids": ["Session/18316"], "source_sha256": "300d982f56ce57ead6824e7ba2fba91e3fd0e145060a6c16a508717acf9327a9", "withdrawn": "", "abstract": "We study the dynamics of an electron in a magnetic field that is piecewise constant. In some settings, it is convenient to consider the system through the lens of mathematical billiards. We show the existence of periodic trajectories of all rational rotation numbers, determine the linear stability of low-period trajectories, and more. Comparisons are made with (standard) magnetic billiards inside a connected domain.", "id": "Paper/66676", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66676"}, {"title": " A Generalized Nonlinear Conic Scalarization Function: Properties and Applications ", "webprogram_exclude": "0", "session_ids": ["Session/19336"], "source_sha256": "8f2ab9100c9815637ec2fd2e5675c798c5bb29294c5162d2980cf732fdddc7c4", "withdrawn": "", "abstract": "We present a generalized nonlinear scalarization function that expands upon Kasimbeyli’s conic scalarization framework. After establishing the function's core mathematical properties—namely convexity, positive homogeneity, $u$-monotonicity, and continuity — we demonstrate its utility across distinct classes of optimization problems. First, we utilize the function to characterize optimality conditions for $u$-minimal and weak $u$-minimal solutions in set-valued optimization. Second, we combine this approach with image space analysis to construct a generalized weak separation function, successfully deriving optimality conditions for generalized Ky Fan inequalities. To validate the scope and effectiveness of these novel findings, we provide supporting examples within infinite-dimensional spaces.", "id": "Paper/66677", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66677"}, {"title": " The Degree-Bounded Characteristic Imset Polytope ", "webprogram_exclude": "0", "session_ids": ["Session/18115"], "source_sha256": "31c3122dc6f9d2ef43f400526bf5df703f503e644bb91cdb2a2eb32f75d25d9b", "withdrawn": "", "abstract": "The characteristic imset (CIM) polytope is a 0/1 polytope whose vertices represent Markov equivalence classes of directed acyclic graphs. Several causal discovery problems can be viewed as solving a linear program over the CIM polytope. However, since the dimension of the CIM polytope grows exponentially in the number of nodes of the underlying DAG, solving these linear programs is computationally intractable. We introduce the degree-bounded characteristic imset polytope, whose vertices correspond only to DAGs whose nodes have bounded in-degree $k$. For fixed $k$, the dimension of this polytope grows polynomially in the number of nodes of the DAG. For $k=1$, we show that this polytope is a matroid independence polytope and we give an extensive list of facets for this polytope when $k =2$.", "id": "Paper/66678", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66678"}, {"title": " Small Data Global Existence for Quasilinear Wave Equations in Accelerating FLRW Spacetimes ", "webprogram_exclude": "0", "session_ids": ["Session/17998"], "source_sha256": "f2d710e1f5e684426369edd65f59d009b548551d2210457cd699e9f1ae3f3ab2", "withdrawn": "", "abstract": "Nonlinear wave equations on curved backgrounds are fundamental to geometric analysis and general relativity. Ensuring the small-data global existence of solutions for these equations provides a rigorous foundation for physical models in expanding universes. Quasilinear wave equations, where the nonlinearities depend directly on the solution and its first derivative, present significant analytical challenges compared to their semilinear counterparts. While accelerating cosmic expansion is known to act as a stabilizing mechanism for semilinear wave equations, its effect in the quasilinear regime remains less understood. In this work, we prove that accelerating expansion in Friedmann–Lemaître–Robertson–Walker (FLRW) spacetimes acts as a viable stabilizing mechanism, establishing small-data global existence for a class of quasilinear wave equations. These results offer key insights into broader geometric nonlinear PDE problems, including the stability of the Einstein field equations. Moreover, the adapted vector field methods developed here offer potential applications to wave equations on more complex cosmological backgrounds, such as black hole spacetimes.", "id": "Paper/66688", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66688"}, {"title": " Nairian Models and the Total Failure of Square ", "webprogram_exclude": "0", "session_ids": ["Session/18646"], "source_sha256": "ed04ebd6872f16eefca09a1d9954333db2b2873137b9d2c2d3f33b07fbe39928", "withdrawn": "", "abstract": "Nairian models form a new class of determinacy models, having additional structure\nbeyond their sets of real numbers. Forcing over a Nairian model with Woodin’s $\\mathbb{P}_{\\mathrm{max}}$\nforcing, we show how to make Jensen’s square principle fail at every regular cardinal\nwith cofinality greater than $\\omega_{1}$. Since suitable Nairian models can be produced from\na hypothesis weaker than a Woodin limit of Woodin cardinals, this rules out one proposed route for showing that Martin’s Maximum is equiconsistent with a supercompact\ncardinal. In the same model, every uncountable regular cardinal is $\\omega$-strongly measurable in HOD. This shows that Woodin’s HOD hypothesis is not provable from ZFC.\nThis is joint work with Grigor Sargsyan and Douglas Blue.", "id": "Paper/66690", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66690"}, {"title": " Bifurcation Analysis of a Human African Trypanosomiasis Model ", "webprogram_exclude": "0", "session_ids": ["Session/19359"], "source_sha256": "4029aa4bb1214cec7fed04810abb838ea2e1f398d24eb395c35d9a7ab01f4415", "withdrawn": "", "abstract": "Human African \\textit{trypanosomiasis} (HAT), also known as African sleeping sickness, is a Neglected Tropical Disease (NTD) endemic to rural regions of sub-Saharan Africa. Although large-scale outbreaks have historically resulted in substantial mortality, the long-term impact of HAT extends beyond death rates through chronic infection, neurological complications, and the social and economic burden experienced by affected communities. Infection is modeled by a two channel system wherein vectors can simultaneously infect both human and zoonotic compartments. The zoonotic compartment also serves as a reservoir for the disease in the environment. The basic reproductive number and the equilibrium states of the model are found, as well as local stability conditions for both equilibrium. We simulate the model numerically to show the conditions under which the stability of each equilibrium state is achieved. To investigate the organization of equilibria across parameter space, we introduce a transmission scaling parameter $\\kappa$ preserving the relative contribution of each transmission pathway while allowing the overall transmission intensity of the system to vary continuously. For each value of $\\kappa$, equilibrium solutions were computed numerically using continuation, with the previous equilibrium serving as the initial approximation for the next parameter value. Stability was determined by evaluating the eigenvalues of the Jacobian matrix at each equilibrium and tracking the dominant eigenvalue. The resulting bifurcation structure provides insight into the transition between disease elimination and endemic persistence and serves as the foundation for future analytical work involving center manifold reductions, persistence theory, and global stability analysis.", "id": "Paper/66692", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66692"}, {"title": " The effect of how two PDEs “meet” on the growth and concentration properties of their joint eigenfunctions ", "webprogram_exclude": "0", "session_ids": ["Session/17442"], "source_sha256": "7f7f6ec8d7bf0a805265cb9246161970bbe0963edc5821ca1317fc7df85bfe52", "withdrawn": "", "abstract": "Many physical phenomena, such as heat diffusion, wave propagation, and the behavior of quantum particles, can be described in terms of Laplace eigenfunctions $\\phi$ with eigenvalue $\\lambda$, which satisfy $-\\Delta \\phi=\\lambda \\phi$, where $\\Delta$ is the Laplace-Beltrami operator. The high-frequency (large $\\lambda$) eigenfunctions have been of particular interest due to their correspondence with high-energy quantum particles. In 1988, to understand the growth and concentration of these eigenfunctions, Sogge obtained estimates on the growth of their $L^p$ norms. Since then, there has been much interest in understanding the conditions in which Sogge’s estimates can be improved. In this talk, we will describe how the growth of the $L^p$ norms can be improved by assuming that the eigenfunctions $\\phi$ satisfy a second equation. We call such functions joint eigenfunctions. As it turns out, the growth and concentration of the joint eigenfunctions depend on how the two equations “meet.” We obtain a sharp estimate for the growth of the $L^p$ norm under the assumption that the equations “meet” with kth order contact. We will define the notion of equations “meeting” with kth order contact and discuss our key tools. This is joint work with Melissa Tacy.", "id": "Paper/66693", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66693"}, {"title": " Lessons From Deploying AI Feedback on Student Proofs ", "webprogram_exclude": "0", "session_ids": ["Session/18346"], "source_sha256": "d6fa8453cbfd040db6662eae9daa7be0654413acfe69d57478f2e823295c36ef", "withdrawn": "", "abstract": "HaLLMos (hallmos.com) is a free online tool that gives students feedback on their proof attempts. We describe its two-stage design. First, a frontier reasoning model, the Critic, walks through a submission step by step and produces a structured list of concerns: what is wrong, what is missing, and what is unclear. Students never see this output. Instead, a second, fine-tuned model, the Coach, turns the Critic's concerns into feedback for the student. Separating the two stages lets the Critic be as capable as current models allow while the Coach is aligned for tone and consistency, and lets us evaluate \"did the system correctly identify the errors in the proof, if there are any?\" separately from \"did it communicate them well to the student?\" The Coach is guided by a written constitution developed with a panel of mathematicians and mathematics educators, whose principles include beginning with what is good about the attempt, distinguishing logical errors from issues of clarity, naming false statements directly, and giving the student enough information to make needed repairs themselves. HaLLMos has now received more than 35,000 proof submissions, and we discuss how this has gone, what we have learned, and what our surveys and interviews of students say.", "id": "Paper/66695", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66695"}, {"title": " Simulating alcohol consumption for non-human Primates ", "webprogram_exclude": "0", "session_ids": ["Session/17972"], "source_sha256": "a7a45ca528a4edf1aa0c78d906e36764060693978fd73fe0a048af64afff9501", "withdrawn": "", "abstract": "We present two models for the alcohol intake of non-human primates (rhesus monkeys).  The first is a probabilistic model that utilizes a Markov Chain to simulate various drinking behavior in the controlled intake phase  of the experiment.   The second is a system of differential equations that describes the change in blood ethanol concentrations accounting for the presence of food in the open access phase of the experiment.  We combine these two models, updating the parameters in the first model for open access, to simulate binge drinking as well as other drinking behaviors.  Using data from the Monkey Alcohol Tissue Research Resource from the Oregon National Primate Research Center,  we calibrate our model to find the best parameters such as rates of absorption and metabolism.", "id": "Paper/66696", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66696"}, {"title": " A weak Allee growth model with predator-induced emigration ", "webprogram_exclude": "0", "session_ids": ["Session/18289"], "source_sha256": "182cecd003422c4c028361b5933af5e06cc9e81402f9c5fa0b7f82bcc3a2fdc8", "withdrawn": "", "abstract": "We analyze the structure of positive steady states for landscape ecological models of the form:\n\\[\n\\left\\lbrace \\begin{matrix}-\\Delta u= \\lambda \\left[\\frac{u}{a}(u+a)(1-u)-h(u)\\right];~\\Omega\\\\\n\\frac{\\partial u}{\\partial \\eta} + \\sqrt{\\lambda} \\gamma g(u) u=0; ~\\partial \\Omega\n\\end{matrix} \\right.\n\\]\nwhere $\\lambda> 0$ is a parameter that is proportional to patch size square, $\\gamma > 0$ is a parameter that quantifies the exterior matrix hostility, $a \\in (0,1)$, $\\Omega$ is a bounded domain in $\\mathbb{R}^N$; $N > 1$ with smooth boundary $\\partial \\Omega$ or $\\Omega =(0,1)$, and $\\frac{\\partial u}{\\partial \\eta}$ is the outward normal derivative of $u$. Here, $h$ represents harvesting and $g$ the emigration pattern.\n\nWe compare the structure of the positive solutions to cases where emigration, $g$, is affected by harvesting, $h$, to the case when it is not.  We establish existence, non-existence, and multiplicity results via the method of sub and super solutions.  When $N=1$, namely $\\Omega = (0,1)$, we obtain bifurcation diagrams via a quadrature method and Mathematica computations.  We also discuss the biological implications of our results.", "id": "Paper/66697", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66697"}, {"title": " Inhibitory Subtypes Shape the Stability and Wandering of Memory Bumps ", "webprogram_exclude": "0", "session_ids": ["Session/18320"], "source_sha256": "fd72140b6ec97f778b39152b90a156b043b2933da087a0a880deaed32d347924", "withdrawn": "", "abstract": "Persistent, localized patterns of cortical activity (\"bumps\") are a leading substrate for storing continuous variables in working memory, and neural field models provide a natural setting for analyzing them. Nearly all such models collapse inhibition into a single homogeneous population, yet cortical interneurons are heterogeneous: parvalbumin-expressing (PV) cells deliver fast, local, perisomatic inhibition; somatostatin-expressing (SST) cells target distal dendrites over a broader footprint; and the two classes inhibit one another asymmetrically.\n\nWe introduce a three-population stochastic neural field with excitatory, PV, and SST layers. In the high-gain (Heaviside) limit, stationary bumps are characterized exactly by their six threshold-crossing interfaces, and reflection symmetry splits the resulting eigenvalue problem into three-dimensional shifting and scaling blocks. This decomposition identifies not only when a bump loses stability but how: slow inhibitory timescales destabilize it through either the shifting subspace, producing drift and traveling waves, or the scaling subspace, producing oscillatory width changes that annihilate the memory. Sweeping thresholds, connection strengths, and spatial scales, we find that even weak inhibitory-to-inhibitory coupling reshapes the stable region nonmonotonically, while broadening inhibitory projections both enlarges that region and strengthens the linear restoring rate within it. Projecting weak noise onto the translational null mode yields an effective diffusion coefficient for bump wandering that agrees with simulation and decreases as the SST footprint grows. Interneuron diversity thus shapes both the deterministic robustness and the stochastic precision of continuous-attractor memories, and yields a tractable testbed for dynamical-systems questions involving symmetry, bifurcation, and noise-driven motion along a neutral direction.", "id": "Paper/66698", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66698"}, {"title": " A Time-Dependent Information Bottleneck Trade-Off Parameter ", "webprogram_exclude": "0", "session_ids": ["Session/19345"], "source_sha256": "072eccc09f26b1ff2184b1d1875beda9470cd49a3d245ea964cf42a54ce0d3b9", "withdrawn": "", "abstract": "The Variational Information Bottleneck (VIB) provides a framework for learning compressed representations that retain information relevant to a prediction task. Standard formulations control the trade-off between compression and predictive information via a fixed Lagrange multiplier, which may be restrictive for temporally evolving data. In this work, we investigate a time-dependent trade-off parameter whose value reflects the expected mutual information between known statistics of a time series input and learned representations produced by a neural network. This formulation allows the information constraint to vary with the temporal structure of the data rather than remaining fixed throughout training.", "id": "Paper/66701", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66701"}, {"title": " Surgery and Me: A guide to surgery on 3-manifolds and its applications to HQFTs in 4-dimensions from Hopf algebras ", "webprogram_exclude": "0", "session_ids": ["Session/17907"], "source_sha256": "9b4bcb849cd7dfd9b2d7e15db8f3112cc77ebfad440070e09caa81c8584de329", "withdrawn": "", "abstract": "Surgery on manifolds has proven to be incredibly lucrative for constructing invariants. Famously, the Reshetikhin-Turaev quantum invariant is defined from performing surgery on 3-manifolds along framed links. Recently, the authors gave a construction for finding Heegaard diagrams of 3-manifolds post-link-surgery. \n\nMoving up a dimension, surgery rears its (lovely) head when constructing 4-manifolds via handle attachments. Specifically, a 4-manifold can be built by attaching 4-dimensional handles of increasing index, homotopy equivalent to k-cells in a CW complex. The boundary of each attachment is a 3-manifold, and thus is given as the result of surgery on another 3-manifold. In this talk, we review the 3-manifold surgery story, explore trisection diagrams, a 4-dimensional analogue to Heegaard diagrams, and discuss surgery in relation to 3-handle attachments. For motivation, we will present two 4-dimensional homotopy quantum field theories based on 3-dimensional versions from Hopf algebras.\n\nThis talk is based on work in progress with Shawn Cui.", "id": "Paper/66703", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66703"}, {"title": " On the Cuspidal Cohomology of Congruence Subgroups of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"8.301ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 3574.2 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathrm {SL}(3, \\mathbb {Z})</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-53\" d=\"M55 507Q55 590 112 647T243 704H257Q342 704 405 641L426 672Q431 679 436 687T446 700L449 704Q450 704 453 704T459 705H463Q466 705 472 699V462L466 456H448Q437 456 435 459T430 479Q413 605 329 646Q292 662 254 662Q201 662 168 626T135 542Q135 508 152 480T200 435Q210 431 286 412T370 389Q427 367 463 314T500 191Q500 110 448 45T301 -21Q245 -21 201 -4T140 27L122 41Q118 36 107 21T87 -7T78 -21Q76 -22 68 -22H64Q61 -22 55 -16V101Q55 220 56 222Q58 227 76 227H89Q95 221 95 214Q95 182 105 151T139 90T205 42T305 24Q352 24 386 62T420 155Q420 198 398 233T340 281Q284 295 266 300Q261 301 239 306T206 314T174 325T141 343T112 367T85 402Q55 451 55 507Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-4C\" d=\"M128 622Q121 629 117 631T101 634T58 637H25V683H36Q48 680 182 680Q324 680 348 683H360V637H333Q273 637 258 635T233 622L232 342V129Q232 57 237 52Q243 47 313 47Q384 47 410 53Q470 70 498 110T536 221Q536 226 537 238T540 261T542 272T562 273H582V268Q580 265 568 137T554 5V0H25V46H58Q100 47 109 49T128 61V622Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJAMS-5A\" d=\"M39 -1Q29 9 29 12Q29 23 60 77T219 337L410 648H364Q261 648 210 628Q168 612 142 588T109 545T97 509T88 490Q85 489 80 489Q72 489 61 503L70 588Q72 607 75 628T79 662T81 675Q84 677 88 681Q90 683 341 683H592Q604 673 604 666Q604 662 412 348L221 37Q221 35 301 35Q406 35 446 48Q504 68 543 111T597 212Q602 239 617 239Q624 239 629 234T635 223Q635 215 621 113T604 8L597 1Q595 -1 317 -1H39ZM148 637L166 648H112V632Q111 629 110 622T108 612Q108 608 110 608T116 612T129 623T148 637ZM552 646Q552 648 504 648Q452 648 450 643Q448 639 266 343T77 37Q77 35 128 35H179L366 339L552 646ZM572 35Q581 89 581 97L561 77Q542 59 526 48L508 37L539 35H572Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-53\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-4C\" x=\"556\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"1182\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-33\" x=\"1571\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2C\" x=\"2072\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJAMS-5A\" x=\"2517\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"3184\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/17903"], "source_sha256": "fb485b8f29c1ee1bb0f7c82e3b104b1b854fcd859af7eed6e6f079e937d5db24", "withdrawn": "", "abstract": "In this talk, we will discuss recent advances made in computations related to $\\mathrm{GL}(3)$ automorphic forms.  In particular, we will talk about how to compute the action of Hecke operators on the cuspidal cohomology of congruence subgroups of $\\mathrm{SL}(3, \\mathbb{Z})$.  As an example, we will introduce the Iwahori congruence subgroup $\\mathcal{I}(3, p)$, detailing how we identified levels with nonzero cuspidal classes and computed the action of Hecke operators at two of these levels. These are the first examples of non-essentially-self-dual automorphic representations of trivial cohomological weight that are Steinberg at $p$ appearing at Iwahori level.", "id": "Paper/66706", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66706"}, {"title": " Classification of gapped states of quantum spin chains ", "webprogram_exclude": "0", "session_ids": ["Session/17925"], "source_sha256": "41bebe6fb08d72fe922d79a37a8b9fe7cfc0345fb1ce28db7f825fbc1d262b2e", "withdrawn": "", "abstract": "We study gapped ground states of local Hamiltonians in one-dimensional spin chains. Using recent techniques, we prove that any such ground state is short-range entangled (SRE): it can be connected to a product state by a finite-time evolution generated by an exponentially quasi-local Hamiltonian. This makes precise the idea that one-dimensional gapped systems are topologically trivial in the absence of symmetries.\n\nWhen a symmetry is imposed, however, SRE states can display non-trivial topological features. Symmetry Protected Topological (SPT) phases are defined as equivalence classes of G-invariant SRE states, where two states are equivalent if they can be smoothly deformed into one another while preserving the symmetry. We show that the set of one-dimensional SPT phases for a compact topological group $G$ forms a group isomorphic to $H^2_{Borel}(G, U (1))$, yielding a complete classification of unique gapped ground states with symmetry in one dimension.", "id": "Paper/66707", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66707"}, {"title": " On the Unique Recovery of Transport Maps and Vector Fields from Finite Measure-Valued Data ", "webprogram_exclude": "0", "session_ids": ["Session/18280"], "source_sha256": "fb57ae2309cd3c32109b3311de6586466be7c6ab2e98142b6c1f5d7c27645eda", "withdrawn": "", "abstract": "We establish conditions under which transport maps and vector fields are uniquely recoverable from finitely many measure-valued observations. In particular, we show when a diffeomorphism (f) is uniquely determined by its action on finitely many densities, and derive a metric on diffeomorphisms based on discrepancies between these pushforward densities. We prove analogous infinitesimal results showing when a vector field (v) is uniquely determined from finitely many weighted divergence observations. Using Whitney and Takens embedding theory, we obtain bounds on the required number of densities that depend only on the problem's intrinsic dimension. We connect these results to Perron--Frobenius and Koopman operators and apply them to establish new well-posedness guarantees for inverse problems arising in continuity, advection, Fokker--Planck, and advection-diffusion-reaction equations. Numerical experiments illustrate the recovery of both transport maps and vector fields from finite measure-valued data.v", "id": "Paper/66710", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66710"}, {"title": " A structural property of generic initial ideals ", "webprogram_exclude": "0", "session_ids": ["Session/18285"], "source_sha256": "da1fb7584348d9e1e90a6072108a759cda732f8c83997e5ac3f8818e16b88a29", "withdrawn": "", "abstract": "For over a century mathematicians have studied how to transfer information between a homogeneous ideal and its initial ideal. In this talk I will consider this topic in the context of regular sequences. I will present an asymptotic structural property of generic initial ideals. This single phenomenon yields results on Hilbert functions, persistence, hyperplane restriction, graded Betti numbers, combinatorial shadow minimization, and Lefschetz properties.", "id": "Paper/66712", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66712"}, {"title": " Higher Brauer groups ", "webprogram_exclude": "0", "session_ids": ["Session/18000"], "source_sha256": "77d31fa5678bc00c415b730b7107da4b307340dd316a5e1fbde784c25baaa4e6", "withdrawn": "", "abstract": "I will discuss joint work with David Gepner on higher Brauer groups and the associated Azumaya algebras.", "id": "Paper/66714", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66714"}, {"title": " Can one hear where a drum is struck? ", "webprogram_exclude": "0", "session_ids": ["Session/17965"], "source_sha256": "b25a81813bd40231547de02ada02b017a8c5ca68c56b6f81b8dd362ab1981023", "withdrawn": "", "abstract": "We give an overview of a variation on Kac's famous question, \"Can one hear the shape of a drum?\" Instead of asking if the Weyl counting function determines the isometry class of a Riemannian manifold, we ask if the local Weyl counting function, evaluated at a point, determines the isometry-group orbit of this point. We will state the problem, present its physical justification, work through a few of the simpler examples, and sketch some of the more involved results---the last of which was a surprise uncovered by a cohort of undergraduate researchers.", "id": "Paper/66716", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66716"}, {"title": " Bounds, Existence and Extremal Results on Fault Tolerant Zero Forcing ", "webprogram_exclude": "0", "session_ids": ["Session/19354"], "source_sha256": "b6fc486abc7301ca3584ae825ee3234fb79f80b9bd877c4899a9f77383b0f8ec", "withdrawn": "", "abstract": "Zero forcing is a recent branch of Graph Theory, primarily for its application to linear algebra, quantum walks and disease pathology. For zero forcing, an initial set of the graph's vertices are chosen and colored blue the other vertices are colored white. The iterative process of the color change rule then starts, where a blue vertex forces an adjacent white vertex to be colored blue if that is its only white neighbor. If the initial set of blue vertices successfully colored every other vertex blue, then the initial set is called a zero forcing set. Recently a new variant of zero forcing called $k$-fault tolerant zero forcing was defined, which introduced $2$ new definitions. A set $B$ is a $k$-fault tolerant zero forcing set if, every subset of size $|B|-k$ is a zero forcing set. Then the $k$-fault tolerant zero forcing number, is the smallest set $B$ such that $B$ is $k$-fault tolerant zero forcing set. Previous works focused on values for $k=1$, in this presentation we focus on generalizing this to any positive integer value $k$. From this, we got lower bounds for the $k$-fault tolerant zero forcing number, existence of forts and results for extremal values of $k$. These findings also give new upper bounds for the original definition of zero forcing.", "id": "Paper/66717", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66717"}, {"title": " FunDiff: diffusion models over function spaces for physics-informed generative modeling ", "webprogram_exclude": "0", "session_ids": ["Session/18447"], "source_sha256": "fc8e2d457a10c853693d4dd8049b32634afbb8462011bee737e8513a5e87b77d", "withdrawn": "", "abstract": "Recent advances in generative modeling-particularly diffusion models and flow matching-have been widely used for synthesizing discrete data such as images and videos. However, adapting these models to physical applications remains challenging, as the quantities of interest are continuous functions governed by complex physical laws. To address this, we introduce FunDiff, an efficient and robust framework for generative modeling in function spaces. FunDiff combines a latent diffusion process with a function autoencoder architecture to handle input functions with varying discretizations, generates continuous functions that can be evaluated at arbitrary locations, and seamlessly incorporate physical priors. These priors are enforced through architectural constraints or physics-informed loss functions, ensuring that generated samples satisfy fundamental physical laws. We theoretically establish minimax optimality guarantees for density estimation in function spaces, demonstrating that diffusion-based estimators achieve optimal convergence rates under suitable regularity conditions. We further demonstrate the practical effectiveness of FunDiff across diverse applications in fluid dynamics and solid mechanics. Empirical results indicate that our method can generate physically consistent samples with high fidelity to the target distribution, and exhibit robustness to noisy and low-resolution data.", "id": "Paper/66720", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66720"}, {"title": " Efficient flow in crowded collectives ", "webprogram_exclude": "0", "session_ids": ["Session/17370"], "source_sha256": "1057cc5ec45a7ad809588c3fa041df91a299c1a7bfc8ce3b82a695087948d995", "withdrawn": "", "abstract": "Heterogeneous crowds manage to share space every day in plazas, train stations, and other city spaces. We present progress on theory, simulation, and robotics for understanding emergent patterns and optimal behavior in crowds and flows. First, we discuss analytical work on estimating the “optimal number of cooks to use in a kitchen” for settings where individuals move in different directions and seek to reach different goal points. Next, inspired by pedestrians walking on a train platform, we examine unidirectional flows of robots with varying speeds and study how the collective behavior changes as density rises. Our work integrates ideas from physics, engineering, and statistics, and is applicable to coordinating robot swarms and designing infrastructure for dense populations.", "id": "Paper/66728", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66728"}, {"title": " Quantum Cellular Automata and Algebraic <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.066ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 889.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">K</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-4B\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-theory ", "webprogram_exclude": "0", "session_ids": ["Session/18217"], "source_sha256": "c9cd09bee2b6c86a1a8a5a4da9d41ec475eb2cdf84f4b069cdf38dc0f1f313a3", "withdrawn": "", "abstract": "The purpose of this talk is to explain an application of algebraic $K$-theory to the classification of quantum cellular automata (QCA), which are models for the dynamics of many-particle quantum systems. Over an arbitrary commutative ring $R$ and for a general class of metric spaces $X$, we use algebraic $K$-theory to construct a space of QCA whose homotopy type depends only on the large-scale (coarse) geometry of $X$. We then show that the classification spaces for algebraic QCAs on Euclidean lattices assemble into an $\\Omega$-spectrum indexed by spatial dimension. As a corollary, we obtain a nonconnective delooping of the $K$-theory of Azumaya $R$-algebras whose negative homotopy groups are the QCA classification groups. This realization also has applications to studying anomalies on quantum systems. Our key insight is that QCA admit a multiplicative analogue of the Pedersen–Weibel model for negative algebraic $K$-theory, and our construction is obtained by adapting their bounded-propagation framework from direct sums of modules to tensor products of matrix algebras. This talk is based on joint work with Bowen Yang.", "id": "Paper/66729", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66729"}, {"title": " Partition of Unity Neural Networks for Interpretable Classification ", "webprogram_exclude": "0", "session_ids": ["Session/17945"], "source_sha256": "0132200ae8cd6c4b853bcf8df79e0e872e52abcf55a3ef989478ddd22a749312", "withdrawn": "", "abstract": "We introduce Partition of Unity Neural Networks (PUNNs), a neural-network architecture for multiclass classification based on the classical notion of a partition of unity. PUNNs replace the characteristic functions of ideal class regions by learned continuous partition functions whose values are interpreted directly as class probabilities. These functions are generated recursively from input-dependent gates, guaranteeing nonnegative probabilities that sum to one without a separate normalization such as softmax, while providing an explicit factorization of each class probability.\n\nWe prove that PUNNs are dense in the space of continuous probability maps from compact subsets of Euclidean space into the probability simplex, including maps whose components may vanish. We also discuss multiple partition components per class and geometry-informed gates. Numerical examples on synthetic data, MNIST, and CIFAR-100 illustrate the learned partitions, the effect of class ordering, and cases in which incorporating geometric information yields comparable accuracy with substantially fewer trainable parameters.", "id": "Paper/66730", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66730"}, {"title": " On algorithms for computing the zeta function of varieties in characteristic p ", "webprogram_exclude": "0", "session_ids": ["Session/18263"], "source_sha256": "0d011c2958baa1a66db02155a974f95dbdabf933411f51ea05364e384b579df9", "withdrawn": "", "abstract": "We will survey some recent advances in the computation of zeta functions in characteristic p, including the use of GPU compute to compute zeta functions.", "id": "Paper/66731", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66731"}, {"title": " How does mucus plug size and location influence airflow resistance in a simplified bronchial model? ", "webprogram_exclude": "0", "session_ids": ["Session/18240"], "source_sha256": "167070a4a65e634b6028511c263e3782ef8a091fffe7b0765ffad095328ac0ad", "withdrawn": "w", "abstract": "This research will investigate how partial mucus obstruction affects airflow resistance in a bronchial\ntube using Navier-Stokes equations to model the flow. The study uses Direct Numerical Simula-\ntion(DNS) and FreeFEM++ to examine how the obstruction size, location, and mucus properties\ninfluence airflow resistance. The research simulates the airflow using flow past a full step, consid-\nering mucus as a solid obstruction as well as air and mucus interaction using classical fluid-fluid\ninteraction problems.", "id": "Paper/66732", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66732"}, {"title": " Nonlinear dynamics of energetic particles in 3D magnetic fields ", "webprogram_exclude": "0", "session_ids": ["Session/18316"], "source_sha256": "9c22eeb7b1a8dbeaded3f79baf2ddc6729e2c966c170224c79d54e0fc54b05e3", "withdrawn": "", "abstract": "Stellarators are toroidal fusion devices that magnetically confine plasma with 3D magnetic fields. While toroidal symmetry is lost, stellarators can be designed to have hidden symmetries, enabling integrability of the guiding center trajectories. While \"precisely quasisymmetric\" configurations have been obtained through numerical optimization, stellarator magnetic fields generally have deviations from symmetry that lead to loss of confinement of energetic particles (EPs). There is also the potential for enhanced EP losses due to interaction with plasma waves, such as Alfvén waves. This talk will provide an overview of the 2 or 2.5 DOF Hamiltonian dynamics of EP guiding center motion. Poincaré sections highlight the non-twist structure due to reversal in the characteristic drift frequency. Diagnostics of phase-space integrability, such as quasi-periodic psuedo-orbits and the weighted Birkhoff average, will be discussed.", "id": "Paper/66733", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66733"}, {"title": " Statistical Properties of Latent Weights of Idealized Models ", "webprogram_exclude": "0", "session_ids": ["Session/17953"], "source_sha256": "902606e27a67710e8c2f807c5b00f6323e4b801fd83706c9ac980f36e13754c6", "withdrawn": "", "abstract": "Consider a discrete probability model $P$ that generates a random sample, and let $Q$ be an idealized version of $P$, for example, based on theoretical considerations or expert knowledge. The latent weight of $Q$ in $P$, denoted $\\lambda_Q(P)$, is the largest expected fraction of samples from $P$ that can be attributed to $Q$. In particular, $P$ may be represented as a mixture in which $Q$ is a component with weight $\\lambda_Q(P)$. A large latent weight therefore indicates that most samples from $P$ can be attributed to the model $Q$. The general notion of latent weight was introduced in 2020 and, in the context of a single idealized model, may serve as an alternative to testing the hypothesis $H_0:P=Q$ when sampling errors or corruption are unspecified. We study properties of these latent weights when $P$ is assumed known, as well as when it must be estimated from data, and use them to revisit Gregor Mendel's controversial genetic experiment data on pea plants (\\textit{Pisum sativum}), which he used to validate his laws of inheritance.", "id": "Paper/66734", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66734"}, {"title": " Rank-Metric Intersecting Codes ", "webprogram_exclude": "0", "session_ids": ["Session/18387"], "source_sha256": "80b5708fb25eaf99e047d920090e0da2d84fde406fc2a6ddbf4e635d116b93d3", "withdrawn": "", "abstract": "Intersecting codes are a classical topic in coding theory, and their recently introduced rank-metric analogue displays several striking differences from the Hamming-metric setting. In this talk, we investigate the existence and parameters of linear rank-metric intersecting codes through their geometric interpretation via $q$-systems. By relating the dual systems of these codes to evasive and scattered subspaces, we obtain new bounds on their parameters and characterize the extremal case of maximum length. In particular, we show that the upper bound $n=2m-3$ can be attained only in dimension three, where the existence problem becomes equivalent to the existence of suitable scattered subspaces. This connection yields new families of examples and also allows us to prove the non-existence of $[6,3,3]_{q^5/q}$ rank-metric intersecting codes, resolving a previously open problem.\nThis is joint work with Martino Borello and Olga Polverino.", "id": "Paper/66736", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66736"}, {"title": " Top Cohomology for Finite-Index Subgroups of the Braid Group ", "webprogram_exclude": "0", "session_ids": ["Session/18240"], "source_sha256": "09ac18fa0b86e008aa1a7584784c1200b79156dfe3b1b641b8808b226ab68b48", "withdrawn": "", "abstract": "The Artin Braid Group $B_n$ can be viewed as the mapping class group of a disk with $n$ punctures. Associated to $B_n$ is a dualizing \\emph{Steinberg module} $\\operatorname{St}(B_n)$, which gives a Bieri-Eckmann duality structure for any finite-index $\\Gamma \\trianglelefteq B_n$. Namely, if $A$ is a $\\mathbb{Z}[B_n]$-module, then $H^k(\\Gamma;A) \\cong H_{n-1-k}(\\Gamma; \\operatorname{St}(B_n) \\otimes A).$\nUsing this duality, we study the top cohomology of several finite-index normal subgroups of $B_n$ with $\\mathbb{Z}$-coefficients. Building on recent work giving an explicit reduced presentation of $\\operatorname{St}(B_n)$, we compute the top cohomology of kernels arising from evaluations of the reduced Burau representation over finite fields and the complex numbers. We also give a closed formula for the top cohomology of the kernel of the writhe homomorphism modulo $m$, for $m\\in\\mathbb{N}$.", "id": "Paper/66740", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66740"}, {"title": " Interlace Polynomials of Nested Circle Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18206"], "source_sha256": "67bb09f54070868e3055c66801945af4b7b67696968bd6a7e53e18b6665fd15e", "withdrawn": "i", "abstract": "In this talk, we study the interlace polynomials of a family of nested circle graphs that we call cartoon flower graphs, denoted by $CF(n,k)$ ($n, k\\ge 2)$. The graph $CF(n,k)$ is obtained by attaching a cycle $C_{k+1}$ to every edge of $C_n$ with the edge of $C_n$ serving as one of the edge of $C_{k+1}$.  In the case $k=2$, the inner cycle forms the center of the flower, with $n$ triangular petals. We show that the coefficients of the interlace polynomials of $CF(n,2)$ are strictly log-concave. We also discuss the interlace polynomials for the general family $CF(n,k)$ when $k\\ge 3$ and explore some of their properties.", "id": "Paper/66742", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66742"}, {"title": " Explainable topological data analysis using persistence heatmaps ", "webprogram_exclude": "0", "session_ids": ["Session/18304"], "source_sha256": "2fd9770223bdd8bb11ade46a2c9ff392990c13b44d4f0a974b9f3455d0f6775d", "withdrawn": "", "abstract": "Topological data analysis (TDA) leverages tools from algebraic topology to aid in various machine learning tasks. Numerous TDA constructions are provably stable in the sense that changes in the input produce linearly bounded changes in the output, with a specified bound. We use representative cycles, which are unstable TDA constructions, to produce stable visualizations to aid in explaining TDA. For example, we produce stable heatmaps on images containing the data such that summing the values of the pixels gives the value of a learned regression function.", "id": "Paper/66744", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66744"}, {"title": " An HVZ Theorem for Discrete Many-Particle Systems ", "webprogram_exclude": "0", "session_ids": ["Session/18296"], "source_sha256": "b385f62e48fddef83d57f2f9c95d86e77cbdf241687c246025f219a7f4bdac61", "withdrawn": "", "abstract": "I will discuss a proof describing the essential spectrum of a discrete many-particle operator in terms of the spectra of certain comparison operators which are more accessible to direct calculation. I show this under rather mild assumptions on the adjacency operator and interaction potential.", "id": "Paper/66747", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66747"}, {"title": " Communication-efficient decentralized optimization over compact submanifolds with data heterogeneity ", "webprogram_exclude": "0", "session_ids": ["Session/19352"], "source_sha256": "e63be993ee111159f54ab2e0b1877c207550067d6537c6ca59c39b866e72c5be", "withdrawn": "", "abstract": "We consider decentralized optimization over a compact Riemannian submanifold in a network of agents, where each agent owns a smooth nonconvex local objective defined by private data and communication is restricted to neighboring agents. We propose projection-based Riemannian EXTRA (REXTRA) and a retraction-based counterpart. Both methods inherit the primal EXTRA correction and require only one local-variable-sized message and one communication round per optimization iteration, even under data heterogeneity. For the projection-based method, we establish vanishing consensus, stationary accumulation points, and an O(1/k) best-iterate stationarity-consensus bound under a sufficiently small constant stepsize and local initialization. For the retraction-based method, we show that the retraction update differs from the projection update by a uniformly second-order term; combined with a finite rooted-tree synchronization phase, this yields an arbitrary-initialization convergence guarantee with the same O(1/k) best-iterate rate. Numerical experiments on decentralized principal component analysis, generalized eigenvalue problems, and low-rank matrix completion demonstrate improved communication efficiency over existing decentralized Riemannian methods.", "id": "Paper/66748", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66748"}, {"title": " The Topology of Mapping Class Groups ", "webprogram_exclude": "0", "session_ids": ["Session/18379"], "source_sha256": "b578a70ad7ee174a2e4a292a0ad6016550bb8a1815f71084d070482715713b21", "withdrawn": "", "abstract": "Mapping class groups are important algebraic invariants of topological spaces, defined as the group of orientation-preserving homeomorphisms of a surface up to homotopy. If the fundamental group of a surface is finitely generated, the surface is of finite type; otherwise, it is of infinite type. For infinite-type surfaces, the homeomorphism type is determined by (1) the genus, (2) the number of boundary components, and (3) the topology of the space of ends (Kerékjártó–Richards classification). In this talk, we survey several structural results on big mapping class groups, which are the mapping class groups of infinite-type surfaces. We show that big mapping class groups are neither locally compact nor compactly generated, yet are homeomorphic as topological spaces to the Baire space $\\mathbb N^{\\mathbb N}$. Lastly, building on work of Mann–Rafi identifying which big mapping class groups admit a coarsely-bounded generating set, we exhibit an infinite family of examples for which this holds, yielding in each case a well-defined quasi-isometry class.", "id": "Paper/66751", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66751"}, {"title": " Euler–Bonnet Curvature: A Discrete Gauss–Bonnet for Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/19358"], "source_sha256": "a71b6bcd73d041596b12612f3b54a708324e4611e5ddba3da4ab93766285fd48", "withdrawn": "", "abstract": "Discrete curvature measures---Ollivier--Ricci, Forman--Ricci, resistance\ncurvature---quantify local shape around a node, yet none relates to the global\ntopology of the graph: no local-to-global theorem guarantees that node\ncurvatures compose into a graph-level invariant. The smooth Gauss--Bonnet\ntheorem supplies exactly that, integrating local curvature to the Euler\ncharacteristic. We develop the discrete analogue for graphs.\n\nThe Euler characteristic transform indexes a family of Euler characteristic\ncurves by \\emph{direction}. We index by \\emph{basepoint} instead: for each\nvertex $i$, geodesic distance from $i$ is the filtration function, giving one\ncurve $k \\mapsto \\chi(G_i^{(k)})$ over the $k$-hop neighborhoods---no\nembedding, no direction, no restriction on the graph. Normalizing the marginal\nchange contributed by the $k$-th shell, the $n_k(i)$ vertices at distance\nexactly $k$, gives $\\hat\\kappa_k(i) = -\\Delta\\chi_k(i)/n_k(i)$, which behaves\nas a curvature and reports how clustered, tree-like, or grid-like the structure\naround $i$ is. Its defining property is a discrete Gauss--Bonnet: the shell\ncontributions telescope exactly to $\\chi(G) = 1 + \\sum_k \\Delta\\chi_k(i)$ from\nevery basepoint. We call this Euler--Bonnet curvature.\n\nBuilding from the Euler characteristic rather than a Riemannian analogy makes\nthe computation combinatorially \\emph{exact}---integer arithmetic, no\noptimization---at cost comparable to Forman--Ricci, and yields a family, not a\nsingle scalar. A compact scalar summary competes with existing measures on\nbenchmarks such as BREC at far lower cost, while the shell decomposition\nrecords an interpretable profile per node. Truncating at a horizon $h$ splits a\nnode's curvature into local and distal parts, additive and lossless by\nconstruction---a scale separation no existing discrete curvature offers.", "id": "Paper/66753", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66753"}, {"title": " Games Galore: A Comparison of Stationary and Stochastically Stable Distributions Across Learning Dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "6407df41873883415baf2b752dfd96f347012a1e62b5e25784216b6e77a5cd06", "withdrawn": "", "abstract": "Strategic interactions are often modeled using game theory, but a repeated game’s long-run outcome depends heavily on the learning dynamic players follow. Stochastic game dynamics combine learning (or response) rules with small perturbations, or \"mistakes,\" to study how repeated play evolves over time. This project compares finite-noise stationary behavior to stochastically stable behavior across a collection of two-player games with finite action sets, to examine whether different stochastic learning dynamics converge to the same outcomes as noise (ε) vanishes. Perturbed Markov chains were constructed under several stochastic learning dynamics and stationary distributions computed across multiple perturbation levels for comparison with stochastic stability predictions. Preliminary results suggest that stationary behavior approaches the stochastic stability prediction as perturbations decrease, providing insight into when finite-noise simulations capture long-run behavior.", "id": "Paper/66754", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66754"}, {"title": " Approximating Flow through an Approximate Deconvolution Time Relaxation Model ", "webprogram_exclude": "0", "session_ids": ["Session/18258"], "source_sha256": "571876343db0a1fac9d343baeb5936ac326bf2b242a3044e0657650bbd88ddf3", "withdrawn": "", "abstract": "This work studies a new time relaxation model that incorporates stabilization terms into the time-dependent incompressible Navier-Stokes equations to address oscillations and effects from small scales in fluid flows. To resolve these small scales, we implement spatial filtering and approximate deconvolution operators. This model acts as a sequel to a Dunca and Neda (2014) model by omitting fluctuation on the test function in the stabilization term, which previously made the model impossible to be implemented in the Crank-Nicolson algorithm. We explore numerical stability, convergence, and computational simulations.", "id": "Paper/66756", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66756"}, {"title": " A Decomposition Lemma in Convex Integration via Classical Algebraic Geometry ", "webprogram_exclude": "0", "session_ids": ["Session/18306"], "source_sha256": "fa5f5e6edcb9f623551340591b0cde570a2a755bc579deec422440f0c969baed", "withdrawn": "", "abstract": "In this paper, we prove a decomposition lemma for symmetric matrix fields $D$ on bounded domains: $D+\\mathrm{Sym}\\nabla\\Phi=\\sum_i a_i^2\\xi_i\\otimes\\xi_i$\nwith uniform control on $\\Phi$ and $a_i^2$, using  fewer than the usual $n(n+1)/2$ rank-one symmetric terms. Except possibly in dimensions $n=8,16$, the decomposition is shown to be optimal through algebraic arguments. This reduces the number of steps in convex integration for a nonlinear PDE system, improving H\\\"older regularity of flexible solutions in dimension $n\\ge3$. This PDE is a partial linearization of the codimension-one local isometric embedding equation in the Nash–Kuiper theorem, and also yields $C^{1,\\alpha}$ very weak solutions of related Monge--Amp\\`ere systems and $2$-Hessian systems. For $n\\ge3$, the improved H\\\"older exponent is any $\\alpha<(n^2+1)^{-1}$ for $n=4,8,16$ and any $\\alpha<(n^2+n-2\\rho(n/2)-1)^{-1}$ otherwise, where $\\rho$ is the Radon--Hurwitz number, related to Bott periodicity.\n\nThe proof involves novel applications of  algebraic geometry and topology that yield the optimality of decomposition, including Adams' theorem on vector fields on spheres,  intersections of projective varieties, and projective duality, combined with an elliptic method that avoids loss of differentiability.", "id": "Paper/66759", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66759"}, {"title": " Quantitative uniqueness for bi-Laplace equations with ptentials ", "webprogram_exclude": "0", "session_ids": ["Session/18265"], "source_sha256": "11961e4b9ed25930fc47b919a4b1951f325580962cd427b92763d1d084473dfe", "withdrawn": "", "abstract": "We study quantitative unique continuation for bi-Laplace equations\n\t\t\\[\n\t\t\\Delta^{2}u+V(x)u=0\n\t\t\\]\nby introducing some new weighted frequency functions. We establish quantitative three-ball inequalities and vanishing-order bounds for bounded and H\\\"older continuous potentials. Three-ball inequalities are built on rescaling invariant weighted frequency functions. The vanishing order results are shown by related, but different weighted frequency functions.", "id": "Paper/66761", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66761"}, {"title": " Dispersal and Heterogeneity in Metapopulation Dynamics: Network Structure and Population Persistence ", "webprogram_exclude": "0", "session_ids": ["Session/18009"], "source_sha256": "05dfa30fa75ba5fbd20794f578b7e47c0483ff1d5f9b1ad816a0d932fd43f2f0", "withdrawn": "", "abstract": "Spatial heterogeneity and dispersal jointly shape population dynamics across fragmented landscapes, yet their combined effects on population persistence remain challenging to characterize analytically. In this talk, we develop a metapopulation framework based on coupled ordinary differential equations on networks, with particular emphasis on regimes in which dispersal occurs on a faster timescale than local population growth. Using tools from matrix analysis and perturbation theory, including new rank-one results for group-invertible matrices, we quantify how local changes in movement and network connectivity influence the dominant eigenvalue governing population persistence. In particular, we show that increasing symmetric connectivity in weight-balanced networks can inhibit population growth under fast dispersal. These results highlight how the interaction between dispersal and spatial heterogeneity can produce counterintuitive effects on population persistence, with implications for understanding biodiversity and ecological dynamics in fragmented and changing environments.", "id": "Paper/66762", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66762"}, {"title": " CoBaLiOn-RS: Code-Based Linkably-Optional Ring Signatures ", "webprogram_exclude": "0", "session_ids": ["Session/18073"], "source_sha256": "9c344e9f94cde590370debcecf5679aaf1b1c7689d925c49c6ee5351c9bc6eac", "withdrawn": "", "abstract": "Linkable ring signatures (LRS) let a member of a group sign anonymously on the coalition's behalf, while allowing any verifier to detect when two signatures were signed by the same individual. \nWe present an advanced post-quantum LRS based entirely on coding-theoretic assumptions. \nReplacing the Stern-style zero-knowledge proof from the state-of-the-art code-based LRS of Liu and Wang with a CVE-style protocol reduces the soundness error from $2/3$ to roughly $1/2$, and combining this with the restricted errors of CROSS yields two instantiations: one whose signature size grows linearly in the ring size $N$, and one that grows logarithmically, at $13.55 + 0.9\\log_2(N)$ kB for NIST security level I. \nBoth variants outperform existing code-based proposals for all practical ring sizes, and the logarithmic variant is competitive with leading lattice- and isogeny-based schemes. \nWe prove correctness, anonymity, linkability, and nonframeability in the random oracle model under variants of the restricted syndrome decoding problem. \nFinally, we introduce \\emph{opt-in linkability}, a functionality where two rings signed with the same secret key remain unlinkable until the signer voluntarily demonstrates the connection, even across rings instantiated with different parity-check matrices. \nThis grants signers plausible deniability by default, resolving real-world anonymity failures caused by automatic linking, and is the first code-based construction to achieve this property.", "id": "Paper/66764", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66764"}, {"title": " Integrating physics and topology to dissect the development of bacterial biofilms ", "webprogram_exclude": "0", "session_ids": ["Session/18303"], "source_sha256": "ca9fbda6f3e172a4265a7295a72b128880bde4189ee0eacaa9061b24fb09ac87", "withdrawn": "", "abstract": "Bacterial biofilms—surface-attached bacterial communities encased within self-produced extracellular matrices—are paradigmatic examples of prokaryotic multicellular systems that grow to exhibit remarkable morphologies and internal ordering. In particular, biofilms that exhibit phenotypic heterogeneity, in which individual cells fluctuate between matrix-producing and non-producing states, can spontaneously self-organize throughout development. Here, we integrate agent-based simulations, physical modeling, and a topological framework for modeling multicellular networks to decipher the physical mechanisms through which biofilm-dwelling cells can achieve such self-organization. Using experimentally calibrated simulations of biofilm growth in which cells switch between matrix-producing and non-producing states, we demonstrate that differential cell-cell, cell-matrix, and cell-surface interactions can mediate spontaneous segregation of these phenotypes. We then analyze the phenotypic patterns that arise in these simulations by modeling the network of matrix-producing cells as a dynamic 3D simplicial complex, for which can identify a minimal basis for the first homology group—thus localizing the “holes” within the network—as well as more detailed topological information such as temporal zigzag persistence. Using this approach, we show that a phenotypically heterogeneous biofilm can grow to form robust networks of matrix-producing cells, whose topological features depend on the strength of cell-cell adhesion. We also discuss how these topological features depend on the various types of mechanical interactions within the biofilm, other phenotypes such as growth rate and cell shape, and aspects of the biofilm lifecycle. In sum, this work elucidates the mechanical basis for phenotypic patterning within developing biofilms, and illustrates the utility of algebraic topology as a toolkit for quantifying complex morphogenetic outcomes in multicellular systems.", "id": "Paper/66767", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66767"}, {"title": " Linearization of small-scale Lipschitz functions on operator spaces ", "webprogram_exclude": "0", "session_ids": ["Session/17834"], "source_sha256": "3d37f125adebc5ce77c435eab266828349bbeae1c60a3dc98c1b58986f59bf12", "withdrawn": "", "abstract": "Operator spaces, as noncommutative or quantum versions of Banach spaces, provide a natural environment for a potential Godefroy-Kalton program: to study Lipschitz equivalence between them through some associated Lipschitz-free spaces.\n\nAlas, it was previously shown by B. Braga and the presenter that the natural notion of a Lipschitz function on an operator space is trivial: it only yields (real) linear functions. However, we more recently introduced a small-scale notion of Lipschitz functions for operator spaces which does give rise to a rich nonlinear theory.\n\nIn this talk, we study the corresponding small-scale Lipschitz-free spaces and the associated Lipschitz-lifting property in the style of Godefroy-Kalton. While the theory has many similarities, there are also significant differences since the functions of interest are defined only on a ball and not on a whole Banach space. In particular, the notion of Lipschitz equivalence is more complicated.", "id": "Paper/66768", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66768"}, {"title": " Student Views on GenAI use in Proof-Based Courses ", "webprogram_exclude": "0", "session_ids": ["Session/18346"], "source_sha256": "d071cc9c266d05f9d656c63006d98c9b5152fde639c663f57089659dcc40a8fa", "withdrawn": "", "abstract": "This exploratory study examines student use and perceptions of\ngenerative AI across three proof-based undergraduate mathematics courses. In each case, course policy permitted some use of generative AI. Drawing on survey responses and student interviews, we discuss how students engaged with AI tools as well as their perceptions of GenAI’s usefulness, accuracy and limitations. We also discuss students' views on how GenAI impacted peer-interactions and instructor-student interactions.", "id": "Paper/66769", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66769"}, {"title": " Prüfer Transformation of the Discrete Non-Uniform Sturm–Liouville Problem ", "webprogram_exclude": "0", "session_ids": ["Session/18385"], "source_sha256": "3fce87aa5792bda64bd103ed4f9a1bb62f671613a75122d9ebd6a647107f29d4", "withdrawn": "", "abstract": "We derive the Prüfer transformation for the discrete Sturm–Liouville equation on a non-uniform grid, converting the second-order difference equation into a coupled system for amplitude and phase. The resulting phase equation is independent of the amplitude, which reduces the Dirichlet eigenvalue problem to the condition that the terminal phase be an integer multiple of pi. Knowing this allows us to back track and solve the original problem.", "id": "Paper/66775", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66775"}, {"title": " Numerical Implementation of the Sturm–Liouville Problem via Prüfer-Based Shooting ", "webprogram_exclude": "0", "session_ids": ["Session/18385"], "source_sha256": "b8df6da9dc7a36fc916335c3ee3ba00aeb54a72e28941ba8d510e3759a85429e", "withdrawn": "", "abstract": "We compare regular shooting with Prüfer-based shooting for computing eigenvalues of a discrete Sturm–Liouville problem on uniform, clustered, and graded grids. Because the phase variable stays bounded while the amplitude can overflow, Prüfer shooting recovers eigenvalues to near machine precision on all three grids, including cases where regular shooting returns no usable value at all.", "id": "Paper/66776", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66776"}, {"title": " Machine Learning and Microplastics: Classifying Particles on Whole Filter Images ", "webprogram_exclude": "0", "session_ids": ["Session/19345"], "source_sha256": "3bdbf1de3654cd4683dd5b9b95813ad448a436218c449e721d811005a14eb40c", "withdrawn": "", "abstract": "Microplastics are ubiquitous across the Laurentian Great Lakes (and globally), reported in water, sediments, and biota, including treated drinking water and the fillets of sport fish. Despite the significant attention that microplastic contamination in the environment, water, and food supplies has garnered, the ability to rapidly analyze samples remains a bottleneck. This project proposes to drastically lower the labor involved in the analysis process of microplastics by testing and validating an automated pipeline based on Machine Learning (ML) and computer vision tools. A critical first step in this process is to standardize the labeling, treatment, and digital workflow of whole filter images for microplastics. A hierarchy of models were trained and tested to analyze whole filter sample images for particle detection as well as identifying information such as particle morphology, color, and material in order to investigate the extent to which machine learning models can predict the boundary, shape, and color of particles on a whole filter. In this talk, we will discuss the results of trained YOLO26 segmentation models for instance segmentation of microplastics and organic particles filtered in lab and environmental samples.", "id": "Paper/66779", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66779"}, {"title": " Upper and Lower Solution Method for Difference Equation with Mixed Boundary ", "webprogram_exclude": "0", "session_ids": ["Session/18240"], "source_sha256": "df793b3e02753855817893ac3172bcfc439a534433b368a8deda3895293e12ff", "withdrawn": "", "abstract": "We establish upper and lower solution method for a second order discrete boundary value problem with non homogeneous mixed boundary condition. We employ Brouwer’s fixed point theory to obtain the existence result.", "id": "Paper/66781", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66781"}, {"title": " Anti-van der Waerden numbers of products of paths and cycles ", "webprogram_exclude": "0", "session_ids": ["Session/18011"], "source_sha256": "048d12d598b1413a00cca1a878ff37843c2b89606d2652d0590a2533bc0dc949", "withdrawn": "", "abstract": "The anti-van der Waerden number, denoted $\\textrm{aw}([n],k)$, is the minimum number of colors $r$ needed so that every coloring of $[n]$ with exactly $r$ colors contains a rainbow $k$-AP, which is a $k$-term arithmetic progression in which each of the $k$ terms receives a different color. A $k$-AP in a graph is a tuple of vertices $(x_1, x_2, \\dots, x_k)$ such that the distance from $x_i$ to $x_{i+1}$ is the same for all $1 \\leq i \\leq k-1$. Thus the anti-van der Waerden number of a graph $G$, $\\textrm{aw}(G, k)$, can be defined as the minimum number of colors $r$ needed so that every vertex-coloring of $G$ with exactly $k$ colors contains a rainbow $k$-AP. Note that for the path graph on $n$ vertices $P_n$, $ \\textrm{aw}(P_n,k) = \\textrm{aw}([n],k)$.\n\nWhen $G$ is the Cartesian product of two graphs, it is known that $3 \\leq \\textrm{aw}(G,3) \\leq 4$, and exact results are known when $G$ is the product of two paths, two cycles, or a path and a cycle. In this talk, we will extend that result to give the exact value of $\\textrm{aw}(G, 3)$ when $G$ is a Cartesian product of any number of paths and cycles. This is joint work with Katie Ansaldi, Erin Bela, Anna Halfpap, Emily Heath, and Nathan Warnberg.", "id": "Paper/66782", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66782"}, {"title": " Analysis of Ergodic Literature with Digraphs and Multilinear Algebra ", "webprogram_exclude": "0", "session_ids": ["Session/17091"], "source_sha256": "ecacb70efa8a818f96742564b95cb72c1591ef570553589bac0813e00bcde639", "withdrawn": "", "abstract": "This presentation explores how concepts from linear and multilinear algebra, combined with graph theory, can be used to analyze ergodic literature—a specific type of literature in which the reader’s choices actively shape the path and the end of the story.  Such texts, seen in works like Eugenios Trivizas  (Professor of criminology, children’s book author) interactive books and the Choose Your Own Adventure series, contain multiple possible storylines and endings.\nBuilding on existing research, this work focuses on identifying important sections of ergodic books using ranking algorithms, with particular attention to PageRank. A central component is the multilinear PageRank model proposed by D. Gleich (2014), which extends the classical algorithm using tensors and second-order Markov chains. By retaining information about the previous step, the model examines how the importance of a section may depend on the path through which the reader arrived there.", "id": "Paper/66783", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66783"}, {"title": " Finite Involutory Quandles of Montesinos Links ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "887a02aeb743305e371ff297568f712d4feae546212f864def8b4f64a65017b3", "withdrawn": "", "abstract": "Similarly to how every knot has an associated fundamental group, every knot has an associated fundamental quandle, which classifies the knot up to orientation. For any $n$, one can define a fundamental $n$-quandle of the knot as a ``quotient'' of the fundamental quandle. Because almost all fundamental quandles are infinite, we investigate links known to have finite $n$-quandles. Specifically, we compute the size and structure of the finite 2-quandles associated with the infinite family of Montesinos knots and links, $M(p_1/2, p_2/3, p_3/q; k)$ when $q = 3, 4, 5$, continuing the work of Shanahan, Hoste, and Mellor.", "id": "Paper/66784", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66784"}, {"title": " Efficient Soft-Output Guessing for Enhanced Quantum Tanner Code Decoding ", "webprogram_exclude": "0", "session_ids": ["Session/18020"], "source_sha256": "93c7e21c9db16e44f00b624621d051de2d37b7d018c2a1ffea146f42a11dcfc5", "withdrawn": "", "abstract": "Quantum error correction is an essential component of large-scale quantum computing. One of the key obstacles to quantum error correction is efficient decoding. Quantum Tanner codes are a particularly interesting class of quantum error correcting codes, promising asymptotically good performance and low density. They can be interpreted as generalized low-density parity-check codes that concatenate small component codes into powerful long codes. However, standard quantum LDPC decoding algorithms do not exploit this structure.\n\nIn this talk, we introduce a decoding framework for quantum Tanner codes that directly exploits this structure by utilizing soft-output guessing random additive noise decoding (SOGRAND). By soft-output decoding entire component codes rather than individual parity checks, we mitigate the effects of trapping sets and cycles, resulting in improved convergence. Because our decoder preserves the message-passing structure of standard belief propagation (BP), it is compatible with many BP enhancements, including ordered-statistic decoding (OSD) postprocessing, BP over GF(4), and RelayBP. Standalone SOGRAND outperforms the BP+OSD baseline by over two orders of magnitude in logical error rate. In combination with the Relay principle, SOGRAND outperforms RelayBP by over one order of magnitude, providing a way forward for scalable decoding of the emerging class of Tanner-code-based quantum codes.", "id": "Paper/66787", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66787"}, {"title": " A Non-Archimedean Commutative Positivstellensatz ", "webprogram_exclude": "0", "session_ids": ["Session/17377"], "source_sha256": "6ac310cd616db9783156a04a0563ea6cf598f4385d9cc04364bc3f8fe6cf86cd", "withdrawn": "", "abstract": "Classical positivstellens\\\"{a}tze often rely on an Archimedean hypothesis, corresponding geometrically to boundedness of the underlying positivity domain. In this talk, we consider a non-Archimedean setting in which positivity is tested on tuples of commuting unbounded operators acting on a common invariant dense domain.\n\n    We first consider tuples \\((T_1,\\ldots,T_d)\\) satisfying\n    \\(\n        \\operatorname{Re}\\langle T_j\\xi,\\xi\\rangle\\geq0\n    \\)\n    on their common domain, and obtain a positivstellensatz characterizing matrix polynomials positive on all such tuples in terms of membership in an associated quadratic module.\n    We then extend the construction from coordinate half-plane conditions to positivity domains determined by a matrix-valued linear pencil \\(\\Gamma\\).\n    Under a positivity condition on the homogeneous part of \\(\\Gamma\\), we obtain an analogous positivstellensatz for this class of non-Archimedean domains.", "id": "Paper/66788", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66788"}, {"title": " The Diamond-Alpha Kalman Filter ", "webprogram_exclude": "0", "session_ids": ["Session/17446"], "source_sha256": "0062a2bbafd2dc602d5a6e70d87c194f98d1dc5282ae7d82a78add102a034be6", "withdrawn": "", "abstract": "In this preliminary talk, we construct a diamond-alpha Kalman filter for linear systems. Such a filter design incorporates both a forward and backward shift component. Here we consider isolated time scales. We make use of an alpha-matrix exponential to establish our results, where the error propagation is updated through an integrator.", "id": "Paper/66792", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66792"}, {"title": " Star Coloring Stencil Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17882"], "source_sha256": "68680783b293166626e3d02f1fc8064829a4b28fbbee8b94d5381bc3f3154961", "withdrawn": "", "abstract": "We consider the star chromatic numbers of Cayley graphs generated by stencils used to discretize partial differential equations (PDEs) on regular grids. Some of these graphs have been studied independent of the PDE interpretation, such as the 2-dimensional king's graph, which is the strong product of two path graphs ($P_m \\boxtimes P_n$) and its 3-dimensional analogue. In the PDE context, the star chromatic number is of interest because it equals the minimum number of forward sweeps of automatic differentiation needed to directly recover the Hessian of a function coming from the discretization of a nonlinear PDE. We provide exact chromatic numbers for graphs arising from discretizations based on box- and star-stencils with radius 1 or 2 on 2-dimensional grids, and upper and lower bounds for their 3-dimensional analogues.", "id": "Paper/66794", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66794"}, {"title": " A structure theorem for Cuntz–Pimsner algebras associated to quantum graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17834"], "source_sha256": "fb04b7f270b91a0adfee390d7e474d4d759befdee50019bb0c99b65dda382bc6", "withdrawn": "", "abstract": "Given a finite $\\{0,1\\}$-matrix, one can build an associated Cuntz--Krieger algebra. Witnessing the matrix as an adjacency matrix for a finite, simple directed graph, the Cuntz--Krieger algebra agrees with the graph $C^*$-algebra for the associated graph. The relations on the generators of this graph $C^*$-algebra obey a structure theorem according to adjacency of vertices in the underlying graph.\n\nA quantum graph replaces the vertex set in a classical graph with a finite-dimensional C*-algebra and the $\\{0,1\\}$-matrix with a quantum adjacency matrix from which one can construct the quantum graph's {\\em local quantum Cuntz--Krieger (LQCK) algebra}. These algebras are particularly difficult to classify--the defining relations for the LQCK algebra of a given quantum graph are in terms of matrix relations for matrices containing the generators as coefficients, rather than relations on the generators themselves. In this talk, we present a new structure theorem and apply it to characterize the local quantum Cuntz--Krieger algebras for examples of quantum graphs.", "id": "Paper/66795", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66795"}, {"title": " On a density problem related to a theorem of Szegő ", "webprogram_exclude": "0", "session_ids": ["Session/17815"], "source_sha256": "1242e9afa365afb51a481110cecaf2c94654bc064677e8db66cda0f66e25a30f", "withdrawn": "", "abstract": "A classical theorem of Szegő states that for any probability measure\n\\(\\mu = w \\frac{d\\theta}{2\\pi} + \\mu_s\\) on the unit circle\nthe polynomials are dense in \\(L^2(\\mathbb{T},\\mu)\\) if and only if\n\\(\\log(w) \\notin L^1(\\mathbb{T})\\). A related question asks\nwhether the monomials with exponents in some subset\n\\(\\Lambda \\subseteq \\mathbb{N}_0\\) already have dense span in\n\\(L^2(\\mathbb{T},\\mu)\\) if \\(\\log(w) \\notin L^1(\\mathbb{T})\\).\nWe construct suitable sets \\(\\Lambda\\) for which this is true depending on decay\nproperties of the Verblunsky coefficients of \\(\\mu\\).", "id": "Paper/66797", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66797"}, {"title": " Attractor Dynamics in Small Spiking Systems ", "webprogram_exclude": "0", "session_ids": ["Session/18007"], "source_sha256": "6b9ded0565a539f73943c1621ada0890c69ebecc7fc1d0b1128cb8a438c93922", "withdrawn": "", "abstract": "Previous work has shown that a ring attractor can arise in finite rate networks with as few as 6–8 neurons, but only under highly fine-tuned parameter choices. Whether analogous continuous attractor dynamics can be realized in small stochastic spiking networks remains unclear. We characterize the conditions under which a finite spiking network can support a stable bump on a continuous ring. For nonlinear Hawkes networks, we use spectral and covariance analyses of the linearized stochastic dynamics to characterize bump stability, finite-size fluctuations, and the radial fluctuations which destabilize the bump’s amplitude and phase. We show that at biologically realistic synaptic timescales, intrinsic spiking variability can become sufficiently large to destroy the bump altogether; even when a bump persists, rapid phase diffusion can preclude a useful ring attractor. We extend this analysis to integrate-and-fire networks using Fokker–Planck methods and find that fast subthreshold dynamics facilitate stable bumps at biological timescales. We use linear-response and renewal theory to solve for the self-consistent response properties of the circuit. Finally, we analyze how polysynaptic feedback loops reshape the response spectrum, suppress destabilizing fluctuations, and increase phase persistence, providing biological mechanisms by which small stochastic circuits may recover robust ring-attractor dynamics.", "id": "Paper/66798", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66798"}, {"title": " Chromatic Quasisymmetric Functions of Oriented Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18360"], "source_sha256": "3270c0686fce347dda7edcb0c3dd8084e54cb814c825d2dc04025a6ff57fe960", "withdrawn": "", "abstract": "The chromatic quasisymmetric function (CQF) on labeled graphs, introduced by Shareshian and Wachs for acyclic orientations and extended by Ellzey to arbitrary digraphs, generalizes Stanley’s chromatic symmetric function. The CQF lies in the ring $\\operatorname{QSym}[q]$, and we call a digraph \\emph{symmetric} if its CQF lies in $\\operatorname{Sym}[q]$. \n\nWe construct several families of symmetric oriented graphs, including wedges of directed cycles, chorded cycles, and certain extended chorded cycles. We also derive necessary conditions for symmetry that apply to arbitrary oriented graphs. In this talk, I will discuss our recent progress on the CQF of oriented graphs.", "id": "Paper/66800", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66800"}, {"title": " Non-commutative harmonic analysis and non-commutative Diophantine approximation ", "webprogram_exclude": "0", "session_ids": ["Session/18279"], "source_sha256": "8993cef23af414dda8e9e2bffaddf881f488ac3618b7a5a522e360410e4cfca4", "withdrawn": "", "abstract": "We will begin by giving a short exposition of a variety of problems in non-commutative Diophantine approximation. These will include  rate of Diophantine approximation, effective equidistribution, and counting solution to  Diophantine approximation problems. \n     We will then briefly note some cases where some of these problems have been solved recently, and briefly indicate the non-commutative harmonic analysis methods used, as time permits.", "id": "Paper/66801", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66801"}, {"title": " AI as Augmented Intelligence: Results from Pilots in Introductory Mathematics Service Courses ", "webprogram_exclude": "0", "session_ids": ["Session/18199"], "source_sha256": "255adf16a7c9cffa92086d7290cb1e4c9aa57308e44f5cefa2d844e15a4b7665", "withdrawn": "", "abstract": "Large language models reached universal adoption before communities developed methods to use them. This gap has been exacerbated by the near-zero cost of producing artifacts traditionally used to measure performance and learning (homework problems, projects, tests, etc.). The prevailing institutional response is to advise caution and restraint with little practical guidance. We report on an ongoing pilot (2026--2028) at the University of Texas at San Antonio in College Algebra, Precalculus, Calculus I, and Calculus II intended to produce evidence to guide practices in teaching and learning. The experiment compares ambient AI (which all students have access to) with constrained AI (which is offered through pilot courses). This preliminary report presents the design principles behind the constraints, the delivery platform, the experimental design, the outcome measures, and results from the fall 2026 semester. We discuss the faculty training required before deploying the pilots. We close with lessons learned and what the remaining pilot semesters will test.", "id": "Paper/66803", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66803"}, {"title": " Strong edge coloring and D-coloring ", "webprogram_exclude": "0", "session_ids": ["Session/18085"], "source_sha256": "eac4ae0d1b94527ee02c491351cbd846c1f4156e7f0eae38900abb51a40a4474", "withdrawn": "", "abstract": "In a graph $G$, the distance between two edges is the distance between the corresponding vertices in the line graph of $G$. Under a strong edge coloring of $G$, any two edges of distance at most $2$ get distinct colors. Introduced as a relaxed version of strong edge coloring, a D-coloring of $G$ is a proper edge coloring such that every diamond subgraph is rainbow. In this talk, we will introduce some recent results on strong edge coloring and D-coloring.", "id": "Paper/66807", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66807"}, {"title": " Mathematics Faculty Professional Development at the Two-Year College Level ", "webprogram_exclude": "0", "session_ids": ["Session/18199"], "source_sha256": "e4b5151e8ce63878ffd5100af700e25fd77aecc435a5211c8d1ebe143771bcae", "withdrawn": "", "abstract": "In this talk we share about the NSF-funded Reconnect Mathematics Project (RMP). RMP is a collaboration between Kellogg Community College (KCC) and the Michigan Mathematical Association of Two-Year Colleges (MichMATYC) that aims to improve mathematics instruction at the community college level in the state of Michigan through professional development on research-based effective pedagogical practices.", "id": "Paper/66810", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66810"}, {"title": " Endpoint Estimates for Stein’s Purely Quadratic Carleson Operator ", "webprogram_exclude": "0", "session_ids": ["Session/17815"], "source_sha256": "4163a13b62e49574c571d867e69f86015d93e2780baa9b9ad53c77308b04b982", "withdrawn": "", "abstract": "We study the near $L^1$ behavior of the maximally quadratically modulated Hilbert transform\n$$\n\\mathcal{C}_2f(x) := \\displaystyle{\\sup_{\\lambda}} \\left|\\operatorname{p.v.} \\int_{\\mathbb{R}}f(x-y)e^{2 \\pi i \\lambda y^2} \\frac{\\mathrm{d} y }{y} \\right|\n$$\nand its lacunary counterpart obtained by restricting $\\lambda$ to $2^{\\mathbb{Z}}.$ We prove that if $\\Phi$ is a Young function satisfying $ \\Phi(t)=o\\bigl(t\\log_2t\\bigr)$ then $\\mathcal{C}_{2,\\mathsf{lac}}$, and therefore $\\mathcal{C}_2$ as well, does not satisfy a corresponding $\\Phi$-modular estimate. In particular, neither the lacunary nor the full quadratic operator is of weak type $(1,1)$. In the positive direction, we establish an $L\\log_1 L$ modular estimate for $\\mathcal{C}_2$ and a $L (\\log_2L)^2 \\log_4L$ estimate for $\\mathcal{C}_{2,\\mathsf{lac}}.$", "id": "Paper/66812", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66812"}, {"title": " Random Matrix Models for the Class Group as a Galois Module ", "webprogram_exclude": "0", "session_ids": ["Session/19355"], "source_sha256": "64ef3bf3cf26f5d0fff713e46260cf043ed83212e919d9fdd5703bb2dec57d4c", "withdrawn": "", "abstract": "We prove universality results for the cokernels of random module homomorphisms. In particular, we replicate the distribution conjectured by Cohen and Martinet for the class group of a random number field as a Galois module. This generalizes Wood’s result that, subject to very weak requirements, the cokernels of random integral matrices  satisfy the distribution conjectured by Cohen and Lenstra for the class group of a random quadratic number field.", "id": "Paper/66815", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66815"}, {"title": " Norhaus-Gaddum Upper Bounds for Laplacian Eigenvalues ", "webprogram_exclude": "0", "session_ids": ["Session/18146"], "source_sha256": "e871663b1eaf63f2cc5664afb7e415aae74525671f123e63444718bfbdd5fad3", "withdrawn": "", "abstract": "Nordhaus-Gaddum type problems concern bounding expressions involving a graph parameter for a graph and its complement simultaneously.  We will discuss upper bounds on the sum of the algebraic connectivity of a graph and that of its complement.  We will further discuss conjectures relating to the normalized Laplacian and other invariants related to the algebraic connectivity.", "id": "Paper/66816", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66816"}, {"title": " Cyclic sieving, plane triangulations, and tridiagonal harmonics ", "webprogram_exclude": "0", "session_ids": ["Session/18376"], "source_sha256": "9911b61336bbcd5750c58f4da309bc1bb04c8e23e76bc5cbad40cdfb03b9d5e6", "withdrawn": "", "abstract": "We conjecture a family of cyclic sieving phenomena (CSPs) relating the tridiagonal harmonics studied by Bergeron and Pr\\'eville-Ratelle to the enumeration of triangulations of rooted plane polygons with internal vertices by Brown, including his counts for those with cyclic symmetry. To do this, we introduce a family of polynomials $\\text{TriCat}_{n,k}(q,t)$ defined as sums over pairs of Dyck paths related in the Tamari lattice with a prescribed number $k$ of contacts for the lower path. We conjecture that these polynomials are symmetric in $q,t$ and derive a recursive method to compute them. We then show how they specialize at $t=q^{-1}$ to simpler formulas in the cases $k = n,n-1,n-2,n-3$, some conjectural, and how these simpler formulas support the CSP conjecture.", "id": "Paper/66819", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66819"}, {"title": " Characteristic Dependence and Thresholds for Betti Numbers of Monomial Ideals ", "webprogram_exclude": "0", "session_ids": ["Session/17373"], "source_sha256": "bf6e2cc118e70da691c8968fe627cbc2904fa7fb8514141c9064591bfe506b28", "withdrawn": "", "abstract": "The Betti numbers of a monomial ideal can depend on the characteristic of the underlying field, with this dependence governed by torsion in the homology of associated simplicial complexes. I will discuss recent work showing that the Betti numbers of monomial ideals in at most five variables are independent of the characteristic of the field. The proof combines a reduction to the squarefree case with Hochster’s formula and restrictions on torsion in simplicial complexes with few vertices. This bound is sharp: characteristic dependence can occur in six variables. I will then describe how these ideas lead to a more refined question: for a given prime $p$, what is the smallest number of variables in which the Betti numbers of a monomial ideal can depend on characteristic $p$? I will conclude with ongoing work on the seven- and eight-variable cases.", "id": "Paper/66820", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66820"}, {"title": " Bifurcation for elliptic problems with nonlinearities in the domain and on the boundary ", "webprogram_exclude": "0", "session_ids": ["Session/17998"], "source_sha256": "e5f282ee33b8732842a359d57fb30cfee1212839e3c59c0c8ae83e7dbf3eca76", "withdrawn": "", "abstract": "We study a parameterized elliptic problem in which superlinear, subcritical nonlinearities appear both in the domain and on the boundary. A rescaling argument together with degree theory gives a branch of positive solutions bifurcating from infinity as the parameter tends to zero. Under additional conditions near zero, the branch emanates from the trivial solution at the first eigenvalue of an associated eigenvalue problem, and we determine the direction of bifurcation. We also establish nonexistence of positive solutions for large parameter values.", "id": "Paper/66821", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66821"}, {"title": " Phase Retrievability and State Distinguishability for Quantum Channels ", "webprogram_exclude": "0", "session_ids": ["Session/18277"], "source_sha256": "4ee3a26a6f3f9db9bb48c7ee95f87463f38c98fa0ecd08ad106c99ec48d0f886", "withdrawn": "", "abstract": "Phase retrieval provides a natural framework for studying when quadratic measurements determine a vector up to a global phase, and this perspective has a direct connection with the identification of pure quantum states. In this talk, I will discuss how ideas from frame theory and operator theory can be used to study phase retrievability and state distinguishability for quantum channels. The main theme is to understand when a channel retains enough information to distinguish pure input states, and how this question can be analyzed through operator-valued measurements, channel adjoints, Kraus representations, and related frame-theoretic structures. I will also indicate how these ideas connect with broader questions concerning distinguishability, structured quantum channels, and information encoded through operator systems.", "id": "Paper/66822", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66822"}, {"title": " Trait-mediated dispersal at habitat edges and hump-shaped density–area relationships ", "webprogram_exclude": "0", "session_ids": ["Session/18325"], "source_sha256": "3c9b40ce9e0d726f6752471e20c6b0c53f8193c0abbbedc5cdbea37687d14be1", "withdrawn": "", "abstract": "We study steady states of a reaction–diffusion model for two species in a habitat patch surrounded by a hostile matrix, where the inferior species adjusts its emigration rate at the patch edge in response to the density of the dominant species. Both dominant-avoidance and refuge-seeking responses are considered. We establish existence and nonexistence results for coexistence states and describe the resulting density–area relationships, showing that edge behavior alone can make a larger patch support a lower average density.", "id": "Paper/66825", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66825"}, {"title": " Solvability of the random stable roommates problem ", "webprogram_exclude": "0", "session_ids": ["Session/18312"], "source_sha256": "fe142b392299726d4fecc012de49b946777f73bb7072a83beebcb8eaef0e0aac", "withdrawn": "", "abstract": "Assume that $n = 2k$ potential roommates each have an ordered preference of the $n-1$ others. A stable matching is a perfect matching of the $n$ roommates in which no two unmatched people prefer each other to their matched partners. When the preferences are chosen uniformly at random, Gusfield and Irving predicted in 1989 that there is no stable matching with high probability. I will discuss our proof of this conjecture, based on a new approach to understanding the landscape of stable matchings.", "id": "Paper/66826", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66826"}, {"title": " Multiple solutions for higher-order dynamic equations with mixed boundary conditions ", "webprogram_exclude": "0", "session_ids": ["Session/18254"], "source_sha256": "a54174ca45fa4f7c1c03772267d887705e4c1a6e73b5d906df61eba6637f3bb8", "withdrawn": "", "abstract": "We consider a class of nonlinear higher-order dynamic equations on time scales subject to mixed boundary conditions, where the nonlinearities in the equation and in the boundary conditions satisfy polynomial growth. Using fixed-point theorems for expansive mappings together with completely continuous operators, we establish the existence of at least one classical solution, and under stronger hypotheses, the existence of at least three non-negative solutions. Examples on discrete and mixed time scales illustrate the results.", "id": "Paper/66827", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66827"}, {"title": " Resolving Monomial Modules Over Numerical Semigroup Rings ", "webprogram_exclude": "0", "session_ids": ["Session/18318"], "source_sha256": "c06d81947323cc919f06f50864ff76f732bb3e43d89ef7ca6a00f77929d5803c", "withdrawn": "", "abstract": "Recent work in numerical semigroups has capitalized on the polyhedral Kunz cone, a discrete parameter space for fixed multiplicity semigroups. This talk describes recent work with Chris O'Neill which generalizes the Kunz cone to a space of monomial modules over numerical semigroup rings.", "id": "Paper/66828", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66828"}, {"title": " Zeros of characters and orders of elements in finite groups ", "webprogram_exclude": "0", "session_ids": ["Session/17832"], "source_sha256": "be4eb6ea8fc9134debcff3bb4de136e7f0982c1f0f03fb0de92d992473f711cb", "withdrawn": "", "abstract": "We discuss our recent joint work with Gabriel Navarro and Gunter Malle on a conjecture of T.~Wilde concerning character values and\nelement orders of finite groups. We reduce it to a statement on nearly simple\ngroups that can be checked ``prime by prime''. For these groups, we show that a\nstrong form of Wilde's conjecture holds in many important cases, and for primes\n$p>5$ we are able to show the required statement for most classes of nearly\nsimple groups.", "id": "Paper/66831", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66831"}, {"title": " Taking High School Students to Mathematical Horizons—and Beyond ", "webprogram_exclude": "0", "session_ids": ["Session/18212"], "source_sha256": "9fa1b8f4fbec8305907464660c42baf6295ee42175e57b9237d37560dd046ec6", "withdrawn": "", "abstract": "We will show examples of how we transformed the MAA’s Math Horizons journal articles and problems into diverse and engaging math circle sessions that combine hands-on activities, problem solving, and open-ended exploration. The activities are flexible and adaptable for participants with a wide range of ages and mathematical backgrounds, from students in the early high school grades—and even younger students—to those studying calculus and undergraduates.", "id": "Paper/66832", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66832"}, {"title": " The Asymptotic Winner of Niedermaier’s Dart Game ", "webprogram_exclude": "0", "session_ids": ["Session/18159"], "source_sha256": "29d6b3a40d82816df025f5432b05954de3319eb6f8342b4ce644577a12fe20b3", "withdrawn": "", "abstract": "In Niedermaier’s dart game, \\(p\\) players begin in a fixed order and take turns throwing darts. A player remains in the game and moves to the back of the line if their dart is closer to the center than every previous dart; otherwise, that player is eliminated. The game continues until only one player remains. Let \\(W_p\\) denote the initial position of the winner and let \\(P_{p,k}=\\mathbb P(W_p=k)\\).\n\nElizalde previously obtained combinatorial recurrences for the probabilities \\(P_{p,k}\\) and asked whether the properly rescaled winning-player distribution converges as \\(p\\to\\infty\\). We answer this question by showing that\n\\[\n\\frac{W_p}{p}\\xrightarrow{d}\\operatorname{Uniform}(0,1).\n\\]\nMoreover, for every fixed \\(k\\) \\[\npP_{p,k}\\longrightarrow1+\\frac1k.\n\\]\nThis allows us to discuss the distributions of successful throws as record positions in a random permutation and couples the winner to the location of the best dart thrown during the first round. We also describe the joint limiting distribution of the highest-ranking players.", "id": "Paper/66837", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66837"}, {"title": " Minimal Surface Spectrum Rigidity ", "webprogram_exclude": "0", "session_ids": ["Session/17960"], "source_sha256": "a320c4138bb728fd391c37b6e62d83c7ad8ba6194e6e633c7e246a272a51c69d", "withdrawn": "", "abstract": "There is a fairly well-developed existence theory for minimal submanifolds in Riemannian manifolds, but still little is known about the space of minimal submanifolds in even the simplest closed Riemannian manifolds. For example, one can ask whether a Riemannian manifold is determined up to isometry by the minimal submanifolds that it contains? In the case of one-dimensional minimal submanifolds, or geodesics, there is a rich theory falling under the heading of \"marked length spectrum rigidity.\" This talk will focus on what can be said for minimal submanifolds of dimension greater than one.  Like the one-dimensional case we use tools and ideas from dynamical systems, but new to the higher dimensional case our proofs also rely in a crucial way on rigidity phenomena for scalar curvature (joint work with Yangyang Li and James Marshall Reber.)", "id": "Paper/66840", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66840"}, {"title": " Properties of the Dichromatic Polynomial ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "169f6f464b8189c3daf03d3abfb6b1ce4f4455d5ee3c5d660ee50d8781b46ed1", "withdrawn": "", "abstract": "The chromatic polynomial of a graph counts its proper vertex colorings and has been extensively studied. For a digraph $D$, the dichromatic polynomial $P_D(q)$ instead counts the $q$-colorings in which no directed cycle is monochromatic. Despite being a natural directed analogue, the dichromatic polynomial has been directly studied in only a few papers, with most of this work appearing recently. We investigate the coefficients, roots, and structural information encoded by the dichromatic polynomial.", "id": "Paper/66841", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66841"}, {"title": " On the relationship between Newton polygons and F-singularities ", "webprogram_exclude": "0", "session_ids": ["Session/17929"], "source_sha256": "3f92dffeb4c3fd156067ebc53c5345543147fbb943a1ba2d2980c3afa223c8f9", "withdrawn": "", "abstract": "We will survey some recent results on the relationship between various generalizations of the F-split condition (such as quasi-F-splitness and higher F-injectivity) of cones of projective varieties, and the crystalline cohomology, zeta functions, and newton polygons of those projective varieties.", "id": "Paper/66842", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66842"}, {"title": " Homomorphisms and Chromatic Numbers of Borsuk Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18352"], "source_sha256": "7c3ef1c5bcf270df8e8effa1062365b0a256954955558047013e80f58f05c41e", "withdrawn": "", "abstract": "Vietoris--Rips complexes connect data points that are sufficiently close, while anti-Vietoris--Rips complexes reverse this perspective and connect points whose dissimilarity exceeds a prescribed threshold. On the sphere $S^k$, with geodesic metric, the Borsuk graph $\\mathrm{Bor}[S^k;r]$ is the $1$-skeleton of the anti-Vietoris--Rips complex at scale $r$. Meaning that, vertex set is $S^k$ and the edges are between two vertices when they are at least $r$ distance apart. Thus, it can be viewed as a dissimilarity graph on the sphere at a threshold. We study for $k>n$, when does a graph homomorphism $f\\colon \\mathrm{Bor}[S^k;r] \\to \\mathrm{Bor}[S^n;t]$ exist? In earlier joint work with Henry Adams, Alex Elchesen, and Michael Moy, the topology of anti-Vietoris--Rips metric thickenings provides an obstruction that for $k>n$, no such graph homomorphism exists when $r<\\pi$ and $t> 2\\pi/3$. In particular, this obstruction is related to the fact that the anti-Vietoris--Rips metric thickening of $S^n$ has the homotopy type of $\\mathbb{RP}^n$ for scales between $2\\pi/3$ and $\\pi$. In ongoing joint work with Henry Adams, we give further bounds when $n=1$ (using chromatic numbers of graphs) or when $f$ is measurable (using independence ratios of graphs). Dually, we produce explicit graph homomorphisms $f$ when $r$ is large and $t$ is small compared to sphere coverings and packings. Further, we investigate how many points need to be uniformly sampled from a sphere until the chromatic number of the resulting random Borsuk graph reaches a certain threshold.", "id": "Paper/66844", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66844"}, {"title": " On the Carleson-Radon transform and the Hybrid Trilinear Hilbert transform ", "webprogram_exclude": "0", "session_ids": ["Session/17815"], "source_sha256": "184bd0aa2552a1a97c88ae019d17253281457d5f431fa13ec4be5778d1e29115", "withdrawn": "", "abstract": "In this talk we will briefly review some very recent progress on two main themes within harmonic analysis area:\n\n1) The study of the Carleson Radon transform\n\n2) The boundedness properties of the Trilinear Hilbert transform along flat/non-flat curves", "id": "Paper/66846", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66846"}, {"title": " Commutative algebra versus classification theory ", "webprogram_exclude": "0", "session_ids": ["Session/18559"], "source_sha256": "d7f886c80d4223cd02fde84ab7179c6c18bbcbf1311cd18dd721a9759c1f9d38", "withdrawn": "", "abstract": "This talk investigates how concepts arising from \"pure logic\" interact with structures arising in the \"real world\" of the rest of mathematics.  In model theory, a central role is played by dividing lines like stability, simplicity, and NIP, which arose out of Shelah's work on classification theory.  It's natural to ask how these dividing lines intersect with concepts from commutative algebra.  For example, which Noetherian rings are stable?  Which UFDs are NIP?  Although we have no complete answers to any of these questions, many partial results are known, especially if one assumes that fields are classified.  I will discuss some of the most interesting of these results.  On the whole, it seems that there is a tension between model-theoretic niceness and algebraic niceness: most natural examples from commutative algebra fail to be model-theoretically tame.", "id": "Paper/66847", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66847"}, {"title": " Shotgun Assembly in the Non-Uniform Lattice Labeling Model ", "webprogram_exclude": "0", "session_ids": ["Session/18312"], "source_sha256": "1c4c7fa9d6a5f8c0c76485461cab243095018688a1bbe5dbd16d8b6719d3e65e", "withdrawn": "", "abstract": "In this talk, we discuss the shotgun assembly problem on the labeled lattice, as proposed by Mossel and Ross (2019). Given a d-dimensional n-lattice with vertices labeled i.i.d. from a discrete probability distribution \\pi, we ask whether it is possible to reconstruct the labeling of the lattice given the k-deck, the collection of all labeled subgrids with side length k. While previous work by Ding and Liu (2023) and Demidovich, Panichkin, and Zhukovskii (2023) has identified the threshold for reconstruction when \\pi is uniform, we examine the non-uniform case. Using information-theoretic arguments, we identify a regime for k under which reconstruction is impossible with high probability, which depends on the Shannon entropy of \\pi. Our negative result coincides with the known information-theoretic threshold in the uniform case.", "id": "Paper/66848", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66848"}, {"title": " Splitting and Gluing in Real Seiberg–Witten Theory ", "webprogram_exclude": "0", "session_ids": ["Session/18344"], "source_sha256": "634aaaa88863c06ca5f7084fca139e86bf4260e17f666d354af14328648d0a50", "withdrawn": "", "abstract": "Real Seiberg–Witten theory is a variant of Seiberg–Witten theory that appears to provide useful and interesting invariants of surfaces in 4-manifolds. In this talk I will explore cutting and gluing techniques, studying how the invariants are related under operations of cutting along hypersurfaces and gluing along boundaries. I will focus on certain vanishing and rigidity theorems for numerical invariants of 2-knots in the 4-sphere.", "id": "Paper/66849", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66849"}, {"title": " AI and Deepening Mathematical Thinking: Designing for Productive Engagement ", "webprogram_exclude": "0", "session_ids": ["Session/19349"], "source_sha256": "9119f98dfc1d37d71c33744e8f9aced7fb7d7c0075f42b878978d75c66c20840", "withdrawn": "", "abstract": "This presentation treats AI use in the mathematics classroom as a design problem: we know students are using AI, so the question is how to create the conditions under which they choose to use it in ways that deepen their thinking or decline to use it in order to protect productive struggle. A framework will be presented that names aspects of a learning environment a teacher can attempt to adjust and asks of each how far it still reaches when a student is working alone. Multiple courses at various levels – introduction to proof, precalculus, introductory statistics, and discrete mathematics – were adjusted with that framework in mind for 2026–2027, and structured prompts for problem solving, metacognition, revision, and self-testing were built into assignments. Preliminary data will be reported on whether students in that environment sought help in ways that returned the work to them, protected their struggle by declining it, or defaulted to ease regardless.", "id": "Paper/66854", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66854"}, {"title": " CANCELLED Gazing into the abyss? Recent AI-assisted endeavors in noncommutative algebra \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/19342"], "source_sha256": "006ddf5959159b66e17bafc8ff58bbbcef87951a969e25cc155d413d92975512", "withdrawn": "", "abstract": "I will discuss recent solutions to problems and developments in research programs in noncommutative algebra that have become possible thanks to the dramatic rise in AI capabilities. The focus will be on methodology, an attempt to put my finger on the role AI played in this progress, and an invitation to discuss philosophical and practical questions we face in this new era.", "id": "Paper/66860", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66860"}, {"title": " On the growth of Lie algebras and Jordan algebras ", "webprogram_exclude": "0", "session_ids": ["Session/17666"], "source_sha256": "63eada6bb8fada7b0e1ca0ca67b1147974941467deca5256ccbc49493ee7638c", "withdrawn": "", "abstract": "We discuss the inverse problem for growth functions of Lie algebras and Jordan algebras, illustrate differences between the polynomially bounded and intermediate realms, and describe the connection with associative algebras.", "id": "Paper/66861", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66861"}, {"title": " Adventures in AI-Sitting ", "webprogram_exclude": "0", "session_ids": ["Session/17765"], "source_sha256": "1e2744806771ff4d005d584f9dc0d1a16c3644b31d9a44cb0b08eca223cf1210", "withdrawn": "", "abstract": "Artificial intelligence assistants such as OpenAI's GPT, Anthropic's Claude, and Google's Gemini are rapidly increasing their abilities in mathematics (and many other technical areas).  Moreover, they are widely used by college students.  Where does the introductory ODEs course fit in a world where many traditional problems can be solved by just asking the assistant? To try to answer this, the author will present the results of inputting problems from standard introductory textbooks into AI assistants, as well as discussing some general issues that arise with the use of such assistants.  Some possible directions for future teaching will be outlined, but the primary intent is to start a conversation rather than presenting a definitive word.", "id": "Paper/66864", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66864"}, {"title": " Highlights from a survey of homology theories for hypergraphs ", "webprogram_exclude": "0", "session_ids": ["Session/18114"], "source_sha256": "4543d067e6e3dd983a37727d8d0fbc965170e2ff405ff812d7f8b08e33df2e69", "withdrawn": "", "abstract": "Hypergraphs have seen widespread application in network and data science communities in recent years. Hypergraph structure in the form of hypernetwork science measures and hypergraph motifs have been among the common approaches. Meanwhile, there have also been theory advances in understanding hypergraph structure from a topological lens. In a recent survey article my colleagues and I defined and described nine different homology theories for hypergraphs found in the literature based on constructing auxiliary structures---specifically simplicial, relative, and chain complexes. This talk will cover some highlights from this survey including how properties of some of the homology theories relate to hypergraph structural features, category theory approaches and functoriality of the auxiliary constructions, and illustrative examples to show variability and build intuition. I will also point out open questions in this area. This is joint work with Ellen Gasparovic, Radmila Sazdanovic, Bei Wang, Yusu Wang, and Lori Ziegelmeier.", "id": "Paper/66868", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66868"}, {"title": " Selfdual Hopf algebras arising as biproducts ", "webprogram_exclude": "0", "session_ids": ["Session/17907"], "source_sha256": "c791584257834fb42fd4ea8637dd746288baf6b22c6d25b66a1eb0c9f2a17d6f", "withdrawn": "", "abstract": "In joint work with Yorck Sommerh\\\"auser, we constructed two families of eight-dimensional semisimple Yetter-Drinfeld Hopf algebras over the Klein four-group. Both families are cocommutative, but one is commutative, and the other is noncommutative. Each family consists of four Yetter-Drinfeld Hopf algebras, corresponding to a fourth root of unity. We will show that Yetter-Drinfeld Hopf algebras in the first family are selfdual.\n\nVia the Radford biproduct construction, these Yetter-Drinfeld Hopf algebras give rise to semisimple Hopf algebras of dimension 32. Selfduality of Yetter-Drinfeld Hopf algebras in the first family leads to selfduality of their biproducts. We will also show that even though Yetter-Drinfeld Hopf algebras in the second family are not selfdual, their biproducts are isomorphic to the ones for the first family, and therefore are selfdual.", "id": "Paper/66870", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66870"}, {"title": " Generalized noise sensitivity of eigenvectors: All eigenvectors, inhomogeneous variance profiles, and dependent resampling ", "webprogram_exclude": "0", "session_ids": ["Session/19370"], "source_sha256": "3336db3d9c9238e76fa4472d73c535fd533695ff2f6368d539eecfaf1be46461", "withdrawn": "", "abstract": "Chatterjee (2008) proved, as an application of his general framework relating superconcentration and chaos, that after the entries of an $n \\times n$ matrix drawn from the Gaussian unitary ensemble undergo an entrywise Ornstein-Uhlenbeck (OU) process for time greater than $n^{-1/3}$, the top eigenvector of the matrix becomes almost completely decorrelated from its initial position.\nMore recently, Bordenave, Lugosi, and Zhivotovskiy (2020) showed that the same happens under a discrete resampling model, once more than $n^{5/3}$ randomly chosen entries of a Wigner random matrix are resampled.\nWe generalize these results in several directions: (1) we analyze the decorrelation of \\emph{any} eigenvector under continuous and discrete resampling dynamics, (2) we analyze the discrete resampling process for generalized Wigner matrices with inhomogeneous variance profiles, (3) we analyze a combination of continuous and discrete resampling where an OU process is repeatedly run for a certain time on randomly chosen entries, and (4) we analyze a dependent version of resampling where entries grouped into ``blocks'' of arbitrary shapes are resampled together.\nIn each case, we show that a given eigenvector decorrelates provided that enough entries have been resampled or that the associated dynamics have been run for a long enough time. Our proofs take a different approach from prior work, relying more directly on the characterization of eigenvectors as derivatives of eigenvalues and reducing the problem of establishing eigenvector noise sensitivity to variants of standard and robust properties of random matrices such as bounds on eigenvalue spacings and eigenvector delocalization.", "id": "Paper/66872", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66872"}, {"title": " Higher-Order Divergence in Ultrapower and IST Constructions of the Hyperreal Numbers ", "webprogram_exclude": "0", "session_ids": ["Session/19340"], "source_sha256": "4727678b57720a9e9720b30fe57cdaa65805b11f4cd2fda435b6bf769e57a711", "withdrawn": "", "abstract": "There are multiple existing approaches to constructing the hyperreal numbers, most notably Abraham Robinson’s ultrapower construction and Edward Nelson’s Internal Set Theory (IST). Each follows a distinct logical path: the ultrapower method extends the real numbers via ultrafilters and the model-theoretic transfer principle within ZFC, while IST enriches ZFC directly with new axioms introducing a predicate for standardness. Although both provide rigorous formalization for nonstandard analysis, and agree at the first-order level, equivalence does not necessarily extend to higher-order logic. We show how higher-order logic is expressed within each framework and that differences in construction lead to divergence beyond first-order equivalence. In particular, we analyze how IST’s transfer axiom and the ultrapower transfer principle generate distinct higher-order consequences. This comparison clarifies the logical strength of each framework and the extent to which axiomatic differences affect their higher-order theories. Additionally, we further investigate this result with automated theorem proving to formalize the logical structure to compare their axiomatized and theorem-derived transfer directly. We verify the divergence through the formalization of internal and external sets of each construction in Isabelle/HOL.", "id": "Paper/66873", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66873"}, {"title": " Reservoir–Immunity Thresholds, CTL Exhaustion, and Bifurcation Mechanisms in HIV Post-Treatment Control. ", "webprogram_exclude": "0", "session_ids": ["Session/19351"], "source_sha256": "2e43f4d64da4e1e243e8aed25402092b40a79fdefbf891efd88348b0323af1d8", "withdrawn": "", "abstract": "Antiretroviral therapy suppresses HIV replication but does not eliminate the latent reservoir, so viral rebound commonly follows treatment interruption. We analyze an extended Conway–Perelson within-host HIV framework coupling uninfected CD4\\(^+\\) T cells, latently and productively infected cells, free virus, cytotoxic T lymphocytes (CTLs), and an exhaustion variable. The model incorporates latent-cell activation, CTL-mediated killing, antigen-driven CTL expansion, and exhaustion-mediated impairment of effector function. We derive the disease-free equilibrium and a basic reproduction number that depends explicitly on CTL killing strength. By reducing the chronic-equilibrium conditions to a scalar equation in the infected-cell level, we characterize the existence and multiplicity of positive equilibria. Using CTL killing efficiency as a bifurcation parameter, we identify forward and backward bifurcation regimes, saddle-node structure, and parameter regions supporting bistability. Numerical simulations show that small changes in initial reservoir burden can redirect trajectories toward viral control or rebound, while exhaustion parameters reshape the bifurcation structure. These results provide a dynamical-systems framework for understanding reservoir-immunity thresholds governing post-treatment HIV outcomes.", "id": "Paper/66876", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66876"}, {"title": " The Berezin integral as a limit of Riemann sums ", "webprogram_exclude": "0", "session_ids": ["Session/17978"], "source_sha256": "f209ba8ef53099368d6ffa6b84a59a302c804cc313962efeb61112e6875729ab", "withdrawn": "", "abstract": "Berezin integration of functions of anticommuting Grassmann variables is usually seen as a formal operation, sometimes even defined via differentiation. Using the formalism of geometric algebra and geometric calculus in which the Grassmann numbers are endowed with a second associative product coming from a Clifford algebra structure, we show how Berezin integrals can be realized in the high dimensional limit as integrals in the sense of geometric calculus. We then show how the concepts of spinors and superspace transform into this framework.", "id": "Paper/66878", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66878"}, {"title": " Closed vortex filament are excellent candidates for the preferred magnetic axis of quasisymmetric fusion devices ", "webprogram_exclude": "0", "session_ids": ["Session/18104"], "source_sha256": "f43980309f715498531070b6ebb6490337693a7d443017b21e83794fffeca3fa", "withdrawn": "", "abstract": "Recently, enormous progress has been made in obtaining quasisymmetry (QS) of outstanding precision through numerical optimization. Significant analytical progress has also been made possible by the asymptotic expansion near the magnetic axis (NAE). A critical factor in realizing good QS at second order in the NAE is the choice of the magnetic axis. However, because of the complexity of the second-order NAE equations, a characterization of the preferred magnetic axes from those equations themselves has remained out of reach. Our previous results connected the quasisymmetric field strength to the Korteweg-de Vries and Gardner equations. In this work we connect the magnetic axis geometry to the Euler-Kirchhoff elastic rod centerlines (Langer and Singer, SIAM Review 1996, Pfefferlé et al. PoP 2018), which are the curves that move rigidly under the vortex filament equation. We present analytical results in the small rotational transform limit and ample numerical evidence for a broad range of quasi-axisymmetric stellarators over the full range of rotational transform reached by present designs.", "id": "Paper/66882", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66882"}, {"title": " Banach Space-valued Neural Network Approximation: An Air-Quality Application ", "webprogram_exclude": "0", "session_ids": ["Session/19362"], "source_sha256": "0ee425e57d2434e3896e889c94746b927df9a81ff9d747a32d1110a866747431", "withdrawn": "", "abstract": "We develop an approximation framework based on an\nadjustable half-hyperbolic activation function for vector-valued functions\nassociated with finite-dimensional Banach spaces. The derived multivariate kernel has been shown to possess the positivity, normalization, discrete unit section,\nand localization properties required for the approximation\nunder certain conditions on the activation parameters. Using this kernel, we construct a family of\nneural network operators: normalized operators\nin compact fields, quasi-interpolation operators in the entire space,\nKantorovich-type operators, and quadrature-type operators. Quantitative\npointwise and uniform approximation estimates\nare obtained in terms of the first continuity modulus, and the effects of the tuning parameter\nare preserved in the relevant constants and tail terms.\n\nThis theoretical framework is supported by a causal vector-valued \nforecasting experiment conducted using the Beijing Multi-Site Air Quality \ndataset. Hourly $\\mathrm{PM}_{2.5}$ and $\\mathrm{PM}_{10}$ concentrations \nare treated jointly as an $\\mathbb{R}^{2}$-valued response, while lagged \npollutant measurements and meteorological variables available at the \nforecast origin constitute the predictor space. The four operator families \nare evaluated for one-step-ahead forecasting under a strictly chronological \ntraining--validation--test protocol. All preprocessing choices and operator \nparameters are determined without access to the test period. Forecasting \nperformance is assessed using errors measured in the vector norm, together \nwith componentwise MAE, RMSE, and $R^{2}$. Seasonal ARIMA and a multilayer \nperceptron are included as external empirical benchmarks. All numerical \nexperiments are implemented in Python~3.13 using double-precision arithmetic \nand fixed computational settings across the four operator families. The \ncomputational analysis examines how the adjustment parameter, sampling \nresolution, and operator construction affect out-of-sample accuracy, \nnumerical stability, and the distribution of normalized kernel weights.", "id": "Paper/66886", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66886"}, {"title": " Uniform Laws of Large Numbers for Subdifferentials: Failure and Remedies ", "webprogram_exclude": "0", "session_ids": ["Session/18245"], "source_sha256": "f28e87dd251810b3451daa4552eb28dc8b8a1986ea5f3a4abb70b61041d4c4f8", "withdrawn": "", "abstract": "We study uniform laws of large numbers for the subdifferentials of random functions. We begin with counterexamples showing that such laws can fail even for univariate random Lipschitz functions and bivariate random convex functions. These examples resolve questions posed by Shapiro and Xu (2007) in the negative and reveal a fundamental barrier to stationary-point consistency in sample-average approximation for nonsmooth stochastic programs. We then identify broad conditions that rule out these failure phenomena. In particular, we establish strong laws of large numbers in the Lipschitz pseudometric under either topological or model-theoretic assumptions. Consequently, we obtain uniform laws of large numbers for both limiting and Clarke subdifferentials.", "id": "Paper/66892", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66892"}, {"title": " A model theory interpretation of quantum physics. ", "webprogram_exclude": "0", "session_ids": ["Session/18321"], "source_sha256": "4f5ff59bf25be109ce6f10e3d4ac6d4e45f603b522209106298aa6c20e69b155", "withdrawn": "", "abstract": "This project develops a framework for analysing physical theories and their interpretations through the methods of continuous model theory. I show that the standard Hilbert-space axiomatisation of quantum mechanics can be reformulated as a theory in the language of Continuous Logic (CL), in which wave functions appear as CL‑predicates on a suitable metric structure. Building on this reformulation, I introduce notions of local and global approximation based on CL‑ultraproducts. A central result establishes that the Dirac–von Neumann model of quantum mechanics admits local approximation by finite structures—equivalently, that there exists a pseudo‑finite model of quantum mechanics.\n\nUsing similar techniques, I prove the existence of a pseudo‑finite structure that locally approximates Lorentz‑invariant Minkowski spacetime, with a pseudo‑finite analogue of $\\mathrm{SO}^+(1,3)$.\n The same structure globally approximates a complexified Minkowski spacetime, in a manner reminiscent of Penrose’s complexification.\n \n  Finally, I construct a pseudo-finite structure that global approximates the Veneziano model, complex numbers with the Euler beta-function,   whose historical significance lies in its role in the emergence of string theory.", "id": "Paper/66893", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66893"}, {"title": " Prime and two-sided ideals of homomorphic images of the Witt algebra ", "webprogram_exclude": "0", "session_ids": ["Session/17666"], "source_sha256": "fb46a41b7edfbcd2891ad5630d20bf0449847eb0463069a28b2d7518db318383", "withdrawn": "", "abstract": "One of the main open problems in ring theory and Lie algebra is whether a Lie algebra $\\mathfrak{g}$ is finite-dimensional if and only if $U(\\mathfrak{g})$ is left or right Noetherian. In 2014, Sierra and Walton proved a notable result that the enveloping algebra of the Witt algebra $U(W)$ is not Noetherian by considering its homomorphic image. Since then, there has been a lot of works generalizing their result, but their interesting conjecture that $U(W)$ satisfies ACC on two-sided ideals remains mysterious. \n\nIn this talk, we will give significant evidence for their conjecture by showing that the image $B_n$ of $U(W)$ over an infinite family of so-called \"orbit homomorphisms\" satisfies ACC on two-sided ideals. These orbit homomorphisms are the key in generalizing the Dixmier map for finite-dimensional solvable Lie algebra to $W$ and the image $B_n$ approximates $U(W)$ as n grows larger. We completely characterize the prime and primitive spectrum of $B_n$ and show that $B_n$ satisfies the Dixmier Moeglin Equivalence. Lastly, I will motivate some interesting conjectures for suggested by our results for the prime and primitive spectrum of the Witt and Virasoro algebras.", "id": "Paper/66894", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66894"}, {"title": " Using linear Kakeya sets to study curved Kakeya sets ", "webprogram_exclude": "0", "session_ids": ["Session/17815"], "source_sha256": "d941dca29f058057eacf74aae29aef8719f71e536d06a24fd1705a1afbeb1dc7", "withdrawn": "", "abstract": "Kakeya sets of curves underlie many oscillatory integral problems, generalizing the linear Kakeya conjecture that underlies the restriction conjecture. As first discovered by Bourgain, Kakeya sets of curves in dimension 3 and greater can behave very differently from Kakeya sets of lines, and may compress more than expected. This leads to a complicated landscape of curved Kakeya problems. We describe how the linear Kakeya conjecture can help us better understand these curved Kakeya problems, and the limitations to using techniques from the linear Kakeya theory. This is based on work by the author and work in collaboration with Shaoming Guo, Larry Guth, Minxing Shen, and Ruixiang Zhang.", "id": "Paper/66900", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66900"}, {"title": " Learning Cell Lineage with Topology-Guided Optimal Transport ", "webprogram_exclude": "0", "session_ids": ["Session/18353"], "source_sha256": "0f243464fd833856994cd27e03e042ee843ff009f49f9ed87752b327476f839d", "withdrawn": "", "abstract": "Spatial transcriptomics tracks gene expression and position across developmental stages, but sampling is destructive: no cell is observed twice, so cell lineage must be learned, not measured. Current methods infer this correspondence by transporting cells to match expression and geometry, discarding the topological features — cavities and loops — that emerge, persist, split, or close as tissue develops.\nWe present ProTopOT, which learns cell correspondence jointly with topological feature correspondence: persistent features extracted from each section are themselves optimally transported alongside the cells, coupled through a nonconvex objective. Beyond this biological setting, the construction is a recipe for any learning problem where instance-level correspondence and topological structure should be inferred jointly", "id": "Paper/66903", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66903"}, {"title": " Mathematical Functions in Desmos Arts ", "webprogram_exclude": "0", "session_ids": ["Session/17091"], "source_sha256": "419fc314f22886b5b41202822dd6768f3b59d4bab47ece030b6dbf2a6748425d", "withdrawn": "", "abstract": "In this talk, a student club event will be introduced. It is a competition on animated art works built from mathematical functions by applying the graphical software “Desmos”. In the process of creating such animated art works, students need to apply a large set of mathematical functions to simulate the desired actions. Through the process, student not only produced beautiful animated art works, but also learned deep mathematical concepts, such as gradients and modeling functions, in a hands-on game-like environment. A few pieces of art works will be demonstrated along with the roles of the mathematical functions behind them.", "id": "Paper/66906", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66906"}, {"title": " The Artin-Springer Theorem for Algebras with Involution over Semiglobal Fields ", "webprogram_exclude": "0", "session_ids": ["Session/18214"], "source_sha256": "63c0b36e189d4d4a828048666fdadc00b5f6ee90c9df8e3f6101f5e7892f4b5d", "withdrawn": "", "abstract": "Let $q$ be a quadratic form over a field $K$ and $L/K$ a field extension of odd degree. It is a well-known result of Artin and Springer that $q$ is isotropic if and only if $q_L$ is isotropic. More generally, it is an open question that if $(A,\\sigma)$ is a central simple algebra with involution over $K$ and $L/K$ is a finite extension of degree relatively prime to $2\\text{Ind}(A$), then $(A,\\sigma)$ is isotropic if and only if $(A_L,\\sigma_L)$ is isotropic. Let $K$ be a complete discrete valued field with residue field $k$ such that char($k)\\neq 2$ and $F=K(X)$ the function field of a smooth, projective, geometrically integral curve $X$ over $K$. We give a positive answer to this question for any central simple algebra with involution over $K$ assuming a positive answer over finite extensions of $k$ and for any central simple algebras with involution $(A,\\sigma)$ over $F$ with $\\text{Ind}(A)=2^n$ assuming a positive answer over finite extensions of $k$ and $k(t)$.", "id": "Paper/66908", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66908"}, {"title": " Counting codes and their equivalence classes ", "webprogram_exclude": "0", "session_ids": ["Session/18389"], "source_sha256": "7bae26f08c6a7637f21c9fe7f07fb2b5ce000856a0eb6b1d0d263ab166778e18", "withdrawn": "", "abstract": "Counting the number of codes with prescribed length, dimension, and correction capability is a notoriously difficult problem (in fact, intractable in full generality). The first part of this talk will provide evidence for this claim by establishing an equivalence between counting codes and computing the invariants of certain posets, a problem that has remained open since the 1950s.\n\nThe second part of the talk turns to the asymptotic version of the problem: Estimating the number of codes and their equivalence classes as one of the code parameters tends to infinity. While the problem remains challenging, considerably more can be said in this setting. In particular, when considering equivalence classes for certain parameter classes, their asymptotic behaviour is often governed by the same distributions that arise in the study of Brownian motion.", "id": "Paper/66909", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66909"}, {"title": " Indistinguishability of Linear Compartmental Models ", "webprogram_exclude": "0", "session_ids": ["Session/18319"], "source_sha256": "205c6a25dacb5bfb9f3e8229d912fc5764de9fad5d7a78c7198ba080deabdb3b", "withdrawn": "", "abstract": "Linear compartmental models describe the movement of material through a system of interconnected compartments, with the underlying directed graph encoding the structure of the model. Two models are indistinguishable when they produce the same input-output behavior despite having different graph structures. We will first discuss results on permutation indistinguishability of skeletal path models, where models with distinct structures and leak arrangements can have identical input-output equations up to permutation. We will then consider a graph theoretic approach that connects the coefficients of the input-output equation to combinatorial features of the underlying graph, yielding an alternative proof of these results. Finally, these graph theoretic ideas will be applied to directed cycle models to identify additional families of indistinguishable models. Together, these results highlight the role of graph structure in determining when distinct linear compartmental models exhibit identical input-output behavior.", "id": "Paper/66910", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66910"}, {"title": " Eventually Nondecreasing Quasi-polynomials ", "webprogram_exclude": "0", "session_ids": ["Session/18379"], "source_sha256": "038e12747baa224919edd6089d25a8027fb571ac1db8c6ef693b29a6d95e3f51", "withdrawn": "", "abstract": "Quasi-polynomials are ubiquitous in combinatorics and algebra, as they arise in a variety of enumeration problems. Because quasi-polynomials consist of constituent polynomials, their behavior is more subtle than for a single polynomial. In particular, unlike for a polynomial, it is possible for a quasi-polynomial defined on the positive integers to have infinitely many points at which it is decreasing. We characterize quasi-polynomials of degree $d$ and period dividing $p$ that are eventually nondecreasing, i.e., that have only finitely many values at which they decrease. We then give a detailed analysis of the space of eventually nondecreasing quasi-polynomials with fixed degree $d$ and period dividing a fixed $p$ such that the $h$-vector of the quasi-polynomial is nonnegative. Using this analysis, we determine the rate of growth of the number of such quasi-polynomials as a function of the sum of the $h$-vector entries for the 0-th constituent polynomial.", "id": "Paper/66912", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66912"}, {"title": " Quasi-isometric Higman embeddings and the Dehn function ", "webprogram_exclude": "0", "session_ids": ["Session/17922"], "source_sha256": "757b2a0771ab45beccb3ca5654ad4313a38e4b2fa292b686764be81ac307cf73", "withdrawn": "", "abstract": "A fundamental algorithmic question in group theory is the Word Problem for finitely generated groups, which asks whether there exists an algorithm to decide whether two words on the generators represent the same group element.  A related notion is the Dehn function of a finitely presented group, the smallest isoperimetric function of the presentation's Cayley complex.  While the Dehn function gives an upper bound for the complexity of the Word Problem for that group, this bound is only meaningful in the class of finitely presented groups and is very far from sharp even in this class.  I resolve this disconnect by instead considering the Dehn functions of the finitely presented groups into which a group embeds, demonstrating a refinement of the Higman embedding theorem that gives a potentially quasi-optimal bound on the Dehn function of the ambient group.", "id": "Paper/66913", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66913"}, {"title": " Upward-Closed Sets in the Dominance Order ", "webprogram_exclude": "0", "session_ids": ["Session/18299"], "source_sha256": "faaba26b1a8bd1c2d4ba63fc62fc02900882b9f07d0cbe1dde9d0913492db2ce", "withdrawn": "", "abstract": "The majorization relation orders all partitions of a fixed positive integer into a poset, generally known as the dominance order. For even integers, all the nontrivial graphic partitions form an ideal (a downward closed set) within this order. If we restrict our attention to this ideal, we then obtain the dominance order on graph degree sequences having a common sum. This talk introduces a forbidden subgraph approach that allows for the characterization of upward-closed sets in the dominance order, including the first known non-split family.", "id": "Paper/66914", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66914"}, {"title": " Variance and higher moments in the DNA coverage depth problem ", "webprogram_exclude": "0", "session_ids": ["Session/18389"], "source_sha256": "26fa0c6ef12dd37c3107b865427b834a507ca0268f800481d3f0b2411bb2f40a", "withdrawn": "", "abstract": "The coverage depth problem in DNA data storage aims to improve the efficiency of DNA sequencers in recovering the information previously stored using artificial DNA. The main difference between retrieving data from DNA and traditional storage media is that DNA strands must be read randomly.\n\nIn the language of coding theory, this translates into considering the generator matrix $G$ of an $[n,k]_q$ code $\\mathcal{C}$ and computing the expected number of columns that one has to draw until the entire space $\\mathbb{F}_q^k$ is spanned. This quantity has been extensively studied in previous works; however, the expectation represents the first moment of the variables that arise in the coverage depth problem.\n\nThis talk will present results concerning the derivation of general formulas and bounds for higher moments and variance in the context of coverage depth, as well as the identification of optimal code families.", "id": "Paper/66921", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66921"}, {"title": " Counting entries on anti-diagonals of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.211ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 521.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">k</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-6B\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-regular arrays ", "webprogram_exclude": "0", "session_ids": ["Session/19361"], "source_sha256": "a0d5ad5e7818139bbb70e284a8477ba9d99194d6c2b44992a729b1990abde186", "withdrawn": "", "abstract": "For a $2$-dimensional array of integers and each $n \\geq 0$, consider the finite generating series (that is, polynomial) $f(n, x)$ that records, on the $n$th anti-diagonal, the number of occurrences of each integer. We study arrays that are $k$-regular, in the sense of Allouche and Shallit, and for which $f(n, x)$ is a $k$-regular function of $n$. The motivating example is the enumeration of binomial coefficients on the $n$th row of Pascal's triangle by their $p$-adic valuation, for which the generating series is known to be a $p$-regular function of $n$.", "id": "Paper/66924", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66924"}, {"title": " The Feynman propagator for the wave equation with inverse square potential ", "webprogram_exclude": "0", "session_ids": ["Session/17999"], "source_sha256": "e6a8c251f668de2f15641cee534cf2f4d4a0ddaa1cf918c5c7bea3358f69f4a0", "withdrawn": "", "abstract": "I will describe a construction of the Feynman propagator for the wave equation with an inverse square potential on Minkowski space.  The construction defines Sobolev-type spaces characterizing the Feynman property on which the operator is invertible and relies on microlocal propagation estimates through the singularity of the potential.  I will also describe the asymptotic behavior of the propagator, which in this model setting can be characterized in terms of hypergeometric functions.", "id": "Paper/66925", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66925"}, {"title": " Recent Advances in the Real Solution Maximization Problem ", "webprogram_exclude": "0", "session_ids": ["Session/18042"], "source_sha256": "ffe7117621e8bbb1ffaf7c0262d11e1b72fde4f3df3e4143258ca4049c648c5e", "withdrawn": "", "abstract": "Given a real parameterized polynomial system, the Real Solution Maximization Problem (RSMP) is to obtain parameters which maximize the real solution count of the system. This is a difficult problem. Known approaches to the RSMP in the literature are qualitatively distinct from one another. For instance, Dietmaier optimization attempts to push conjugate solutions together using gradient descent on a certain vector field over the parameter space, whereas degeneration techniques try to find totally real instances over exceptional parameters of the projection of the solution set onto the parameter space, then perturb to find many real solutions over generic parameters. We survey these methods, demonstrating problems for which they have enjoyed success. We present novel approaches to the RSMP, in particular an alternative framework for Dietmaier optimization.", "id": "Paper/66932", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66932"}, {"title": " Ramsey numbers with wild edges ", "webprogram_exclude": "0", "session_ids": ["Session/18011"], "source_sha256": "857092a8f9ab67df4985a4d60e8c0a9dc57fa6b216b267eea51a7a005446d8ea", "withdrawn": "", "abstract": "Ramsey numbers determine the minimum number of vertices required in a complete graph to guarantee the existence of some monochromatic structure. Motivated by recent work of Lesgourgues, Liebenau, and Taylor, we investigate a variant of Ramsey numbers where a matching simultaneously receives every color, which we call a wild matching. We consider how the addition of this sparse structure affects the Ramsey number for various graphs, determining the stability of particular Ramsey numbers. We study pairs of cliques, stars, paths, cycles, and wheels; we also prove several multicolor results.", "id": "Paper/66938", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66938"}, {"title": " A cyclic projections approach to the minimum enclosing ball problem ", "webprogram_exclude": "0", "session_ids": ["Session/18069"], "source_sha256": "37fa66de65edec2a86b3bd27b5973f7c7286856212d728267dd45a4e19345bac", "withdrawn": "", "abstract": "The method of cyclic projections is a simple and classical algorithm for convex feasibility problems. It is especially attractive in certain metric spaces where basic tools like gradients are difficult to define, but the notion of metric projection is completely natural. In this talk we present an algorithm for solving the minimum enclosing ball problem by solving a sequence of cyclic projection problems. The algorithm works by maintaining upper and lower bounds on the optimal enclosing ball radius, and thus, by design, provides certificates of approximate optimality.", "id": "Paper/66943", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66943"}, {"title": " A geometric approach to nonlocal 2-Hessian equations ", "webprogram_exclude": "0", "session_ids": ["Session/18378"], "source_sha256": "66e1d7743b5096ac43afdb248a3458deb77757abb5c43f260bb751174e3e1f21", "withdrawn": "", "abstract": "We study a nonlocal 2-Hessian equation, given by an infimum of linear deformations of the fractional Laplacian, that is,\n$\n\\inf_{A\\in \\mathcal{A}_2}\\Delta^s (u\\circ A)(A^{-1}x)\n$.\n We characterize the class of coefficient matrices $\\mathcal{A}_2$, which determines the behavior of the operator, and provide a detailed geometric description of the possible degeneracies.\nOur main theorem shows that the nonlocal 2-Hessian equation remains uniformly elliptic for strictly positive right-hand sides, which leads to regularity estimates.  \nThe results hold under weaker hypotheses than those previously considered in the literature, and for the full range $s\\in(0,1)$. In particular, no convexity on the solutions is required. Our hypotheses can be interpreted as nonlocal counterparts of the local notions of  semiconcavity and \n2-convexity.\nMoreover, all the results are stable as $s\\to1$, recovering the local case.\nThe geometric methods developed here are new, even in the local setting, and may be relevant to a broader class of nonlocal fully nonlinear equations and curvature-type problems.", "id": "Paper/66944", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66944"}, {"title": " Discrete Meijer G functions ", "webprogram_exclude": "0", "session_ids": ["Session/17446"], "source_sha256": "cc661e67e71ac5814382afcae1c2dda2a9c878d157dc9f5d7a7bb46a48835876", "withdrawn": "", "abstract": "The Meijer G function is a classical special function defined by a Mellin-Barnes integral. We shall explore a discrete analogue of this function and see some of its properties. We will also discuss the difficulties in extending this definition to time scales.", "id": "Paper/66948", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66948"}, {"title": " Density of reproducing kernels in Model spaces ", "webprogram_exclude": "0", "session_ids": ["Session/18277"], "source_sha256": "543c562dcc7634d93de616496a688d8c32fb962ea6f2af1b7cb5e6accec707d1", "withdrawn": "", "abstract": "Model spaces associated with meromorphic inner functions provide a natural generalization of Paley--Wiener spaces, with Clark bases playing the role of exponential bases on a lattice. We study density conditions for systems of reproducing kernels in these spaces. Using a density measured relative to a Clark basis, we obtain sufficient Beurling--Landau-type criteria: sufficiently small upper density yields a Riesz sequence, while sufficiently large lower density yields a frame.", "id": "Paper/66951", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66951"}, {"title": " Divergence Criteria for Matrix Generalized Hypergeometric Series with Singular Upper Parameter Matrices ", "webprogram_exclude": "0", "session_ids": ["Session/18254"], "source_sha256": "362efad0eaeb6e9eca2d220a981c5e4eeb1962a8031d0e81d5e6191c26c45f32", "withdrawn": "", "abstract": "We investigate divergence criteria for matrix generalized hypergeometric series under certain assumptions. While the divergence criteria for scalar generalized hypergeometric series are currently well understood, the matrix case is not due to the added complexity brought about by the behaviors and properties of matrices. In this talk, we present our current progress in extending previous work on this topic, focusing on the 3x3 matrices case. Here, we consider when the upper parameter matrices are not of full rank. We will outline the method used and discuss our ongoing work toward determining explicit divergence conditions and implications for higher dimensions.", "id": "Paper/66952", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66952"}, {"title": " Controlling Adaptive Invasive Species: A Bioeconomic Model of Wild Pigs ", "webprogram_exclude": "0", "session_ids": ["Session/18327"], "source_sha256": "97b162c44d929032319b8e7227fa709fe5c7bd704cc3b4bdfbfcaabce1dad163", "withdrawn": "", "abstract": "Ecological adaptation to human control measures can significantly complicate natural resource management efforts. Adaptation increases future management costs and, in the case of wild pigs, exacerbates both ecosystem disservices and financial losses to agricultural producers. Wild pigs are highly intelligent, enabling them to evade various private and government-implemented control efforts, making them one of North America's most challenging invasive species to manage. Unsuccessful removals from trapping or hunting allows escapees to spread and reinforce learned avoidance behavior in their offspring. This study examines optimal culling efforts that maximize representative crop producer’s net present benefits while accounting for wild pig population dynamics and the consequences of learned avoidance behaviors by survivors. This work introduces a representation of the evolution of avoidance learning/forgetting processes, thus providing a more realistic bio-economic framework for effective and sustainable control strategies. Interestingly, the evolution of avoidance leads to strong incentives, in many situations, for early eradication of wild pigs, even if their presence is discovered late in the invasion and growth process.  To avoid higher future culling costs of more adaptable wild pigs, early eradication often leads to temporary negative net benefits in short-term. However, if the producer is financially unable to cover these near-term losses, then the second-best option for maintaining an acceptable level of wild pigs becomes the feasible outcome. However, the control rule for this option can lead to one of two outcomes, with one significantly worse than the other. To avoid the managerial challenges associated with the second best option, public intervention may be necessary to achieve the producer’s first-best outcome.", "id": "Paper/66953", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66953"}, {"title": " The fields generated by character values of linear and unitary group. ", "webprogram_exclude": "0", "session_ids": ["Session/17832"], "source_sha256": "0ac5bcef1bfaf43c4fceace7de8e192314a3bde0453617a3a80b2c0025b4a418", "withdrawn": "", "abstract": "For a finite group $G$, define the field $\\mathbb{Q}(G) := \\mathbb{Q}(\\chi(g) : \\chi \\in \\operatorname{Irr}(G) , g \\in G)$. In this talk we discuss generating sets for the fields $\\mathbb{Q}(G)$ when $G$ is a linear group, a unitary group, or one of the simple groups $\\operatorname{PSL}_n(q)$ or $\\operatorname{PSU}_n(q)$. We then apply these result to classify all number fields $F$ of degree $2$ or $3$ over $\\mathbb{Q}$ such that $F = \\mathbb{Q}(S)$ for some non-abelian  simple group $S$.", "id": "Paper/66954", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66954"}, {"title": " Many-body localization for the random XXZ spin chain in fixed energy intervals ", "webprogram_exclude": "0", "session_ids": ["Session/18296"], "source_sha256": "bee19e45613fb42ed4d5cf14f9e4bd7c2736c5962896235a8a7e702b22e3eb4a", "withdrawn": "", "abstract": "It is shown that  the infinite random Heisenberg XXZ spin-$\\frac12$ chain exhibits slow propagation of information  (logarithmic light cone), a   key signature of many-body localization (MBL),   in any fixed energy interval at the bottom of the spectrum.  The relevant parameter regime, which covers both weak interaction and strong disorder, is determined solely by the  energy interval.  (Joint work with Alexander Elgart)", "id": "Paper/66955", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66955"}, {"title": " Fast One-Pass Sparse Approximation of the Top Eigenvectors of Huge Approximately Low-Rank Matrices? Yes, <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"7.738ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 3331.8 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">MAM^*</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4D\" d=\"M289 629Q289 635 232 637Q208 637 201 638T194 648Q194 649 196 659Q197 662 198 666T199 671T201 676T203 679T207 681T212 683T220 683T232 684Q238 684 262 684T307 683Q386 683 398 683T414 678Q415 674 451 396L487 117L510 154Q534 190 574 254T662 394Q837 673 839 675Q840 676 842 678T846 681L852 683H948Q965 683 988 683T1017 684Q1051 684 1051 673Q1051 668 1048 656T1045 643Q1041 637 1008 637Q968 636 957 634T939 623Q936 618 867 340T797 59Q797 55 798 54T805 50T822 48T855 46H886Q892 37 892 35Q892 19 885 5Q880 0 869 0Q864 0 828 1T736 2Q675 2 644 2T609 1Q592 1 592 11Q592 13 594 25Q598 41 602 43T625 46Q652 46 685 49Q699 52 704 61Q706 65 742 207T813 490T848 631L654 322Q458 10 453 5Q451 4 449 3Q444 0 433 0Q418 0 415 7Q413 11 374 317L335 624L267 354Q200 88 200 79Q206 46 272 46H282Q288 41 289 37T286 19Q282 3 278 1Q274 0 267 0Q265 0 255 0T221 1T157 2Q127 2 95 1T58 0Q43 0 39 2T35 11Q35 13 38 25T43 40Q45 46 65 46Q135 46 154 86Q158 92 223 354T289 629Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-41\" d=\"M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2217\" d=\"M229 286Q216 420 216 436Q216 454 240 464Q241 464 245 464T251 465Q263 464 273 456T283 436Q283 419 277 356T270 286L328 328Q384 369 389 372T399 375Q412 375 423 365T435 338Q435 325 425 315Q420 312 357 282T289 250L355 219L425 184Q434 175 434 161Q434 146 425 136T401 125Q393 125 383 131T328 171L270 213Q283 79 283 63Q283 53 276 44T250 35Q231 35 224 44T216 63Q216 80 222 143T229 213L171 171Q115 130 110 127Q106 124 100 124Q87 124 76 134T64 161Q64 166 64 169T67 175T72 181T81 188T94 195T113 204T138 215T170 230T210 250L74 315Q65 324 65 338Q65 353 74 363T98 374Q106 374 116 368T171 328L229 286Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-4D\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-41\" x=\"1051\" y=\"0\"></use>\n<g transform=\"translate(1802,0)\">\n <use xlink:href=\"#E1-MJMATHI-4D\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-2217\" x=\"1521\" y=\"513\"></use>\n</g>\n</g>\n</svg>! ", "webprogram_exclude": "0", "session_ids": ["Session/17718"], "source_sha256": "f5fac19bc55d536fc7ac99526add2799de217daceb2aa44b7df9492dc557b5ba", "withdrawn": "", "abstract": "Motivated by applications such as sparse PCA, we present provably accurate one-pass algorithms for the sparse approximation of the top eigenvectors of extremely massive matrices based on a single compact linear sketch. The resulting compressive-sensing-based approaches can approximate the leading eigenvectors of huge approximately low-rank matrices that are too large to store in memory based on a single pass over its entries while utilizing a total memory footprint on the order of the much smaller desired sparse eigenvector approximations. Moreover, the compressive sensing recovery algorithm itself can also be formulated to run in a time which principally depends on the size of the sought sparse approximations, making its runtime sublinear in the size of the large matrix whose eigenvectors one aims to approximate. Preliminary experiments on huge matrices having approximately $10^{16}$ entries illustrate the developed theory and demonstrate the practical potential of the proposed approach. The talk will include a discussion of open problems and ongoing work.", "id": "Paper/66959", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66959"}, {"title": " The interior of dynamical black holes ", "webprogram_exclude": "0", "session_ids": ["Session/18148"], "source_sha256": "3bede01a4ef38ae75fb8aab7fd8cd2b0826e0530f2ef47592a7040953d5f3d58", "withdrawn": "", "abstract": "It is well-known that the Schwarzschild black hole features a curvature singularity, while in contrast the exact Kerr black hole possesses a Cauchy horizon across which spacetime is smoothly extendible.\n\nHowever, stationary black holes like Schwarzschild or Kerr are too idealized to capture the generic behavior of black holes formed dynamically in nature, such as through gravitational collapse. For dynamical black holes, the presence and structure of interior singularities remain a fundamental open problem.\n\nIn this talk, I will survey recent mathematical progress on black hole interior dynamics and its connections to Penrose's Strong Cosmic Censorship conjecture.", "id": "Paper/66962", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66962"}, {"title": " A proof of Rubey’s lattice conjecture ", "webprogram_exclude": "0", "session_ids": ["Session/18334"], "source_sha256": "fb2101c4fed8118836bf219d94e9519d0ca6d3e1fb1f6b329feb6e039a2de8cb", "withdrawn": "", "abstract": "In 2011, Rubey generalized chute and ladder moves on the set of reduced pipe dreams for a permutation $w$ and conjectured that the induced poset on reduced pipe dreams is a lattice. In recent work, we prove this conjecture. Our key tool is a new type of move operation $M_{ij}$, defined as a composite of certain generalized ladder moves and later simplified in terms of swaps on a partition shape. We show that joins and meets exist in Rubey's poset by proving simple recursive formulas in terms of $M_{ij}$ operations. In addition, we give an explicit criterion to determine if two elements of the Rubey lattice are comparable using an injective map from reduced pipe dreams to tableaux on the diagram of a permutation. The pipe dream tableaux construction also gives an exact formula for the maximal length of any chain in the Rubey lattice and bounds on the number of reduced pipe dreams for $w$, or equivalently the number of terms in the corresponding Schubert polynomial.\n\nThis talk is based on joint work with Sara Billey and Connor McCausland. An independent proof of Rubey's conjecture was simultaneously given by Ilani Axelrod-Freed, Colin Defant, Hanna Mularczyk, Son Nguyen, and Katherine Tung.", "id": "Paper/66964", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66964"}, {"title": " Quasi-isometric embeddings of Ramanujan complexes ", "webprogram_exclude": "0", "session_ids": ["Session/18121"], "source_sha256": "18a6894c77ca0a12d4f6efa1f5285d47ae5e0e4c3855cc721000689bbd7a918b", "withdrawn": "", "abstract": "Euclidean buildings (a.k.a. affine buildings and Bruhat-Tits buildings) are considered as a $p$-adic analogue of symmetric spaces. We show that there is no quasi-isometric embedding between the symmetric space of $SL(n,\\mathbb{R})$ and the Euclidean building of  $SL(n,\\mathbb{Q}_p)$. Generalizing this, we distinguish Ramanujan complexes constructed by Lubotzky-Samuels-Vishne as finite quotients of Euclidean buildings of $SL(n,\\mathbb{F}_p((y)))$ up to quasi-isometric embeddings. These complexes serve as high dimensional expanders with fruitful applications in mathematics and computer science.", "id": "Paper/66965", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66965"}, {"title": " Non-Parametric Testing of Exponentiality: A Dynamic Extropy Perspective ", "webprogram_exclude": "0", "session_ids": ["Session/19364"], "source_sha256": "7afde7e737fcf3bbb0bd3b71dc039714990d64551bd31ec4d734cf804026c0f4", "withdrawn": "", "abstract": "Numerous researchers study information measures such as entropy and extropy to solve real-world challenges. Jahanshahi et al. (2020) replaced the density function with the distribution function in extropy to define the cumulative residual extropy (CRJ). In this study, an updated version of the cumulative residual extropy (CRJ) with dynamic features is introduced as the normalized dynamic survival extropy (NDSE). We also observe that NDSE captures attention in reliability theory, since the NDSE of the relevant random variable in the age replacement model is always equal to the CRJ of that variable. We provide an NDSE-based nonparametric test to assess whether a data set follows an exponential trend. The proposed test is unique due to its exact distribution of the test statistic, scale-invariant property, consistency, asymptotic normality, high power, and simplicity of calculation. Aware of the problem of censored observations, we explained how our test will be applied to them. A power comparison with five other tests using different alternatives is also provided. A few real-life examples are also included.", "id": "Paper/66966", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66966"}, {"title": " Limitations of the Mean-field Approximation for Modeling Yeast Metabolism ", "webprogram_exclude": "0", "session_ids": ["Session/19363"], "source_sha256": "e6c592212b87370b1f103fbed4393ef502a25a8a23c275a36a1a58bbd455f8d6", "withdrawn": "", "abstract": "Mean-field theory approximates systems of interacting particles by evolving probability distributions. Rigorous justifications of this transition from discrete to continuous settings generally rely on fixed-time analysis and an assumption of asymptotic particle independence. However, these assumptions can obscure the stability of the mean-field and the role of particle correlations. We study a simple yet highly correlated model for yeast metabolism that highlights these issues. Adapting a coupled-systems argument of Golse and Tadmor, we first validate a mean-field limit connecting particle dynamics to a nonlinear transport equation. We then use numerical simulation and stability analysis to show the resulting mean-field model can fail to consistently reproduce important qualitative features of the system, especially in long-time dynamics with a large (but finite) number of particles. To more faithfully transition from discrete to continuous settings, we consider closed higher-order truncations of the BBGKY hierarchy, which explicitly evolve particle correlations.", "id": "Paper/66967", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66967"}, {"title": " Ergodic Optimization with Linear Constraints ", "webprogram_exclude": "0", "session_ids": ["Session/19357"], "source_sha256": "4106d9946db73892fa8aaefea61c0f816b63ec22aec022e4867a5cf79d4f5cb4", "withdrawn": "", "abstract": "Let $T : X \\to X$ be a continuous map of a compact metrizable space, and let $\\phi : X \\to \\mathbb{R}$ be a continuous function. The ergodic optimization problem is to  maximize the integral $\\int \\phi  \\, d\\mu$ as $\\mu$ ranges over all $T$-invariant Borel probability measures on $X$. In this paper we consider a constrained version of the ergodic optimization problem. Given a `constraint set' $\\mathcal{C}\\subset C(X)$, let $M_\\mathcal{C}(X,T)$ be the set of $T$-invariant Borel probability measures $\\mu$ on $X$ such that $\\int g \\, d\\mu = 0$ for all $g \\in \\mathcal{C}$. We investigate the problem of maximizing the integral $\\int \\phi \\, d\\mu$ over the constrained set $M_\\mathcal{C}(X,T)$. We address basic properties of this optimization problem, beginning with non-emptiness of $M_\\mathcal{C}(X,T)$ and existence of optimal solutions. Additionally, we establish the generic and prevalent uniqueness of optimal measures, we provide a realization result, and we give a characterization of the dual problem. This framework provides a common generalization of several previously considered optimization problems in dynamical systems and optimal transport.", "id": "Paper/66968", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66968"}, {"title": " Minimality and stability of the ball in the liquid drop model with screened interactions ", "webprogram_exclude": "0", "session_ids": ["Session/18378"], "source_sha256": "399b302c8d91c2552cb49169a85eee7f0e53974b6dc59a9af3bb7d344d5d3d37", "withdrawn": "", "abstract": "I will present on the volume-constrained minimization of a functional given the sum of the perimeter functional and a nonlocal repulsive term defined through the Yukawa kernel. In this functional the competition between surface tension and repulsion is governed by two independent quantities: the screening rate and the volume. For this problem, above an explicit critical screening rate, minimizers exist at every volume, and below an explicit volume threshold minimizers exist for every screening rate. Moreover at small volume the ball is the unique minimizer up to translation, uniformly in the screening rate. Finally, there exists a sharp volume threshold, depending on the screening rate, for the ball to be a stable volume-constrained critical point. This is a joint work with Lia Bronsard and Kenneth DeMason.", "id": "Paper/66975", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66975"}, {"title": " Equity-based Grading of Communication in PreCalculus ", "webprogram_exclude": "0", "session_ids": ["Session/18081"], "source_sha256": "54d3a984c5e734050c32e5626120b2f584afc400f51291b535451b0cb430f458", "withdrawn": "", "abstract": "The Precalculus sequence at the University of Minnesota emphasizes mathematical communication and problem-solving as a significant portion of the grade. This differs from most traditional approaches to participation points. The growth mindset is foundational to this work and rubrics have been developed based on ELIPSS. The major indicator of success is the reduction of failure rates in the Underrepresented Minority population and the success of these students in subsequent calculus courses.", "id": "Paper/66988", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66988"}, {"title": " Computational Study of the Partial Coverage Weighted Set Covering Problem ", "webprogram_exclude": "0", "session_ids": ["Session/19322"], "source_sha256": "e161bd9b50c92990b5836a358acf90f5f1065a652e80ba2aa7538b34a7174186", "withdrawn": "", "abstract": "This study investigates the computational performance of Gurobi for the partial coverage weighted set covering problem (PCWSCP). Using 420 instances derived from 105 benchmark problems at coverage levels of $80\\%$–$95\\%$, approximately $86\\%$ of instances with up to 800 rows and 8,000 columns were solved optimally within 300 seconds. Solution times generally decreased with lower coverage requirements. Warm-starting with greedy, carousel greedy, or local branching solutions provided no significant advantage over a cold start. These results demonstrate that many PCWSCP instances can be solved optimally using commercial software without specialized algorithms and provide the first computational study of the weighted PCWSCP.", "id": "Paper/66991", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/66991"}, {"title": " <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.029ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 873.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\ell ^p</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2113\" d=\"M345 104T349 104T361 95T369 80T352 59Q268 -20 206 -20Q170 -20 146 3T113 53T99 104L94 129Q94 130 79 116T48 86T28 70Q22 70 15 79T7 94Q7 98 12 103T58 147L91 179V185Q91 186 91 191T92 200Q92 282 128 400T223 612T336 705Q397 705 397 636V627Q397 453 194 233Q185 223 180 218T174 211T171 208T165 201L163 186Q159 142 159 123Q159 17 208 17Q228 17 253 30T293 56T335 94Q345 104 349 104ZM360 634Q360 655 354 661T336 668Q328 668 322 666T302 645T272 592Q252 547 229 467T192 330L179 273Q179 272 186 280T204 300T221 322Q327 453 355 590Q360 612 360 634Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-70\" d=\"M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-2113\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-70\" x=\"590\" y=\"513\"></use>\n</g>\n</svg> improving estimates for multilinear forms motivated by distance graphs ", "webprogram_exclude": "0", "session_ids": ["Session/19339"], "source_sha256": "c2e3b92948122e8d0aecd2235f436826275b01ba8be4897c602019fafc9a3f4f", "withdrawn": "", "abstract": "Spherical averaging operators are ubiquitous, appearing in solutions to the wave equation, inverse problems, and point configuration questions. Results on \\(L^{p}\\) improving estimates for the spherical averaging operator in the continuous setting have been studied classically by Littman and Strichartz in the 1970s. In contrast, it is only recently that \\(\\ell^{p}\\) improving results have been obtained in the discrete setting for the spherical averaging operator, with both Hughes and Kesler-Lacey finding estimates in \\(\\mathbb{Z}^{d}\\). These ideas can be used to study multilinear geometric averaging operators and forms motivated by Falconer type problems and how the underlying graph structure of the point configuration impacts the mapping properties of the operators. For example, Iosevich, Palsson, Zhai, and Wyman conducted a study of \\(L^{p}\\) improving estimates for operators based on connected graphs in the continuous setting. We present a similar study of forms based on connected graphs over the integers. Building on work done by Bhowmick, Iosevich, Koh, and Pham on finite fields, we seek to understand how graph structure of the underlying configuration impacts mapping properties. We obtain \\(\\ell^{p}\\) improving estimates for this collection of forms motivated by the work on the spherical averaging operator over the integers.\\\\", "id": "Paper/67001", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67001"}, {"title": " Improved Bounds on the Degree of Homogeneous Bent Boolean Functions ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "d8e7bc0684d801b812d38f62522421f1cfd87927e4c10d970037a6cf7aa7c74e", "withdrawn": "", "abstract": "Bent homogeneous Boolean functions are maximally non-affine under the Hamming metric and such that every term in the algebraic normal form has the same degree. No such functions of degree 4 have been found. We show that the nonexistence bound on the degree of homogeneous bent Boolean functions can be strengthened; for such a function $f: \\mathbb{F}_2^n \\to \\mathbb{F}_2$, the maximum degree is shown to be bounded by $d \\leq \\frac{n}{4} + \\frac{1}{4}\\log_2(n+3) + \\left(\\frac{3}{2} + \\frac{1}{4}\\log_2\\left(\\frac{\\pi}{2}\\right)\\right)$, improving the prior bound from a $\\sqrt{n}$ factor to $\\log_2(n)$, and explicitly calculating the constants. Additionally, analysis of the Krawtchouk moment polynomials along with linear programming techniques offered more succinct proofs of known bounds on the degree, while also providing an exact characterization of the weight distributions for specific $n \\in \\{6,8,10,12\\}$ and $d \\in \\{3,4,5\\}$. Vectorial bent Boolean functions were also studied resulting in its bound being analogously strengthened.", "id": "Paper/67010", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67010"}, {"title": " Representations and primitive ideals of the Virasoro algebra ", "webprogram_exclude": "0", "session_ids": ["Session/19342"], "source_sha256": "a60f41670a7e199f7cdb358d675f01c38c827fd1dafc62baff55879aded1ccde", "withdrawn": "", "abstract": "Since representation theory of the Virasoro algebra $Vir$ is extremely rich, following Dixmier philosophy, we study and construct a large class of primitive ideals of its enveloping algebra instead. Although $Vir$ does not have an adjoint algebraic group, we are still able to generalize a version of the Dixmier map for finite-dimensional solvable Lie algebra to $Vir$ using Poisson theory. This is a map from the Poisson primitive spectrum of the symmetric algebra of $Vir$ to the primitive spectrum of the enveloping algebra of $Vir$.\n\nIn the process, we construct irreducible representations of the Virasoro algebra following the classical Kirillov's orbit method. We also define an infinite family of homomorphisms from $U(W)$ to $A_1\\otimes U(\\mathfrak{g}_n)$, where $A_1$ is the first Weyl algebra and $\\mathfrak{g}_n$ is a finite-dimensional solvable subquotient of the Witt algebra $W$, for each $n$. By pulling back representations and primitive ideals of $\\mathfrak{g}_n$ to $W$ and $Vir$, we managed to extend the Dixmier map of $\\mathfrak{g}_n$ to $W$ and $Vir$. As a result, we prove that the enveloping algebra $U(Vir)$ does not satisfies the Dixmier-Moeglin equivalence and motivate interesting questions about the properties of this Dixmier map.", "id": "Paper/67018", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67018"}, {"title": " Transitional geometries and Higgs bundles ", "webprogram_exclude": "0", "session_ids": ["Session/18268"], "source_sha256": "e1a0b377a64cba50d8abd4a5b5b11c12eb6a7e21b9c9cff04d3b7ba8a4198400", "withdrawn": "", "abstract": "Under the right conditions surface group representations, i.e. homomorphisms from the fundamental group of a topological surface into a Lie group, are intimately connected to geometric structures modeled on homogeneous spaces, and also to Higgs bundles on Riemann surfaces. This creates opportunities for using Higgs bundles to investigate geometric structures, and also for using geometric structures to shed light on Higgs bundles.  This talk will explore these themes.", "id": "Paper/67024", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67024"}, {"title": " In-Context Kernel Ridge Regression with Transformers ", "webprogram_exclude": "0", "session_ids": ["Session/18305"], "source_sha256": "e7af49461898e034368fc735ecd3b0ef2d83f12820a8be69b5447983a7665cae", "withdrawn": "", "abstract": "In this talk, we study in-context kernel ridge regression (KRR) with Gaussian\nkernels and show that a standard softmax-attention transformer can approximate\nthe KRR predictor during its forward pass. Under bounded-data assumptions,\nwe construct a single-head transformer whose forward pass approximately\nimplements preconditioned Richardson iteration on the associated kernel\nsystem. The construction uses $\\mathcal{O}(\\log(1/\\varepsilon))$ blocks and\nMLP width $\\mathcal{O}(\\sqrt{N/\\varepsilon})$ to achieve $\\varepsilon$-accurate\nprediction for prompts of length $N$. Softmax attention produces a\nrow-normalized Gaussian-kernel operator for cross-token interactions, while\nMLP layers approximate the intra-token scalar arithmetic required by the\nupdate. Empirically, we train GPT-2-style transformers on Gaussian-process\nregression tasks and observe that they progressively align with the exact\nGaussian KRR estimator across depth in terms of both prediction error and\ninduced weights.", "id": "Paper/67027", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67027"}, {"title": " Transforming AI through Modern Mathemnatics ", "webprogram_exclude": "0", "session_ids": ["Session/18026"], "source_sha256": "a73d8ac7118effeb4fb42484c4fa7278cfacb52907fdba0a4c4d056501b5134c", "withdrawn": "", "abstract": "Despite the tremendous success of artificial intelligence (AI) in science, engineering, and technology in the past decade, its explainability, generalizability, and reliability have been a major concern. The solution to these challenges holds the future of AI.  Topological deep learning (TDL), a new paradigm in rational learning introduced by us in 2017, offers interpretable and generalized AI approaches. TDL utilizes topological data analysis (TDA), which is originally rooted in persistent homology, an algebraic topology technique. However, persistent homology has many limitations, including the lack of localization, being restricted to point cloud data, and the inability to represent non-topological information. To address these challenges, we generalized TDA to combinatorial spectral theory (e.g. Topological Laplacian and Dirac), differential topology (e.g. de Rham-Hodge theory), and geometric topology (e.g. Khovanov homology) to handle data on graphs, differentiable manifolds, and curves embedded in 3-space, respectively (see Artif Intell Rev 59, 58, (2026) for a review). To further advance AI through modern mathematical theories, we introduced commutative algebra as a new frontier in data science and machine learning.", "id": "Paper/67028", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67028"}, {"title": " <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"5.082ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 2188.2 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">(p,q)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-70\" d=\"M23 287Q24 290 25 295T30 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-250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-70\" x=\"389\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2C\" x=\"893\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-71\" x=\"1338\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"1798\" y=\"0\"></use>\n</g>\n</svg>-Percolation Forcing ", "webprogram_exclude": "0", "session_ids": ["Session/18207"], "source_sha256": "9c686e48ced21432e1cb931b4908ffe6aaac8c7e163bffc1a111723aa8c7058b", "withdrawn": "", "abstract": "We consider two variants on zero forcing.  The first we call $(p,q)$-Percolation Forcing.  In this forcing variant, we allow either percolation or forcing to turn a vertex from white to blue.  We also consider the another variation we call $(p,q)$-Repeated Forcing.  In this forcing variant, we require that both percolation and forcing conditions are met in order to turn a vertex from white to blue.  In this talk, we will discuss some preliminary results we have about each of these zero forcing variants including their values on certain graph classes, how they compare to other more studied zero forcing variants, and properties of these color-change rules.", "id": "Paper/67030", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67030"}, {"title": " Gaussian solutions to the Quantum Yang–Baxter equation and their twists ", "webprogram_exclude": "0", "session_ids": ["Session/17907"], "source_sha256": "dc05f3e0fc9b76f255ac11d2bbf64bf832e3c20ae431d9a1d4be53b7c59960d9", "withdrawn": "", "abstract": "The Yang–Baxter (YB) equation is ubiquitous due to its vast connections to diverse areas such as quantum information theory, representation theory, knot and link theory, and quantum groups. While Hietarinta’s classification of solutions in dimension $n=2$ has been known for nearly 35 years, the classification question remains open in dimensions $n \\geq 3$. Towards this end, Martin and Rowell have suggested a strategy of studying families of solutions which can be generalized to every dimension, an example of which is Gaussian solutions. In this talk, we examine Gaussian solutions in dimension $n=2$ and classify all valid twisting pairs, as defined by Huang, Nguyen, Ure, Vashaw, Veerapen, and Wang. In doing so, we apply the Faddeev--Reshetikhin--Takhtajan (FRT) construction to produce coquasitriangular bialgebras from the Gaussian solutions in dimension 2. As a result, we conclude that a twist of a Gaussian solution does not necessarily remain Gaussian. This suggests that novel solutions may be found by twisting Gaussian solutions in higher dimensions. This is joint work with Padmini Veerapen.", "id": "Paper/67031", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67031"}, {"title": " A SoTL Study of Business Calculus ", "webprogram_exclude": "0", "session_ids": ["Session/18091"], "source_sha256": "7e91e4d2c9464d3fe498139cedf3bf45789a122dede45b1674f12854f5694c34", "withdrawn": "", "abstract": "We will present initial results of a 3 year SoTL study of Business Calculus students at University of Denver exploring the relationship between students’ prior knowledge of algebra, attitude towards mathematics, and math anxiety and their course performance. At University of Denver, business calculus is a 40-60 student, multi-section, coordinated course which is required for all students majoring in business. The course has no prerequisites, so students in the course have a wide range of mathematical backgrounds. The course also has a large number of students receiving final grades of D, F, and W (withdraw). Our study seeks to understand the greatest barriers to student success to inform future interventions and changes to course curriculum. This study originated as part of the SoTL Faculty Fellows program at University of Denver, which seeks to build a community of SoTL scholars within the university.", "id": "Paper/67032", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67032"}, {"title": " Pseudo-Anosov flows, hyperbolic geometry, and the curve graph ", "webprogram_exclude": "0", "session_ids": ["Session/17916"], "source_sha256": "9494c2d749ad34ecd433e78f498844688a0970fd90e202704ec3e9a4034684d4", "withdrawn": "", "abstract": "In this talk, I will discuss a joint work with Samuel J. Taylor, where we consider embedded non-fiber surfaces in a hyperbolic 3-manifold transverse to a pseudo-Anosov flow. Utilizing foundational work on Kleinian surface groups, we connect the hyperbolic geometry of the surface to the dynamics of the flow via the curve graph. More specifically, the flow gives a pair of special multicurves on the surface, and we show that they are also geometrically distinguished, enabling us to extract geometric information, such as the position of short curves and the volume, from the relation of the pair of multicurves in the curve graph. Our result also connects to recent study of the geometry of endperiodic mapping tori.", "id": "Paper/67033", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67033"}, {"title": " Width Stability of 3-Manifolds ", "webprogram_exclude": "0", "session_ids": ["Session/18290"], "source_sha256": "a436d256c388a968fc22f30bebbd98dcf379a305c45e9672b5b06e1bc6e3b732", "withdrawn": "", "abstract": "In the 1990’s, researchers such as Colding and Petersen investigated the stability of invariants such as the radius, volume, and Laplace eigenvalues $\\lambda_k$ of closed Riemannian manifolds with $\\mathrm{Ric}\\geqslant(n-1)g$. They showed that almost maximality of either the radius or volume, or minimality of $\\lambda_{n+1}$ (listed with multiplicity), is equivalent to the closeness of the manifold of interest to the unit round sphere.\n\nWe contribute another invariant to this list in dimension $n=3$, by studying the almost-rigid properties of the first Almgren-Pitts width $\\omega_1$ as a non-linear, minimal-surface-based analogue of Petersen's work with the Laplace spectrum.", "id": "Paper/67034", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67034"}, {"title": " Explicit bounds on value sets of polynomials over finite fields ", "webprogram_exclude": "0", "session_ids": ["Session/19355"], "source_sha256": "87177a60e0b1de6a5b9152a16f8b1dc92d373cb06c101839036388d25c7ea4b8", "withdrawn": "", "abstract": "An extension of a result of Birch and Swinnerton-Dyer asserts that, for every prime power \\(q\\) and every polynomial \\(f\\in\\mathbb F_q[X]\\) of degree \\(n\\ge1\\), there is a rational number \\(c\\), with denominator dividing \\(n!\\), such that\n\n$$ \\bigl|\\#f(\\mathbb F_q)-cq\\bigr|<d_n\\sqrt q $$\r\n\r\nfor some constant \\(d_n\\) depending only on \\(n\\). We give an explicit version of this result, showing that one may take \\(d_n=n2^{n+3}\\). We also prove that no polynomial bound in \\(n\\) is possible: for every \\(a>0\\) and every positive integer \\(k\\), there are \\(n,q\\), and a degree-\\(n\\) polynomial \\(f\\) such that\n\n$$ \\bigl|\\#f(\\mathbb F_q)-cq\\bigr|>a n^k\\sqrt q. $$\n\nThe upper bound is obtained using effective Chebotarev estimates for monodromy covers, while the lower-bound construction uses low-degree higher-dimensional models of polynomial maps over extension fields.", "id": "Paper/67035", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67035"}, {"title": " A primary subalgebra of the Monster Lie algebra ", "webprogram_exclude": "0", "session_ids": ["Session/18270"], "source_sha256": "16d9eec0b7df28e39497fb6911a59ac81f500449750200644c729a3b82bcdaac", "withdrawn": "", "abstract": "The Monster Lie algebra $\\mathfrak{m}$, constructed by Borcherds in his proof of the Monstrous Moonshine conjectures, is a $\\mathbb{Z}\\oplus\\mathbb{Z}$-graded generalized Kac–Moody algebra constructed from the Moonshine module $V^\\natural$ whose graded pieces encode the representation theory of the Monster group $M$.  We introduce a new proper Borcherds subalgebra $\\mathfrak p \\subset \\mathfrak m$, built from the primary vectors of $V^\\natural$, and show that it mirrors the structure of $\\mathfrak m$ itself: it decomposes as $\\mathfrak p = \\mathfrak u^- \\oplus \\mathfrak{gl}_2 \\oplus \\mathfrak u^+$, with $\\mathfrak u^\\pm$ free Lie algebras for which I will give explicit free generators. Every graded component of $\\mathfrak p$ carries a natural $M$-module structure, and we provide a denominator formula for $\\mathfrak p$ that leads to recursive formulas for the dimensions of its root spaces and for its characters.", "id": "Paper/67037", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67037"}, {"title": " <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.162ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 500.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">1</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-31\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-cross intersecting set pair systems are small ", "webprogram_exclude": "0", "session_ids": ["Session/18011"], "source_sha256": "264532f36717373b739c9a0bb5e442aa1cc394e23b59c82c54dff80c253cf436", "withdrawn": "", "abstract": "Let $\\{(A_i,B_i)\\}_{i=1}^m$ be a family of $m\\geq 2$ pairs of finite sets, called a \\emph{set pair system}. Such a system is \\emph{cross-intersecting} if $|A_i \\cap B_j| \\geq 1$ for $i\\neq j$, while $|A_i \\cap B_i|=0$. A classical result of Bollob\\'as shows that if $|A_i| \\leq n$ and $|B_i| \\leq n$ for all $i$, then $m \\leq \\binom{2n}{n}$. By taking each~$(A_i,B_i)$ to be a complementary pair of~$n$-sets in~$[2n]$, we see that this upper bound on~$m$ is best possible. \n\nF\\\"uredi, Gy\\'arf\\'as, and Kir\\'aly suggested the following variant of the cross-intersecting problem. We say a set pair system $\\{(A_i,B_i)\\}_{i=1}^m$ is \\emph{$1$-cross-intersecting} if $|A_i \\cap B_j| = 1$ whenever $i \\neq j$, while $|A_i \\cap B_i|=0$. That is, we ask that the~$A_i$ and~$B_j$ not only intersect, but do so in precisely~$1$ element. Let~$m(n)$ denote the largest value of~$m$ one can obtain in a~$1$-cross-intersecting system with~$|A_i| \\leq n$ and $|B_i| \\leq n$ for all $i$. The theorem of Bollob\\'as implies immediately that~$m(n) \\leq \\binom{2n}{n}$, but the tight construction above is \\emph{not}~$1$-cross intersecting.\n\n\nF\\\"uredi, Gy\\'arf\\'as, and Kir\\'aly were able to obtain constructions of~$1$-cross-intersecting systems showing~$m(n) = \\Omega(5^{n/2})$, and they conjectured that~$m(n) = o(\\binom{2n}{n})$.\nThe first progress on this problem was obtained by Holzman who proved (answering another question of F\\\"uredi, Gy\\'arf\\'as, and Kir\\'aly) that~$m(n) \\leq \\frac{29}{30} \\binom{2n}{n}$.\nThe coefficient~$\\frac{29}{30}$ was later improved\nto $\\frac{5}{6}$ by Kostochka, McCourt, and Nahvi.\nWe confirm the conjecture by showing that, in fact,~$m(n) \\leq e^{n}$.\nOur proof method, different from that of Holzman and of Kostochka, McCourt, and Nahvi, uses elementary linear algebra.", "id": "Paper/67038", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67038"}, {"title": " Stability Patterns for Spherical Braid Groups ", "webprogram_exclude": "0", "session_ids": ["Session/18287"], "source_sha256": "221b6fcd3667aa6c11ecc3a7becc3bf7a9afbd23e5c02ad4763a49c18674cdc5", "withdrawn": "", "abstract": "Representation stability is a ubiquitous pattern for sequences of cohomology groups with group actions. It was proven by Church--Farb that the cohomology of the pure braid groups exhibits representation stability. Church later generalized the result to ordered configuration spaces of points in manifolds. In this talk, I will describe a further generalization of the result to the equivariant homology of ordered configuration spaces of manifolds with group actions. Then I will discuss how this generalization helps\nprove that the homology of spherical braid groups exhibit homological periodicity.", "id": "Paper/67039", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67039"}, {"title": " Two Matrix Weight Bump Conditions For Commutators ", "webprogram_exclude": "0", "session_ids": ["Session/17442"], "source_sha256": "2a1fb1ded879287187470156bc2ab49f37ae02ddc7807ca7c848903354c5be91", "withdrawn": "", "abstract": "The modern study of boundedness of commutators in the scalar setting began with Coifman, Rochberg, and Weiss proving that given a Calder\\'{o}n-Zygmund operator $T$ and a BMO function $b$, then the commutator $[b,T]$ is bounded on $L^p(\\mathbb{R}^n)$.  Further results have been shown extending these results in various weighted settings.  My talk concerns the boundedness of commutators in a two weight matrix setting.  We will discuss recent results and the inherent limitations of moving from a scalar to a matrix setting.", "id": "Paper/67043", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67043"}, {"title": " Knots, Chirality, and the Hidden Topology of RNA Folding ", "webprogram_exclude": "0", "session_ids": ["Session/18358"], "source_sha256": "85b88003b72844ce485cb49b845ce30a3214c4848811fe7fd6aee42b505e1cd4", "withdrawn": "", "abstract": "RNA molecules fold into intricate three-dimensional shapes whose entanglement — how the chain crosses and threads through itself — is central to their function, yet is largely invisible to the distance-based methods used to compare and predict structures. I will describe a topological characterization of RNA folds, built from classical knot-theoretic quantities such as linking and writhe, that captures this entanglement directly. As a central example, a ribozyme's native fold and a long-lived misfold are geometrically nearly identical yet differ by a single topological crossing — invisible to distance-based comparison, immediate topologically, and the reason the misfold is a long-lived kinetic trap. I will close with how this viewpoint exposes errors in machine-learned structure predictions that purely geometric scores miss. No background in biology will be assumed.", "id": "Paper/67046", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67046"}, {"title": " To Kick or Receive, that is the question. ", "webprogram_exclude": "0", "session_ids": ["Session/18205"], "source_sha256": "f73dafb365cf6cdd6886b505fe4192a560dcf88b4820cd0a773cddfeabe4eb4b", "withdrawn": "", "abstract": "In 2025, the NFL changed the overtime rules to ensure both teams get possession of the ball at least once.  In previous years, it was possible for teams to lose in overtime without ever receiving possession of the ball.  Prior to the most recent rule change, overtime models favored choosing to receive the ball first, consistent with the teams’ decision making.  In this talk, we will present a Markov chain model that incorporates the most recent overtime rule changes and demonstrates that, under the revised rules, electing to kick first is more optimal than electing to receive first. The result is consistent with the choices made in the 2025-2026 season.", "id": "Paper/67048", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67048"}, {"title": " Taut foliations dual to flows in Dehn surgeries ", "webprogram_exclude": "0", "session_ids": ["Session/18267"], "source_sha256": "cac2eb4d8201ee2463d93e6b1a5c48fc23f8af62d11866e463bd173e5d504233", "withdrawn": "", "abstract": "Taut foliations are an important and historically significant structure on 3-manifolds.The modern L-space conjecture makes a prediction about which rational homology spheres can admit a taut foliation. But where could the predicted taut foliations \"come from\"? Must they be compatible with “natural” geometric structures on the 3-manifold? In this talk, I'll discuss work with John Baldwin and Matt Hedden, where we address a type of geography problem for taut foliations in manifolds obtained by Dehn surgeries along knots. I'll explain why our result is surprising, and if time permits, sketch the proof. All are welcome!", "id": "Paper/67054", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67054"}, {"title": " Non-characterizing surgeries of hyperbolic L-space knots ", "webprogram_exclude": "0", "session_ids": ["Session/18087"], "source_sha256": "d1ec901825b602bf50ca6decb5f2a66afeb4ca6461cb2ea701b067751eee552f", "withdrawn": "", "abstract": "Dehn surgery is one of the primary ways to study 3- and 4-dimensional manifolds. In the past 10 years, there has been an explosion in the study of \"non-characterizing slopes\" of knots, i.e. a study of when distinct knots can both admit an $r$-framed Dehn surgery to the same 3-manifold. In this talk, we explore this story for \"hyperbolic L-space knots\", an important family of knots from both the Dehn surgery and Heegaard Floer perspectives. We will present some new (and surprising to us) examples, and sketch the proof idea and strategy.", "id": "Paper/67057", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67057"}, {"title": " Equivariant concordance of periodic 2-knots ", "webprogram_exclude": "0", "session_ids": ["Session/18344"], "source_sha256": "da6017f11443e86c9faeaa8a216d9fa44dfaefded0525decd00f639f7061a3bc", "withdrawn": "", "abstract": "It has been known since the 1960's that all 2-knots are slice, meaning that all 2-spheres embedded in the 4-sphere bound embedded 3-balls into the 5-ball, and thus are concordant to the unknotted sphere. However, when we restrict to the class of \"periodic\" 2-knots, meaning 2-knots which are invariant under a certain finite cyclic group action on 4-sphere, there are actually two concordance classes. In this talk, we'll discuss the technique used by Kervaire to slice 2-knots, and then illustrate an invariant which completely classifies periodic 2-knots up to equivariant concordance.", "id": "Paper/67058", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67058"}, {"title": " Counting hypergraphs without linear cycles of fixed length ", "webprogram_exclude": "0", "session_ids": ["Session/18011"], "source_sha256": "de4e41a84377ef4d8e1adcd61bd1ebcdb69eb076d445fd22c42347a8812d4ff5", "withdrawn": "", "abstract": "Let $C_k^{(r)}$ denote the $r$-uniform linear cycle with $k$ hyperedges. An $r$-graph is $C_k^{(r)}$-free if it contains no copy of $C_k^{(r)}$. Write $\\text{ex}_r(n,C_k^{(r)})$ for the maximum number of hyperedges in an $n$-vertex $C_k^{(r)}$-free $r$-graph. Balogh, Narayanan and Skokan asked whether, for every pair of integers $r,k\\ge 3$, the number of $C_k^{(r)}$-free $r$-graphs on $n$ labelled vertices is $2^{(1+o(1))\\text{ex}_r(n,C_k^{(r)})}$.\n\nAlthough the analogous statement fails for graphs ($r=2$), as shown by a construction of Morris and Saxton, the general question remained open for hypergraphs. Very recently, Jiang and Longbrake answered it affirmatively for $r\\ge 5$.\n\nIn this talk, I will present a complete resolution of the problem, establishing an affirmative answer for all $r,k\\ge 3$. Joint work with J\\'ozsef Balogh and Abhishek Methuku.", "id": "Paper/67061", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67061"}, {"title": " Elliptic fibrations, spherical braid groups, <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"3.93ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 1691.9 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathrm SL_2</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-53\" d=\"M55 507Q55 590 112 647T243 704H257Q342 704 405 641L426 672Q431 679 436 687T446 700L449 704Q450 704 453 704T459 705H463Q466 705 472 699V462L466 456H448Q437 456 435 459T430 479Q413 605 329 646Q292 662 254 662Q201 662 168 626T135 542Q135 508 152 480T200 435Q210 431 286 412T370 389Q427 367 463 314T500 191Q500 110 448 45T301 -21Q245 -21 201 -4T140 27L122 41Q118 36 107 21T87 -7T78 -21Q76 -22 68 -22H64Q61 -22 55 -16V101Q55 220 56 222Q58 227 76 227H89Q95 221 95 214Q95 182 105 151T139 90T205 42T305 24Q352 24 386 62T420 155Q420 198 398 233T340 281Q284 295 266 300Q261 301 239 306T206 314T174 325T141 343T112 367T85 402Q55 451 55 507Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4C\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-53\" x=\"0\" y=\"0\"></use>\n<g transform=\"translate(556,0)\">\n <use xlink:href=\"#E1-MJMATHI-4C\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-32\" x=\"963\" y=\"-213\"></use>\n</g>\n</g>\n</svg> character varieties and complex reflection groups. ", "webprogram_exclude": "0", "session_ids": ["Session/17904"], "source_sha256": "29f7c135f24a0d8e5d0dc2fc0fc209ae3a8f3b1a396993a46be4b1416e30240c", "withdrawn": "", "abstract": "Elliptic fibrations are a basic class of 4-manifolds, and are the total space of ``families of elliptic curves (tori) with degenerations''.  In this talk I will explain how the topics in the title are all related.  The only background assumed will be standard first-year graduate courses.", "id": "Paper/67065", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67065"}, {"title": " Mean viability theorems and second-order Hamilton–Jacobi equations ", "webprogram_exclude": "0", "session_ids": ["Session/17800"], "source_sha256": "1c4fb0a697bb7d7e22daca88bd445157823b56e67ede8a8409509bc489c54aca", "withdrawn": "", "abstract": "We introduce\n the notion of mean viability for controlled stochastic differential equations\n  and establish counterparts of Nagumo's classical viability theorems  (necessary and sufficient \n  conditions for mean viability).\nAs an application, we  provide  a purely probabilistic proof\nof a comparison principle and of\nexistence \nfor contingent and viscosity solutions of\nsecond-order  fully nonlinear path-dependent Hamilton--Jacobi--Bellman\nequations. We do not use \n  compactness and optimal stopping arguments, which are usually employed \n   in the literature on viscosity solutions for second-order path-dependent  PDEs.", "id": "Paper/67066", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67066"}, {"title": " Uncovering identifiability of epidemiological models: basic reproduction number and complementary data streams ", "webprogram_exclude": "0", "session_ids": ["Session/18127"], "source_sha256": "c8716f1470ce4623b457afe0effa974b50be0f0ee5eee6ba94176d36f163d5bc", "withdrawn": "", "abstract": "Mathematical models of infectious disease dynamics are routinely fitted to surveillance data to estimate epidemiological parameters and inform public health decisions. Such data are typically discrete and noisy, but before attempting estimation, it is essential to ask whether the model structure itself permits unique parameter identification at least under perfect (continuous, noise-free) observations. This mathematical property of a model with respect to observation(s), known as structural identifiability, serves as a necessary precondition for reliable inference, since a model that fails this test cannot yield unique parameter estimates even from perfect data. In this study, we systematically investigate structural identifiability in various classes of compartmental epidemic models and establish two main findings. First, we present and deploy a methodology for assessing structural identifiability of epidemiological quantities of interest and demonstrate that the basic reproduction number exhibits identifiability across diverse model structures (including models with multiple transmission pathways and host-vector dynamics) even when individual parameters are not uniquely identifiable. These findings challenge the assumption that complete model identifiability is necessary for reliable epidemiological inference and suggest reformulating the central question from “is the model identifiable?” to “are the quantities that matter for the decision-making identifiable?” Second, we prove that incorporating minimal complementary data, as little as a single time-point measurement from an additional state variable, can make otherwise nonidentifiable models globally identifiable.", "id": "Paper/67071", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67071"}, {"title": " Complex structures on S^{6} ", "webprogram_exclude": "0", "session_ids": ["Session/17904"], "source_sha256": "02f336019e20020ceee5038087d2d72eae1be6c66dcbaeb293bd80337fe8e160", "withdrawn": "", "abstract": "A recent manuscript written by Claude under the direction of Levent Alpoge constructs a 1-parameter family of compact complex threefolds diffeomorphic to S^6. I will describe the main geometric ideas behind the construction and outline the proof. If time permits, I will remark on possible future research directions.", "id": "Paper/67073", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67073"}, {"title": " Counterexamples to boundary regularity for the monopolist’s problem in the plane ", "webprogram_exclude": "0", "session_ids": ["Session/18331"], "source_sha256": "21ab49896f55e359948e5b27fc7848f6207072f7e271009cb058171d11e93c3b", "withdrawn": "", "abstract": "Rochet and Chone's (1998) version of the monopolist's problem can be reformulated as the minimization of a Dirichlet energy among nonnegative convex functions on a convex domain in the plane. We present new counterexamples to boundary regularity of the solution. \n\nSuch counterexamples complicate the identification of the region of strict convexity,  which represents the set of consumer types who will opt to buy customized products, and turns out to be an obstacle problem with an endogenous obstacle.", "id": "Paper/67079", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67079"}, {"title": " Spectral inequalities for Schrödinger operator with singular potentials ", "webprogram_exclude": "0", "session_ids": ["Session/17749"], "source_sha256": "df39f7b403f9c50ecc011cb6fe49138077b609bedeb0708d8acab28bb72adf37", "withdrawn": "", "abstract": "We establish spectral inequalities for Schr\\\"odinger operators\n$H=-\\Delta_g+V$ on compact connected manifolds with Lipschitz metrics,\nwhere $V\\in L^p(M;\\R)$ and $d/2<p<\\infty$.\r\nFor every nonempty open set $\\omega\\subset M$, the $L^2(M)$ norm of a\r\nfunction in the spectral subspace corresponding to $(-\\infty,\\lambda]$\r\nis controlled by its $L^2(\\omega)$ norm with cost\r\n$C\\exp\\bigl(C(1+\\norm{V}_{L^p(M)}^{2p/(2p-d)}+\\sqrt\\lambda)\\bigr)$.\r\nThis is a joint work with Prof. Jiuyi Zhu.", "id": "Paper/67083", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67083"}, {"title": " One-Dimensional Divergence–Gradient Jacobi Operators with Random and Doubling-Map Coefficients ", "webprogram_exclude": "0", "session_ids": ["Session/17804"], "source_sha256": "e1489b10222890960dc4d6818872b6227d36978b9100bfb13b1d0847d09d662a", "withdrawn": "", "abstract": "We study one-dimensional Jacobi operators of divergence--gradient type with strictly positive, uniformly bounded coefficients generated either by independent random variables or by the doubling map. In the random setting, whose spectral properties are well understood, we establish upper and lower power-law bounds on the time growth of the \\(q\\)-moments of the position operator. The lower bound implies dynamical delocalization, while the upper bound rules out ballistic transport. Numerical evidence suggests nearly diffusive behavior at large moments. For coefficients generated by the doubling map, the spectral properties are less well understood. Near the bottom of the spectrum, we obtain square-root asymptotics for the integrated density of states and a linear expansion of the Lyapunov exponent. We also establish large-deviation estimates for transfer matrices, implying H\\\"older regularity of the integrated density of states and the Lyapunov exponent, as well as Anderson localization. The key ingredients of the proofs are the Figotin--Pastur modified Pr\\\"ufer formalism and the Bourgain--Schlag martingale approach to Schr\\\"odinger operators generated by the doubling map.", "id": "Paper/67088", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67088"}, {"title": " Beyond Traditional Point Systems: The Impact of Specifications Grading in Calculus 1 ", "webprogram_exclude": "0", "session_ids": ["Session/18440"], "source_sha256": "ae9b34473f8223419db745978a1ceea349693e9eae4d6bb632069682eb525209", "withdrawn": "", "abstract": "Traditional points-based grading systems often emphasize the accumulation of partial credit rather than the demonstration of meaningful learning outcomes. Specifications grading offers an alternative approach by evaluating student work against clearly defined standards and emphasizing mastery, transparency, and student agency. This presentation examines the implementation of specifications grading in a Calculus I course over multiple semesters and explores its impact on student math identity and subsequent course grades in Calculus 2. Course design elements, including mastery-based assessments and revision opportunities will be discussed. Challenges associated with implementation, such as student adjustment to the grading model and instructor workload, will also be addressed. Attendees will gain practical insights into the benefits and considerations of adopting specifications grading in introductory mathematics courses and will leave with strategies for adapting this approach to their own teaching contexts.", "id": "Paper/67089", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67089"}, {"title": " New families of convex partitions in the plane ", "webprogram_exclude": "0", "session_ids": ["Session/18072"], "source_sha256": "30c4c24122b9b82fd419ed2fef2007f99a22cb97af8c921dba154b94b1ea61a4", "withdrawn": "", "abstract": "A family $\\mathcal{F}$ of convex partitions of $\\mathbb{R}^d$ into $k$ regions is called \\emph{equitable} if for every finite absolutely continuous measure $\\mu$ on $\\mathbb{R}^d$ with bounded support there exists a partition $(C_1,\\ldots,C_k)\\in\\mathcal F$ such that $\\mu(C_i)=\\frac{\\mu(\\mathbb{R}^d)}{k}$. More generally, $\\mathcal{F}$ is called \\emph{disproportionate} if for every finite absolutely continuous measure $\\mu$ on $\\mathbb{R}^d$ with bounded support, and every choice of positive numbers $\\alpha_1,\\ldots,\\alpha_k$ with $\\sum_{i=1}^{k}\\alpha_i=1$, there exists a partition $(C_1,\\ldots,C_k)\\in\\mathcal F$ such that $\\mu(C_i)=\\alpha_i$, for all $i=1,\\ldots,k.$ In this paper, we introduce new disproportionate families of convex partitions in $\\mathbb{R}^2$ and prove a new bound on a problem of Rold\\'an-Pensado and Sober\\'on on equitable partitions. To obtain our results, we use the KKM theorem and its colorful extension due to Gale. \n\nThis is joint work with Daniel McGinnis, Alex Parker, and Shira Zerbib.", "id": "Paper/67090", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67090"}, {"title": " How do demand-side incentives relate to insurance transitioning behavior of public health insurance enrollees? A novel voting ensemble approach for ranking factors of mixed data types ", "webprogram_exclude": "0", "session_ids": ["Session/18328"], "source_sha256": "132518a48da09152afb352e3d53ce829aee53bacac63b98ab767feeeafcbbff5", "withdrawn": "", "abstract": "We conduct factor importance analysis on the insurance transitioning behavior of the public health insurance enrollees in the U.S., based on the Medical Expenditure Panel Survey (two-year longitudinal files, 2011 - 2018). The factors in the dataset consist of both numerical and categorical type data, which makes it more difficult to compare their importances. In\norder to measure the effects of these factors of mixed data types, two relatively “model-free” ranking scores are introduced: vote count and average partial dependence ranking score. Different from traditional ranking scores, the novel ranking scores apply to any regression and classification methods and to either numerical or categorical factors. A voting ensemble\nis designed to obtain the above two ranking scores, with four competitive base learners:forward and backward stepwise subset selections, LASSO and random forest. The selected top five driving factors of insurance transitioning are number of physician office visits, family\nsize, chronic condition, age and family income. A predictive model based on the top-ranked factors is provided and model validation result shows that it is competitive to other popular prediction methods.", "id": "Paper/67091", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67091"}, {"title": " Linear Codes with Any Two Coordinates Recoverable from Two Others: From Bounds to Optimal Dimension ", "webprogram_exclude": "0", "session_ids": ["Session/18388"], "source_sha256": "becbb3f17ea656175c1a0170c1dacb12e091d3010a334244ce15da84b0440650", "withdrawn": "", "abstract": "A length-$n$ linear code over a field $\\mathbb{F}$ is said to have the $(t,r)$ local exact-recovery property if, for every target set of $t$ coordinates, there exists a disjoint recovery set of at most $r$ coordinates from which the target set can be recovered. For fixed $n,t,r$ and $\\mathbb{F}$, the problem is to determine the maximum possible dimension of a code with this property. This problem is closely connected to cooperative locality in distributed storage and to single-server private information retrieval with side information. We focus on the case $t=r=2$, where existing constructions and converse bounds on the maximum dimension are separated by a gap that grows linearly with $n$. We close this gap by determining the maximum dimension for every $n\\geq 4$ and every field $\\mathbb{F}$ and providing explicit optimal constructions. The converse translates local recovery into global geometric constraints, using induction and quotient reductions to control coordinate directions and their multiplicities. Matching achievability follows from simple constructions using repeated basis directions and, when needed, at most two nontrivial linear combinations.", "id": "Paper/67092", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67092"}, {"title": " Partitioning Partitions: Analyzing Properties of Type <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.982ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 1284.1 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">B_n</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-42\" d=\"M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-42\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-6E\" x=\"1074\" y=\"-213\"></use>\n</g>\n</svg> and <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"3.143ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 1353.1 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">D_n</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-44\" d=\"M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-44\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-6E\" x=\"1171\" y=\"-213\"></use>\n</g>\n</svg> Partitions ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "70c87497f08ab6b9f1687b19dcd652571575e0edefa0976626c9afc560872428", "withdrawn": "", "abstract": "Partitions arise in many disciplines of mathematics, from combinatorics to number theory.  We look at applications of partitions in Lie theory to parameterize matrices with desirable properties. In Lie theory, there are four types of classical Lie algebras: $A_n$, $B_n$, $C_n$, and $D_n$. This project focuses on analyzing the partitions of type $B_n$ and $D_n$ algebras through generating functions, restrictive properties, and counting their partitions. More specifically, we ultimately develop methods to count the number of partitions in all subsets of these algebras with specific properties utilizing features that relate to the number of even and odd parts in the partitions. We specifically leverage some of the work of Lusztig and Spaltenstein in their classification of the generalized Springer correspondence to do this. We are able to use this information about the number of specific types of partitions to obtain new results relevant about counting the number of nilpotent orbits classified as almost Levi-regular and provide framework to extend to other this to other settings. This work was done under the supervision of Dr. Amber Russell.", "id": "Paper/67093", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67093"}, {"title": " Heegaard Floer obstructions to Anosov flows on 3-manifolds ", "webprogram_exclude": "0", "session_ids": ["Session/17916"], "source_sha256": "b840698815d93e3b2ae0ac69f930cf621c8f8216869bc4f9307af1a1e192feba", "withdrawn": "", "abstract": "We build an Anosov flow obstruction using the Heegaard Floer contact classes of the corresponding bicontact structure. As an application we produce an infinite family of hyperbolic 3-manifolds with $b_1>0$ that cannot admit such a flow. This is joint work with Matthew Hedden and Jeremy Van Horn-Morris.", "id": "Paper/67095", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67095"}, {"title": " Wave decay and the bottom of the spectrum ", "webprogram_exclude": "0", "session_ids": ["Session/18326"], "source_sha256": "0e33d0fe195ff053a4f544ac7f9860129eb91469586611671fb5f06f6de5ba7e", "withdrawn": "", "abstract": "A classic application of high energy resolvent estimates is to wave decay, for example for waves propagating in the complement of an obstacle in Euclidean space.  In these settings the behavior of the resolvent at low energy may be what determines the leading terms in the wave expansion.  We prove a general theorem that allows us to extend a classic wave decay result due to Burq to two-dimensional Euclidean scattering problems for which the cut-off resolvent is unbounded at $0$.", "id": "Paper/67096", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67096"}, {"title": " CANCELLED Finite <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.064ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 888.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\r\n<title id=\"MathJax-SVG-1-Title\">N</title>\r\n<defs aria-hidden=\"true\">\r\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4E\" d=\"M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z\"></path>\r\n</defs>\r\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\r\n <use xlink:href=\"#E1-MJMATHI-4E\" x=\"0\" y=\"0\"></use>\r\n</g>\r\n</svg>-quandles of knots and links \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/19352"], "source_sha256": "84942f5dd3eb67f3745df7fca94fa2f769df632e4bc8df3f4119e54eb2b6ce0d", "withdrawn": "", "abstract": "The {\\em fundamental quandle} of a knot is a complete invariant for tame, unoriented knots.  However, the structure of the quandle can be extremely complex, so it can be useful to consider quotients of the quandle.  For a given $N=(n_1, \\dots, n_k)$, the {\\em fundamental $N$-quandle} of a knot, link or spatial graph is the result of adding relations $x^{y^{n_i}} = x$ to the fundamental quandle, for certain elements $x$ and $y$ of the fundamental quandle. For certain knots and links, some $N$-quandles is finite; previously the author, building of work of Hoste and Shanahan, has provided a complete list of these links. It has been an ongoing project to compute the size and structure of these finite $n$-quandles; that project has now been completed, and we report on the results.", "id": "Paper/67101", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67101"}, {"title": " On the p-rationality of Lusztig induced characters ", "webprogram_exclude": "0", "session_ids": ["Session/17832"], "source_sha256": "21afdb37d75d321a8dd6acf0cd1470167d0e93d9d7e461f3d7d783d0f0792350", "withdrawn": "", "abstract": "Among finite simple groups, character values of alternating and sporadic groups tend to have relatively low irrationality at any prime $p$, whereas those of simple groups of Lie type can have arbitrarily high $p$-irrationality. I will discuss some results supporting this phenomenon. In particular, if $\\chi:=R_{\\textbf{T}}^{\\textbf{G}}(\\theta)$ is a Deligne--Lusztig character of a finite reductive group $\\textbf{G}^F$, with $\\theta$ an irreducible character of a maximal torus $\\textbf{T}^F$, and if $\\chi$ has degree prime to $p$, then the so-called $p$-rationality level of $\\chi$ coincides precisely with that of $\\theta$. I also present further evidence suggesting that Lusztig induction preserves $p$-rationality for characters of $p'$-degree.", "id": "Paper/67103", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67103"}, {"title": " Linear representations of manifolds ", "webprogram_exclude": "0", "session_ids": ["Session/17942"], "source_sha256": "1e21ac7bc83ebe21fe1911b80cd4297e0dfd4bbac2f799b5376418c19f196f6c", "withdrawn": "", "abstract": "To perform optimization over a manifold, a natural first step is to understand how manifolds are represented as matrices, on which our numerical algorithms can run. We classify which manifolds with symmetry admit matrix representations and show how to construct the optimal representations. Along the way, we compute the minimal dimension of equivariant embeddings of these manifolds.", "id": "Paper/67109", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67109"}, {"title": " Modeling Pulsed Vaccinations to Control Sylvatic Plague in Himalayan Marmots ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "2257246e739adb7c35dc41a136963e806fad7829028404750b6925849b4b9e1b", "withdrawn": "", "abstract": "Sylvatic plague is a highly contagious disease resulting from \\textit{Yersinia pestis} bacteria (the same bacteria responsible for the Black Death in Europe from 1346 to 1353) and is transmitted between mammals through flea bites. We developed a mathematical model to characterize the dynamics of plague within a population of fleas and Himalayan marmots (\\textit{Marmota himalayana}), which have been found to express a gene resistant to the deadly disease. Analysis of this epizootic model examines population dynamics without any intervention (a baseline scenario) and with a pulsed vaccination control measure to determine the effectiveness of vaccination in conjunction with the resistance gene. We use uncertainty and sensitivity analysis (utilizing Latin hypercube sampling and partial rank correlation coefficients) to determine the sensitivity of the control effectiveness to uncertain model parameters.", "id": "Paper/67111", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67111"}, {"title": " Goodwillie polytopes: a self-dual family arising from the topology of loop spaces ", "webprogram_exclude": "0", "session_ids": ["Session/18379"], "source_sha256": "03aa9dc5a37d51c94cc7ce3a06be07560dfed0f6377736daaff2df8508dfb6c6", "withdrawn": "", "abstract": "The $S^1$-equivariant homology of the free loop space $LX = Map(S^1, X)$ is a natural setting for important operations in string topology and is closely connected to cyclic homology. In work motivated by this connection, two Koszul-dual chain models for $LX$ appear: a “smallest” model and a larger model in which certain geometric compatibilities become visible. The underlying idea is surprisingly concrete. Adams’ construction regards a singular simplex as a parametrized family of paths from its first vertex to its last. Arranging simplices cyclically into a “necklace” and concatenating the resulting paths produces families of free loops. Applying Adams’ construction directly leads to freehedra; first decomposing the simplices using the Alexander–Whitney diagonal leads instead to a family of larger parameter spaces: the Goodwillie polytopes.\nThese polytopes are interesting mathematical objects in their own right, and their combinatorics give geometric form to algebraic properties of the Hochschild-type constructions that motivate them. We will describe and visualize their structure and the striking self-duality of their face lattices.", "id": "Paper/67112", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67112"}, {"title": " Who Checks the Statement? Fidelity in Two Lean 4 Formalizations of Hamilton’s Theorem ", "webprogram_exclude": "0", "session_ids": ["Session/19345"], "source_sha256": "7c4ebc9cb7bab7299cd385c206491f60958087fc1fc417e2021d1a176539be4b", "withdrawn": "", "abstract": "Machine-checked proof guarantees that a proof establishes its stated conclusion. It does not guarantee that the stated conclusion faithfully renders the informal theorem. As autoformalization scales, statement review rather than proof search becomes the binding constraint on trust — and statement review is the part that requires neither large models nor privileged compute.\n\nWe report preliminary results from a case study. Hamilton’s 1982 theorem, that a closed 3-manifold admitting a metric of positive Ricci curvature admits a metric of constant positive curvature, has recently been formalized in Lean 4. The author independently maintains a formalization blueprint targeting the same result. A line-level comparison of the two formal statements yields a working taxonomy of [N~14] divergence categories, including hypotheses strong enough to trivialize the claim, quantifier scope that silently narrows it, and definitional choices that typecheck but denote a different object than the informal reading supplies.\n\nSome categories admit mechanical detection on commodity hardware: vacuity via attempted derivation of False from the hypotheses, over-weakening via trivial closure under standard automation, outright error via negation-provability. Others appear to require human or learned judgment, and we characterize which. We also discuss what reproducible auditing demands in practice — pinning toolchain and Mathlib commit, content-addressing results — given that Mathlib changes daily and formalization results are routinely reported without either.\n\nAll artifacts are public and the methods require no proprietary model access, which we suggest makes statement auditing a natural locus for user-controlled work in AI for mathematics.", "id": "Paper/67121", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67121"}, {"title": " Higher-Dimensional Dynamical Moduli Spaces ", "webprogram_exclude": "0", "session_ids": ["Session/18259"], "source_sha256": "0241906f6967234f91b731a2d10e8a576e97334483ba396d1e11fd84c13e97dd", "withdrawn": "", "abstract": "Let $\\text{End}_d^N$ be the space of degree $d$ endomorphisms of $\\mathbb{P}^N$. The group $\\text{PGL}_{N+1}$ acts on $\\text{End}_d^N$ by conjugation, leading to the dynamical moduli spaces \n$\\mathcal{M}_d^N :=\\text{End}_d^N/\\text{PGL}_{N+1}.$\nThe geometry of these spaces has been extensively studied in the case $N=1$, with questions concerning, for example, their rationality and the structure of their singular loci. In this talk, we discuss ongoing work on aspects of the geometry of $\\mathcal{M}_d^N$ when $N\\geq 2$, and explore some of the challenges that arise in higher dimensions.", "id": "Paper/67132", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67132"}, {"title": " Closure operations induced by resolution of singularities in equal characteristic zero ", "webprogram_exclude": "0", "session_ids": ["Session/18347"], "source_sha256": "7473653303eb605ffd221e53770033ecfe542c3d1e2385d00c73de77f05e91f6", "withdrawn": "", "abstract": "In positive characteristic, there is a close connection between so-called F-singularities and the theory of tight closure developed by Hochster and Huneke. This has inspired much work investigating closure operations in equal characteristic zero and in mixed characteristic. However, until recently, most closure operations studied in characteristic zero lacked a connection to resolutions of singularities and their associated vanishing theorems. A few years ago, in joint work with Neil Epstein, Rebecca R.G., and Karl Schwede, we proposed several new closure operations defined using resolutions of singularities in characteristic zero. In this talk, I'll discuss recent extensions of this work, including connections to the positive characteristic picture.", "id": "Paper/67133", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67133"}, {"title": " Making a Better Math Marketing Team ", "webprogram_exclude": "0", "session_ids": ["Session/18322"], "source_sha256": "fa683bceb311495742351740739037cbf82b1fc145698b0acfc77dc0316e910e", "withdrawn": "", "abstract": "As a math educator, it is very common for people to tell me they hate math or that they are not a math person. In this talk, I will share why I started making math videos on social media and tips on what worked for me in sharing the message that math can be fun. This session is for those who want to start sharing on social media but just needs a little nudge in doing so.", "id": "Paper/67134", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67134"}, {"title": " A Combinatorial Characterization of Hyperbolic 3-Manifolds ", "webprogram_exclude": "0", "session_ids": ["Session/18267"], "source_sha256": "b5ece691bc9981c0640bf01a7eaa3f824f31fa7c17b8bd90dd1c50ce981ee3c2", "withdrawn": "", "abstract": "In joint work with D. Cooper and P. Patel, we give a combinatorial characterization of closed hyperbolic 3-manifolds using the notion of locally combinatorially defined (LCD) families. More specifically, we show that there is a finite collection of triangulated 3-balls such that a closed 3-manifold has a triangulation whose local neighborhoods are modeled on one of these 3-balls if and only if it is hyperbolic. In previous work, we proved that a family of compact $n$-manifolds $\\mathcal{F}$ is LCD if and only if there exists a compact branched $n$-manifold $W$ such that $\\mathcal{F}$ is precisely the set of manifolds that immerse into $W$. Thus, our result implies the existence of such a universal branched 3-manifold for closed hyperbolic 3-manifolds. In this talk, I will describe the main ideas of the proof, which relies heavily on this equivalence theorem. In particular, I will explain how LCD families capture the thick part of a hyperbolic 3-manifold, while branched manifolds encode the thin part.", "id": "Paper/67136", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67136"}, {"title": " Chromatic number of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.162ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 500.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">3</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-33\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-stable Kneser graphs ", "webprogram_exclude": "0", "session_ids": ["Session/19360"], "source_sha256": "06211d6eee9ce3be89670e67dbd8ea254595a00d607cd50ca227dc572c921905", "withdrawn": "", "abstract": "For an integer $s \\ge 2$, a subset $S \\subseteq [n]$ is {\\em $s$-stable} if $\\min \\{j - i, n + i - j\\}\\ge s$ for every $i,j \\in S$ with $i<j$. Denote the set of all $s$-stable subsets of size $k$ of $[n]$ by $\\binom{[n]}{k}_{s\\text{-stable}}$. Schrijver proved in 1978 that the chromatic number of the Kneser graph $\\mathrm{KG}\\big( \\binom{[n]}{k}_{2\\text{-stable}}\\big)$ is $n - 2k +2$ whenever $n\\ge 2k$. Generalizing this result, Meunier conjectured in 2011 that $\\chi\\left( \\mathrm{KG}\\big( \\binom{[n]}{k}_{s\\text{-stable}} \\big) \\right)= n - sk +s$ for all $n\\ge sk$. This conjecture was previously proven for all even $s$, for $s \\ge 4$ and large enough $n$, and  for $k=2$. We prove the conjecture in the cases $s=3$ and $n$ large enough, or $k=s=3$. To this end, we prove versions of the Hilton-Milner theorem for $s$-stable sets.", "id": "Paper/67139", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67139"}, {"title": " Self-modifying Feedforward Neural Networks for Zero-shot Inference, Continual Learning, and Identifying New Learning Algorithms ", "webprogram_exclude": "0", "session_ids": ["Session/17705"], "source_sha256": "0558d22f0019861957506eae73a424b132fc6c5231772e802ad6f6194e414064", "withdrawn": "", "abstract": "Humans and animals have a unique capacity to generalize and learn in novel circumstances. This capacity manifests in various ways, including 0-shot inference and continual learning—two abilities thought to be foundational in the brain. However, the neural implementations and algorithms underlying these cognitive abilities remain poorly understood, in part due to the lack of deep learning models that are both interpretable and capable of solving 0-shot and continual learning tasks. To address this gap, we introduce a feedforward neural network architecture that learns online via a biologically grounded learning rule (3-factor Hebbian learning) as opposed to a standard gradient-descent-based learning rule. In contrast to recent and established continual learning methods, our model succeeds on multiple 0-shot and continual learning tasks, establishing the model as a suitable candidate for mechanistic analysis. Next, we explain our procedure for extracting the essential learning algorithms implemented by these networks and describe the identified algorithms. Finally, we present theoretical guarantees on learning for specific networks and connect network components and parameters to task performance. Overall, we provide both a theoretical and empirical framework for discovering new neural learning algorithms.", "id": "Paper/67141", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67141"}, {"title": " Algorithms for Multiparameter Persistence ", "webprogram_exclude": "0", "session_ids": ["Session/18072"], "source_sha256": "8bb013169f8099cb7877219b69be29f0252ca8eeee9267820b105ea56d85e48c", "withdrawn": "", "abstract": "Recent focus on multiparameter persistence in Topological Data Analysis (TDA) has resulted in some of the efficient algorithms. Going beyond implementing the linear algebra straightforwardly dictated by the underlying algebraic structures, some of these algorithms derive the efficiency from exploiting special geometric and combinatorial structures hidden behind the algebra. In this talk, we expose this thematic paradigm by presenting recent algorithms designed for (i) computing presentations from input chain complexes, (ii) computing decompositions of the input persistence module from such presentations, and (iii) computing some invariants of the input persistence module such as generalized rank and limits/colimits.\nThese algorithms, because of their efficiency, have been implemented into software that can be used in practice.", "id": "Paper/67142", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67142"}, {"title": " Reproducing Kernels and Random Matrices ", "webprogram_exclude": "0", "session_ids": ["Session/17377"], "source_sha256": "204c8ad5236a828b2fc7ad92feca055bf157a9381a2d3c0dbdc5baed42fba5b3", "withdrawn": "", "abstract": "This talk studies a situation in which the famed Szeg\\H{o} kernel of the Hardy space arises from a sequence of unitary integrals in random matrix theory. Earlier work of two of the authors (Jury and Roman) generalized this phenomenon to a multivariate setting in a non-trivial manner, suggesting a deeper connection between the Hardy space and the group of unitary matrices. With our third author (van Rensburg), we have gone further still.\n\nIn this talk, we discuss our latest results, including the resolution of an earlier conjecture in our work. Time permitting, we will also explore some currently unresolved ideas which offer avenues for future research.", "id": "Paper/67143", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67143"}, {"title": " Computing algebraic and Hermitian <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.066ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 889.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">K</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-4B\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Theory of classifying spaces of cyclic <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.162ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 500.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">2</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-32\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-groups ", "webprogram_exclude": "0", "session_ids": ["Session/17843"], "source_sha256": "0b519892fa61ad07fe21aae7f22762b4b161009841c198ea483eeb5c5753e2cc", "withdrawn": "", "abstract": "Chow groups of classifying spaces have played an important role in algebraic geometry, notably in counterexamples to the integral Hodge conjecture. This motivates the study of classifying spaces through richer invariants. In this talk, I will present the explicit computation of the algebraic and Hermitian $K$-theory of classifying spaces of cyclic $2$-groups. We use the Adams and Atiyah–Hirzebruch spectral sequences to compute these and uncover how these theories detect torsion phenomena and describe the resulting algebraic structure. I will also discuss how the corresponding classical groups embed into their motivic analogues.", "id": "Paper/67144", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67144"}, {"title": " Counting Pairs of Saddle Connections on Translation Surfaces ", "webprogram_exclude": "0", "session_ids": ["Session/17902"], "source_sha256": "0c165090dfdbb5b1d5bce7220302fc1bdec25729aa122c302488188955027c3d", "withdrawn": "", "abstract": "In 2022, Athreya-Fairchild-Masur proved that, for a generic translation surface, the number of pairs of saddle connections of length at most $R$ and cross product at most $A$ grows asymptotically like $c_A R^2$ for some (inexplicit) constant $c_A$. In this talk, I will discuss some further work on understanding these asymptotics. This includes uniform bounds and growth rate of $c_A$ as a function of $A$, pointwise results, and a family of exceptional surfaces for which quadratic growth of the associated counting function fails. I will also discuss exact computations of $c_A$ for Veech curves, as well as families of non-Veech rank-1 subvarieties. This is partially joint work with Samantha Fairchild, Kanishka Katipearachchi, and Howard Masur.", "id": "Paper/67145", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67145"}, {"title": " Arithmetic and Computation in the Boij Soederberg Cone ", "webprogram_exclude": "0", "session_ids": ["Session/18025"], "source_sha256": "671037016f009e5fa25344bc2c979918005d4cef94184546a7166c008f19f1da", "withdrawn": "", "abstract": "When viewed through the lens of Boij Soederberg theory, conjectured bounds for the Betti numbers of graded modules lead naturally to systems of Diophantine equations. Remarkably, some of these systems can actually be solved.  I will describe this translation and our results, which use methods from classical number theory as well as computational algebraic geometry (using Macaulay2).  This is joint work with my two undergraduate students Noah Huang and Harrison Wolf.", "id": "Paper/67148", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67148"}, {"title": " The Force Multiplier Impact of the Polymath Jr Program ", "webprogram_exclude": "0", "session_ids": ["Session/18205"], "source_sha256": "96ecd0a7fd547fc40b955cda699536754a9e0170b1b5b2771420ebe335fdc854", "withdrawn": "", "abstract": "During the pandemic response, when many summer REUs were cancelled, the Polymath Jr program was created to step in and provide research opportunities on a large scale. Run every summer since and now supported by the NSF, on the order of 300 students explore research projects in around 15 groups, where graduate students and postdocs gain valuable experience in mentoring undergraduates and designing research programs. Taking to heart that ``the perfect is the enemy of the good'', we describe the challenges in creating and sustaining an online program, report on some typical results, and discuss how to participate at any level.", "id": "Paper/67149", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67149"}, {"title": " A Combinatorial Characterization of Sol 3-Manifolds ", "webprogram_exclude": "0", "session_ids": ["Session/18380"], "source_sha256": "317a4e99247ecbb30a6f2ddc3ee5ebfa7fd251eb15d227f98f97d12197b265cd", "withdrawn": "", "abstract": "Sol geometry, one of the eight Thurston geometries, has strong connections to geometry, dynamics, and combinatorics. In this talk, I will give a combinatorial characterization of Sol 3-manifolds using the notion of locally combinatorially defined (LCD) families, developed in joint work with D. Cooper and P. Patel. To show that Sol 3-manifolds are LCD, we construct two regular languages: one that detects Anosov monodromies of torus bundles and another that detects the gluing maps of Sol semi-bundles. These languages are then used to build a compact branched 3-manifold. I will explain how this provides a finite combinatorial description of Sol 3-manifolds, revealing a connection between 3-manifold geometry, recognition problems, and formal language theory.", "id": "Paper/67150", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67150"}, {"title": " Generalized chip firing and critical groups of arithmetical structures on trees ", "webprogram_exclude": "0", "session_ids": ["Session/17921"], "source_sha256": "f516daf861fe05d969385306d92dd52416ec68d1a6cdc69bd12e54ed4a3507b0", "withdrawn": "", "abstract": "Chip firing provides a way to study the sandpile group (also known as the Jacobian) of a graph. We use a generalized version of chip firing to bound the number of invariant factors of the critical group of an arithmetical structure on a graph. We also show that, under suitable hypotheses, critical groups are additive under wedge sums of graphs with arithmetical structures. These results allow us to relate the number of invariant factors of critical groups associated to any given tree to decompositions of the tree into simpler trees. We use this to classify those trees for which every arithmetical structure has cyclic critical group. Finally, we show how to construct arithmetical structures on trees with prescribed critical groups. In particular, every finite abelian group is realized as the critical group of some arithmetical structure on a tree.", "id": "Paper/67152", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67152"}, {"title": " From coexistence to selection in protein network competition ", "webprogram_exclude": "0", "session_ids": ["Session/17383"], "source_sha256": "9b8306445595f2c88d263b615998d5ffd0c8b3862e3efc0f0e41f50ea2065595", "withdrawn": "", "abstract": "The cytoskeleton—complex self-organized assemblies of protein filaments and auxiliary proteins—plays important roles in cell shape and mechanics through the dynamics of self-organized higher-order architectures such as networks. Multiple architectures coexist simultaneously in the cell, competing for common limited resources in a dynamic manner that is essential for the cell’s ability to quickly respond to external cues. How such networks coexist in the competitive cellular environment is still poorly understood.\n\nRecently, our collaborators demonstrated the importance of protein turnover for resource distribution between networks (Guerin et al. 2025, Curr. Biol.), showing that turnover permits networks of different strengths to coexist. However, if too many networks compete, a selection process occurs which favors assembly of strong networks over weak ones. Interestingly, they have further found that the critical degree of competition at which selection occurs is highly sensitive to the turnover rate and amount of available protein.\n\nTo understand the mechanisms underlying this coexistence-selection transition in the competition, we developed a mathematical model for the network assembly dynamics as a system of coupled ODEs, incorporating parameters which correspond directly to the action of complementary proteins modulating turnover. Notably, we find that a Michaelis-Menten equation for the network assembly rate, indicative of autocatalytic growth which is constrained, is essential to capture the transition from coexistence to selection with increasing network competition. Our model reproduces key experimental results and reveals the precise mechanism through which turnover, resource constraints, and degree of competition determine the coexistence or selection of multiple competing protein filament networks, with broad implications of how cells can, in general, tune their various dynamic cytoskeletal architectures.", "id": "Paper/67153", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67153"}, {"title": " Kinematics and energetics of a swirling micro-swimmer in complex fluids ", "webprogram_exclude": "0", "session_ids": ["Session/18240"], "source_sha256": "d4389ac4380d6224d184f90f5d004bd36ddda65986c71be914b9c5620d78c32d", "withdrawn": "", "abstract": "Investigating microorganism motility in diverse fluid environments is vital for engineering application-specific micro-robots. While ciliated microswimmers are standard models for these systems, the coupled effects of rotational velocity on their kinematics and energetics remain understudied. In contrast to simple viscous fluids—where rotation and translation are decoupled—complex fluids induce strong coupling between a microswimmer's rotational speed and its translational motion. Here, we present analytical and numerical investigations into the kinematics and energetics of a swirling microswimmer. We employ perturbation analysis to derive closed-form solutions and utilize numerical simulations to validate our analytical predictions while exploring parameter regimes beyond analytical tractability.", "id": "Paper/67156", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67156"}, {"title": " Subquadratic Growth and Uniform Property <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.453ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 625.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\Gamma</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-393\" d=\"M128 619Q121 626 117 628T101 631T58 634H25V680H554V676Q556 670 568 560T582 444V440H542V444Q542 445 538 478T523 545T492 598Q454 634 349 634H334Q264 634 249 633T233 621Q232 618 232 339L233 61Q240 54 245 52T270 48T333 46H360V0H348Q324 3 182 3Q51 3 36 0H25V46H58Q100 47 109 49T128 61V619Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-393\" x=\"0\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18382"], "source_sha256": "30b2681b92a15ff121a7abde8ac8502e158cab834cf106f5ca8cee5b7a513cfd", "withdrawn": "", "abstract": "Considerable attention has been paid to Uniform Property $\\Gamma$ (UP$\\Gamma$) and its recent impact on the classification program of C* algebras. In particular, as proven in 2020 by Castillejos et al., the presence of UP$\\Gamma$ for simple, separable, unital, nuclear C* algebras with nonempty trace space suffices for the Toms-Winter conjecture to hold. We will discuss new tracially localized dimension-growth conditions which guarantee UP$\\Gamma$ for certain classes of AH and ASH algebras.", "id": "Paper/67161", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67161"}, {"title": " Double Plus Ungood: Modeling with Discrete-Time Dynamical Systems ", "webprogram_exclude": "0", "session_ids": ["Session/18271"], "source_sha256": "5cd815b45dd5230dd7e72cc36b39d6c184620e32630bd35640c5ce877e31ece4", "withdrawn": "", "abstract": "While it's indisputable that differential equations need to play a key role in undergraduate education, due to their utility in modeling numerous real world phenomena, there's a lot of choices in how to introduce them. Remembering how games of chance influenced the development of probability (and their appeal to general audiences!), we motivate modeling discrete-time systems by analyzing the infamous ``Double Plus One'' strategy of roulette. We see how the solution leads to difference equations, and then explore generalizations to many important continuous systems and differential equations. We also discuss how to use AI to assist in preparing talks like this, commenting on what changed from a similar presentation in '25 to this one.", "id": "Paper/67162", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67162"}, {"title": " Rational Chains on Fano Varieties and Rationally Connected Fourfolds ", "webprogram_exclude": "0", "session_ids": ["Session/17996"], "source_sha256": "1e70daa53d3082e8fdab5d1069dd91a68387fe8126dd80ef4ceeef87227e43c9", "withdrawn": "", "abstract": "Fano varieties play a very important role in birational geometry. One way of understanding the geometry of Fano varieties is to study rational curves on them. For example, a key step in showing the boundedness of smooth Fano varieties relies on bounding the degree of rational chains through two general points of the variety. This was achieved by Campana and Koll\\'ar-Miyaoka-Mori in 1992. The bound was shown to be exponential in the dimension of the variety, but it is suspected to be far from optimal. In this talk, we prove a much stronger bound for smooth Fano varieties $X$ of dimension $n$ with semistable tangent bundle: There exists a chain of rational curves through at least two general points of total ($-K_X$)-degree at most $2n$. This result has many consequences: we can improve the bound for the anticanonical volume of smooth Fano varieties with semistable tangent bundle, we can improve the degree bound for very free curves in these varieties, and there are also applications in symplectic geometry. In particular, we prove that smooth Fano fourfolds with semistable tangent bundle have a non-vanishing 2-point Gromov-Witten invariant, answering a question of Koll\\'ar in this case. If time permits, we will discuss some work towards the unstable tangent bundle case. This work is joint with Eric Riedl.", "id": "Paper/67165", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67165"}, {"title": " An Individualized and More Efficient Approach to Improving Placement Scores ", "webprogram_exclude": "0", "session_ids": ["Session/18092"], "source_sha256": "93704a3e6edb61e5706e1dfcd9bfec218c407673d03679902c870edfdedc89aa", "withdrawn": "", "abstract": "Mathematics Workshop is a one-credit course developed by the authors to move beyond the “one-size-fits-all” model of developmental mathematics courses and support students as they prepare for their required math course. Students at all levels of preparation can take this class to place into whatever course is required for their program. The course leverages an online placement system to provide online individualized mathematics content support combined with in-person faculty support and community-building. We plan to describe the course structure in detail and discuss its successes and limitations, especially regarding performance in subsequent courses. We will also discuss challenges with implementation and how this type of class may impact students’ attitudes about mathematical thinking.", "id": "Paper/67166", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67166"}, {"title": " A Classification of Indecomposable Unitary <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"4.378ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 1884.9 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathrm {BT}_1</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-42\" d=\"M131 622Q124 629 120 631T104 634T61 637H28V683H229H267H346Q423 683 459 678T531 651Q574 627 599 590T624 512Q624 461 583 419T476 360L466 357Q539 348 595 302T651 187Q651 119 600 67T469 3Q456 1 242 0H28V46H61Q103 47 112 49T131 61V622ZM511 513Q511 560 485 594T416 636Q415 636 403 636T371 636T333 637Q266 637 251 636T232 628Q229 624 229 499V374H312L396 375L406 377Q410 378 417 380T442 393T474 417T499 456T511 513ZM537 188Q537 239 509 282T430 336L329 337H229V200V116Q229 57 234 52Q240 47 334 47H383Q425 47 443 53Q486 67 511 104T537 188Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-54\" d=\"M36 443Q37 448 46 558T55 671V677H666V671Q667 666 676 556T685 443V437H645V443Q645 445 642 478T631 544T610 593Q593 614 555 625Q534 630 478 630H451H443Q417 630 414 618Q413 616 413 339V63Q420 53 439 50T528 46H558V0H545L361 3Q186 1 177 0H164V46H194Q264 46 283 49T309 63V339V550Q309 620 304 625T271 630H244H224Q154 630 119 601Q101 585 93 554T81 486T76 443V437H36V443Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-42\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-54\" x=\"708\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-31\" x=\"2023\" y=\"-213\"></use>\n</g>\n</svg> Modules ", "webprogram_exclude": "0", "session_ids": ["Session/18082"], "source_sha256": "daf65b7116316dbd2c7bee5e34e811baf07fe58ede142fbe2ffb8129df163700", "withdrawn": "", "abstract": "One fruitful method for studying abelian varieties in characteristic p is to study their \\(p\\)-torsion subgroups, to which one may associate a linear-algebra object called a \\(\\mathrm{BT}_1\\)  module. Equipping an abelian variety with extra structure induces a corresponding structure on the associated \\(\\mathrm{BT}_1\\)  module; an action of an order in an imaginary quadratic field, for example, yields a unitary \\(\\mathrm{BT}_1\\)  module. In this talk, we introduce unitary \\(\\mathrm{BT}_1\\)  modules and construct the four possible indecomposable types of these modules. We also show that two of these types give rise to points lying in the intersection of an Ekedahl–Oort and a Newton stratum of a moduli space of abelian varieties in characteristic \\(p\\). This is joint work with E. Andrews, M. Fox, H. Goodson, S. R. Groen, and S. Nair.", "id": "Paper/67167", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67167"}, {"title": " Exploiting Block Toeplitz Structure in Bayesian Inverse Problems for Autonomous Dynamical Systems ", "webprogram_exclude": "0", "session_ids": ["Session/18032"], "source_sha256": "d8dbf4138a9d03be8e241803e35b15bd40e5d5dd00827fd47ab16a86e31d4735", "withdrawn": "", "abstract": "We present a framework for large-scale Bayesian inverse problems governed by autonomous dynamical systems, in which the parameter-to-observable map is linear and time-invariant. Upon discretization, this map and its adjoint become block lower-triangular Toeplitz matrices; exploiting this structure replaces repeated PDE solves with a GPU-performant FFT-based algorithm for Hessian-vector products, achieving near-linear complexity. We demonstrate this framework on several large-scale tsunami early warning applications. First, we construct real-time digital twins for tsunami early warning in the Cascadia Subduction Zone and the Japan Trench, assimilating seafloor pressure data through an acoustic--gravity wave model to infer spatiotemporal seafloor deformation with over one billion parameters, achieving Bayesian inversion and forecasting in a fraction of a second, a ten-billion-fold speedup over the state of the art. Second, we exploit the same block Toeplitz structure to recast Bayesian optimal experimental design as a data-space matrix subset selection problem, enabling scalable multi-GPU greedy sensor placement for tsunami warning networks. Third, we exploit the linear time-invariant structure of coupled earthquake--tsunami dynamics to precompute elastic Green's function and acoustic--gravity adjoint response operators, reducing earthquake-to-tsunami waveform generation to two consecutive FFT-accelerated convolutions, generating full waveforms in milliseconds per rupture. Across these applications, block Toeplitz structure is the common algorithmic thread enabling billion-parameter Bayesian inference and optimal experimental design.", "id": "Paper/67168", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67168"}, {"title": " A Time-Scale Collocation Method for Difference Equations and Discrete Dynamical Systems ", "webprogram_exclude": "0", "session_ids": ["Session/18254"], "source_sha256": "d2dc58af69c44abf6becb56bce49fbb4a91df7cebe835455f669cf04a0e369a6", "withdrawn": "", "abstract": "This work develops a collocation-based numerical method for difference equations and discrete dynamical systems within the framework of time-scale calculus. The proposed approach employs falling factorial basis functions together with Stirling number representations, providing a natural algebraic structure for dynamic equations defined on discrete time scales. By using the recursive and operational properties of the falling factorial basis, the original dynamic problem is transformed into a finite-dimensional system of algebraic equations whose solution determines the coefficients of the collocation approximation.\n\nThe method is first illustrated through scalar nonlinear difference equations, including a discrete Riccati-type problem, in order to demonstrate the construction of the approximation and evaluate its accuracy through residual errors. The framework is then extended to coupled systems of dynamic equations and applied to a discrete HIV infection model. In this way, the HIV model serves as a representative nonlinear dynamical system for examining the performance of the proposed method on a more complex biological application.\n\nNumerical results show that the method produces accurate approximations with small residual errors for both scalar difference equations and coupled discrete dynamical systems. These results suggest that falling-factorial-based collocation provides a flexible and effective computational framework for the numerical treatment of dynamic equations on discrete and, more generally, time-scale domains.", "id": "Paper/67169", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67169"}, {"title": " Traverso’s Isogeny Conjecture & Supersingular Unitary <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.259ex\" height=\"2.009ex\" style=\"vertical-align: -0.671ex; margin-left: -0.089ex;\" viewBox=\"-38.5 -576.1 542 865.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">p</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-70\" d=\"M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-70\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Divisible Groups ", "webprogram_exclude": "0", "session_ids": ["Session/18214"], "source_sha256": "56687f23659392234e8a2276ded8c2962f5bc4a13f172e5b2d21c0abd85cd720", "withdrawn": "", "abstract": "Given a \\(p\\)-divisible group \\(X\\) over an algebraically closed field of characteristic \\(p\\), its \\(p\\)-torsion group scheme \\(X[p]\\) and its Newton polygon are classical invariants. When \\(X\\) arises as the \\(p\\)-divisible group of an elliptic curve, \\(X[p]\\) alone determines the Newton polygon. More generally, there is a \\(b\\) such that \\(X[p^b]\\) determines the Newton polygon. Traverso's Isogeny Conjecture, proven by Nicole and Vasiu in 2007, bounds the minimal such \\(b\\) in terms of the dimension and height of \\(X\\). In this talk, we refine this bound for supersingular \\(p\\)-divisible groups arising from points on a unitary Shimura variety. This is joint work with E. Andrews, M. Fox, H. Goodson, S. R. Groen, and S. Nair.", "id": "Paper/67170", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67170"}, {"title": " A Second-Order Efficient Scheme for the Long-Time Dynamics of Chaotic Models ", "webprogram_exclude": "0", "session_ids": ["Session/19344"], "source_sha256": "ec3ef8f92b087304e4093b77dfd4f2dc270652f10d0c8690b98a13fdb7334662", "withdrawn": "", "abstract": "We propose a highly efficient second-order numerical scheme for approximating the long-time dynamics of a class of nonlinear models, including chaotic systems arising in geophysical fluid dynamics. The method is unconditionally stable and requires solving only a fixed symmetric positive definite linear system at each time step. We prove that the numerical solutions remain uniformly bounded for all time and that the scheme accurately captures the long-time behavior of the underlying system. In particular, the global attractors and invariant measures of the scheme converge to those of the original model as the time step approaches zero. Numerical experiments on the Lorenz-96 system demonstrate that the scheme efficiently approximates long-time statistical properties and captures the invariant measures of the system. We also present additional numerical investigations of the scheme's ability to reproduce long-time statistical and chaotic properties of the underlying dynamics.", "id": "Paper/67171", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67171"}, {"title": " Classification of Collisions of Twisted Foulkes Character Polynomials ", "webprogram_exclude": "0", "session_ids": ["Session/18264"], "source_sha256": "4a5db778eda3ae94fe3d158c1456794e7c0cef01c578bfee652776d66b687fa3", "withdrawn": "", "abstract": "The twisted Foulkes character polynomial is an algebraically defined polynomial attached to an integer partition in terms of generalized Hermite polynomials. In this talk, we will describe the construction of this character polynomial. We determine precisely how much combinatorial information this polynomial encodes by completely classifying all pairs of partitions that give rise to the same polynomial. Our main result shows that equality of twisted Foulkes character polynomials admits a purely combinatorial characterization in terms of two explicit local operations on partitions. As a consequence, we determine precisely which conjugacy classes of the symmetric group have identical character values for every twisted Foulkes character and equal values of the sum of all irreducible characters, also known as the total character.", "id": "Paper/67174", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67174"}, {"title": " Component-by-Component Constructions for Extensible Lattice Sequences with Low Discrepancy for Arbitrary Sample Size ", "webprogram_exclude": "0", "session_ids": ["Session/17807"], "source_sha256": "5f84eace6547149734b84ad713b59b3dff13a2909ce3460eb8fa6cc4e0466fbd", "withdrawn": "", "abstract": "Extensible rank-one lattice sequences allow previously evaluated points to be retained as the sample size increases.  Existing constructions are naturally tied to selected nested lattice sizes, whereas a computation may terminate at any intermediate sample size. We introduce the weighted sum of expected squared discrepancies (WSESD) as a single figure of merit that weights the expected squared discrepancy (ESD) at sample size $n$ with a weight of $n^{1-\\delta}$.  We then implement a component-by-component (CBC) construction for the generating vector.   We establish theoretical error bounds for the resulting CBC construction that provides an ESD of $\\mathcal{O}(n^{-2+\\epsilon})$ for arbitrary $n$, not only preferred sample sizes. The leading constant is dimension-independent if the coordinate weights decay quickly enough.", "id": "Paper/67179", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67179"}, {"title": " Balanced Coloring ", "webprogram_exclude": "0", "session_ids": ["Session/18317"], "source_sha256": "902cd153a387a86cfa534c7a001508d969dc8938ccea70e5de164fb314438681", "withdrawn": "", "abstract": "Neighborhood balance coloring, recently introduced by Freyberg and Marr, has attracted considerable attention. Since then, many variations and generalizations have been studied. In this talk, I will explore the interplay between neighborhood balanced colorings and graph products. This is joint work with Karen L. Collins.", "id": "Paper/67180", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67180"}, {"title": " Constructions of Lagrangian cobordisms ", "webprogram_exclude": "0", "session_ids": ["Session/18218"], "source_sha256": "93da9eaae1a74bde46c1fc6cbd0b7f8efd1e0e527619ee18efbd1a5306430616", "withdrawn": "", "abstract": "Lagrangian cobordisms between Legendrian knots impose an interesting and not well-understood relation on Legendrian knots, and have attracted a lot of attention in recent years. Of particular interest is the special class of such cobordisms called “decomposable,” which are made up of a sequence of elementary cobordisms which smoothly correspond to attaching 0- and 1-handles. A recent significant development by Dimitroglou Rizell and Golovko answered the long-pondered question of whether every (nonribbon) Lagrangian cobordism between Legendrian knots is decomposable in the negative. In this talk we will survey methods for constructing Lagrangian cobordisms and provide a history of results related to decomposability, leading up to and including the work of Dimitroglou Rizell and Golovko. If time permits, we will briefly touch on connections to the theory of trisections of 4-manifolds. Most of the content of this talk comes from a survey paper joint with No\\'{e}mie Legout, Caitlin Leverson, Ma\\\"{y}lis Limouzineau, Ziva Myer, Yu Pan, Samantha Pezzimenti, Lara Simone Su\\'{a}rez, and Lisa Traynor.", "id": "Paper/67182", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67182"}, {"title": " Same Degree, Different Fate: Rates of Convergence to the ESD for 2-level <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.216ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 523.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">d</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-64\" d=\"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-64\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-regular graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17942"], "source_sha256": "80adeaf4e75b75400c7d3a4141b5160307f06cc6790a07ffbace816368ea575a", "withdrawn": "", "abstract": "In this work, we introduce and analyze a new ensemble of regular graphs \nwith a two-level structure. The vertex set is partitioned into two groups \nof equal size, and every vertex has exactly $a$ neighbors within its own \ngroup and $b$ neighbors in the opposite group. We apply the trace method \nto the resulting ensemble by classifying closed walks according to how \nthey move between the two vertex groups. This allows us to distinguish \ncontributions from purely internal walks, walks involving cross-group \nedges, and more complicated configurations containing cycles. We derive \nexplicit formulas for the first several moments and identify the \ncombinatorial structures responsible for their lower-order terms. In this \nway, the model provides a concrete setting for studying how additional \ngraph structure influences the rate at which the spectral distribution \napproaches its limiting behavior. Joint with: Naida Gavranovic, Joshua \nKhan, Mateo Palomares, Devayani Pradhan, Emily Upton, and Connor Yau.", "id": "Paper/67186", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67186"}, {"title": " Characterizations via Generalized Inverses ", "webprogram_exclude": "0", "session_ids": ["Session/18372"], "source_sha256": "9a92b14826f0ffadbcb7665fcc742a27213c23db702715ec0ce41d25e266abb7", "withdrawn": "", "abstract": "The study of generalized inverses has a long history (traced to E.H. Moore’s seminal work on generalized reciprocals for singular matrices in 1920) and occupies a unique position with significant applications in numerical analysis, statistics, optimization, and systems theory.  Many characterizations concerning regularity, unit-regularity, and exchange properties can be reformulated in terms of the existence and structure of generalized inverses. Concepts such as \\emph{annihilator-stability} can be reformulated through generalized inverses that help us answer a long-standing question on left-right symmetry of Kaplansky's uniquely generated rings. We will also formulate a generalized invertibility notion in the skew corners $eRf$ for arbitrary pairs of idempotents. On this foundation, we develop a way to produce units of the corner ring from complementary blocks using the classical Banachiewicz formula for inversion of partitioned matrices. This allows carrying the stable range of Bass and Vaserstein along skew-corners associated with arbitrary idempotents.", "id": "Paper/67192", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67192"}, {"title": " Strong parity edge-coloring of graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18359"], "source_sha256": "b0ab6f986a962be95e06696685f89151fff7cd2eae81a5adf3d0ad1c3fa83f6d", "withdrawn": "", "abstract": "An edge-coloring of a graph $G$ is a {\\it parity edge-coloring} if for each path $P$ in $G$, some color appears on an odd number of edges in $P$.  It is a {\\it strong parity edge-coloring} if for every open walk $W$ in $G$, some color appears an odd number of times along $W$.  The minimum numbers of colors in parity and strong parity edge-colorings of $G$ are denoted $p(G)$ and $\\hat p(G)$, respectively.\n\n\\par\nWe characterize strong parity edge-colorings and use this characterization to prove lower bounds on $\\hat p(G)$ and answer several questions posed by Bunde, Milans, West, and Wu about 20 years ago.  The applications are as follows:\n\n\\par\n(1)~For the complete bipartite graph $K_{r,s}$, we prove the conjectured value of $\\hat p(K_{r,s})$ (it is the value $r\\circ s$ given by the Hopf--Stiefel function).\n\n\\par\n(2)~We show that $\\hat p(G)$ for a connected $n$-vertex graph $G$ equals the general lower bound $\\lceil \\lg n \\rceil$ if and only if $G$ embeds in the hypercube $Q_{\\lceil \\lg n \\rceil }$.\n\n\\par\n(3)~We asymptotically compute $\\hat p(G)$ when $G$ is the $\\ell$th distance-power of a path, proving $\\hat p(P_n^\\ell)\\sim\\ell\\lceil \\lg n\\rceil$.\n\n\\par\n(4)~We disprove the conjecture that $\\hat p(G)=p(G)$ when $G$ is bipartite by constructing bipartite graphs $G$ such that $\\hat p(G)/p(G)$ is arbitrarily large; in particular, with $\\hat p(G)\\ge{1\\over3}k\\ln k$ and $p(G)\\le2k+k^{1/3}$.", "id": "Paper/67193", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67193"}, {"title": " Stability of bounded solutions for the fuzzy Landau equation ", "webprogram_exclude": "0", "session_ids": ["Session/17991"], "source_sha256": "45545ebd834e52fbd23c6d04572004b9262b9eb5252710c01d85f43cf0a3eb5f", "withdrawn": "", "abstract": "The fuzzy Landau equation is an approximation of the Landau equation, a fundamental model in collisional plasma dynamics. This approximation is considerably more tractable, both numerically and in terms of global well-posedness. In this talk we establish a conditional stability estimate in the 2-Wasserstein distance for a class of nonlinear equations generalising the fuzzy Landau equation. This class also contains 2D incompressible Euler in vorticity form, Vlasov–Poisson, and Patlak–Keller–Segel, recovering known uniqueness results for these models within a single framework. The proof is based on the stochastic coupling argument introduced by Fournier and Guérin, for which we provide an analytic interpretation.", "id": "Paper/67194", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67194"}, {"title": " Holonomy limits of SL(2,C) surface group representations ", "webprogram_exclude": "0", "session_ids": ["Session/17283"], "source_sha256": "8107dc1eb2474a454397d79db2fa2dd964a7f2f70b9607463dd3f8c04b9b0a6e", "withdrawn": "", "abstract": "The character variety of SL(2,C) surface group representations is compactified by (projective classes of) actions on R-trees. A natural question is: given a sequence of representations (or, by the non-abelian Hodge correspondence, Higgs bundles) leaving all compact subsets of the moduli space, how do we describe the limiting R-tree and action? The answer is well known for sequences of representations with \"generic\" Higgs bundles. In this talk, we'll discuss joint work in preparation with Sara Maloni and Lam Nguyen in which we answer this question for classes of non-generic Higgs bundles. As in the generic case, we approach this problem using harmonic maps.", "id": "Paper/67196", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67196"}, {"title": " A Muon-Accelerated Algorithm for Low Separation Rank Tensor Generalized Linear Models ", "webprogram_exclude": "0", "session_ids": ["Session/17908"], "source_sha256": "630a06b419a273bf24eacc72326cdc7af2d3bcd4fb826fa32d8d298fa093dfe9", "withdrawn": "", "abstract": "Tensor-valued data arise naturally in multidimensional signal and imaging problems, such as biomedical imaging. When incorporated into generalized linear models (GLMs), naive vectorization can destroy their multi-way structure and lead to high-dimensional, ill-posed estimation. To address this challenge, Low Separation Rank (LSR) decompositions reduce model complexity by imposing low-rank multilinear structure on the coefficient tensor. A representative approach for estimating LSR-based tensor GLMs (LSR-TGLMs) is the Low Separation Rank Tensor Regression (LSRTR) algorithm, which adopts block coordinate descent and enforces factor orthogonality through repeated QR-based projections. However, these repeated projections can increase computational cost. Therefore, we propose LSRTR-M, which incorporates Muon (MomentUm Orthogonalized by Newton-Schulz) updates into LSRTR by replacing the projection-based factor updates while preserving the original block coordinate scheme. Across synthetic linear, logistic, and Poisson LSR-TGLMs, LSRTR-M converges faster in both iteration count and wall-clock time, while achieving lower normalized estimation and prediction errors. On the Vessel MNIST 3D task, it further improves computational efficiency while maintaining competitive classification performance.", "id": "Paper/67197", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67197"}, {"title": " Crystals and spherical Schubert varieties ", "webprogram_exclude": "0", "session_ids": ["Session/18308"], "source_sha256": "20b95ac58117213a06d186e763a2e0bf4ce0ecd47a12045456a58aee5a6103ab", "withdrawn": "", "abstract": "Let a general linear group act on a partial flag variety transitively, and consider the induced action of its Levi subgroup $L$. A Schubert variety is \\emph{$L$-spherical} if it is stable under $L$-action and contains a dense open orbit of a Borel subgroup of $L$. It is \\emph{toric} if $L$, in addition, is a torus. In this talk, we will give a combinatorial classification of $L$-spherical Schubert varieties in partial flag varieties. This is achieved by applying Lakshmibai-Seshadri paths forming crystal graphs of Demazure modules. Previously, Hodges and Lakshmibai classified $L$-spherical Schubert varieties in Grassmannians. $L$-spherical Schubert varieties in complete flag varieties were treated independently by Gao--Hodges--Yong and Can--Saha. Our classification generalizes and unifies these results.", "id": "Paper/67198", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67198"}, {"title": " Generative Modeling of Resilience Trajectories in Alzheimer’s Disease ", "webprogram_exclude": "0", "session_ids": ["Session/17970"], "source_sha256": "f96e68b191b7f1ccbcf7e06e6045608bc2903c942508261cb7fff5105c0508a5", "withdrawn": "", "abstract": "Biological data is often high-dimensional and complex, making the direct analysis and prediction of such data difficult. Variational autoencoders (VAEs) encode high-dimensional data into a lower-dimensional probabilistic latent space, and analyses in these latent spaces can uncover complex dynamics and interactions in the original, higher-dimensional space. Traversal through latent spaces learned from high-dimensional biological data can enable the identification of sets of features contributing to specific continuous outcomes. However, such traversal is challenging due to the complexity and nonlinearity of these spaces, particularly across data types (e.g., genetic and behavioral). In this talk, we will present novel methods for trajectory generation and sampling in structured biological latent spaces, with emphasis on spaces learned by a conditional-Gaussian mixture VAE. In particular, to facilitate continuous generation through areas of the latent space corresponding to highly variable input features, we created a method for constructing uniform samples in small hyperspheres along a generated trajectory, revealing the local properties of that region. We further developed a procedure using barycenters of generated distributions to characterize between-condition latent space regions. We will show applications of these novel techniques to characterizing mechanisms of resilience in Alzheimer’s disease via trajectory generation and analysis in cognitively aligned VAE latent spaces.", "id": "Paper/67199", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67199"}, {"title": " MSRI-UP 2027 Projects ", "webprogram_exclude": "0", "session_ids": ["Session/17987"], "source_sha256": "c6689106db25a12e02ab37367ca8265b0a4b014c7bd6d3cfed0cf83f01a5b9ea", "withdrawn": "", "abstract": "The association between waist circumference and type 2 diabetes prevalence is well established as nonlinear, but whether it has shifted as U.S. obesity patterns have changed over the past two decades remains largely unexamined. This talk presents an REU 2027 project that addresses this gap. The project models the association using a varying-coefficient generalized additive model (GAM) with automated variable selection, applied to NHANES data spanning 1999–2023. The model allows this relationship to change smoothly across survey years, rather than assuming it remains the same over time. This makes it possible to assess whether the diabetes risk threshold associated with waist circumference has shifted. It also identifies which covariates help explain that shift. Existing NHANES studies have not addressed these questions, since they typically rely on regression models with a fixed functional form or on smoothing methods applied to a single time period. These findings could help public health researchers better target screening and prevention efforts toward the populations most at risk. Beyond presenting this project, the talk will briefly introduce two additional REU research components: education statistics and labor economics. All three are situated within a broader six-week undergraduate research program in applied statistics.", "id": "Paper/67200", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67200"}, {"title": " Cluster Structures on Semisimple Groups ", "webprogram_exclude": "0", "session_ids": ["Session/18278"], "source_sha256": "c3ec630747955a957846acd695a1ab7d7d5b6a4ca152295035807bb261f91586", "withdrawn": "", "abstract": "Cluster algebra structures on simply connected complex semisimple Lie groups were introduced by Bernstein, Fomin, and Zelevinsky as well as by Gekhtman, Shapiro, and Vainshtein.  In this talk, I will discuss cluster algebra structures on semi simple groups without assuming that they are simply connected.", "id": "Paper/67203", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67203"}, {"title": " The Stability of Folk Theorem Equilibria with Imperfect Costly Monitoring ", "webprogram_exclude": "0", "session_ids": ["Session/19353"], "source_sha256": "c682ee59747de8bb4166168e0edcb532f82a0fdc6533e1d74f13975f751cc095", "withdrawn": "", "abstract": "We study the stability of Folk Theorem outcomes in indefinitely repeated Prisoner's Dilemma games in which monitoring is imperfect and, critically, \\emph{costly and endogenous}: players choose not only a stage-game action but also an information-acquisition intensity that controls the precision of the private signal they subsequently receive about their opponent's behavior. We show that a version of the Folk Theorem survives this extension: for any feasible, individually rational payoff vector and any admissible cost function, there exists a discount factor threshold above which the payoff vector is sustainable as a subgame-perfect equilibrium, with monitoring intensity chosen optimally along the equilibrium path. Our principal theoretical contribution is a stability analysis of the equilibrium payoff correspondence $V(\\sigma^2,c)$: we prove that this correspondence is upper hemicontinuous in the baseline noise variance $\\sigma^2$ and the cost function $c$, establish a comparative-statics result showing that the correspondence is monotonically shrinking (in the Hausdorff sense) in both arguments, and derive an explicit threshold cost level above which sustaining near-efficient outcomes requires strictly greater patience. We complement the analytical results with an evolutionary agent-based simulation in which a heterogeneous population of monitoring strategies -- blind free-riders, fixed-overhead monitors, and trust-adjusted adaptive monitors -- competes under mutation and selection, alongside a persistent adversarial subpopulation designed to probe for exploitable blind spots. The simulation corroborates the theoretical prediction that endogenous, trust-contingent monitoring dominates both blind cooperation and static monitoring once an adversarial threat is present, while illustrating that the presence of such a threat introduces persistent volatility into aggregate welfare even after the population has converged on the theoretically optimal strategy class.", "id": "Paper/67209", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67209"}, {"title": " Homological properties of invariant rings of permutation groups ", "webprogram_exclude": "0", "session_ids": ["Session/18030"], "source_sha256": "81cefff14b0693c5fda37739e73bf0eb7f5ddd7be832cb5177215f620b72648a", "withdrawn": "", "abstract": "Consider the action of a finite group $G$ on the polynomial ring $S := k[x_1, \\ldots, x_n]$ by degree-preserving automorphisms, and consider the ring of invariants $S^G$. It is well-known that the functor of invariants is not exact in positive characteristic and several key isomorphisms break down in this case. Nevertheless, we show that if $G$ acts by permuting variables and the characteristic of $k$ is not two, then the following are independent of $k$, and may thus be computed using characteristic zero techniques: the $a$-invariant of $S^{G}$, the property of $S^{G}$ being quasi-Gorenstein, and the Hilbert functions of the local cohomology modules $H_{\\mathfrak{m}}^{n}(S)^{G}$ and $H_{\\mathfrak{n}}^{n}(S^{G})$; moreover, these Hilbert functions coincide. Additionally, we determine the ring of $k$-linear differential operators on $S^{G}$, and show that each differential operator lifts to one over $\\mathbb{Z}$.", "id": "Paper/67210", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67210"}, {"title": " Using Sparse Compositional Network Inference to Characterize Coral Microbiome Dynamics During Transplantation ", "webprogram_exclude": "0", "session_ids": ["Session/17756"], "source_sha256": "bdc1d82abe8ceb45b06c4f98ee0b502b18a3815903162d739783ae321e49d905", "withdrawn": "", "abstract": "Coral transplantation is widely used in reef restoration, yet the microbial mechanisms underlying successful acclimatization remain poorly understood. Microbiome studies present significant statistical challenges because 16S rRNA sequencing data are high-dimensional, sparse, and compositional, making standard correlation-based analyses potentially misleading. In this work, we investigate how sparse graphical modeling techniques can be used to infer and compare microbial interaction networks associated with coral transplantation. We focus on two dominant coral species, Porites lobata and Porites cylindrica, monitored during an 18-week transplantation experiment with samples collected at three time points. Microbial association networks were constructed from 16S rRNA amplicon sequencing data using SparCC, SPIEC-EASI, and graphical LASSO (gLASSO), three approaches designed to address the challenges of compositional data while producing sparse network estimates. We compare the resulting networks through graph-theoretic measures, including degree, betweenness, eigenvector centrality, PageRank and quantify changes in network topology across time and host species. Our analysis examines the stability of inferred hub taxa across inference methods and identifies topological features that consistently characterize microbiome restructuring during acclimatization. By evaluating how different sparse network inference procedures influence conclusions regarding keystone taxa and community organization, this work provides a mathematical framework for studying ecological networks in compositional settings. The results offer insight into coral microbiome resilience while highlighting the broader role of sparse graphical models and network theory in the analysis of complex biological systems.", "id": "Paper/67213", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67213"}, {"title": " Assessment of Statistical Coupling Between Bacterial and Algal Microbiomes in Transplanted  Porites  Corals ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "d1f1859e70612fbf9a053007fffdbed0e5835bdab6cd9b3d8836b6bc0dd33776", "withdrawn": "", "abstract": "Rising sea temperatures and other anthropogenic stressors are degrading coral reefs worldwide, and coral resilience depends in part on the coral's microbial partners: its bacterial community and its algal symbionts (\\textit{Symbiodiniaceae}). Whether these two communities shift together during transplantation in cross-domain \"coupling\" is a natural question for restoration monitoring. Using published 16S data and raw ITS2 sequence data from a \\textit{Porites} transplantation experiment on Guam (Lock et al. 2025), we tested for bacterial-algal coupling four weeks after transplantation (48 samples) with Mantel permutation tests, repeated across two dissimilarity metrics (Bray-Curtis and centered log-ratio (CLR)-based Aitchison distance) and two taxonomic resolutions per community. A family-level bacterial table (aggregated from 18,240 16S ASVs) versus algal OTUs under Bray-Curtis showed a statistically significant correlation (Mantel r = 0.29, p = 0.002). The signal collapsed when the algal side was refined to ASVs (r = 0.02, n.s.), under the compositionally corrected Aitchison distance (r = 0.10, n.s.), and when the dominant taxa (\\textit{Cladocopium} C15; \\textit{Endozoicomonadaceae}) were removed. We conclude that the apparent coupling is resolution- and metric-dependent and dominance-driven: it is not evidence of biological interaction between the two communities, though it also does not demonstrate independence. The methodological point stands showing that microbiome coupling claims should be stress-tested across taxonomic resolutions, dissimilarity metrics, and dominance structure before any biological interpretation is drawn.", "id": "Paper/67216", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67216"}, {"title": " Using Network Analysis on Dominant Reef-Flat Porites Corals’ Bacteriomes During Transplantation to Identify Species-Specific Acclimatization Strategies ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "fb137286479d1468ca99788b46c95b4c54c5a001164ebfed78bfc0518d921167", "withdrawn": "", "abstract": "Coral reefs worldwide experience environmental stressors that disrupt coral-bacterial interactions critical to coral health and survival. Coral transplantation is widely used to restore stressed reefs, yet bacteriome dynamics during acclimatization remain poorly understood. To investigate these dynamics, we apply graph-theoretic network centrality measures to characterize the acclimatization strategies of two dominant coral species, \\textit{Porites lobata} and \\textit{Porites cylindrica}, transplanted into coral garden plots. DNA metabarcoding data collected over an 18-week acclimatization period enabled the identification of bacterial genera. Correlations among bacterial genera were inferred using the SparCC algorithm across time points and coral species. The resulting correlation networks revealed notable differences in pre-transplantation network structure between the two \\textit{Porites} species. For both species, closeness and degree centrality scores generally declined over time, whereas betweenness centrality increased throughout the acclimatization period. In addition, the most influential bacteriome families, identified through eigenvector centrality, shifted substantially across time points, with opportunistic taxa occupying increasingly central positions following transplantation. Overall, bacteriomes restructured from densely connected to sparser networks by the end of the 18-week period. These findings provide new insights into coral-associated bacteriome stability and resilience and highlight factors that should be considered in coral reef restoration efforts.", "id": "Paper/67218", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67218"}, {"title": " Linear and Energy-Stable Convex Splitting for the Parabolic Sine-Gordon Equation and Its Applications ", "webprogram_exclude": "0", "session_ids": ["Session/19344"], "source_sha256": "ea7153333485abfe49177067b82109c2ca8dd18dba69fe956f7870757d590466", "withdrawn": "", "abstract": "In this talk, we present an unconditionally energy-stable convex splitting scheme for the parabolic sine-Gordon equation. \nBy decomposing the energy functional into two convex parts, the proposed scheme leads to a linear system at each time step, guaranteeing unique solvability, high computational efficiency, and preservation of the discrete maximum principle. \nTo achieve higher temporal accuracy, we further extend the formulation using the convex splitting Runge--Kutta method to obtain second-order temporal accuracy while preserving energy stability. \nSpatial discretization is performed using a standard finite difference scheme. \nNumerical experiments in two and three dimensions show theoretical accuracy, unconditional energy stability, and expected physical dynamics, such as mean curvature flow. \nFinally, we discuss the applicability and extensions of this linear convex splitting approach.", "id": "Paper/67219", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67219"}, {"title": " Unsuited Hands in Finite and Infinite Decks ", "webprogram_exclude": "0", "session_ids": ["Session/17106"], "source_sha256": "11e4c186437717b44f31dd2efca0d494ec285cba1f5d6974c7cb1b4518851d49", "withdrawn": "", "abstract": "Every hand starts with one suit, but how long must we deal before\nevery player holds at least two? We study a game in which each player\nreceives one card per round and play ends when all hands contain\ntwo distinct suits, or when a finite deck is exhausted. Independent\ndraws from equally likely suits lead to exact stopping distributions\nand moments for any fixed number of players. For two players sharing\na balanced finite deck with two suits, inclusion--exclusion accounts for the dependence\nbetween hands, and every positive integer moment converges to its\ninfinite-deck counterpart as the deck grows. We then replace\none-suitedness by the requirement that a specified suit occupy more\nthan a given proportion of the hand. The ballot theorem gives special\ncases, while Sparre Andersen's one-sided identity gives an exact single-player\nsurvival generating function and recurrence for every real threshold\nbetween zero and one. We characterize the possible first-failure\nrounds and derive moment formulae when the threshold exceeds the suit\nprobability. These variants connect geometric\nwaiting times, inclusion--exclusion, and lattice-path first passage,\nwhile distinguishing the effects of dependence from those of a\nchanging hand condition.", "id": "Paper/67221", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67221"}, {"title": " A fast third-order predictor-corrector method for nonlinear fractional differential equations ", "webprogram_exclude": "0", "session_ids": ["Session/19344"], "source_sha256": "d5e1e237e7558edd6bb6c74e9e1ab4beb9b49d4abd77ba59cf47608072794f2b", "withdrawn": "", "abstract": "We propose a fast predictor-corrector method for nonlinear fractional differential equations with the Caputo fractional derivative, based on piecewise quadratic interpolation and a sum-of-exponentials (SOE) approximation of the power-law kernel.\nThe third-order predictor-corrector method of Nguyen and Jang (2017) attains a convergence rate independent of the fractional order under suitable regularity assumptions, but evaluating its memory term requires $O(N^2)$ operations and $O(N)$ storage.\nThe proposed method reduces these to $O(NN_{\\exp})$ operations and $O(N_{\\exp})$ storage while preserving the accuracy of the original method.\nWe also investigate accuracy loss associated with limited temporal regularity and provide cancellation-safe expressions to address catastrophic cancellation in the evaluation of the history term.\nSeveral numerical examples confirm the convergence rate and the reduction in computational cost.", "id": "Paper/67222", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67222"}, {"title": " Volume-guided selection for hierarchical Vecchia approximation ", "webprogram_exclude": "0", "session_ids": ["Session/18032"], "source_sha256": "af57092569fc753cf3b3b57a98032c295b04b9aa76a29af535a800558ca9204c", "withdrawn": "", "abstract": "Positive-definite matrix approximations are widely used to scale kernel methods in machine learning and statistics to large data sets. Particularly powerful approaches exploit hierarchical off-diagonal low-rank structure. The Vecchia approximation can recover this structure while preserving positive definiteness and accessing only a small fraction of the matrix entries. I will present a volume-guided method for adaptively selecting columns in a hierarchical Vecchia approximation.", "id": "Paper/67223", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67223"}, {"title": " Agentic AI for Linear Algebra Education ", "webprogram_exclude": "0", "session_ids": ["Session/18225"], "source_sha256": "2316261abe01c53e5f81b0240ff4dc296d0495c7ad0b8596c7c88d81f9e2dcc2", "withdrawn": "", "abstract": "This MATLAB demo highlights how agentic AI can help students explore the role of linear algebra across diverse application domains. Students can seamlessly discover how core concepts such as eigenvalues, matrix factorizations, and singular value decomposition underpin real-world problems in science and engineering.", "id": "Paper/67232", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67232"}, {"title": " Asymmetry of curl eigenfields solving Woltjer’s variational problem ", "webprogram_exclude": "0", "session_ids": ["Session/18104"], "source_sha256": "fa01acf7b4925ab7e465362988eeecd8e638019994ea01a88921aa169afdb41f", "withdrawn": "", "abstract": "In the late 50s Woltjer proposed the idea that magnetic fields in astrophysical plasmas tend to relax so as to minimise their energy while conserving a quantity known as \\emph{helicity} - the average linking between pairs of magnetic field lines. Later in the 70s, Taylor applied this idea to other contexts, such as laboratory plasmas where these magnetic fields get the name \\emph{Taylor states}. The variational problem of minimising $L^2$ energy while keeping helicity fixed is known to have minimisers which are certain principle eigenfields of the curl operator. These eigenfields live in a domain of the curl for which its inverse is compact and self-adjoint. \n\nThis talk will be on recent joint work with Peralta-Salas (ICMAT) and Pfefferl\\'e (University of Western Australia) on the construction of rotationally symmetric toroidal domains for which\n\\begin{enumerate}\n    \\item principle curl eigenspace is simple so that all principle eigenfields are symmetric, and \n    \\item others for which \\emph{no} minimiser is symmetric.\n\\end{enumerate}\nThis serves as another counterexample to the folk wisdom that ``principal eigenfields must inherit the symmetries of the domain\" and demonstrates a stark contrast between the curl operator and the Laplacian on functions.", "id": "Paper/67233", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67233"}, {"title": " A <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"5.761ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 2480.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">HOD</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-48\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 219 683Q260 681 355 681Q389 681 418 681T463 682T483 682Q499 682 499 672Q499 670 497 658Q492 641 487 638H485Q483 638 480 638T473 638T464 637T455 637Q416 636 405 634T387 623Q384 619 355 500Q348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504Q674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660Q586 677 588 679T604 682Q609 682 646 681T740 680Q802 680 835 681T871 682Q888 682 888 672Q888 645 876 638H874Q872 638 869 638T862 638T853 637T844 637Q805 636 794 634T776 623Q773 618 704 340T634 58Q634 51 638 51Q646 48 692 46H723Q729 38 729 37T726 19Q722 6 716 0H701Q664 2 567 2Q533 2 504 2T458 2T437 1Q420 1 420 10Q420 15 423 24Q428 43 433 45Q437 46 448 46H454Q481 46 514 49Q520 50 522 50T528 55T534 64T540 82T547 110T558 153Q565 181 569 198Q602 330 602 331T457 332H312L279 197Q245 63 245 58Q245 51 253 49T303 46H334Q340 38 340 37T337 19Q333 6 327 0H312Q275 2 178 2Q144 2 115 2T69 2T48 1Q31 1 31 10Q31 12 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-44\" d=\"M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-48\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-4F\" x=\"888\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-44\" x=\"1652\" y=\"0\"></use>\n</g>\n</svg> Characterization of the Reals of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"6.395ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 2753.4 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">M_{2n+1}</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4D\" d=\"M289 629Q289 635 232 637Q208 637 201 638T194 648Q194 649 196 659Q197 662 198 666T199 671T201 676T203 679T207 681T212 683T220 683T232 684Q238 684 262 684T307 683Q386 683 398 683T414 678Q415 674 451 396L487 117L510 154Q534 190 574 254T662 394Q837 673 839 675Q840 676 842 678T846 681L852 683H948Q965 683 988 683T1017 684Q1051 684 1051 673Q1051 668 1048 656T1045 643Q1041 637 1008 637Q968 636 957 634T939 623Q936 618 867 340T797 59Q797 55 798 54T805 50T822 48T855 46H886Q892 37 892 35Q892 19 885 5Q880 0 869 0Q864 0 828 1T736 2Q675 2 644 2T609 1Q592 1 592 11Q592 13 594 25Q598 41 602 43T625 46Q652 46 685 49Q699 52 704 61Q706 65 742 207T813 490T848 631L654 322Q458 10 453 5Q451 4 449 3Q444 0 433 0Q418 0 415 7Q413 11 374 317L335 624L267 354Q200 88 200 79Q206 46 272 46H282Q288 41 289 37T286 19Q282 3 278 1Q274 0 267 0Q265 0 255 0T221 1T157 2Q127 2 95 1T58 0Q43 0 39 2T35 11Q35 13 38 25T43 40Q45 46 65 46Q135 46 154 86Q158 92 223 354T289 629Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-4D\" x=\"0\" y=\"0\"></use>\n<g transform=\"translate(970,-150)\">\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-32\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-6E\" x=\"500\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-2B\" x=\"1101\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-31\" x=\"1879\" y=\"0\"></use>\n</g>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18589"], "source_sha256": "f40eca357ca133cad6fd8aeabc387c24c3dbd8fa23cd702bd00e37be1dfb76e4", "withdrawn": "", "abstract": "$Q$-theory extends the basis theory of the hyperarithmetic reals to the higher odd levels of the projective hierarchy. Assuming PD, $Q_{2n+1}$ consists of those reals that are $\\Delta^1_{2n+1}$-definable from a countable ordinal. I will focus on $Q_3$, the first case beyond the hyperarithmetic reals, and its connection with $M_1$, the minimal mouse with one Woodin cardinal. I will give a characterization of the reals of $M_1$ as the hereditarily-OD reals of $L[x]$ whenever $x$ computes $M_1^\\sharp$. These techniques can be further extended to characterize the reals of $M_{2n+1}$. This is joint work with Farmer Schlutzenberg.", "id": "Paper/67234", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67234"}, {"title": " Analysis of the Ekman model with general power-law eddy viscosity ", "webprogram_exclude": "0", "session_ids": ["Session/18370"], "source_sha256": "0432116043165165d969d792d737a5d1144bc96c489c0961cc790591b6560737", "withdrawn": "", "abstract": "The Ekman model is a system of first-order linear ODEs, which provides a simplified description of fluid motion under ideal atmospheric conditions. It encodes a balance between wind velocity, Earth's rotational force, and the fluid’s internal friction, the latter of which is modeled by an elevation-dependent quantity $K(z)$, called the eddy viscosity. Remarkably, these forces are enough to describe the spiraling phenomenon of ocean currents at varying heights, i.e., \\textit{Ekman spirals}, that we observe in reality. We study the Ekman model for the power-law viscosities $K(z) \\sim  z^\\alpha$ over the domain $[z_0, \\infty)$ for $\\alpha \\in \\mathbb{R}$ and with the no-slip condition at the bottom layer $z = z_0$. Previous literature has only treated special choices of $\\alpha$, but erroneously. Ultimately, our work extends previous treatments to any possible power $\\alpha\\in\\mathbb{R}$. In doing so, we also correct the literature for the special cases. We furthermore establish exact representations of the velocity components $(u, v)$ for all power-law exponents. Lastly, we propose an alternative approach to studying the dependence of deflection angle, a characteristic quantity of Ekman spirals, on $\\alpha$, by studying ratios of Wronskians of Kelvin functions.", "id": "Paper/67235", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67235"}, {"title": " On polynomial matrix factorization using Trimmed Sylvester matrices ", "webprogram_exclude": "0", "session_ids": ["Session/18229"], "source_sha256": "d02f2399eb4f4397a5173b7c37998bd750ed0025c9dac0fe8cb21caa645b167a", "withdrawn": "w", "abstract": "Factorization of polynomial matrices is a fundamental tool in systems and control theory, playing a central role in isolating controllable and uncontrollable subsystems, computing kernel representations and intersection of several behaviors. While factorization and greatest common divisor computation for scalar polynomials are well established, the factorization of polynomial matrices remains less developed.\n\nWe developed an algebraic framework for the computation of Greatest Common Right Divisor (GCRD) of a set of given polynomial matrices without explicit symbolic computations. We introduce a formulation based on sructured Trimmed Sylvester matrices, a class of submatrices of Sylvester matrices, and establish a central theoretical result: the rank deficiency of a suitably constructed Trimmed Sylvester matrix is related the degree of the determinant of the GCRD.\n\nBuilding on this property, we propose an exact algorithm that employs a QR decomposition directly on the Trimmed Sylvester matrix to recover the coefficients of a GCRD with a special property that the upper triangular matrix can be additionally used to compute some speicific integer invariants related to the given polynomial matrices.", "id": "Paper/67236", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67236"}, {"title": " Robust sensor coverage in the presence of spatial obstacles and exclusion zones ", "webprogram_exclude": "0", "session_ids": ["Session/18245"], "source_sha256": "900499f0c85ba375e56f2e8c572ae263ac57a75900701152b57cfcb13ab42d6d", "withdrawn": "", "abstract": "In this article, we develop a robust optimization framework for obstacle-aware aerial directional sensor networks operating under positional uncertainty using a sector-based sensing model. The monitoring area is discretized into grid points and a unified geometric formulation is developed to model directional sensing while explicitly accounting for obstacle-induced visibility loss and exclusion regions. To enhance sensing performance under uncertainty, three progressive optimization strategies, namely robust aerial grid coverage (RAGC), robust aerial target coverage (RATC) and robust aerial target scheduling (RATS), are proposed. The framework employs robust orientation optimization based on the radius of robust feasibility to maximize effective grid and target coverage under sensor perturbations, followed by a target-aware sleep scheduling mechanism that minimizes the number of active sensors without compromising target monitoring. Extensive simulations under varying target distributions, obstacle configurations, uncertainty levels and sensor failure scenarios demonstrate that the proposed framework achieves robust and energy-efficient sensing while consistently outperforming representative approaches from the literature in terms of coverage quality, target monitoring and sensor utilization.", "id": "Paper/67237", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67237"}, {"title": " <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.066ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 889.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">K</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-4B\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-theory of Segre monoid algebras ", "webprogram_exclude": "0", "session_ids": ["Session/19342"], "source_sha256": "101d4a0215854e14ae588b21f51934478faa1f050bcc1dbd98ab3e38c4c48b21", "withdrawn": "", "abstract": "Let $R$ be a commutative Noetherian regular ring containing $\\mathbb{Q}$ and $R[M]$ the monoid algebra defining the homogeneous coordinate ring of the Segre embedding of $\\mathbb{P}^r_R\\times\\mathbb{P}^s_R$ to $\\mathbb{P}^{r+s+rs}_R$ for all $r, s \\ge 1$. We show that the map $K_1(R)\\to K_1(R[M])$ is an isomorphism. We also calculate the higher $K$-theory of $R[M]$, when $R$ is a field. At the end, we provide an application to the Serre dimension of this monoid algebra.", "id": "Paper/67242", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67242"}, {"title": " Implementation of Mastery Quizzes in Developmental College Algebra Course ", "webprogram_exclude": "0", "session_ids": ["Session/18299"], "source_sha256": "c131feaaf99bac2e1f0c4c8c440b673159e0af795162770fda1859fe4c3e20c6", "withdrawn": "", "abstract": "Mastery based learning (Bergmann, 2023) is a classroom instruction approach that gives students an indefinite number of opportunities to demonstrate their learning through a cycle of preparation, assessment and feedback. In Fall 2026, I incorporated short mastery quizzes into my developmental college algebra course. Throughout the week students will learn about a new topic and take a mastery quiz on that topic the following week. To pass the quiz, students must answer all questions correctly. Otherwise, they will be offered a retake of the mastery quiz the following class. Subsequent retakes will be offered in office hours. Using student evaluation data, I will assess student’s perceptions of the mastery quizzes as a tool for their learning.", "id": "Paper/67245", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67245"}, {"title": " Examination of the Singular Solution and Envelope of the General Solutions of Clairaut’s Equation for Various Discrete Time Scales ", "webprogram_exclude": "0", "session_ids": ["Session/17446"], "source_sha256": "5e9788ff775991180bd2635d0236b603863e7bf46d841444d47d72137780986e", "withdrawn": "", "abstract": "In this work, we examine how the singular solution of the time scale Clairaut dynamic equation varies based on changes to the discrete time scale.  For the classic Clairaut differential equation, it is well known that the singular solution is the envelope of the general solutions.  We explore this relationship in the discrete setting for the time scale Clairaut equation.\n\nThe time scale calculus generalizes and unifies differential and difference equations, but also is a source of many interesting results that do not have a direct analog to these classic cases. A brief introduction to the key results of the time scale calculus that are used in this work will be provided.", "id": "Paper/67246", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67246"}, {"title": " Rees algebras of monomial ideals ", "webprogram_exclude": "0", "session_ids": ["Session/17373"], "source_sha256": "b4e30098ccc2562b05a8697e4e7f87901547a63fb0d9a59a8e963c7b06d2d0d5", "withdrawn": "", "abstract": "The Rees algebra is a classical object in commutative algebra which encodes asymptotic properties of an ideal $I$ such as the syzygies of powers $I^k$. In this talk, we consider the Rees algebra of a monomial ideal in a polynomial ring over a field, and show that the defining ideal of the Rees algebra of $I$ is generated by Sylvester forms.", "id": "Paper/67247", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67247"}, {"title": " Positive Weighted Curvatures on Compact Manifolds with Convex Boundary and Proper Manifolds ", "webprogram_exclude": "0", "session_ids": ["Session/17803"], "source_sha256": "01aed7e3eaf9874259f168802f20c96cc8d9237de772a6bf522b5dd825bd3171", "withdrawn": "", "abstract": "Given a Riemannian manifold $(M,g)$ equipped with a positive density function $f = e^{-\\varphi}$, we study the weighted sectional curvature $\\overline{\\sec}_\\varphi(U,V)$ and the $k$-th intermediate weighted Ricci curvature $\\overline{\\text{Ric}}_{\\varphi,k}(U,V)$. We show that $\\overline{\\sec}_\\varphi(U,V)$ and $\\overline{\\text{Ric}}_{\\varphi,k}(U,V)$, together with the weighted second fundamental form $\\widetilde{\\mathrm{I\\!I}}$, play central roles in controlling the topology of the manifold. Using the theory of $\\widetilde{C}(k)$ functions, variational methods, and Morse theory, we prove that by imposing suitable restrictions on these quantities, an $n$-dimensional compact manifold with boundary or a proper open $n$-dimensional manifold is diffeomorphic to an $n$-ball or to a certain CW complex. This shows that such rigidity phenomena is not confined in the unweighted case, but persist in the weighted setting as well. These results extend classical theorems from the unweighted setting to the weighted case, demonstrating that $\\overline{\\sec}_\\varphi(U,V)$ and $\\overline{\\text{Ric}}_{\\varphi,k}(U,V)$ provide effective tools in Riemannian geometry.", "id": "Paper/67250", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67250"}, {"title": " A Trilogy of Algorithmic Mathematical Art: Polynomiography, Modulography, and Triangulography ", "webprogram_exclude": "0", "session_ids": ["Session/18554"], "source_sha256": "36de8c165941e2b33583c4f2740203b6359a5fb0b41c3fc6fdfeaa7220c26965", "withdrawn": "", "abstract": "This talk presents a trilogy of algorithmic mathematical art arising from my research on properties of polynomials, polynomial root-finding, linear programming, and computational geometry.\n\nPolynomiography visualizes root-finding algorithms for complex polynomials, producing striking images far beyond familiar Newton fractals. Modulography visualizes level curves of the modulus of a polynomial and the regions they enclose. Guided by the Geometric Modulus Principle, it shows how critical points organize ascent and descent in the modulus landscape, giving rise to a distinct class of images called modulographs. Triangulography is based on the Triangle Algorithm, a method I developed for convex-hull membership: determining whether a given point lies in the convex hull of a finite set of points. This simply stated problem is fundamental in linear programming, machine learning, computational geometry, and statistics. In two dimensions, the algorithm is simple enough to be explained to a child, yet its constructions, enhanced by intricate artistic coloring, can produce images reminiscent of the geometric art of Piet Mondrian and other artists of the De Stijl movement.\n\nEach form supports numerous techniques, visual styles, animations, design objects, and educational activities. The images are rendered through implementations of the underlying mathematical algorithms. AI can serve as a conversational interface, allowing the programming layer to recede into the background without making the images “AI-generated.” Because AI systems may produce visually plausible but mathematically inaccurate results, fidelity to the prescribed algorithms must be checked carefully.\n\nRepresentative artworks from all three forms will be presented. The talk will also discuss selected mathematical and computational questions arising from the underlying algorithms. Additional examples and links to related publications will be made available online.", "id": "Paper/67263", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67263"}, {"title": " Computational Modeling of Bayesian Decision-Making in Uncertain Environments: Analysis of Human Behavioral Data ", "webprogram_exclude": "0", "session_ids": ["Session/19322"], "source_sha256": "c1bcae159fa1c517ffec0dfc1be3e26a51bedc9dc22246d66152c24d2d27d88b", "withdrawn": "", "abstract": "People rarely make decisions with complete information in the real world. Humans must often act under uncertainty, drawing on data that is incomplete and noisy. In many situations, additional information can reduce uncertainty, but obtaining that information carries a cost. To model how humans decide to seek costly information to improve their choices, we study information-seeking behavior in a sequential decision-making task under dynamically changing conditions, and compare human behavioral data with the predictions of an optimal Bayesian model. The model combines belief updating with finite-horizon dynamic programming to compute decision policies under stochastic state transitions and costly information gathering. Using computational simulations and policy analyses, we characterize how optimal decision thresholds vary across time as a function of uncertainty and environmental instability. We then compare model predictions with the choices of human participants to evaluate how closely human strategies align with normative computations. Preliminary results suggest that participants often acquire costly information less frequently than predicted by the optimal model, while also displaying suboptimal information-seeking behavior in specific belief regions. These results provide preliminary evidence that human information seeking is shaped not only by uncertainty, but also by systematic biases and constraints that lead to predictable deviations from optimal behavior.", "id": "Paper/67265", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67265"}, {"title": " CANCELLED DG methods for the approximation of multiphase flows in heterogeneous porous media. \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/17850"], "source_sha256": "bf32436cfcb37b135ac43a42bc43c419a5b4ffe344fe6296c6a2a17f3fcb5dd0", "withdrawn": "", "abstract": "Flows in highly heterogeneous media arise in many problems such as oil and gas recovery from subsurface reservoirs, carbon geological storage or groundwater contamination. The mathematical modeling of such processes is given by the coupling of mass conservation equations, one for each phase considered (e.g liquid, gas), leading to a coupled systems of nonlinear partial differential equations with space-time dependent coefficients. To approximate numerically the solution of such problems, we propose to combine a sequential approach with a stabilization technique leading to time-independent stiffness matrices that can be assembled and preconditioned at initialization. After establishing the convergence properties of our method, we will validate numerically on various setups involving either manufactured solution, injection-extraction problems and viscous fingering generation in highly heterogeneous media.", "id": "Paper/67267", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67267"}, {"title": " Permutation Statistics from Random Pipe Dreams ", "webprogram_exclude": "0", "session_ids": ["Session/19321"], "source_sha256": "00a49adfa6ed61576fe06c0d75c91270a25efeeaea70262e8070a03eef33445d", "withdrawn": "", "abstract": "Working in the symmetric group $\\mathfrak{S}_n$, fix a finite word $\\mathsf{w}$ over the alphabet of adjacent transpositions $\\{s_1,\\ldots, s_{n-1}\\}$. For a fixed probability $p \\in (0,1)$, we obtain a random subword $\\mathsf{v}$ of $\\mathsf{w}$ by independently deleting each letter with probability $1-p$. Composing the letters of $\\mathsf{v}$ gives a random permutation $v \\in \\mathfrak{S}_n$. In 2024, Defant, Morales, Panova, Petrov, and Yeliussizov studied this random deletion process via a connection to \\textit{random pipe dreams}. In particular, for a large class of initial words $\\mathsf{w}$, Defant determined an asymptotic formula for the expected number of inversions of $v$. We prove a mixing lemma for pipes in infinite pipe dreams and use it to compute local permutation statistics of $v$. Addressing a question of Morales, Panova, Petrov, and Yeliussizov, we compute permuton limits for random deletion from the word $\\textsf{w}^{(n)}_{\\text{staircase}}= (s_{n-1})(s_{n-2}s_{n-1}) \\ldots (s_1 \\ldots s_{n-1})$ as $n \\to \\infty$ and $p_n \\to 1$.", "id": "Paper/67268", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67268"}, {"title": " Generalizing CROCKER Plots for Two-Dimensional Bifurcation Analysis ", "webprogram_exclude": "0", "session_ids": ["Session/18008"], "source_sha256": "2a93cf0a0b8228d7c46133f36566b55949e0b53f405e087a338c65b93d1f469b", "withdrawn": "", "abstract": "Topological data analysis provides a coordinate-free perspective on how dynamical systems evolve under varying conditions. In our previous work, we utilized CROCKER plots to track topological features—specifically, Betti numbers across varying filtration scales—to detect phase transitions along a single control parameter [1].\n\nThis talk builds on that foundation by extending the methodology to multi-parameter spaces, focusing on systems driven by two independent parameters. Transitioning to a 2D parameter grid introduces significant geometric complexity. Instead of relying on traditional analytical mappings, we generalize the CROCKER representation to capture these multi-parameter boundaries dynamically. By transforming phase space trajectories into multi-dimensional topological surfaces, we can identify structural stability changes and phase transitions purely through the persistence of data shape. We will discuss the theoretical setup for constructing these generalized representations and outline computational strategies for extracting topological signatures across a 2D grid. Ultimately, this approach offers a purely data-driven alternative for mapping complex dynamical behaviors where classical analytical methods become computationally or geometrically prohibitive.\n\nAcknowledgment: This research is supported by the European Union’s Horizon Europe research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 101271995 (TOPOCLIM-EWS).\n\nReferences:\n[1] Güzel, İ., Munch, E., Khasawneh, F.A., (2022). Detecting bifurcations in dynamical systems with CROCKER plots. Chaos: An Interdisciplinary Journal of Nonlinear Science, 32(9), 093111.", "id": "Paper/67270", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67270"}, {"title": " Exploring Body Duress Imposed by Different Dance Styles Through Cluster Analysis ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "ccb7bad98c752f771c1b0823c4297d2478338433430adf332a5c254cd50ce184", "withdrawn": "", "abstract": "There are many styles of dance ranging from fiery salsa to grounded hip hop to light and airy ballet. As a dance and statistics double major, I am excited to investigate how body velocities, alignments and angles of executing the same dance moves in different dance styles can be used to reveal similarities, differences and the duress of the dance movements. This project uses a mixed dataset on performances of similar dance moves by different dance styles and is analyzed using KAMILA (k-means for mixed large data) clustering algorithm to uncover hidden patterns. The patterns are further evaluated in comparison of four well known and seemingly different dance styles. A series of hypothesis tests are used to further confirm the significance of clustering. I will discuss the clustering uncovered and how the dance styles present different or similar strains on the body when performing the different dance movements.", "id": "Paper/67280", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67280"}, {"title": " Pattern-avoiding Cayley permutations ", "webprogram_exclude": "0", "session_ids": ["Session/17943"], "source_sha256": "bfc5be2d2429d94f4839fc2c24c07f30fbf5f44705914b485e078b72518afccc", "withdrawn": "", "abstract": "In this talk, we study pattern avoidance in the context of Cayley permutations, introduced by Mor and Fraenkel in 1984. A Cayley permutation is a finite sequence of positive integers containing at least one copy of each integer between 1 and its maximum value. We take a combinatorial species-first approach, when possible, to enumerating Cayley permutations avoiding patterns of length two and three, as well as pairs of such patterns. Our goal is to describe the corresponding species and derive exponential generating series and explicit counting formulas. We conclude with several conjectures and open problems.", "id": "Paper/67281", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67281"}, {"title": " On the inductive Feit condition ", "webprogram_exclude": "0", "session_ids": ["Session/17832"], "source_sha256": "ac38ae92e570b69944e5b9b55d03e80fc5443e60e6c41a9c0c4f63a7d6cdc371", "withdrawn": "", "abstract": "A long-standing conjecture of Walter Feit, dating back to 1979, can be approached through a more recent character-theoretic problem formulated in the work of R. Boltje, G. Navarro, A. Kleshchev, and P. Tiep. Roughly speaking, the problem asks whether the irrationalities occurring in the character of a non-linear primitive irreducible representation of a finite group can always already be detected inside a proper self-normalizing subgroup.\n\nThe problem admits a reduction to finite simple groups. I will explain what condition needs to be proven and describe some progress in the case of finite groups of Lie type, which is the last open family of simple groups.", "id": "Paper/67282", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67282"}, {"title": " Effects of infinite parameter limits on the structural identifiability of linear compartment models ", "webprogram_exclude": "0", "session_ids": ["Session/18319"], "source_sha256": "eb2aace7b38636cb951e793f3dee41971d3e8b6f876e2be24ac2192619957934", "withdrawn": "", "abstract": "Structural identifiability answers the theoretical question of which parameter combinations of a mathematical model can be uniquely recovered from ideal, noise-free input–output data. However, in many biological applications, systems may operate in near-limiting conditions (e.g. timescale separation). Structural identifiability has been long studied on biological systems, such as those represented by linear compartment models, but the effects of singular parametric limits on a model's structural identifiability has received less attention. In this work, we investigate how structural identifiability of linear compartment models is affected under singular limits in which a single parameter is sent to infinity. Such limits induce a collapse of the underlying graph that resembles an edge contraction and results in a reduced model, potentially changing the identifiability of the system in the process. Here, we show that the limit and the transfer function commute---namely that the transfer function of the original model converges to the transfer function of the collapsed model under the infinite limit of a single parameter. From this result, we can identify which parameter combinations survive the singular limit and characterize the resulting changes to model identifiability, particularly the degeneracies that result and lead to parameter insensitivity. We illustrate these results on several families of linear compartment models, including mammillary, catenary, and cyclic networks, and discuss connections to model reduction and the geometry of parameter space under asymptotic limits.", "id": "Paper/67289", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67289"}, {"title": " On saturation numbers of diameter-4 trees ", "webprogram_exclude": "0", "session_ids": ["Session/18315"], "source_sha256": "db43dca1ce21a2cb1f57cb65d0327796861d245fc071c4996dc30a57315ef967", "withdrawn": "", "abstract": "Complementary to the foundational Tur\\'an number of a graph $H$ is the {\\em saturation number} $\\operatorname{sat}(n,H)$, the minimum size of a maximally $H$-free graph of order $n$ (maximal, that is, in the sense that adding any extra edge creates a copy of $H$). K\\'aszonyi and Tuza proved that $\\operatorname{sat}(n,H) = O(n)$ for every graph $H$, and general lower bounds have been obtained by Cameron and Puleo and by the author and Rombach. Both employ the initial observation that all but a small clique of vertices in any $H$-saturated graph have degrees at least $k_0 = \\min_{uv \\in E(H)}\\bigl\\{\\max \\{d(u), d(v)\\} - 1\\bigr\\}$. While the corresponding lower bound $\\operatorname{sat}(n,H) \\geq \\frac{k_0}{2} n - O(1)$ is sharp for only a few graph classes, such as stars, no trees have been known to have saturation numbers asymptotically greater than $\\frac{k_0 + 1}{2} n$. All paths and all trees of diameter at most $3$, for instance, are such that $\\operatorname{sat}(n,H) \\leq \\frac{k_0 + 1}{2} n + O(1)$. We determine saturation numbers asymptotically for an infinite class of diameter-$4$ trees for which the latter inequality holds. Along the way, we prove that this bound does not hold in general: for any $\\varepsilon > 0$ and any integer $k\\geq 2$, there are diameter-$4$ trees $H$ such that $k_0 = k$ and $\\operatorname{sat}(n,H) > (k - \\varepsilon) n$ for all sufficiently large $n$.", "id": "Paper/67290", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67290"}, {"title": " Quasi-Monte Carlo Beyond Hardy-Krause via Online Thinning ", "webprogram_exclude": "0", "session_ids": ["Session/17807"], "source_sha256": "d22d227f2379b01085c827c75f920267a56ea94f3dab3144ae7f8d425467fd77", "withdrawn": "", "abstract": "Numerical integration studies how well one can estimate the integral of a function $f$ over $[0,1)^d$ using $n$ sample points. The two classical methods, Monte Carlo (MC) and quasi-Monte Carlo (QMC), have complementary strengths and weaknesses, and a fundamental question is to design an approach that combines the benefits of both. \nRecently, building on the transference principle in discrepancy theory, [Bansal, Jiang, SODA 2025] gave a randomized QMC method that bridges MC and QMC guarantees using only i.i.d.\\ samples. Their method also goes beyond the classical Koksma--Hlawka inequality: it achieves integration error $\\widetilde{O}_d(\\sigma_{\\mathsf{SO}}(f)/n)$, where the smoothed-out variation $\\sigma_{\\mathsf{SO}}(f)$ can be substantially smaller than the Hardy--Krause variation that governs the classical bound. However, their algorithm requires $n^2$ i.i.d.\\ samples as input, and this quadratic blowup is inherent to any method based on the transference principle.\n\n\nIn this work, we bypass the quadratic blowup: for any constant $\\varepsilon > 0$, we show that $(1+\\varepsilon)n$ i.i.d.\\ samples suffice to both obtain the beyond-Hardy--Krause guarantee of [Bansal, Jiang, SODA 2025], resolving an open problem posed there, and to produce low-discrepancy point sequences. Our algorithms are variants of the online Haar-thinning method of Dwivedi, Feldheim, Gurel-Gurevich, and Ramdas [Dwivedi, Feldheim, Gurel-Gurevich, Ramdas, Probab. Theory Relat. Fields, 2019].", "id": "Paper/67291", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67291"}, {"title": " Collected Coin Game (Bulgarian Solitaire) ", "webprogram_exclude": "0", "session_ids": ["Session/18062"], "source_sha256": "445cfebd9cd641360834ff2696315c3d90f3005c65be9bbc459457b404bd9171", "withdrawn": "", "abstract": "A player begins with coins arranged in distinct piles. At each turn, she removes one coin from each pile to form a new, single pile. Repeating this operation eventually leads to a previously encountered arrangement, terminating in a cycle. This process raises natural mathematical questions: Where are the fixed points? Do 2-cycles exist? Which states are cyclic and how can we visualize the process?\n\nPopularized by Martin Gardner in his 1980s Scientific American columns and collected in his 1997 book The Last Recreations, Bulgarian Solitaire provides an inviting gateway to discrete dynamical systems, integer partitions, and state graphs. This presentation will explore mathematical properties of this process and share free classroom-ready resources for introducing the game to students.", "id": "Paper/67296", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67296"}, {"title": " A Topological Measure of Stability for the Classical K-Means Algorithm ", "webprogram_exclude": "0", "session_ids": ["Session/18114"], "source_sha256": "1452963f28312f4683465ed68849c487acc709593d5584582a84b6ca426a0802", "withdrawn": "", "abstract": "The classical k-means algorithm is sensitive to perturbations in the underlying data, but its stability is typically studied through the lens of changes in cluster assignments or the value of the clustering objective. This talk develops a topological approach to quantifying such stability. Given a finite point configuration and a k-means clustering, we associate Vietoris--Rips filtrations to the resulting clusters and use persistent homology to quantify topological changes induced by perturbations of the data. \n\nWe establish bounds relating pointwise perturbations of the data to changes in the k-means objective. An objective-gap condition guarantees that sufficiently small perturbations preserve the optimal partition, while a separate Voronoi-margin condition guarantees preservation of pointwise assignments. Under these stability conditions, we bound the Gromov-Hausdorff distance between corresponding clusters and use stability results for Vietoris-Rips persistence to bound the resulting change in persistence diagrams. \n\nThese results lead to a metric-based notion of topological stability that complements assignment-based notions of clustering stability. In particular, we give examples showing that a clustering can remain stable at the level of pointwise assignments while undergoing substantial topological change. The approach provides a connection between geometric perturbation theory, optimization-based clustering, and persistent homology.", "id": "Paper/67297", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67297"}, {"title": " Levi-spherical matrix Schubert varieties ", "webprogram_exclude": "0", "session_ids": ["Session/18308"], "source_sha256": "5ec5d71f985b9592cac96e3e4491679c6fe6e23a98cc621ed81c13ee1a1da9c2", "withdrawn": "", "abstract": "Matrix Schubert varieties, introduced by Fulton in 1992, are certain generalizations of determinantal varieties. They carry Levi group actions, and thus their coordinate rings are Levi-representations. A variety with an action of a Levi group $L$ is called \\emph{spherical} if a Borel subgroup of $L$ has a dense, open orbit, or equivalently, if its coordinate ring is multiplicity-free as an $L$-representation. In this talk, we present a combinatorial classification of Levi-spherical matrix Schubert varieties when the Levi group acting is maximal. This is joint work with Ada Stelzer.", "id": "Paper/67298", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67298"}, {"title": " Homogenization of a free boundary problem in one dimension ", "webprogram_exclude": "0", "session_ids": ["Session/18289"], "source_sha256": "8090f1123930945a1521ba86e5b9a624bdbfeb297ea12210de3e7159cf4f0040", "withdrawn": "", "abstract": "The focus of this talk is a free boundary problem of Hele-Shaw type that arises as a model of tumor growth in heterogeneous tissue. I will present a result on stochastic homogenization for this problem: that is, the coefficients are assumed to oscillate randomly at small scales, and we prove convergence to a deterministic PDE as the scale of oscillation approaches zero. Our result holds only in one spatial dimension; however, it is new even in the setting of periodic coefficients. Based on joint work with Yuming Paul Zhang.", "id": "Paper/67299", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67299"}, {"title": " Dynamics of a nonlocal weighted moving boundary model in time-periodic environments ", "webprogram_exclude": "0", "session_ids": ["Session/18289"], "source_sha256": "ac3759f66389ce3b88771f4f2e031418ed0323c6319159d352896f8bbf382884", "withdrawn": "", "abstract": "In this talk, we study a Fisher–KPP equation with a time-periodic logistic source and a nonlocal weighted moving boundary condition. We first establish a vanishing–balancing–spreading trichotomy for the system in time-periodic environments. In particular, we show that, as time evolves, the moving front may undergo periodic expansion and contraction. Under suitable assumptions, we then derive sharp criteria characterizing species vanishing and persistence. Finally, we present numerical simulations that illustrate and complement the theoretical results.", "id": "Paper/67300", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67300"}, {"title": " Learning from Helpful Feedback: Strategies for Self-graded Mathematics Homework ", "webprogram_exclude": "0", "session_ids": ["Session/18081"], "source_sha256": "4d133898ad70c434b6e32bc50a3a9e6e9257d6b8d05473e261effa1dd8ad3fab", "withdrawn": "", "abstract": "A cornerstone of alternative grading is providing actionable feedback—yet instructors frequently find that students overlook or misunderstand the comments they receive. To help close this feedback loop, I have spent several years implementation-testing self-grading strategies across mid-level and advanced university mathematics courses (including Discrete Mathematics, Linear Algebra, Abstract Algebra, and Graph Theory with class sizes of 20–30 students). This talk examines two primary self-assessment approaches: instructor-annotated solutions and generative AI (LLM) guidance. Findings indicate that students are fully capable of engaging in self-assessment, report higher perceived learning gains compared to traditional grading models, accept self-grading as a meaningful educational exercise, and show reduced reliance on unauthorized AI resources. Additionally, transferring grading responsibilities to students significantly reduces instructor workload, freeing up time for targeted support. I will share practical implementation logistics, assessment outcomes, recommendations for prospective adopters, and personal reflections.", "id": "Paper/67301", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67301"}, {"title": " Global dissipative solutions to the 3D Navier-Stokes and MHD equations ", "webprogram_exclude": "0", "session_ids": ["Session/18306"], "source_sha256": "615b36edb5adb4adc5743e04c2309841c7bde69b60e56ec48faf49bd31201fdf", "withdrawn": "", "abstract": "In this talk we will overview some recent results on dissipative solutions to the 3D Navier-Stokes and MHD equations. We will first show that, for arbitrarily prescribed finite energy divergence-free initial data, there exist infinitely many global-in-time weak solutions with continuous energy profiles to both the 3D deterministic and stochastic Navier-Stokes equations. Moreover, for the critical initial data, we prove the existence of infinitely many dissipative solutions to the 3D Navier-Stokes and MHD equations, whose energy profiles are continuous and decreasing on time. Our proof designs a telescoping convex integration scheme that takes advantage of the dissipative term. This talk is based on joint works with Alexey Cheskidov and Zirong Zeng.", "id": "Paper/67302", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67302"}, {"title": " Solutions of second order iterative boundary value problems with nonhomogeneous boundary conditions ", "webprogram_exclude": "0", "session_ids": ["Session/19369"], "source_sha256": "a7e2f89c86ddbd73e6b132e812b94a8d23adb91a57adfb6bc7b56993a79fe322", "withdrawn": "", "abstract": "We consider the existence and uniqueness of solutions to the second order iterative boundary value problem $u''(t) = f(t, u(t), u^{[2]}(t)), \\, a \\leq t \\leq b,$ where $u^{[2]}(t) = u(u(t))$, with solutions satisfying one of the following boundary conditions $u(a) = a, u(b) = b$ or $u(a) = b, u(b) = a$. The Schauder fixed point theorem is used to establish our results.", "id": "Paper/67304", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67304"}, {"title": " A Lefschetz Fixed Point Formula for Subelliptic Complexes on Contact Manifolds ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "67a9915206e0547140306c6ca4bdce95263534cb81a64b5c99b483f8dbf71a45", "withdrawn": "", "abstract": "In this poster, I present a Lefschetz fixed point formula for subelliptic complexes on contact manifolds, extending the classical Atiyah-Bott theorem from the elliptic setting to the contact/sub-Riemannian setting. Using heat kernel methods, subelliptic Hodge theory, and the Heisenberg tangent groupoid, the formula expresses the Lefschetz\nnumber as a sum of contributions from the fixed points. Examples illustrate how the result connects global topological invariants with local analytic data determined by the contact structure.", "id": "Paper/67308", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67308"}, {"title": " COFI-DQI: Solving Curve Optimal Function Intersection via Decoded Quantum Interferometry ", "webprogram_exclude": "0", "session_ids": ["Session/18020"], "source_sha256": "a2ee84e799aabdf7a194522b49c3c36f7840ad459933164fbd18666130bf641b", "withdrawn": "", "abstract": "In 2025, Jordan et al. introduced Decoded Quantum Interferometry (DQI), a decoding-based quantum algorithm for combinatorial optimization. Their framework uses Reed-Solomon decoding and gives rise to a dual optimization problem, termed Optimal Polynomial Intersection (OPI), for which DQI achieves a superpolynomial speedup over known classical algorithms. More recently, Jordan and Gu extended DQI to Hermitian codes and introduced Hermitian Optimal Polynomial Intersection (HOPI), providing evidence that the apparent quantum speedup of DQI extends to polynomial regression problems on algebraic curves.\n\nMotivated by the well-understood duality and decoding theory of algebraic geometry codes, we extend this framework to additional curve families and introduce Curve Optimal Function Intersection (COFI). We investigate COFI using codes from Suzuki curves and extended norm--trace curves and identify families that improve upon one-point Hermitian codes for the HOPI problem considered by Jordan and Gu. In particular, these curve families can reduce the quantum resources required by DQI while simultaneously allowing a larger number of constraints to be considered.", "id": "Paper/67309", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67309"}, {"title": " LoRA-CRAFT: Cross-layer Rank Adaptation via Frozen Tucker Decomposition of Pre-trained Attention Weights ", "webprogram_exclude": "0", "session_ids": ["Session/19350"], "source_sha256": "0acdfc5050165c45a30d9b13678c6a1e837d1d397520f235a38c81dbde59cc91", "withdrawn": "", "abstract": "Parameter-efficient fine-tuning (PEFT) methods adapt large pre-trained models while updating only a small number of parameters, but most existing approaches treat transformer layers independently. We introduce LoRA-CRAFT, a tensor-based PEFT method that exploits cross-layer structure in pre-trained attention weights. For each adapted projection, attention weight matrices from all transformer layers are stacked into a third-order tensor and decomposed by a Tucker-3 higher-order singular value decomposition (HOSVD). The Tucker core and factor matrices are frozen, and adaptation is performed only through small trainable square matrices acting on the frozen factors, together with a residual formulation that preserves the original pre-trained weights at identity initialization.\n\nFor fixed Tucker ranks, the number of CRAFT adaptation parameters is independent of both model width and depth. We also provide theoretical results on HOSVD approximation, the expressiveness of the resulting tensor orbit, and gradient behavior at initialization. Experiments on GLUE with RoBERTa-base and RoBERTa-large and on commonsense reasoning benchmarks with LLaMA2-7B and LLaMA3-8B show that CRAFT achieves competitive accuracy with extremely small trainable parameter budgets. The results illustrate how multilinear structure in pre-trained attention weights can be used to design highly parameter-efficient adaptation methods for large language models.", "id": "Paper/67316", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67316"}, {"title": " Rotational Control of Sedimentation in a Cone–Fluid System ", "webprogram_exclude": "0", "session_ids": ["Session/18240"], "source_sha256": "bd66ab0be7736580ef37544a18b5c982ad0ecf1f57a863fbdaecf44df839c237", "withdrawn": "", "abstract": "We study the sedimentation of a freely translating, rotating conical body in an incompressible viscous fluid, with the goal of understanding how rotation and geometric asymmetry modify the net hydrodynamic force on the body. A motor-driven cone is released in a water tank, and its vertical trajectory is reconstructed from video under passive and actively rotating conditions. The dynamics are organized using the translational and rotational Reynolds numbers,\n\n$$ Re_U=\\frac{UR}{\\nu}, \\qquad Re_\\Omega=\\frac{\\Omega R^2}{\\nu}, $$\n\ntogether with \\(U/(\\Omega R)\\), which compares translational and rotational velocity scales. For the smallest cone tested, active rotation reduces the mean descent speed from approximately \\(4.27\\) cm/s to \\(1.65\\) cm/s, corresponding to a reduction of about \\(60\\%\\). We compare these measurements with numerical flow fields and examine how rotation modifies the surrounding pressure, vorticity, and wake structure. The results demonstrate a substantial rotation-induced change in sedimentation and provide a simple experimental and computational model for studying coupled rigid-body and viscous-flow dynamics.", "id": "Paper/67320", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67320"}, {"title": " Intertwining Results for Perturbations of Model Operators Associated to a Certain Class of Polydisc Inner Functions. ", "webprogram_exclude": "0", "session_ids": ["Session/17377"], "source_sha256": "b4c159645abb50c77b6f553f581b4fa5393a11bb1d81ed77d5213381eefeacc8", "withdrawn": "", "abstract": "Doubtsov in his seminal 2020 paper extended Clark's theory on the spectral measures associated to inner functions on the disc to inner functions $\\phi:\\mathbb{D}^n\\to\\mathbb{D}$ on the polydisc. Calzi in 2024 extended the theory further to the more general setting of bounded symmetric domains. \n\nAn interesting fact that distinguishes the one variable theory and the multivariable theory is that the Clark embedding operator $J_\\alpha:K_\\phi\\to L^2(\\mu_\\alpha[\\phi])$ is no longer guaranteed to be a unitary operator. Doubtsov gave a characterization for when the embedding operators are unitary, while Arora, Bickel, Liaw, and Sola (ABLS) gave necessary conditions for when these embedding operators intertwine a perturbation of the model operators on $K_\\phi$, and multiplication by the independent variables on $L^2(\\mu_\\alpha[\\phi])$. Furthermore, ABLS showed that for rational inner functions, if $\\alpha$ is a generic point, then the embedding operator is unitary and the intertwining relation holds.\n\nIn this talk, we enlarge the class of functions for which we know the intertwining relation holds. In particular, we show that if we have an inner function $\\phi:\\mathbb{D}^n\\to\\mathbb{D}$, and if there is a partition $P=\\{P_1,P_2,\\ldots,P_k\\}$ of the variables $z_1,\\ldots,z_n$ such that $$\\phi(z_1,\\ldots,z_n)=\\prod_{i=1}^k\\phi_i(P_i),$$ then $J_\\alpha$ is unitary for all $\\alpha$, and we have the intertwining relation between the model operators in each variable. As an intermediate step, we prove a structure result about Clark measures for inner functions of the above type.", "id": "Paper/67322", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67322"}, {"title": " On the well-posedness and solitary waves in higher-order KdV-type equations ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "2711ff85d66be295c812cbaba475b0e7da11ee17412367f91f14de130e562553", "withdrawn": "", "abstract": "We study the Cauchy problem for the fifth-order generalized Korteweg de Vries (5gKdV) equation with power-type nonlinearities, including the sublinear regime $(0<\\alpha<1)$. We prove local well-posedness for initial data in suitable weighted Sobolev spaces that encode spatial decay, and also show how the Kato smoothing-type estimates influence the choice of nonlinearities. These models arise in the study of weakly nonlinear dispersive waves, including plasma waves, gravity-capillary and capillary waves, and internal waves in stratified fluids. In addition, we perform numerical simulations to show solutions dynamics in this model.", "id": "Paper/67323", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67323"}, {"title": " Stories Behind the Graphs: Exploring Countries Through Mathematics ", "webprogram_exclude": "0", "session_ids": ["Session/17961"], "source_sha256": "8152365e8982cff5c257ecefcfa8a3170b7acafd5accda85ef4a754f677ea20a", "withdrawn": "", "abstract": "How can a graph become a starting point for mathematical curiosity, conversation, and real-world investigation? In this session, we share a hands-on Math Circle activity centered on exploring population pyramids. Rather than beginning with formulas or predetermined questions, students first examine population graphs, make observations and predictions, identify patterns and differences, and generate their own questions about what stories the graphs reveal. Students work collaboratively to interpret the graphs, compare trends across countries or time periods, and investigate students’ generated questions about different countries in the world using the available data.\n\nThe activity emphasizes noticing, wondering, prediction, question posing, mathematical reasoning, and collaborative sense-making, providing an accessible entry point for students with varied mathematical backgrounds. We will share prompts that instructors can use to move students from informal observations toward examining meaningful quantitative questions about the world around them. Participants will leave with a self-contained, adaptable lesson structure that can be readily implemented in a Math Circle, classroom, or outreach setting.", "id": "Paper/67324", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67324"}, {"title": " Interactivity, Fidelity, and Polish: Building Modern Math Illustration ", "webprogram_exclude": "0", "session_ids": ["Session/18366"], "source_sha256": "c14fd9b800b90429071ce55fc551111aad1e493419eb4b8664d28f8856239d34", "withdrawn": "", "abstract": "Visual representations of mathematical concepts are as old or older than the subject itself, but the use of technology as a medium remains nascent in comparison. The rapidly changing environment of screen sizes, input methods, and computational abilities presents a challenging space to enter, but also offers one of the most compelling and effective ways to communicate mathematical concepts directly. Over the past eight years, I have created nearly 50 web applets for visualizing math — ranging from art to teaching aids to tools for mathematicians and hobbyists — and I have been fortunate to see my work meet with a wide audience. In this talk, I share the most important lessons I have learned for creating and maintaining beautiful, engaging, and functional mathematical renderings, with the goal of helping people already in the space improve their work and convincing many more to join.", "id": "Paper/67330", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67330"}, {"title": " Ribbon concordance and finitely many fibered predecessors ", "webprogram_exclude": "0", "session_ids": ["Session/17916"], "source_sha256": "cbd550a676c7c9dfa58c91f46595d06a0deacc07e49ff7c363ab0d38b6f94669", "withdrawn": "", "abstract": "A ribbon concordance from one knot $J\\subset S^3$ to another knot $K$ is a smoothly embedded annulus in $S^3 \\times I$ with boundary $K \\sqcup -J$. Agol recently proved that this defines a partial order on  knots, answering a longstanding question of Gordon. But Gordon posed several other, as yet unsolved, questions in his original paper. One of these asks whether there exists an infinite strictly decreasing sequence of ribbon concordant knots. I'll discuss work with Sivek in which we pose and study the stronger conjecture that for each $K$ there are only finitely many $J$ which are ribbon concordant to $K$. We prove this for fibered $J$, using relationships between Floer homology and orbits of flows in fibered knot complements.", "id": "Paper/67331", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67331"}, {"title": " Nonlinear Diffusion and Density-Dependent Emigration: Interactions Governing Population Persistence ", "webprogram_exclude": "0", "session_ids": ["Session/17442"], "source_sha256": "8fe6f9b22e0c67929e563f0ebe6b6430dbc9c5c0c29f981c1143476f970c08eb", "withdrawn": "", "abstract": "We investigate the persistence of a population within a finite one-dimensional habitat patch by analyzing positive steady states of a reaction-diffusion model with nonlinear diffusion and density-dependent emigration. The model incorporates logistic population growth, density-dependent movement within the habitat, and density-dependent loss of individuals across the habitat boundaries. In particular, we study the two-point boundary value problem\n$\n    \\begin{cases}\n        -(\\phi(u)u')'=\\lambda u\\tilde f(u) ~;~ x\\in(0,1) \\\\\n        -u'(0)+\\sqrt{\\lambda}\\gamma G(u(0))u(0)=0 \\\\\n        u'(1)+\\sqrt{\\lambda}\\gamma G(u(1))u(1)=0,\n    \\end{cases}\n$\nwhere $\\lambda$ and $\\gamma$ are positive parameters, $\\phi$ characterizes density-dependent (nonlinear) diffusion, $\\tilde f$ describes density-dependent population growth, and $G$ characterizes density-dependent emigration at the habitat boundaries. We analyze the existence and structure of positive steady states and investigate how nonlinear diffusion, population growth, and boundary emigration interact to determine population persistence. In particular, we identify conditions under which a habitat patch can support a positive population and examine the resulting critical patch-size and bifurcation structure.", "id": "Paper/67332", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67332"}, {"title": " Noncrossing Combinatorics, the Full Twist, and Decategorification of Knot Invariants ", "webprogram_exclude": "0", "session_ids": ["Session/18286"], "source_sha256": "4b9d2b0daeaa4457804e5e3f696991bd999e761f2e4115cb37ea80995e8b7de1", "withdrawn": "", "abstract": "Much work in knot theory has consisted of categorifying, and thereby strengthening, knot invariants. We take the opposite approach: decategorification, more commonly called combinatorics. We introduce a technique that relates the dual braid group generators, the Hecke images of pure braids, and factorization problems in reflection groups to knot invariants. We prove that the $(a,z=0)$-HOMFLYPT polynomial can be computed as a solution to such a problem. This technique was motivated by Coxeter--Catalan combinatorics. For example, we give a new proof of EL-shellability of the noncrossing partition lattice using the image of the full twist in the Hecke algebra; in a surprising sort of combinatorial reciprocity, its inverse computes the homotopy type. Similarly, noncrossing partitions naturally arise from our construction applied to positive powers of the full twist, while cluster complexes come from the same construction applied to negative powers. In crystallographic type, we exploit the conjugacy of all Coxeter elements to give the first reflection subword models for rational noncrossing Catalan objects. Our reciprocity gives two models: one generalizing noncrossing partitions, and one generalizing clusters. Applying the same method produces two (rational) noncrossing parking models.", "id": "Paper/67333", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67333"}, {"title": " Compact strongly <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.678ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 722.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbb C</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJAMS-43\" d=\"M684 131Q684 125 672 109T633 71T573 29T489 -5T386 -19Q330 -19 276 -3T174 46T91 134T44 261Q39 283 39 341T44 421Q66 538 143 611T341 699Q344 699 364 700T395 701Q449 698 503 677T585 655Q603 655 611 662T620 678T625 694T639 702Q650 702 657 690V481L653 474Q640 467 628 472Q624 476 618 496T595 541Q562 587 507 625T390 663H381Q337 663 299 625Q212 547 212 336Q212 249 233 179Q274 30 405 30Q533 30 641 130Q658 147 666 147Q671 147 677 143T684 131ZM250 625Q264 643 261 643Q238 635 214 620T161 579T110 510T79 414Q74 384 74 341T79 268Q89 213 113 169T164 101T217 61T260 39L277 34Q270 41 264 48Q199 111 181 254Q178 281 178 344T181 434Q200 559 250 625ZM621 565V625Q617 623 613 623Q603 619 590 619H575L588 605Q608 583 610 579L621 565Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJAMS-43\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-convex hypersurfaces in <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"4.153ex\" height=\"2.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -1006.6 1787.9 1152.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbb C\\mathbb P^2</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJAMS-43\" d=\"M684 131Q684 125 672 109T633 71T573 29T489 -5T386 -19Q330 -19 276 -3T174 46T91 134T44 261Q39 283 39 341T44 421Q66 538 143 611T341 699Q344 699 364 700T395 701Q449 698 503 677T585 655Q603 655 611 662T620 678T625 694T639 702Q650 702 657 690V481L653 474Q640 467 628 472Q624 476 618 496T595 541Q562 587 507 625T390 663H381Q337 663 299 625Q212 547 212 336Q212 249 233 179Q274 30 405 30Q533 30 641 130Q658 147 666 147Q671 147 677 143T684 131ZM250 625Q264 643 261 643Q238 635 214 620T161 579T110 510T79 414Q74 384 74 341T79 268Q89 213 113 169T164 101T217 61T260 39L277 34Q270 41 264 48Q199 111 181 254Q178 281 178 344T181 434Q200 559 250 625ZM621 565V625Q617 623 613 623Q603 619 590 619H575L588 605Q608 583 610 579L621 565Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJAMS-50\" d=\"M16 666Q16 675 28 683H195Q334 683 370 682T437 672Q511 657 554 611T597 495Q597 343 404 309Q402 308 401 308Q381 303 319 303H261V181Q261 157 262 120Q262 60 267 50T304 36Q310 35 313 35Q352 35 352 17Q352 10 346 3L339 -1H28Q16 5 16 16Q16 35 53 35Q68 36 75 37T87 42T95 52Q98 61 98 341T95 630Q91 640 83 643T53 648Q16 648 16 666ZM235 35Q228 46 227 84Q226 129 226 337V621L230 635L237 648H128Q128 647 133 632Q136 620 136 341Q136 64 133 50L128 35H235ZM301 341H313Q339 341 354 344T389 362T417 410T426 498Q426 586 401 616T322 647Q301 647 293 643Q271 637 264 621Q261 617 261 479V341H301ZM429 350Q431 350 443 353T476 367T515 391T548 432T562 490Q562 550 524 592Q507 607 484 619Q481 621 448 635L433 639L439 621Q462 578 462 506Q462 448 454 413T437 366T428 350H429Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJAMS-43\" x=\"0\" y=\"0\"></use>\n<g transform=\"translate(722,0)\">\n <use xlink:href=\"#E1-MJAMS-50\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-32\" x=\"864\" y=\"581\"></use>\n</g>\n</g>\n</svg> without projective umbilic points ", "webprogram_exclude": "0", "session_ids": ["Session/18295"], "source_sha256": "e7221d41000cd981c38a4cea3e1fe0738b8b222f5cd2d20106c8b7066c89522a", "withdrawn": "", "abstract": "A real hypersurface $S\\subset\\mathbb C\\mathbb P^2$ is said to be {\\em strongly $\\mathbb C$-convex} if it is locally \nprojectively equivalent to a strongly convex hypersurface in $\\mathbb C\\mathbb P^2$. A {\\em projective umbilic point}\n$p \\in S$ is a point lying in a projective image of the sphere $S^3$ having third-order (or\nbetter) contact with $S$.\n\nIn earlier work the authors showed that all compact circular $S$ as above must contain\nat least one projective umbilic point.  The current talk will explain a (Claude-assisted) method for building\n(non-circular) $S$ with no projective umbilic poin", "id": "Paper/67334", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67334"}, {"title": " On Autoencoders for Inverse Problems ", "webprogram_exclude": "0", "session_ids": ["Session/18446"], "source_sha256": "40760c14fbd2a6f61ff8e5642446a4853b3cec6ebba6d3282a30c488467319f5", "withdrawn": "", "abstract": "In this talk, I will discuss a data-driven framework for inverse problems that combines dimensionality reduction with surrogate modeling by learning a pair of autoencoders trained on observations and target parameters.  By creating mappings between the low-dimensional, informative latent spaces of these autoencoders, the method provides efficient surrogate models for the forward and regularized inverse operators, enabling fast inversion during inference time and bypassing the need for an explicit forward model.  The approach is grounded in Bayes risk and empirical Bayes risk minimization theory, connected to classical techniques like principal component analysis in the linear setting.  The framework extends naturally to a nonlinear setting, with error and residual bounds under certain assumptions that are related to inexpensive metrics that the network structure affords.  These metrics can be used empirically to detect when a new sample lies out-of-distribution of the samples on which the network was trained, helping identify the scope of a trained model. The framework also provides natural ways to refine solutions using the learned latent spaces, which can be used to extend the applicability of a network to problems with different experimental setups.  Numerical illustrations show the applicability of this framework on challenging ill-posed problems in many imaging domains.", "id": "Paper/67337", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67337"}, {"title": " Practical Encrypted Face Recognition via Homomorphic Similarity Search ", "webprogram_exclude": "0", "session_ids": ["Session/18307"], "source_sha256": "d6e701e41d46780c17ceb4cdd387b88f627d678d35af66d32d394723af760fe0", "withdrawn": "", "abstract": "Face recognition matches a query template against a database of enrolled biometric vectors, an operation that is privacy-sensitive. Homomorphic encryption allows a server to perform the search directly on encrypted data, revealing nothing of the sensitive data, in this case, the facial images. In this talk, we present our practical encrypted face-recognition system using the fully homomorphic encryption CKKS scheme, which supports approximate arithmetic over a cyclotomic ring. The computation reduces to encrypted matrix–vector products, whose cost is dominated by ciphertext rotations, i.e., Galois automorphisms composed with key switching, and by the memory these keys consume. A baby-step/giant-step restructuring of the encrypted diagonal product lowers the rotation count from linear to square-root in the vector dimension and shrinks the rotation-key set by an order of magnitude. Further optimizations, including a packing technique that exploits the ring's conjugation automorphism to carry two coordinates per slot, together with system-level techniques, pushes the search to a million encrypted vectors in under a second.", "id": "Paper/67349", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67349"}, {"title": " Algebraic Structures on Sets of Partitions ", "webprogram_exclude": "0", "session_ids": ["Session/18239"], "source_sha256": "ea08765f0c185410f68db782c04188097cc353340f3cb5841375b986c2efda65", "withdrawn": "", "abstract": "A partition of an integer $n$ is a weakly decreasing sequence of positive integers which sum to $n$. Denote the set of all partitions by $\\mathcal{P}$. In this talk, we explore various binary operations on partitions to find an algebraic structure on $\\mathcal{P}$. In particular, we discover that $\\mathcal{P}$ is an abelian group under modified versions of concatenation, component-wise addition, and component-wise multiplication. We extend two partition groups to vector spaces over the finite field $\\mathbb{Z}_p$, where $p$ is a prime. We further discover that partitions are equipped with a commutative ring structure. Next, we consider subgroups, subspaces, and ideals of our algebraic partition structures to investigate properties of related types of restricted partitions. Finally, we explore various bijections between types of restricted partitions that appear in our algebraic structures.", "id": "Paper/67351", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67351"}, {"title": " Investigation of Thermal Instability in Inclined Couette–Poiseuille Flow ", "webprogram_exclude": "0", "session_ids": ["Session/19343"], "source_sha256": "c4f76178939789d4617f8217ba9d8a13f7a1d3baa97e2a6e95a856fa2025dc71", "withdrawn": "", "abstract": "This study investigates the onset of thermal instability in an inclined fluid layer subjected to Couette–Poiseuille flow, with one boundary maintained at a constant temperature and the other subjected to a constant heat flux. The stability characteristics are examined using a Chebyshev polynomial-based collocation method, with the thermal Rayleigh number serving as the principal instability parameter.\n\nThe results reveal the existence of a critical angle of inclination that separates two distinct instability regimes. Below this threshold, the system becomes unstable through longitudinal rolls, and the critical Rayleigh number remains unaffected by the superimposed Couette–Poiseuille flow. Beyond the critical angle, transverse modes become dominant, and the critical Rayleigh number exhibits a pronounced dependence on the imposed flow. Furthermore, the onset of instability is strongly influenced by the Prandtl number of the fluid.\n\nThese findings demonstrate the coupled effects of inclination, shear flow, and fluid properties on the transition to thermal convection and provide insight into the mechanisms governing the stability of inclined fluid layers under mixed boundary conditions.", "id": "Paper/67356", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67356"}, {"title": " The Math of Conservation: Why Preventative Control is Essential for Saving Tasmanian Wildlife ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "d46468d87ea485b3e809a734c1342a1fbc73315645f336630a8b587517a37aee", "withdrawn": "", "abstract": "Since European settlement, 34 Australian terrestrial mammal species have gone extinct, with invasive feral cats (Felis Catus) identified as a driving factor in these ecosystem losses. Determining which management strategies achieve meaningful, long-term increases in the native prey population remains a critical challenge for conservation efforts. To investigate this, we developed a mathematical model using non-linear ordinary differential equations to simulate predator-prey interactions between feral cats and native prey species in Tasmania, such as the Tasmanian swamp rat (Rattus lutreolus). Parametric variations were used to model specific control interventions, and then a sensitivity analysis was performed to understand which methods of control would have the largest effect on prey population. We evaluated control combinations varying in frequency, duration, and intensity, concluding that regular, preventative population control is necessary to produce sustained, meaningful protection for native prey species.", "id": "Paper/67367", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67367"}, {"title": " Hybrid Neural-Classical Correction for Frozen Time Series Foundation Models: A Comprehensive Ablation Study on High-Frequency Stock Prediction ", "webprogram_exclude": "0", "session_ids": ["Session/18124"], "source_sha256": "51b19d50538a037b524f20efd4ccdc6220660d75755dfaef783dd8da0f42a2a5", "withdrawn": "", "abstract": "Foundation models for time-series forecasting provide strong zero-shot performance across many domains, but their accuracy may deteriorate in specialized settings such as high-frequency financial markets. We study a hybrid correction framework for adapting a frozen TimesFM model to one-minute stock-return prediction during the opening trading hour. Premarket information is combined with the foundation-model forecast through lightweight neural correction modules, followed by Random Forest residual learning. We compare an attention-based architecture with a parameter-efficient bilinear-gated architecture and perform a systematic ablation study across 10 large-cap technology stocks and more than two million observations.\n\nThe hybrid models substantially improve predictive performance over frozen TimesFM. The best model achieves mean per-day correlation of 0.373 and pooled correlation of 0.597, compared with 0.059 and 0.061 for the uncorrected foundation model. The ablation results show that classical residual learning contributes as much as, and in some cases more than, the neural correction component, while self-attention provides the strongest positive neural-only contribution. A simpler bilinear-gated model attains the best overall performance using approximately nine times fewer neural parameters than the attention-based model.\n\nThese results suggest that effective adaptation of foundation models for financial time series can benefit from combining modern neural representations with classical statistical learning, while maintaining computational efficiency and strict temporal separation between training inputs and future returns.", "id": "Paper/67370", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67370"}, {"title": " Learning, Creating, Bonding, and Healing with Topological Crochet ", "webprogram_exclude": "0", "session_ids": ["Session/18216"], "source_sha256": "86520c21e646d8f695e2da68fba5924c48b0db758c3ce3f5dca5352b67ccfc19", "withdrawn": "", "abstract": "What if abstract topological surfaces could be explored not only through diagrams and equations, but by making them with our own hands? Topological crochet turns ideas from algebraic topology into tangible objects that can be constructed, manipulated, and explored through creative practice. In doing so, it offers an accessible, hands-on approach to learning mathematical ideas that are often considered highly abstract.\n\nIn this talk, I will introduce topological crochet through concrete examples including M\\\"{o}bius bands, connected sums, projective planes, and Klein bottles. A topological skeleton provides a blueprint for growing a crocheted surface, allowing mathematical structure to guide the making process. At the same time, the process of making can provide new ways of seeing and understanding mathematical structures and relationships. Thus, the interaction is not simply mathematics translated into art, but a two-way exchange between mathematical thinking and creative practice.\n\nI will share how this approach grew from my own journey from theoretical physics and mathematics to fiber art, and how it has developed into workshops, exhibitions, collaborations, and a forthcoming book. I will also reflect on experiences of sharing topological crochet with diverse communities, where making together has created opportunities for learning, connection, joy, and healing. Through these experiences, I hope to show how the arts can provide not only new ways to teach and learn mathematics, but also new ways to experience mathematics together.", "id": "Paper/67378", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67378"}, {"title": " Bicrystalline ideals ", "webprogram_exclude": "0", "session_ids": ["Session/18253"], "source_sha256": "c4b51cda243769acedd05d5f0a89cc9e4ce3ab8751096e8f129a78db8d172252", "withdrawn": "", "abstract": "When an ideal $I$ carries an action of some reductive group $G$, $I$ decomposes into a direct sum of irreducible $G$-representations. In this talk, we give a combinatorial rule for computing these irreducible multiplicities when $I$ is \\emph{bicrystalline} and $G$ is a product of general linear groups. We present various examples of bicrystalline ideals and describe an algorithm that decides whether a given ideal is bicrystalline. This is joint work with Ada Stelzer and Alexander Yong.", "id": "Paper/67380", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67380"}, {"title": " A Weak Modified Euler Method and its Stability Analysis. ", "webprogram_exclude": "0", "session_ids": ["Session/19344"], "source_sha256": "5b89d4d66603fac12a1cfb21b3b29cbe26b30ca2ec46576ee726a37468f05ee9", "withdrawn": "", "abstract": "The proposed weak modified Euler method effectively mitigates the numerical instabilities frequently encountered in standard explicit Euler method. Local and global approximation theorems are rigorously established to formalize its convergence properties. Furthermore, we determine the mean-square stability domain of the weak scheme for linear stochastic differential equations (SDEs) subject to multiplicative noise and derive explicit step-size bounds that ensure controlled error propagation. Finally, illustrative numerical examples are presented to validate the theoretical findings.", "id": "Paper/67385", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67385"}, {"title": " Battling Invasive Cats in Tasmania: Mathematical Models on Population Reduction of Feral Cats ", "webprogram_exclude": "0", "session_ids": ["Session/19353"], "source_sha256": "85eadb31885091840b2f03e8fd8e14dbe1c4503ff90e17722e1e1ac1e34c5c76", "withdrawn": "", "abstract": "The introduction of feral cats to Australia has caused native species populations to collapse, leading to frighteningly low population numbers and extinction. Tasmania has one of Australia’s most intact ecosystems, making it imperative that we protect and preserve its native flora and fauna. Our goal is to determine meaningful management strategies to increase native prey populations over the coming years. We developed a mathematical model using non-linear ordinary differential equations to simulate predator-prey interactions between feral cats and native prey species in Tasmania, such as the Tasmanian swamp rat (Rattus lutreolus) and the long-tailed mouse (Pseudomys higginsi). Parametric variations were used to model specific control interventions, and then a sensitivity analysis was performed to understand which methods of control would have the largest effect on prey populations. We evaluated control combinations varying in frequency, duration, and intensity, and predicted population dynamics in the coming years.", "id": "Paper/67386", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67386"}, {"title": " Candidate and voter incentives for strategic voting under instant runoff voting and Condorcet methods ", "webprogram_exclude": "0", "session_ids": ["Session/18097"], "source_sha256": "8b6e1c7d23fe96f735bb9d6bade8cdc5edd4dafdb1c7506d17a81f19f4da5413", "withdrawn": "", "abstract": "Instant runoff voting (IRV) and Condorcet methods are two of the most prominent alternatives to plurality voting for single-winner elections. Using ranked-ballot data from real-world elections and large collections of synthetic elections, we compare the incentives for strategic voting created by these methods. We find that under IRV, strategic incentives tend to occur near the top of the ballot, where voters may benefit from abandoning a sincere favorite for a more viable candidate. Under many Condorcet methods, strategic incentives instead arise farther down the ballot, particularly through truncation and burying. We also find that some Condorcet methods are much more resistant to strategic voting than others. We discuss what these differences mean for both voters and political campaigns.\n\nWe supplement these results with survey data collected in collaboration with the Electoral Competition Center. These surveys allow us to examine what happens when IRV and Condorcet methods select different winners. In particular, we consider how the two methods can reward different patterns of voter support and how the treatment of lower-order preferences affects both election outcomes and opportunities for strategic behavior.", "id": "Paper/67392", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67392"}, {"title": " Hopf algebras on graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18134"], "source_sha256": "9b798c4db36a517cb53f87db16ae9086ca435e7bfc20c766f00d72614fe386c2", "withdrawn": "", "abstract": "Combinatorial Hopf algebras are a fundamental organizational tool for ranked combinatorial data.  Categorifying these structures via the representation theory of a tower of finite groups has the effect of selecting natural bases to work with that generally have beneficial structural properties (integral structure constants, orthogonality with respect to a canonical inner product, etc.).  There are a wide variety of graph types (trees, labeled vertices, unlabeled vertices, etc) where one might want a representation theoretic interpretation of the corresponding Hopf algebras.  This talk explores a more comprehensive approach using the additive group of finite nilpotent upper triangular matrices.", "id": "Paper/67393", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67393"}, {"title": " Computing <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.583ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 681.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">L</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4C\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-4C\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-polynomials of genus 2 and genus 3 curves ", "webprogram_exclude": "0", "session_ids": ["Session/18263"], "source_sha256": "40fcc9056c8ffbc3f157003591a4f3bf901a3c8ec92ddccacc0bd4a5d0dc674e", "withdrawn": "", "abstract": "Let $C$ be a curve over $\\mathbb{Q}$ of genus 2 or 3. At a prime $p$ of good reduction, its $L$-polynomial is the numerator of the zeta function of the reduction of $C$ at $p$. For genus 2 curves, Harvey and Sutherland’s implementation of Harvey’s average polynomial-time algorithm computes these $L$-polynomials modulo $p$ at all primes of good reduction in a given range. For genus 3 curves that arise as smooth plane quartics, the work of Costa, Harvey, and Sutherland also provides an average polynomial-time algorithm for $L$-polynomials modulo $p$ at good primes in a given range.\n\nIn this talk, I will present Las Vegas algorithms that compute the $L$-polynomials by lifting these modulo $p$ coefficients to integer coefficients. The genus 2 lifting algorithm runs in average polynomial time. The genus 3 lifting algorithm has an average running time of  $O(p^{1/4+o(1)})$ , under heuristic assumptions. Combined with the work to compute the modulo $p$ coefficients, these lifting algorithms yield significant speedups over existing methods for computing $L$-polynomials.", "id": "Paper/67394", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67394"}, {"title": " Making room for all: A UDL-aligned inquiry-oriented approach to Sequence and Series ", "webprogram_exclude": "0", "session_ids": ["Session/18200"], "source_sha256": "943fe1354225f64ceaf986bcb49d1fd872cb8b78838be08a85f0479c013a58bd", "withdrawn": "", "abstract": "A growing body of research highlights the potential of inquiry-oriented (IO) instruction to enhance undergraduate student learning. During IO instruction, students are guided to build their own knowledge by engaging in mathematical practices. This type of instruction is built around social interaction, such as contributing and sharing reasoning with peers and instructors. Thus, instruction must be carefully designed to accommodate the different ways students participate. In our NSF project titled \"Collaborative Research: Designing for All - An Inquiry-Oriented Approach to Calculus Sequence and Series with Universal Design for Learning,\" we are developing an inquiry-oriented approach for a unit on sequence and series (IOSS) in Calculus that incorporates Universal Design for Learning (specifically, UDL-Math) principles to attend to students’ unique strengths and needs. During this presentation, we will share tasks designed to support students' reinvention of some of the theorems typically covered in the calculus unit on sequences and series such as the Monotone Convergence Theorem and the Test for Divergence. Throughout, we will share the instructor’s role in this reinvention, including how the instructor can provide diverse opportunities for student participation, as well as ways that students experienced these tasks and instruction. We will further engage the audience in discussing UDL-aligned IO practices and how they might open up opportunities to participate in inquiry classes, inviting interested instructors to join our ongoing work adapting the task sequence for their own context and instructional strengths.", "id": "Paper/67397", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67397"}, {"title": " Multi-Scale Visualization of Mapper Graphs via Filtration ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "f88d247024cef024154ca7041470fd55ef88ea10b8b12e51f3fb97d2da426a61", "withdrawn": "", "abstract": "Topological Data Analysis (TDA) provides powerful tools for understanding high-dimensional data by capturing its underlying shape and structure. Mapper, a widely used TDA algorithm, creates a graph that enables the visualization of complex data structures and can reveal significant patterns that may not be evident through traditional statistical methods. One of the main challenges in using Mapper is parameter selection; small variations in parameter choices can significantly impact the resulting graph structure. In this work, we use a filtration of Mapper graphs to visualize Mapper's output from a multi-scale perspective.\n\nWe focus on parameter changes that produce a filtration of Mapper graphs (or more generally Mapper simplicial complexes),\n\\[\nK_1 \\xrightarrow{f_1} K_2 \\xrightarrow{f_2} \\cdots \\xrightarrow{f_{m-1}} K_m,\n\\]\nwhere consecutive complexes are connected by simplicial maps. We develop computational methods for constructing, validating, and visualizing these maps. This framework allows us to track vertex correspondences, node mergers, and other structural changes across consecutive Mapper complexes, helping us identify which features persist across parameter choices and which appear only at particular settings.", "id": "Paper/67398", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67398"}, {"title": " Alexander- and Markov-Type Theorems for Flat Virtual Singular Braids ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "db4a6bcdb5bf35aaf4efcc02c6b55d19914c29afcf63919f4be1d270853c38c4", "withdrawn": "", "abstract": "We introduce and study flat virtual singular braids and links. Motivated by classical results in knot theory, we develop a braiding algorithm for flat virtual singular links using L-moves adapted to this setting. We prove an Alexander-type theorem showing that every flat virtual singular link can be represented as the closure of a flat virtual singular braid, and a Markov-type theorem characterizing when two flat virtual singular braids have equivalent closures.", "id": "Paper/67400", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67400"}, {"title": " Islamic art beyond periodicity ", "webprogram_exclude": "0", "session_ids": ["Session/18216"], "source_sha256": "114d43572c4eac568bf4ec9d7a215f5db1e37a4d4ececfdf4e10b843b22e22ad", "withdrawn": "", "abstract": "Traditional Islamic art builds on different notions of periodicity (rotational symmetry, tessellations, construction lines) to create beautiful designs. We present three different sets of activities to broaden students' conceptions of creativity in math. We discuss traditional Islamic art principles, Jennifer Padilla's Islamic art based on Penrose tilings, and expand to the more recent \"Einstein\" hat tiling.", "id": "Paper/67401", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67401"}, {"title": " Average twin prime conjecture for elliptic curves in arithmetic progressions ", "webprogram_exclude": "0", "session_ids": ["Session/18380"], "source_sha256": "30360320802890f80b70131f26757208f0174ed99067c8411865aefaaacd2441", "withdrawn": "", "abstract": "In 1988, Koblitz conjectured an asymptotic formula for the number of primes $p \\le x$ for which the reduction of an elliptic curve over $\\mathbb{Q}$ has prime order. Building on the work of Balog, Cojocaru, and David, who proved this conjecture on average in 2011, we extend the result to primes $p$ lying in arithmetic progressions. Our asymptotic formula holds uniformly for moduli up to a fixed power of $\\log x$. We also show that the resulting average constant matches the theoretical constant predicted by Lee, Mayle, and Wang in 2025 using Galois representations.", "id": "Paper/67402", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67402"}, {"title": " Bond-failure in peridynamics: nonequivalence of critical stretch and critical energy density criteria ", "webprogram_exclude": "0", "session_ids": ["Session/18378"], "source_sha256": "e5bc7dfa7c7330c1b2bcb86d31ff17249263b735756e2417d72c7b4c14fb6dc9", "withdrawn": "", "abstract": "To model material fracture, peridynamics introduces the concept of bond-failure, meaning that a bond is no longer able to transfer forces between material points. We prove that the two most used bond-failure criteria in the literature, namely, the critical stretch and critical energy density criteria, are not equivalent in general. In fact, using them indistinctly result in different bond-breaking dynamics and fracture phenomena. We also show how to precisely identify the influence functions for which the two criteria coincide. Numerical examples showcase the striking differences between the effect of the two criteria for different choices of influence functions on crack dynamics, including the crack tip evolution, crack propagation, and crack branching. This is joint work with Pablo Seleson (Oak Ridge National Laboratory) and Mary Vaughan (Texas State University).", "id": "Paper/67404", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67404"}, {"title": " A Transfer Approach for Unfitted Discretizations of Glacier Flow ", "webprogram_exclude": "0", "session_ids": ["Session/18367"], "source_sha256": "d31413cb1e3193afdc9f9e9a5bb8e3c0e60c0a8409d7d0025365cb54e1771ef0", "withdrawn": "", "abstract": "Glacial ice can be modeled as an incompressible and highly viscous fluid. Its evolution over time is governed by mechanical properties such as internal stress, pressure, and velocity as well as its interactions with the environment through temperature variations, snowfall, and melting. Mathematically, this can be modeled by a system of PDEs that is obtained from conservation of mass and momentum together with constitutive laws. Further analysis of the relevant physical parameters leads to simplifications resulting in a nonlinear system known as “the full Stokes model” in the glaciology community. A major computational challenge arises from the complex and evolving geometry of the glacier domains. Fitted meshes may require computationally expensive remeshing along the glacier boundary, thus motivating the use of unfitted discretization techniques. We investigate a transfer approach in which the physical boundary is represented independently of the computational mesh.", "id": "Paper/67408", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67408"}, {"title": " Hyperfiniteness of generic Z wr Z actions. ", "webprogram_exclude": "0", "session_ids": ["Session/18213"], "source_sha256": "1d1caca7caba52c2f3ccf0216417bf8e599661c5513e9139ec893fc8fdeb8733", "withdrawn": "", "abstract": "Given a countable group G, there is a natural Polish space of continuous actions of G on the cantor space. There is then hope that one can gain understanding of the dynamics of G actions by studying which properties hold generically (i.e., on a comeager set) in this space. \n\nFor example, Weiss's question asks whether the (orbit equivalence relations of) actions of amenable G are hyperfinite. A weaker but still very open question is whether the generic action of such a G is hyperfinite. Iyer and Shinko initiated this line of research and proved that if G (amenable or not) has finite asymptotic dimension, its generic action is hyperfinite. In joint work with Shinko, we prove a generalization of this result, a special case of which is that the generic action of Z wr Z is hyperfinite. We discuss extensions to solvable and even elementary amenable groups.", "id": "Paper/67410", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67410"}, {"title": " Knitting a Gyroid ", "webprogram_exclude": "0", "session_ids": ["Session/18232"], "source_sha256": "7e0aba55254976cd1a0ba2c91c1c75e07811fe724696f85c84216e7516ab3211", "withdrawn": "", "abstract": "Making a gyroid has been a long-term goal of mine as a math artist. In this talk, I describe a fiber-art construction of the gyroid, a triply periodic minimal surface, using a discretization based on Alan Schoen’s uniform gyroid. The resulting structure can be viewed as hyperbolic hexagons with four hexagons meeting at each vertex, unlike the familiar hexagonal wallpaper tiling, where three meet at each vertex. I first construct paper-strip skeletons to explore this structure, then translate the same system into knitting, using foundation chains to help with the cast-on. Partial hexagons form the boundary, which is supported by a 3D-printed frame. I will also compare the knitted surface with a crochet realization. Knitting is particularly well suited to visualizing minimal surfaces: its natural stretchiness allows the fabric to conform to the geometry and bring the mathematical structure to life.", "id": "Paper/67413", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67413"}, {"title": " Multilinear Averages on Curves ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "16b6e40a51214b55d8f94779b9b97a35e08aaae09746e73dbfeb56ef10597e2e", "withdrawn": "", "abstract": "We prove endpoint strong-type bounds for a general class of multilinear weighted averaging operators associated with polynomial curves. Our results extend earlier work of Stovall by adapting the methods developed by Christ, Dendrinos, Stovall, and Street to the multilinear setting.", "id": "Paper/67415", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67415"}, {"title": " Computing Generalized Puiseux Series ", "webprogram_exclude": "0", "session_ids": ["Session/18356"], "source_sha256": "14086a37c50a8f11835294935c42a0ea0314b369e91b9f0348a6e469d0b0bb21", "withdrawn": "", "abstract": "Moving towards a robust numerical path tracker for polynomial homotopies, one must properly choose the step size while still avoiding potential singularities. Finding the closest singularity reveals a need for solving systems with coefficients that are power series with floating-point exponents. These systems arise when polyhedral homotopies are induced by floating-point lifting values.\n\nMethods from tropical geometry have proven useful in the solving of these systems. These methods give us access to tools from combinatorial optimization that can give us insight into the original systems. We apply the Hungarian Algorithm when solving the linear systems in Newton's method to compute the power series. Tools from combinatorial optimization also allow for solutions to storage limitations that arise when computing power series with real powers. We will also address the computational scalability of this problem.", "id": "Paper/67420", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67420"}, {"title": " Conditional Gambler’s Ruin Problem with Arbitrary Winning and Losing Probabilities with Applications ", "webprogram_exclude": "0", "session_ids": ["Session/19370"], "source_sha256": "2bcb676669120ec2ef2eb1eaa0198037a9be65ce9140daff34206157c3cfba8c", "withdrawn": "", "abstract": "We provide formulas for the expectation of a conditional game duration in a finite state-space one-dimensional gambler’s ruin problem with arbitrary winning \\(p(n)\\) and losing \\(q(n)\\) probabilities (i.e., depending on the current fortune). The formulas are stated in terms of the system’s parameters. Beyer and Waterman (\\emph{Math. Mag.}, 50(1):42–45, 1977) showed that for the classical gambler’s ruin problem, the distribution of a conditional absorption time is symmetric in \\(p\\) and \\(q\\). Our formulas imply that, for non-constant winning and losing probabilities, the expectation of a conditional game duration is symmetric in these probabilities (i.e., it remains the same if we exchange \\(p(n)\\) with \\(q(n)\\)), as long as their ratio \\(q(n)/p(n)\\)) is constant.\n\nMost of the formulas are applied to a non-symmetric random walk on a circle/polygon. Moreover, for a symmetric random walk on a circle, we construct an optimal strong stationary dual chain, which turns out to be an absorbing, non-symmetric birth-and-death chain. We apply our results to provide a formula for its expected absorption time, which is the fastest strong stationary time for the aforementioned symmetric random walk on a circle. In this way, we improve upon a result of Diaconis and Fill (\\emph{Ann. Prob.}, 18(4):1483–1522, 1990), where a strong stationary time -- though not the fastest -- was constructed. The expectations of the fastest strong stationary time and the one constructed by Diaconis and Fill differ by \\(3/4\\), independently of the circle’s size.\n\nThis is joint work with P. Markowski and has been published as: Lorek, P., Markowski, P. Conditional Gambler’s Ruin Problem with Arbitrary Winning and Losing Probabilities with Applications. \\emph{Methodol. Comput. Appl. Probab.} 27, 54 (2025).\n\nA version of this talk was previously presented at the 2025 AMS Fall Eastern Virtual Sectional Meeting.", "id": "Paper/67423", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67423"}, {"title": " Nonlinear Semigroup Methods for Coupled Fluid-Elasticity PDE Systems and Data Assimilation ", "webprogram_exclude": "0", "session_ids": ["Session/18283"], "source_sha256": "528f6e40f2297a994d6e65031983b5d336e97866b2e44fea721bca9911a1242d", "withdrawn": "", "abstract": "We apply a novel use of nonlinear semigroup methods, in combination with a new nonlinear pressure elimination technique, to establish new qualitative results for a well-known fluid-structure model over general Lipschitz domains. This nonlinear fluid–structure interaction (FSI) is a coupling of Navier–Stokes flow with a system of linear elasticity, which constitutes a coupled parabolic-hyperbolic system. The coupling between these two distinct PDE dynamics is realized via transmission boundary conditions, for a boundary geometry that is assumed to be merely Lipschitz. Due to the boundary coupling, there is a lack of classically well-defined traces in the topology of the energy-level solutions. Our novel pressure elimination method enables an explicit operator representation of this coupled PDE, previously established for the linear case of this system. We apply this representation, in combination with a novel use of nonlinear semigroup techniques, to show the static and local in time well-posedness for the coupled PDE system. To deal with the Navier–Stokes and associated boundary nonlinearities we construct a truncated nonlinear semigroup approximation, and give a new proof of maximality of the static resolvent PDE, which is now well-posed in nonsmooth (general Lipschitz) domains. We illustrate further applications of our method in FEM where the approximating fluid subspace does not require the divergence-free condition. We also illustrate the consequences of our results for related problems of data assimilation and observer design, for partial observation that is continuous in time. This work was done in collaboration with George Avalos.", "id": "Paper/67429", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67429"}, {"title": " GAISE-ing Into the Future ", "webprogram_exclude": "0", "session_ids": ["Session/18064"], "source_sha256": "c9d5f22ac5581bdfbbeb05746287c40a24638af066017a63fb57f90f5db351d4", "withdrawn": "", "abstract": "The 2026 GAISE College Report (Guidelines for Assessment and Instruction in Statistics and Data Science Education) includes many resources for improving teaching and learning in Introductory Statistics and Introductory Data Science.  Recommendations in the report include using real data, prioritizing conceptual understanding, building communication skills, and using technology effectively.  The presenter is a co-chair of the GAISE author team and will discuss how the recommendations support a modeling first mindset and support the use of resampling methods in statistical inference.", "id": "Paper/67434", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67434"}, {"title": " On Lin’s type Hessian estimates for a class of singular-degenerate parabolic equations ", "webprogram_exclude": "0", "session_ids": ["Session/18265"], "source_sha256": "ca856eb1c46188e3828c4dc5a28d181f25b998bbcad66d668adf828dff5599d0", "withdrawn": "", "abstract": "In this talk, I will present recent work on weighted Hessian estimates for a class of parabolic equations in non-divergence form. The leading coefficients may be singular, degenerate, or both, through a weight belonging to a suitable Muckenhoupt class. We introduce a class of weighted parabolic cylinders intrinsically adapted to these equations. Under a small, weighted BMO condition on the weight, we derive local quantitative lower-bound estimates for solutions, which serve as key ingredients in establishing the weighted Hessian estimates. I will also present several examples of admissible weights to which our results apply. This is joint work with Tuoc Phan.", "id": "Paper/67436", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67436"}, {"title": " Chemotaxis models with signal-dependent sensitivity and a logistic-type source: Boundedness and global existence of solutions ", "webprogram_exclude": "0", "session_ids": ["Session/18445"], "source_sha256": "855eef8934831351cc67377eaf48371f0dcdd3e7381811f2dbc8f8e6abc8fbbd", "withdrawn": "", "abstract": "In this talk we will consider a chemotaxis model with signal-dependent sensitivity and a logistic-type source on a bounded smooth domain in R^N. We investigate the boundedness and global existence of positive classical solutions from three different perspectives: the role played by the negative chemotaxis sensitivity coefficient, the role of the nonlinear cross diffusion rate, and the role of the logistic-type source. Given a positive smooth initial, we prove that all positive classical solutions stay bounded provided that the chemotaxis sensitivity is negative, or the nonlinear cross diffusion rate is relatively weak, or the logistic source is relatively strong.\n\nBased on a joint work with Dr. Wenxian Shen and Dr. Le Chen.", "id": "Paper/67437", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67437"}, {"title": " Real Data, Fast: A Web-Based Tool for Teaching Statistical Inference ", "webprogram_exclude": "0", "session_ids": ["Session/18092"], "source_sha256": "4ce6312e64ea459d38c50562994cd2324a308271e034845df0b55b455458aef3", "withdrawn": "", "abstract": "The statistics education literature consistently supports the use of real and relevant data to improve student engagement and learning. One of the easiest ways to make data meaningful is to have students collect and analyze their own data, but the process can be slow and cumbersome. We present a simple web-based platform designed to make the entire process of data collection, visualization, and statistical inference fast and seamless. The platform focuses on randomized experiments and simple linear regression. An instructor sets up the activity and receives a four-digit code that students use to enter data without creating an account. As the data are collected, the platform automatically displays descriptive statistics, appropriate graphs, and inferential results. Students can also return to the results after the activity is complete. The goal is to make it easy to move from asking a research question to collecting data, describing the data, and making an inference within a single class period.", "id": "Paper/67438", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67438"}, {"title": " The shape of spiking neural computation ", "webprogram_exclude": "0", "session_ids": ["Session/18114"], "source_sha256": "ba67ab0279d71245b7db21a24aecfb4bfb80b52d31bf85a59fa2365442446b39", "withdrawn": "", "abstract": "Action potentials, or spikes, in the brain support neural computation through coordinated patterns of activity across neurons and time.  In this talk, I will present a mathematical framework for constructing combinatorial and topological objects directly from the spiking activity and synaptic connectivity of a spiking neural network. In this construction, individual spikes are vertices, synaptically mediated causal interactions between spikes are edges, and higher-order structures correspond to higher-order patterns of interaction.   This construction differs from standard neural population analyses in that it does not require binning spikes in time or representing activity as a sequence of population state vectors. I will also present a method that identifies recurring isomorphic substructures in the resulting complexes, which we interpret as candidate reusable computational motifs.  Our construction suggests a natural connection between the physiology of spiking networks and core ideas in algebraic topology, pointing toward new mathematical questions about compositionality and information flow in spiking neural systems.\nSNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525", "id": "Paper/67439", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67439"}, {"title": " A model of an online social network ", "webprogram_exclude": "0", "session_ids": ["Session/19343"], "source_sha256": "cd3873743e513967d6e40f4459c1d46b89b3a88bd39f2f76417942ff1467f1e8", "withdrawn": "", "abstract": "We introduce a new epidemic framework to model the adoption and abandonment dynamics of users on an online social network (OSN), with special emphasis on the novel compartment pauci-engaged. Pauci-engaged individuals have been exposed to an invitation to an OSN, but remain undecided about joining, thus reflecting real-world hesitation and trial behaviors. Building on the infectious–recovery dynamics studied by Chen, Kong, and Wang, we derive the basic reproduction number $\\mathscr{R}_0$ and establish threshold conditions for the stability of both the user-free equilibrium and the user-prevailing equilibrium. Local stability analysis using the Jacobian matrix, together with global stability results based on Lyapunov functions, shows that when the basic reproduction number $\\mathscr{R}_0 < 1$, the OSN cannot sustain an engaged user base, while when $\\mathscr{R}_0>1$, a persistent engagement state emerges. Our findings highlight the pivotal role of the decision-making phase in the growth of the digital platform and offer actionable insights to optimize user recruitment and retention strategies in OSNs.", "id": "Paper/67440", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67440"}, {"title": " Normalized distance Laplacian cospectrality for trees ", "webprogram_exclude": "0", "session_ids": ["Session/18146"], "source_sha256": "513b79d9f428dbe16aae602445afd662875216de40948d1c3631c74beff9fdf0", "withdrawn": "", "abstract": "The normalized distance Laplacian is a matrix defined in terms of a graph and considers both the distances between each pair of vertices as well as the transmission of each vertex. It is a normalized version of the distance Laplacian matrix and is defined analogously to the normalized Laplacian matrix. Two non-isomorphic graphs are called cospectral for a given matrix if they share the same spectrum for that matrix. A graph is called spectrally determined for a given matrix if no other graph is cospectral for that matrix. In this talk, we will consider the cospectality or lack thereof of trees for the normalized distance Laplacian. We will provide conditions which must hold for a graph to be cospectral to a tree. Furthermore, we will show that for the normalized distance Laplacian, the star graph is spectrally determined and the double star graphs and path graph are spectrally determined among trees.", "id": "Paper/67441", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67441"}, {"title": " The Gel-Buffer Potential ", "webprogram_exclude": "0", "session_ids": ["Session/17988"], "source_sha256": "489de8f58b5360f69fb96e7a8047206381c1da7b40bedb01c68de066c043911e", "withdrawn": "", "abstract": "We establish existence and uniqueness of a saddle-saddle connection as a result of a boundary layer calculation in the Poisson-Nernst-Planck (PNP) equations. This boundary layer trajectory corresponds to a potential difference we describe as the Gel-Buffer Potential, in analogy to a Donnan Potential for an impermeable membrane.", "id": "Paper/67443", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67443"}, {"title": " A Normal Form for the Thin Flat Surfaces Category ", "webprogram_exclude": "0", "session_ids": ["Session/18385"], "source_sha256": "60b94a2cf52b6b32e95cd0ecb225348c0a61487617f06d8172562f571a1a985d", "withdrawn": "", "abstract": "The category \\textbf{TFS} of thin flat surfaces, introduced by Khovanov, Qi, and\nRozansky, is a strict symmetric monoidal category whose morphisms are compact oriented\nsurfaces with corners arising as neighborhoods of immersed graphs in a strip. In this talk, I will explain my work with Dr. Carmen Rovi proving\ntwo main results. First, a normal form theorem: every connected viewable tf-cobordism\nis equal, in \\textbf{TFS}, to a canonical composite determined by its topological type. Second, a\nsufficiency theorem: we establish a list of relations in the \\textbf{TFS} category which are sufficient, meaning that any two composites of generators representing the same tf-cobordism\nare related by a finite sequence of the listed relations. If time allows, I will discuss current work on a decorated version of \\textbf{TFS}, whose morphisms are those of \\textbf{TFS} with embedded 1-manifolds.", "id": "Paper/67444", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67444"}, {"title": " Bounds on Betti Numbers of General Koszul Algebras ", "webprogram_exclude": "0", "session_ids": ["Session/18025"], "source_sha256": "54eda31b6ce5fc90ac85c929e000faabf8a4cb6a4809fec8da58b09a592cf31f", "withdrawn": "", "abstract": "Let $S = \\mathbb{k}[x_1,\\ldots,x_n]$ be a standard graded polynomial ring, $I$ a homogeneous quadratic ideal, and $R = S/I$. In 2009, Avramov, Conca, and Iyengar asked whether $R$ being Koszul (i.e., $\\mathbb{k}$ has an $R$-linear resolution) implies that the $i$-th Betti number of $R$ is bounded above by $\\binom{r}{i}$, where $r$ is the number of generators of $I$. If $I$ is generated by at least $\\lceil n^2/4 + n/2 \\rceil$ general quadrics, then $R$ is known to be Koszul by a result of Fr\\\"oberg and L\\\"ofwall. In joint work with Elo\\'isa Grifo and Mark Walker, we prove that Avramov, Conca, and Iyengar's question has an affirmative answer for the class of general Koszul algebras.", "id": "Paper/67446", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67446"}, {"title": " Inertial Stochastic eASAP for Nonsmooth Coupled Tensor Optimization with Nonseparable Coupling ", "webprogram_exclude": "0", "session_ids": ["Session/19322"], "source_sha256": "bd184409ed996d5b9a86e918c0c8b9af31a2b5056438b6737e70012ff0565b1e", "withdrawn": "", "abstract": "We consider a class of nonsmooth nonconvex multiblock optimization problems in coupled tensor decomposition. The objective is the sum of smooth but nonconvex data-fitting terms and a nonsmooth nonconvex coupling term. The main difficulty arises from the coupling term, which is nonseparable across blocks and links factors across modalities. Besides, repeatedly evaluating the full gradients of the data-fitting terms is expensive. In this paper, we propose an inertial stochastic extended alternating structure-adapted proximal gradient method (nest-eASAP), which can be viewed as an extension of inertial stochastic optimization to problems with nonsmooth nonseparable coupling. The principal analytical difficulty arising from this extension is that blockwise stochastic inertial updates generate residuals at mixed Gauss--Seidel points, whereas stationarity is evaluated at the actual iterate. Under suitable local regularity conditions, including blockwise restricted prox-regularity  and the Aubin property, we prove that nest-eASAP reaches a blockwise stochastic $\\varepsilon$-stationary point in $\\mathcal{O}(\\varepsilon^{-2})$ iterations. Subdifferential compatibility of the coupling term extends the same complexity from blockwise to full stochastic $\\varepsilon$-stationarity. Additionally, with the Kurdyka--{\\L}ojasiewicz property, this condition further ensures finite expected length. Numerical experiments on synthetic coupled tensor decomposition and hyperspectral--multispectral image fusion show improved reconstruction accuracy.", "id": "Paper/67447", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67447"}, {"title": " Risk-Neutral Pricing of Random-Expiry Options Using Trinomial Trees ", "webprogram_exclude": "0", "session_ids": ["Session/18058"], "source_sha256": "d175a115c3dc90260a0288e8470123a23f6098b826b0bbdc9a20ede9230ec8fc", "withdrawn": "", "abstract": "Random-expiry options are nontraditional derivative contracts that may expire early based on a random event.  We develop a methodology for pricing these options using a trinomial tree, where the middle path is interpreted as early expiry.  We establish that this approach is free of arbitrage, derive its continuous-time limit, and show how it may be implemented numerically in an efficient manner.", "id": "Paper/67448", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67448"}, {"title": " Refined inertia sets for structured sign patterns ", "webprogram_exclude": "0", "session_ids": ["Session/18227"], "source_sha256": "151cbdbc6b76537fa8ceaf328a8f370a072cf4745ddab2aae862cc3b23942e9a", "withdrawn": "", "abstract": "The  {\\em refined inertia} of  an $n\\times n$ matrix $A$  is the 4-tuple ri$(A)=(n_+,n_-,n_z,2n_p)$ where $n_+,n_-$ equal the number of eigenvalues of $A$ with positive, negative (respectively) real parts, $n_z$ is the number of eigenvalues of $A$  equal to zero and $2n_p$ is the number of nonzero pure imaginary eigenvalues of $A$ (note that $n_+ + n_-+ n_z+2n_p = n$).   We investigate  refined inertia sets of sign patterns of the form \n$\\mathcal{C}=\\left[\\begin{array}{c|c} \\mathcal{A} &\\mathcal{D}\\\\ \\hline \\mathcal{D}&O\\\\ \\end{array}\\right]$, where $\\mathcal{A}$ is an irreducible sign pattern and $\\mathcal{D}$ denotes the positive diagonal pattern.  Our  focus is on characterizing patterns $\\mathcal{C}$ that allow the maximum number of refined inertias within this class.\nWe give necessary structural conditions  for the directed graph of such patterns and identify families of sign patterns of this form that achieve the maximum number of refined inertias.", "id": "Paper/67450", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67450"}, {"title": " The Simultaneous Conjugacy Search Problem in Contracting Groups: A Heuristic Attack ", "webprogram_exclude": "0", "session_ids": ["Session/19339"], "source_sha256": "4e11e4c664cef6924120d7435c870194f35161801e2937ca886e39c5ae71790a", "withdrawn": "i", "abstract": "Advances in quantum computing motivate the search for cryptographic methods based on computational problems that may remain difficult for quantum computers. Several proposed protocols use problems in non-commutative groups, including the simultaneous conjugacy search problem (SCSP), which asks for a common conjugator between several pairs of group elements. We study this problem for self-similar contracting groups acting on regular rooted trees of arbitrary degree and develop an efficient heuristic attack. Our method reconstructs an unknown conjugator recursively from the given conjugate pairs. We test the attack on several known contracting groups as well as on randomly generated examples, using a heuristic procedure for constructing such groups. Our experiments show that the SCSP is often vulnerable in this setting, suggesting that contracting groups may not provide sufficient security for cryptographic protocols based on this problem. We then consider a modified version of the SCSP involving families of groups that are more resistant to the original attack and adapt our method to this setting.", "id": "Paper/67451", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67451"}, {"title": " The quadratic density of prime gaps and Legendre’s conjecture ", "webprogram_exclude": "0", "session_ids": ["Session/19367"], "source_sha256": "e22dc48361b04ea3d37f8c614dd88d8fcc51ff3639a21b11933fba2426d03160", "withdrawn": "", "abstract": "We study Eratosthenes sieve as a discrete dynamic system.  At every stage of the sieve there is a cycle of gaps \n${\\mathcal G}(p^\\#)$ between the remaining numbers, known as the p-rough numbers.  There is a 3-step recursion that produces the next cycle from the current one ${{\\mathcal G}(p_k^\\#)\\rightarrow {\\mathcal G}(p_{k+1}^\\#)}$.  The cycles under this recursion constitute a discrete dynamic system.\n\nWe count initial populations of gaps and constellations in the cycle ${\\mathcal G}(p_0^\\#)$.  From the eigenstructure of the iterative system we obtain {\\bf exact} models $w_{s,J}(p_k^\\#)$ for the relative population of any admissible constellation $s$ of length $J$ and span $|s|<2p_1$, across all subsequent stages of the sieve.\n\nWe introduce a statistic $\\eta_s(p_k)$, the quadratic density of $s$ in the interval $(p_k^2,p_{k+1}^2]$.  The quadratic density is the average population of $s$ across the quadratic intervals $(n^2,(n+1)^2]$ for ${p_k \\le n < p_{k+1}.}$  The expected quadratic density $\\widehat{\\eta_s}(p_k)$ reflects the relative population models $w_{s,J}(p_k^\\#)$ to first order. \n\nFor gaps, we show that once a gap $g< 2p_1$ appears in ${\\mathcal G}(p_k^\\#)$, its expected quadratic density\n$\\widehat{\\eta_g}(p_k)$ is increasing.", "id": "Paper/67455", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67455"}, {"title": " Discovering Relationships in College Students’ Academic Preferences Through Association Rules Mining ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "827e543202344ec3628c16d73ffb2a259f2b8f70eef379c1608b2f9a60050694", "withdrawn": "", "abstract": "Knowing the academic program preferences of students can help colleges improve advising strategies, better promote their existing programs, and design new interdisciplinary programs. By examining deidentified academic records of the past ten graduating classes from Butler University, this research aims to uncover meaningful relationships among different fields of study based on student preferences. Unsupervised machine learning algorithms, such as the Apriori, ECLAT, and FP-Growth algorithms, are used to generate association rules between major and minor degree programs completed by students of the graduating classes. These program preferences are further analyzed with a special focus on how students’ primary major selections influence the selection of secondary programs. A series of objective interestingness measures such as support, confidence, and interest factors, are applied to select and evaluate the association rules. This poster discusses the uncovering of relationships among the academic programs commonly completed together, helping institutions better understand the academic interests of students.", "id": "Paper/67456", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67456"}, {"title": " Bridging Low-Dimensional Topology and Representation Learning in AI ", "webprogram_exclude": "0", "session_ids": ["Session/18357"], "source_sha256": "c81923428d116b1e93f856898837bd0d3e55ec0d8173e1b2f78a31867e476170", "withdrawn": "", "abstract": "Topology is naturally suited to studying structure that is nonlinear, multiscale, and nonstationary. Yet within machine learning, its use has remained largely confined to topological data analysis. In this talk, we discuss a broader perspective, namely the tools such as Morse theory from low-dimensional topology which provide a complementary and largely unexplored framework for understanding the hidden structure of data-generating processes and the learning tasks built upon them. We show how the ideas of discrete Morse theory, together with concepts from cobordism theory, can be used to guide graph diffusion models. In particular, we describe a Morse-theoretic approach to induced diffusion guidance, discuss its theoretical guarantees, and illustrate how these constructions can facilitate graph diffusion models in applications to spatio-temporal surveillance and graph regeneration. More broadly, the talk will illustrate how low-dimensional topology can serve not only as a tool for analyzing data after the fact, but as a source of mathematical structure that can be incorporated directly into the design of learning algorithms. These applications represent only a small window into what low-dimensional topology may have to offer machine learning and artificial intelligence.", "id": "Paper/67459", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67459"}, {"title": " Multiplicative Updates Analysis for Quadratic Programming with Convex Domain Constraint ", "webprogram_exclude": "0", "session_ids": ["Session/18124"], "source_sha256": "3b779d20c97ebb17dafa05e58155904609e7c128293568b105f09e64f59679e0", "withdrawn": "", "abstract": "Many problems in statistical learning and neural computation involve linear optimizations with convex domain constraints. In this article, we study a large set of optimization problems in quadratic programming where the optimization is confined to any closed convex domain in $\\mathbb R^p$, with $p\\ge1$. We extend Sha et al.'s multiplicative updates for quadratic programming with nonnegative constraint to arbitrary closed convex domain constraint. Compared to existing methods for the same problems, our novel numerical scheme improves the value of the objective function iteratively and converges monotonically to the global optimizer, and we achieve closed form updates without the need of tuning. As an advantage to other multiplicative updates methods used in the machine learning literature, our algorithm can be easily hard-coded in any  languages, such as Python, $R$ and $MATLAB$. We show that this algorithm provides solutions to linear regularizations with any convex penalty functions. Examples include ridge, lasso, elastic net and $L^p$ ($p\\ge1$) penalties. We also provide convergence analysis, simulation study with coding in Python to show the consistency and simplicity of our algorithms.", "id": "Paper/67460", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67460"}, {"title": " LeafRank: A phylodynamic framework for inferring relative fitness from single-cell phylogenies in chromosomally unstable tumors ", "webprogram_exclude": "0", "session_ids": ["Session/18350"], "source_sha256": "95e80ec0767a9fdf10b0aebb4ecc55fabba59718eed78ef602f9008ad86a2693", "withdrawn": "", "abstract": "Tumors contain cancer cells with diverse growth potentials that shape evolutionary trajectories, yet this fitness diversity remains difficult to quantify in cases of whole-genome duplication (WGD) and chromosomal instability. We present LeafRank, a mathematical framework that leverages single-cell DNA-seq phylogenies to infer the relative fitness of individual cells. Using a multi-type branching process model, LeafRank integrates full tree topology, including branch lengths and bifurcation patterns, to estimate marginal fitness probabilities under punctuated evolutionary regimes driven by rare driver events. To account for elevated aberration rates following WGD, we introduce a tree-rescaling strategy that adjusts for lineage-specific genomic instability. Unlike methods focused on predefined subclones, LeafRank ranks all sampled cells, enabling flexible assessment of growth heterogeneity. Simulations demonstrate high accuracy across spatial and non-spatial virtual tumors. Applied to ovarian cancer, LeafRank reveals directional and parallel selection in WGD tumors and identifies recurrent copy number events enriched in high-fitness lineages. WGD lineages do not show immediate growth advantages but acquire fitness through subsequent alterations.", "id": "Paper/67461", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67461"}, {"title": " Comparison of hyphal growth in fusing and non-fusing3 mycelia using a multiscale model of fungal growth ", "webprogram_exclude": "0", "session_ids": ["Session/19371"], "source_sha256": "9f8e602550cd86ea28d7e4abe6880dda549612f4556261b8fc4a8a95fc4a07ee", "withdrawn": "", "abstract": "Bacterial-fungal interactions play a fundamental role in many processes including crop biofuel development and biosystem design. In this work, we focus on the interactions between the fungus, \\textit{Laccaria bicolor}, and the bacterium, \\textit{Psuedomonas fluorescens}, and their integral role in the fitness of the roots of  \\textit{Populus} species. \\textit{Laccria bicolor} synthesizes malate which stimulates growth and chemotaxis of \\textit{P. flourescens}. Furthermore, \\textit{P. flourescens} provides \\textit{L. bicolor} with thiamine thereby increasing fungal mass. We developed a multiscale computational model to investigate these interdependent interactions. The growth and branching of the fungal mycelia are modeled using an off-lattice spatial discrete submodel which is dependent on both diffusive and active translocation of internal nutrients and uptake of external nutrients. Malate secretion acts as a source of diffusive chemoattractant for \\textit{P. fluorescens}. The bacteria colony are represented by point sources of diffusing thiamine.", "id": "Paper/67464", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67464"}, {"title": " Leading Undergraduate Teams in COMAP Mathematical Modeling for the first time, what is needed? ", "webprogram_exclude": "0", "session_ids": ["Session/18066"], "source_sha256": "e45d278c7a97e3076156f062ba618a7eede550b32a80285c669d40bf2ae70003", "withdrawn": "", "abstract": "As a COMAP MCM/ICM coach at UC Riverside, I mentored two undergraduate teams totaling six students in the 2026 competition. My coaching emphasized mathematical modeling, collaborative problem-solving, and clear technical communication, helping students connect classroom knowledge with real-world challenges. Both teams earned the “Successful Participant” designation. Through this work, I supported undergraduate engagement in applied mathematics while strengthening my leadership and mentoring skills. My goal is to help students build confidence as independent thinkers, effective collaborators, and emerging mathematical modelers.", "id": "Paper/67466", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67466"}, {"title": " The Hausdorff Dimension of the Folklore Set ", "webprogram_exclude": "0", "session_ids": ["Session/18261"], "source_sha256": "43a9865841617b468c1a80cd9337344266f642f36b2a325ebc9a224d83b82b53", "withdrawn": "", "abstract": "In 1970, Davenport and Schmidt proved that Dirichlet-improvable numbers are either rational or badly approximable. The Folklore Conjecture asserts that such phenomenon does not persist in higher dimension and that the set of vectors that are Dirichlet-improvable but neither singular nor badly approximable has full Hausdorff dimension. In this talk, I will briefly recall previous progress toward this conjecture and discuss recent work by Kim, Kleinbock, Nekrasov, Rao, and myself resolving it. I will illustrate connections to homogeneous dynamics and, time permitting, I will give a rough idea of the proof.", "id": "Paper/67467", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67467"}, {"title": " Making Sense of \"Boundary Conditions\": Surprises in the Truncated-Fractional Framework ", "webprogram_exclude": "0", "session_ids": ["Session/17883"], "source_sha256": "f7632504c8745e3dd76f9014dbcd72c7e061c9070d8ab46f7d9031b91783ce8d", "withdrawn": "", "abstract": "Fractional vector calculus has found great success in a variety of applications, and the truncated-fractional framework developed by Bellido, Cueto, Foss, Kreisbeck, Mora-Corral, Radu, Sch\\\"onberger, and others provides the mathematical setting for applying these modeling tools to problems on bounded domains. However, when formulating models on bounded domains, an important question arises: what is the appropriate notion of \"boundary conditions\" for truncated-fractional PDEs and Variational Problems? Because the operators are nonlocal, one natural choice is to enforce Dirichlet-type volume constraints on the collar, a set of positive measure in a neighborhood of the topological boundary.\n\nIn this work, we explore the mathematical aspects of the Fractional Sobolev spaces associated with this type of constraint. Surprisingly, the most straightforward approach fails to capture a number of key properties familiar from the classical setting: the fractional analogs of the Hardy and Poincar\\'e inequalities fail, as do the nonlocal Green's Identity and the boundedness of the extend-by-zero operator. All of these properties play a key role in the mathematical analysis of classical PDEs as well as the numerical approximation of their solutions. We instead propose an alternate choice of Sobolev space and show establish that it satisfies the fractional analog of these desirable properties.", "id": "Paper/67468", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67468"}, {"title": " Atoroidal surface bundles and restrictions on their geometry ", "webprogram_exclude": "0", "session_ids": ["Session/18297"], "source_sha256": "b5579660ea91cf61a4b055bb1a1f02963d968266cf34a1dc064447dfc7121852", "withdrawn": "", "abstract": "I will discuss work with Leininger showing that our atoroidal surface bundles over surfaces are typically not complex surfaces nor hyperbolic manifolds.", "id": "Paper/67472", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67472"}, {"title": " Fisher information in kinetic equations ", "webprogram_exclude": "0", "session_ids": ["Session/17991"], "source_sha256": "cfdfc6307257a15c78f52579d749b1ee4bbbd5b5ec4d3a6ee3528fef30a095c1", "withdrawn": "", "abstract": "The Fisher information has recently played a significant role in the study of kinetic equations. Guillen and Silvestre proved that the Fisher information is monotone decreasing along solutions of the Landau equation with Coulomb potential, leading to global regularity for sufficiently regular initial data. In this talk, I will discuss two results concerning the Fisher information for Landau-type equations. First, for an isotropic modification of the Landau equation introduced by Krieger and Strain, we prove that the Fisher information is also monotone decreasing. As a consequence, we obtain global existence of smooth solutions for a suitable class of initial data. Second, for the Landau equation with Coulomb potential, we establish an a priori estimate on the dissipation of the Fisher information. This estimate allows us to extend the global existence theory to rough initial data in (L^1_5 \\cap L\\log L). The first result is joint work with David Bowman.", "id": "Paper/67473", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67473"}, {"title": " Cohomology of Hecke congruence subgroups ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "4060643f69df018c9a2e00f8de84f80bd779f26dafcb36cbba8c3d551584a0e2", "withdrawn": "", "abstract": "The Hecke congruence subgroup $\\Gamma_{0,n}(p)\\leq \\operatorname{SL}_n(\\mathbb{Z})$ is the subgroup of matrices whose first column is of the form $(*,0,\\dots,0)^t\\bmod p$. The cohomology of these groups has connections to problems in number theory and algebraic $K$-theory. Borel--Serre showed that the rational cohomology of $\\Gamma_{0,n}(p)$ vanishes above degree $\\binom{n}{2}$. I prove that the top-dimensional cohomology group \n$H^{\\binom{n}{2}}(\\Gamma_{0,n}(p);\\mathbb{Q})$\n vanishes for $p\\in\\{2,3,5,7,13\\}$ when $n\\geq 3$, as well as whenever $n$ is sufficiently large relative to $p$. In contrast, I show that this group is nonzero when $n=2$ for every prime $p$, recovering a known result, and when $n=3$ for every prime $p\\notin\\{2,3,5,7,13\\}$. Thus, the top-dimensional cohomology exhibits a transition from nonvanishing in small rank to vanishing as the rank grows relative to $p$. In joint work with Jeremy Miller, I show that this vanishing phenomenon persists in the two neighboring degrees: the groups \n$H^{\\binom{n}{2}-1}(\\Gamma_{0,n}(p);\\mathbb{Q})$ and $H^{\\binom{n}{2}-2}(\\Gamma_{0,n}(p);\\mathbb{Q})$ also vanish when $n$ is sufficiently large relative to $p$.", "id": "Paper/67475", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67475"}, {"title": " Algebraic Geometry Codes on Surfaces ", "webprogram_exclude": "0", "session_ids": ["Session/18388"], "source_sha256": "87bd758065460ce4e255db3de3e7dac1ac17bf7169260347ccb56fb98ad82c49", "withdrawn": "", "abstract": "We use tools from algebraic geometry to improve the parameters of error-correcting codes. In particular, we use Bézout’s theorem to improve the minimum distance of codes constructed on surfaces. We construct locally recoverable codes with hierarchy from surfaces in $\\mathbb{A}^3$ admitting a fibration by curves of Artin-Schreier or Kummer type. We derive the parameters of our codes by leveraging the geometry and arithmetic of the fibration, which is obtained by projection onto one of the coordinates.", "id": "Paper/67476", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67476"}, {"title": " Representation Stability and Stable Periodicity of Spherical Braid Groups ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "208212e70b4110386c970bcee039c066b0cde77ac334b06208d293454c0d9165", "withdrawn": "", "abstract": "Stability patterns for the homology of spaces has been studied for decades. It was proven by Arnol'd-McDuff-Segal that unordered configuration spaces on non-compact manifolds exhibit homological stability. Later, Church-Farb proved that ordered configuration spaces on any manifold exhibit representation stability. Since configuration spaces on surfaces other than $S^2$ and $RP^2$ are Eilenberg-Maclane spaces, the stated results extend to braid groups and pure braid groups (respectively) on surfaces other than $S^2$ and $RP^2$. However, the stability patterns for the homology of braid groups and pure braid groups on $S^2$ and $RP^2$ have remained unknown. This poster will explore my result which uses group actions and equivariant homology to describe the stability patterns for the homology of both the braid group and pure braid groups on $S^2$ and $RP^2$.", "id": "Paper/67477", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67477"}, {"title": " Divisibility, Periodicity, and Prime Outputs in the Modified Narayana Cow’s Sequence 1, 1, 1, 2, 3, 4, 6, 9, 13, etc. ", "webprogram_exclude": "0", "session_ids": ["Session/18235"], "source_sha256": "16f7af3fa0191ebe00521446bb4b110f2ec5aef1d9fae341545a2fed54d81ed1", "withdrawn": "", "abstract": "The Narayana Cow Sequence is named after the fourteenth century Indian mathematician Narayana Pandita and considered the birth patterns in cows, akin to the Fibonacci sequence dealing with the birth patterns in rabbits. Each of the first three terms in the modified Narayana Cow sequence has a value of one while every term thereafter can be obtained as the sum of the previous term and the term three places prior. The initial dozen terms of the sequence are 1, 1, 1, 2, 3, 4, 6, 9, 13, 19, 28, and 41 respectively. I am starting with term one. In the standard Narayana Cow Sequence, the terms are the same as mine, but the initial term would be term zero rather than term one. All of my terms are shifted by one place. Thus my fourth term has value two while the third term in the standard sequence has value two. This paper explores divisibility and periodicity in the sequence modulo n for the initial one hundred terms as well as securing any prime outputs. Using a variety of software programs including MATHERMATICA 13.0.1, Dario Alpern's website and dcode.fr/prime-factors-decomposition, I was able to secure the complete factorizations for the first seven hundred thirteen terms. We conclude by examining the ratios of successive terms which approach what is known as the super Golden ratio which is somewhat analogous to the Golden ratio in Fibonacci-like sequences. Moreover, every prime enters the sequence as a factor akin to the Fibonacci and Padovan sequences. This is in contrast to the Lucas sequence, where one-third of the primes never enter the sequence as factors. Lastly, we consider two easily derived identities involving sums of terms in the Narayana Cow sequence, one using mathematical induction and the other that considers applying the recursion relation in the sequence twice. Such excursions highlighted in this paper would be amenable to undergraduate and graduate students engaged in numerous areas including research in number theory, computational number theory, discrete mathematics, recreational mathematics, coding, and computer science. K-12 teachers and mathematics education professionals could utilize these ideas in fostering curiosity and perseverance in problem solving. While the Fibonacci and Padovan sequences are widely studied, the Narayana Cow sequence is a companion to them in the sprit of fostering mathematical enrichment.", "id": "Paper/67478", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67478"}, {"title": " Efficient Solvers for Linear Optimization via the Hierarchically Semi-Separable Matrix Factorization ", "webprogram_exclude": "0", "session_ids": ["Session/18032"], "source_sha256": "1ba62d3d289da2c014a9ba50bcae1bc2b3bf1088fd3d4b1f4754ec389e472539", "withdrawn": "", "abstract": "Many structured matrices arising in practical settings have hierarchical low rank structures that make storage and computation especially efficient. While much work has focused on the square matrix case, we consider fast solvers for rectangular systems. In particular, we present a new direct method for computing the least squares solution to an underdetermined system involving hierarchical semi-separable matrices. Our method avoids exacerbating the condition number and has a complexity that is near-linear in the size of the matrix.", "id": "Paper/67479", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67479"}, {"title": " Turing Instabilities in Multi-Species Reaction Networks ", "webprogram_exclude": "0", "session_ids": ["Session/18257"], "source_sha256": "62f4c359a6a476a6c2cdf11c79d3855cbe25ffc80b04f4720158da85bebdc4f4", "withdrawn": "", "abstract": "Turing instabilities provide a mechanism by which a spatially homogeneous steady state can become unstable and give rise to nonhomogeneous spatial patterns. Reaction networks with spatially non--homogeneous species concentrations are frequently modeled by reaction--diffusion systems. While pattern formation mechanisms are well understood for two-species networks, general criteria for networks with many interacting species remain limited. We establish algebraic conditions for diffusion--driven instabilities in reaction networks with an arbitrary number of species. If the underlying spatially homogeneous system admits a positive steady-state parameterization, we analyze the characteristic polynomial of the linearized reaction--diffusion system to determine whether diffusion destabilizes a constant  steady state. Our conditions for diffusion--driven instability reduce to explicit inequalities involving the rate constants and the diffusion parameters, providing criteria that are readily verifiable. Finally, for systems where only a single species diffuses, we derive a criterion for a Turing--Hopf instability, demonstrating how diffusion can destabilize a steady state through a pair of complex conjugate eigenvalues.", "id": "Paper/67481", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67481"}, {"title": " Infinitely many Lefschetz pencils on ruled surfaces ", "webprogram_exclude": "0", "session_ids": ["Session/17904"], "source_sha256": "a2646dfcaaa334cc630f2bed1468bd1dc3fab3d55fd2553076d6224b8407c6e3", "withdrawn": "", "abstract": "Works of Donaldson and Gompf show that a closed, oriented 4-manifold admits a symplectic structure if and only if it admits the structure of a Lefschetz pencil. However, the question of how many Lefschetz pencils (or fibrations) a given symplectic 4-manifold admits remains open. Works of Park--Yun and Baykur construct 4-manifolds admitting arbitrarily large (but finite) numbers of Lefschetz pencils or fibrations of the same genus. In this talk, we will construct infinitely many non-isomorphic Lefschetz pencils of the same genus on ruled surfaces of negative Euler characteristic. In fact, our construction gives the first example of infinitely many non-isomorphic but diffeomorphic Lefschetz pencils and fibrations of the same genus. This is joint work with Carlos A. Serván.", "id": "Paper/67482", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67482"}, {"title": " Singly Generated Dynamical Frames and Their Redundancy ", "webprogram_exclude": "0", "session_ids": ["Session/18277"], "source_sha256": "a8a3f5d595ae5905e4ebb4060ed1870fe4c4cd082a2f0807515bbbaa117ed1f0", "withdrawn": "", "abstract": "A singly generated dynamical frame for a Hilbert space $\\mathcal{H}$ is a frame of the form $\\{T^kf\\}_{k=0}^\\infty$ where $T \\in B(\\mathcal{H})$ and $f \\in \\mathcal{H}$. It has been observed that, for certain operators $T$, such frames possess unusually high redundancy not observed in other classes of frames. The positive spectrum Carleson frames, i.e. those dynamical frames for which $T$ is diagonalizable and has positive real spectrum, satisfy the property that $\\{T^{Nk+j_k}f\\}_{k = 0}^\\infty$ is also a frame for any $N \\in \\mathbb{N}_0$ and $j_k \\in [0,N)$. In this talk, we discuss the extent of this redundancy for positive spectrum Carleson frames, as well as other classes of dynamical frames which possess these strong redundancy properties.", "id": "Paper/67483", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67483"}, {"title": " Monad-comonad pairs in operator algebras ", "webprogram_exclude": "0", "session_ids": ["Session/17834"], "source_sha256": "7cdfedfad9a2aac99d9ca55411cff021854c2f2a7cd3c19cf6c5b3d276924019", "withdrawn": "", "abstract": "Several constructions in operator algebras have given rise to closely linked subcategories. These involve universal properties, which are sometimes not easy to verify. We continue to study a recently-discovered method - involving monads and comonads - to make this easier. And we apply it to a new example: Fell bundles over locally compact Hausdorff groupoids. Work in progress. Joint with Erik Bedos, S. Kaliszewski, and Jeri Ann Spiker.", "id": "Paper/67484", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67484"}, {"title": " Exploring Student Engagement Across the Precalculus to Calculus Pathway: A Pilot Study ", "webprogram_exclude": "0", "session_ids": ["Session/19355"], "source_sha256": "391c6f57d5b59fbd7a94f77240767581d45e49829b6a88328005e128ed039e6c", "withdrawn": "", "abstract": "The pilot study employed a descriptive, cross-sectional design, using self-report survey measures collected over two consecutive semesters, to examine how students’ engagement-related experiences intersect with academic progression in Precalculus and Calculus, specifically Calculus for Life Sciences. The study was exploratory and was not designed to examine individual change over time. In the Precalculus study, the survey was administered to 88 students across six classes, who reported generally strong instructional support and strong beliefs that their mathematical ability could improve through effort, but comparatively lower levels of interest, participation, collaboration, and help-seeking. To provide a broader picture of course progression, final course-grade records were also examined for all 246 students enrolled across the six Precalculus sections; 71.5\\% earned a C or higher and were eligible to progress to Calculus, while 28.5\\% did not meet the progression requirement. In the subsequent Calculus study, the survey was administered to 37 students who reported relatively strong behavioral and cognitive engagement in areas such as attendance, attention to lectures, task completion, persistence, and resource-seeking, but responses also indicated lower participation in class, less emphasis on understanding the reasoning underlying calculus concepts, weaker affective engagement, and more limited social engagement with peers. Across the two course contexts, a recurring pattern emerged: students reported willingness to persist and confidence in their ability to succeed, while opportunities to participate, collaborate, seek help, and engage more deeply with mathematical reasoning appeared comparatively limited. Although the survey samples were not intentionally matched, the findings provide a foundation for future longitudinal research examining how engagement relates to mathematical learning, course performance, and persistence across the Precalculus-to-Calculus pathway. It also allows researchers to move from broad, retrospective descriptions of engagement to a direct examination of engagement during authentic calculus problem solving.", "id": "Paper/67486", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67486"}, {"title": " Structured representations of biomolecules: from geometry and topology to graph learning ", "webprogram_exclude": "0", "session_ids": ["Session/18026"], "source_sha256": "4b1fc5b588b5e091f6b2f62acbf827b12c45e89c32f7b94a6027dfa9c98df3d0", "withdrawn": "", "abstract": "Biomolecular systems exhibit intricate multiscale organization shaped by geometric, topological, and interaction constraints. Developing representations that capture this structural complexity while remaining amenable to learning remains a fundamental challenge.\n\nIn this talk, I present a series of mathematical frameworks integrating multiscale differential geometry, algebraic topology, and graph theory to construct low-dimensional yet information-rich representations of biomolecules. We develop curvature-informed geometric descriptors, topological summaries, and atom-type-specific interaction decompositions that encode multiscale structural organization in stable and interpretable forms. Building on these ideas, we introduce a hierarchical Multi-level, Multi-color Graph Neural Network that decomposes molecular graphs into chemically and geometrically colored subgraphs, addressing expressivity limitations and information bottlenecks inherent in standard message-passing architectures.\n\nThese topology-, graph-, and geometry-informed representations achieve competitive performance across molecular benchmarks and have supported repeated top-tier results in the D3R Grand Challenges, illustrating how mathematically structured representations can considerably improve biomolecular modeling.", "id": "Paper/67487", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67487"}, {"title": " Transversal Pooling for Group-Lipschitz Neural Networks ", "webprogram_exclude": "0", "session_ids": ["Session/18273"], "source_sha256": "c648474a2e28a9c8057d34ca546e6404b40015a42d93818dbc295a74de939629", "withdrawn": "", "abstract": "Invariance and Equivariance play a key role in the design of neural networks by allowing the network to exploit natural symmetries in the data. However, for some applications, it is desirable to only have invariance to ``small\" translations or rotations (e.g., an image of a six versus a nine).\n\nThis motivates us to introduce a family of Group-Lipschitz Neural Networks with Transversal Pooling. These networks rely on a continuous wavelet transform with filters parameterized by a group $G$. We then reduce our filter bank to be parameterized by a subgroup $\\Lambda \\leq G$ by pooling over coset representatives (i.e., over a transversal) and prove that our networks have natural invariance and equivariance properties. We demonstrate the utility of our method on real and synthetic data, including predicting whether a tropical cyclone will experience rapid intensification.", "id": "Paper/67493", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67493"}, {"title": " Irregular Solutions to Uniformly Elliptic Nonlinear PDEs ", "webprogram_exclude": "0", "session_ids": ["Session/18364"], "source_sha256": "611a2cef09e28420bbfad74a1ee410a7e7a56688c686e9b0b40bc0bea098632a", "withdrawn": "", "abstract": "We discuss the application of convex integration to the construction of irregular solutions to nonlinear partial differential equations in certain classes of Sobolev spaces. For a given domain \\(\\Omega\\subset\\mathbb{R}^2\\) and a mapping \\(A:\\mathbb{R}^2\\to\\mathbb{R}^2\\), we study solutions \\(u:\\Omega\\to\\mathbb{R}\\) satisfying\n$$\n\\begin{cases}\n\\operatorname{div}(A(\\nabla u))=0 & \\text{in }\\Omega,\\\\\nu=0 & \\text{on }\\partial\\Omega.\n\\end{cases}\n$$\nWe present an example of a smooth and uniformly elliptic mapping \\(A\\) with essentially linear growth that fails to be monotone and asymptotically Uhlenbeck, for which the associated equation exhibits non-uniqueness of solutions and the failure of a priori Calder\\'on--Zygmund estimates below a critical exponent.", "id": "Paper/67496", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67496"}, {"title": " On function Bayesian optimal experimental design for inverse problems: existence and differential struture ", "webprogram_exclude": "0", "session_ids": ["Session/18446"], "source_sha256": "f9aa44a2d46c5140244d01202772352b7c7547ece8e92df8dca940858dda07c1", "withdrawn": "", "abstract": "Optimal experimental design seeks observations that reduce uncertainty in an unknown parameter. For inverse problems governed by partial differential equations, both the unknown and the experimental design may be functions: examples include spatially distributed parameters and moving sensor trajectories. A function-space formulation provides a foundation for computational methods whose structure is independent of a particular discretization.\n\nThis talk presents existence and differentiability results for Bayesian experimental design with infinite-dimensional design variables. We first discuss conditions ensuring the existence of designs that maximize expected information gain, including settings with function-valued observations. We then focus on Bayesian A-optimality for linear inverse problems with Gaussian priors and noise, where uncertainty is measured by the trace of the posterior covariance. We derive first and second Frechet derivatives with respect to the design and obtain gradient and Hessian representations together with constrained optimality conditions. These formulas provide a basis for derivative-based design optimization. For finitely many measurements, observation space representations avoid forming the full posterior covariance and use matrix solves whose size is determined by the number of measurements.\n\nWe discuss sensor design for diffusion equations, motivated by heat transfer and contaminant monitoring, and outline extensions to Fourier sampling in MRI. The emphasis is on linking function space analysis to computationally tractable uncertainty reduction.\n\nThe talk is based on joint work with Tapio Helin and Phuoc-Truong Huynh, and on ongoing joint work with Babak Maboudi Afkham.", "id": "Paper/67497", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67497"}, {"title": " An infinite family of 1-cylinder pillowcase-tiled surfaces ", "webprogram_exclude": "0", "session_ids": ["Session/17902"], "source_sha256": "5042a88c3314cb5f6382fd9e50d97dd1c3e0f7e093429ad5e2da85d32d544c2b", "withdrawn": "", "abstract": "Apisa-Wright conjectured that all branched covers of quadratic differentials in $\\mathcal{Q}(-1^4)$ with at most one cylinder in each direction are cyclic covers. This talk will present an infinite family of counterexamples, and discuss the challenges of classifying these 1-cylinder pillowcase-tiled surfaces.", "id": "Paper/67498", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67498"}, {"title": " Reflected waves in excitable media and their implications for the onset of cardiac arrhythmias ", "webprogram_exclude": "0", "session_ids": ["Session/17988"], "source_sha256": "4b3f91dd167e6384b259bb369c46425d57921d5debdab715986d1d4a45d36095", "withdrawn": "", "abstract": "The heart is an excitable medium - Each beat of our heart is triggered by a wave of excitation, called an action potential, that propagates in a coordinated manner through our heart tissue. Usually, when a propagated cardiac action potential interacts with a local tissue heterogeneity such as a region of depressed excitability or an abrupt change in geometry, either the action potential is blocked and annihilated, or it successfully propagates across the heterogeneity. However, in some cases, action potentials can successfully cross the heterogeneity and then give rise to a reflected action potential, i.e., an action potential that propagates in the retrograde direction. These reflected pulses are thought to lead to the onset of life-threatening arrhythmias. The mechanisms that generate reflected pulses in excitable media are not well understood, but their existence has been linked to the existence of an unstable spatiotemporal periodic orbit that has been referred to as a one-dimensional (1D) spiral wave. 1D spiral waves are 'source defects' that consist of a non-excited core that sheds anti-phase counter-propagating pulses. The link between reflection, 1D spiral waves, and the induction of cardiac arrhythmias make it crucial to clarify the underlying mechanisms that give rise to 1D spiral waves and to identify conditions for which they exist. In this talk, I will discuss the link between reflected waves and 1D spirals in excitable media, and give an overview of our work that attempts to elucidate the bifurcation scenario leading to the existence of 1D spirals. \n\nThe origins of this work go back to my time as a graduate student with Jim Keener, and the work was later continued with Eric Cytrynbaum (UBC), another of Jim’s students. More recent work with Stephanie Dodson (Colby), a former postdoc in my group, and Vincent Lovero (LBNL), a recent graduate student, has carried this line of research forward — a small illustration of the lasting influence of Jim Keener.", "id": "Paper/67499", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67499"}, {"title": " Pólya-Szegö Inequality on Submanifolds of Manifolds with Nonnegative Curvature, and Applications ", "webprogram_exclude": "0", "session_ids": ["Session/18265"], "source_sha256": "dcf7c06135944965234e3d794bc45e55acea14082479915c288b9af8f44cc816", "withdrawn": "", "abstract": "We prove a P\\'olya--Szeg\\\"o inequality for functions defined on an $n$-dimensional submanifold $\\Sigma$ of a complete noncompact Riemannian manifold with nonnegative sectional curvature. The associated rearrangement is a Schwarz rearrangement on $\\mathbb R^n$, and the constant depends on the $L^n$-norm of the mean curvature of $\\Sigma$ and an isoperimetric inequality obtained by Brendle. As applications, we derive Sobolev, Log-Sobolev, Hardy, and Gagliardo--Nirenberg inequalities on submanifolds of arbitrary codimension under a small total mean curvature assumption. In the critical Sobolev case, we obtain Moser--Trudinger inequalities on finite-volume submanifolds and exact growth inequalities on submanifolds with infinite volume. Under suitable assumptions, the P\\'olya--Szeg\\\"o constant equals one; in this case, the critical constants in the inequalities coincide with the sharp Euclidean ones.", "id": "Paper/67503", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67503"}, {"title": " A pipe dream basis for Schubert modules ", "webprogram_exclude": "0", "session_ids": ["Session/18067"], "source_sha256": "c752c5107b3672641f3f385472588a5b21d3a8aa3863de006e78e9affbbe5cd8", "withdrawn": "", "abstract": "The Schubert module $M_{D(w)}$ is a representation of the group $B$ of upper triangular matrices, and its character is the Schubert polynomial. Using filtrations constructed by Anderson, we offer a representation-theoretic interpretation of the pipe dream formula. One output of our work is a weight basis of $M_{D(w)}$ which intrinsically ``knows'' the combinatorics of pipe dreams.", "id": "Paper/67504", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67504"}, {"title": " Curl-measure fields and the Stokes’ theorem for weakly differentiable vector fields ", "webprogram_exclude": "0", "session_ids": ["Session/18342"], "source_sha256": "3caba6c5617e612e9175eeaede78bf0153abd8634d11409f01272b91bb2eb335", "withdrawn": "", "abstract": "We introduce and analyze the class $\\mathcal{CM}^{p}$ of curl-measure fields, consisting of $p$-integrable vector fields whose distributional curl is a vector-valued finite Radon measure. \nThese spaces provide a unified framework for the study of problems involving vorticity. We establish Stokes-type theorems for curl-measure fields\nby introducing Stokes functionals on {\\it good manifolds}, \ncharacterized through the finiteness of manifold-adapted maximal operators, and by developing new trace theorems for curl-measure fields.", "id": "Paper/67505", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67505"}, {"title": " On Translative Packing Densities of Finite Cylinders ", "webprogram_exclude": "0", "session_ids": ["Session/19346"], "source_sha256": "7329a6d809ca2f2beca38bf2b2ab1d971f237a19433a7b710028d2dbc803edf2", "withdrawn": "", "abstract": "In 1951, C.A. Rogers proved that for every planar convex disk $K$ the  maximum translative packing density $d_T(K) $ is equal to the  maximum lattice packing density $d_L (K)$. The first half of the paper concerns the question whether this equation extends to nonconvex disks. We list\nseven counterexamples  (including four  previously unrecognized ones, as they were designed for different purposes) and also list four positive results.  The second half of the paper  concerns the 3D analogue of Rogers' planar result. We show that for every  finite cylinder $C$ with base $B$ the planar Rogers' equation $d_T(B) = d_L(B)$  implies the 3D Rogers' equation $d_T(C) = d_L(C)$. We also  present a cylinder to show that the  opposite implication does not hold.", "id": "Paper/67506", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67506"}, {"title": " Scott Analysis of Ordered Structures ", "webprogram_exclude": "0", "session_ids": ["Session/17922"], "source_sha256": "4197f21d66e0de940a3de8d2f71f64856b2b0768b7243e7d42ba5f385b60ebd6", "withdrawn": "", "abstract": "Scott analysis yields a method for measuring the complexity of countable structures. In particular, it describes the complexity of describing a structure up to isomorphism, the complexity of automorphism orbits, and the difficulty of building isomorphisms between copies of a structure. We apply this analysis to ordered algebraic structures such as Presburger groups, divisible ordered abelian groups, and real closed fields. We also make use and compare these results to past work that was done with linear orders and models of Peano arithmetic.", "id": "Paper/67509", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67509"}, {"title": " The Shape of Emotion in Speech: Improving Performance and Interpretability with Persistent Homology ", "webprogram_exclude": "0", "session_ids": ["Session/18304"], "source_sha256": "e810d113785a9406a50441c225319b0f388524668b63b91ccc34fe57934a76ca", "withdrawn": "", "abstract": "Speech emotion recognition commonly relies on spectral representations, which although can provide strong classification performance give limited interpretability. In this talk I present a new framework to perform speech emotion recognition through the use of persistent homology. Mel-spectrogram frames are treated as points, which are used to calculate Vietoris-Rips filtrations with three different distance metrics: Euclidean, Time-Weighted Euclidean and Wasserstein, which characterize spectral similarity, temporal variation, and distributional characteristics in speech respectively. We compute the zeroth and first homology groups and vectorize them using persistence images. \n\nWe evaluate the persistence images through the use of a multilayer perceptron or fusion with conventional spectrogram based models. Across four datasets, the persistence images only model achieves non-trivial performance and improves pooled performance when combined with spectral features. \n\n\nBeyond this, the framework allows for understanding which topological features are important for emotional classification through channel based ablations. The time-weighted Euclidean zeroth homology group is the most informative, which suggests that the temporal organization of spectral components is particularly important for distinguishing emotions. Additionally, first homology groups provided complementary information. This demonstrates that persistent homology can be used to complement conventional spectral speech emotion recognition while providing interpretable insights into the shape of emotion.", "id": "Paper/67510", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67510"}, {"title": " Active sensing with predictive-coding based perception ", "webprogram_exclude": "0", "session_ids": ["Session/18007"], "source_sha256": "e6c3ce552ef66388bdff4d02f0194e0989a6bbe2b69ebfc91560d9b572732327", "withdrawn": "", "abstract": "Animals effectively navigate dynamically changing, noisy environments by sampling behaviorally relevant information through body movements—a process known as active sensing. For example, animals actively sample relevant visual scenes through head and eye movements or touch different parts of an object with their fingers or whiskers to recognize its shape. Action selection is driven by the animals’ internal model of the world, which is shaped by learning the statistical regularities of the environment and continuously updated by incoming novel observations—a process known as predictive coding.\nWe devised an algorithm for predictive-coding-based perception and active sensing in which sequential observations are selected through perceptual inference to minimize uncertainty in an exploratory behavioral mode and maximize expected rewards in an exploitative behavioral mode. By visualizing the latent geometry of the perception model, we showed that exploratory action selection promotes latent geometries that more closely resemble the structure of the environment.  We further extended the model to integrate information across multiple sensory modalities, constructing modality-specific information landscapes over the action space. Finally, by developing a lexicographic algorithm that switches between two behavioral modes—information gathering and reward exploitation—based on perceptual uncertainty obtained from a perception model with multimodal sensory inputs, we show how agents can support biologically plausible active sensing and behaviorally relevant embodied exploration.", "id": "Paper/67512", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67512"}, {"title": " Using Non-Archimedean geometry to study algebraic geometry ", "webprogram_exclude": "0", "session_ids": ["Session/17996"], "source_sha256": "45eda21f154ee8f73b477ad9db86554feca53768574c111df84ade291102ddd3", "withdrawn": "", "abstract": "Non-Archimedean geometry can be viewed as a degenerating limit of algebraic geometry. Berkovich analytification is a systematic way of translating algebraic varieties into non-Archimedean spaces using valuations. This allows us to carry out analytic and geometric constructions on varieties over general fields, while simultaneously encode tropical information. I will introduce the construction of Berkovich spaces and discuss some applications to the study of canonical metrics and measures on algebraic varieties, in particular on Fano and Calabi–Yau manifolds.", "id": "Paper/67513", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67513"}, {"title": " Global solutions to the Boussinesq equations and the planetary geostrophic approximation ", "webprogram_exclude": "0", "session_ids": ["Session/18283"], "source_sha256": "53ae6d1bef74bab6d9641d3a5f1252687eb3f311c7f4e68b2b9ee05dd338592b", "withdrawn": "", "abstract": "We investigate the three dimensional Boussinesq equations in the planetary geostrophic scale, where the buoyancy/gravity driven flow is near geostrophic balance in the large horizontal spatial scale. By establishing the uniform (with respect to the characteristic number) estimates, we are able to obtain the global weak solutions and the unique global strong solutions to the Boussinesq equations without restriction on the initial data. Furthermore, sending the characteristic number to zero with the established compactness rigorously justifies the planetary geostrophic approximation of the Boussinesq equations. We employ the novel buoyancy flow-free flow decomposition to overcome the singularity caused by the buoyancy/gravity.", "id": "Paper/67515", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67515"}, {"title": " Gap junction architecture and synchronization clusters in the Thalamic Reticular Nuclei ", "webprogram_exclude": "0", "session_ids": ["Session/19343"], "source_sha256": "9ad1b5e2f04bb89f012024611c08d07e17a0c5e0523eac93eb60b43c4d3bc559", "withdrawn": "", "abstract": "Neuronal synchronization can emerge through various coupling mechanisms, but its expression\ndepends strongly on how these connections are organized. Gap junctions, in particular, can\nreshape inhibitory synchrony, sometimes reinforcing coherence, other times fragmenting it.\nBuilding on the classic Rinzel-Golomb model of the thalamic reticular nucleus (TRN), we extend\nan inhibitory network to include gap-junction coupling arranged in biologically motivated\nclustered patterns. In particular, we explore the effects of the size, strength, and spatial\ndistribution of gap-junction clusters on synchronization, and how these effects are modulated by\nthe level of background inhibition. Across conductance regimes, weak electrical coupling can\ntransiently destabilize synchrony, while stronger or more extensive clustering promotes\ncoherence or dampens oscillations. These results suggest that the spatial organization of\nelectrical connectivity, together with inhibitory tone, plays a decisive role in shaping rhythmic\ncoordination within TRN-like networks.", "id": "Paper/67517", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67517"}, {"title": " The Kessler Trap: Modeling Structural Invariance and Adaptive Control in Coupled Orbital Logistics ", "webprogram_exclude": "0", "session_ids": ["Session/19005"], "source_sha256": "fda31526c9e16343fe50c30a4195f02d5c4bd6ede5f299d80ce786318a4e35bf", "withdrawn": "", "abstract": "Balancing high-throughput transport systems against endogenous environmental degradation presents a classic non-linear optimization challenge. Investigating Problem B of the 2026 Mathematical Contest in Modeling (MCM), this work models the long-term logistical deployment of a lunar construction base supported by a dual-mode transport architecture: high-capacity rocket launches and a delicate geostationary space elevator.While naive linear models suggest maximizing rocket launch frequency accelerates mission timelines, our coupled stochastic framework reveals a pronounced \"Logistics Cliff\". Beyond a critical launch threshold ($u \\ge 0.8$), rapid orbital debris accumulation degrades tether reliability, forcing the transport fleet into a permanent sustainment trap where life-critical cargo displaces construction payload. By testing structural invariance across linear, quadratic, and cubic debris growth regimes, we show that the optimal transport corridor remains strictly interior ($u \\in [0.4, 0.5]$). To address exogenous collision shocks and parameter uncertainty, we formulate an observable, threshold-based adaptive control policy that throttles launch cadence upon detecting infrastructure degradation. This presentation outlines the modeling architecture, discusses the educational insights gained from formulating non-monotonic physical constraints under contest time pressure, and reflects on transitioning competition models into robust systems analyses.", "id": "Paper/67521", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67521"}, {"title": " Energy spectrums of Turbulent Fluid Images ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "470faa9da07342c94ad114cc69cd2f54e6adfa7eb83b9c63d14207f1034b476c", "withdrawn": "", "abstract": "We study recent conjectures on whether particular paintings of turbulence satisfy physical laws of turbulent fluid flow, in particular that energy decays by wavenumber with a slope of -5/3 in the inertial range.  We develop code to transform image intensity, including value, saturation, and temperature, into Energy by wavenumber, and expand recent studies by considering pieces created through different art historical movements with a wide variety of image types, croppings, and reproductions. Overall, we find that the story is much more complex than the recent literature suggests.", "id": "Paper/67523", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67523"}, {"title": " Approximation of Degenerate Parabolic Problems Using WENO Reconstructions ", "webprogram_exclude": "0", "session_ids": ["Session/17926"], "source_sha256": "2595a9fbc150be0c9269d9ddeeb2e77813d6a7560ee903e84b92d950fbd23cc0", "withdrawn": "", "abstract": "We discuss approximation of the scalar degenerate parabolic PDE $u_t + \\nabla\\cdot[F(u) - D(u)\\nabla B(u)] = G(u)$ using weighted essentially non-oscillatory (WENO) finite volume reconstructions.  The diffusive flux $-D(u)\\nabla B(u)$ may vanish, leading to hyperbolic behavior in which $u$ may exhibit a discontinuity or a steep front. We present a general approach in which the normal diffusive flux at a point on a mesh cell facet is approximated using a one-dimensional sampling line of spacing $\\eta$. Multi-level WENO reconstructions are used to evaluate $u$ accurately on the sampling line on each side of the facet.  Polynomial interpolation is used to reconstruct the solution and its derivative. The procedure is accurate when $u$ is smooth, and approximates a discontinuity to $O(1/\\eta)$. The scheme is accurate and efficient in any spatial dimension on general unstructured computational meshes using, e.g., multilevel WENO reconstructions.  Numerical results in two space dimensions show the efficacy of the scheme by considering three prototypical examples: the porous medium equation, the Allen-Cahn equation, and the Stefan problem (with no mushy region). We also present analytical and numerical studies that relate $\\eta$ to the mesh spacing.", "id": "Paper/67524", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67524"}, {"title": " Self-Organized Vegetation Patterns in Drylands ", "webprogram_exclude": "0", "session_ids": ["Session/18222"], "source_sha256": "ddf33ddc39dc94fe89bef0b9b7a175e003b2e32258b4e2c69cc926d1bdf4a75a", "withdrawn": "", "abstract": "Drylands are water-limited ecosystems, where the water arrives via rare, discrete and unpredictable rainstorms. One strategy for concentrating this resource where it is needed by the consumers involves feedbacks that drive the formation of regularly-spaced bands of vegetation. These bands form transverse to gentle slopes and can capture rain run-off. Such large-scale vegetation patterns, readily observed via satellite images, have been found in semi-arid and arid regions around the globe. We use a PDE framework to model the consumer-resource interactions between biomass and soil moisture, with soil water replenished by rainstorms that we model as impulses to the system. We use this framework to explore the effect of storm variability on vegetation pattern formation by introducing randomness into the timing and the total amount of water deposited by each storm. We investigate how storm variability impacts vegetation pattern formation, which may give insight into the resilience of these dryland ecosystems in the face of climate change.", "id": "Paper/67526", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67526"}, {"title": " Chromatic Subspaces ", "webprogram_exclude": "0", "session_ids": ["Session/18359"], "source_sha256": "faa93b582db4adf7e8798a4ef8ccbb7bfe27d503c05941c447c09f8dab0831cc", "withdrawn": "", "abstract": "The chromatic symmetric function encodes rich combinatorial information about a graph. In fact, the Tree Isomorphism Conjecture asserts that non-isomorphic trees have distinct chromatic symmetric functions. In this talk, I will study the linear algebraic structure of chromatic symmetric functions arising from families of graphs, focusing on the subspaces of symmetric functions spanned by the chromatic symmetric functions of trees and connected graphs. I will also discuss linear relations among the coefficients that arise when chromatic symmetric functions are expressed in the star basis. Our main tool is the deletion-near-contraction relation, which provides a recursive framework for studying these spaces and coefficient relations.", "id": "Paper/67528", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67528"}, {"title": " Semilinear wave equations on the Witten bubble spacetime ", "webprogram_exclude": "0", "session_ids": ["Session/18148"], "source_sha256": "3c3042444a7611ef58e3e8d03a872fb52d16c18bdc42d0c8a8a4ad2a1b51791d", "withdrawn": "", "abstract": "We initiate the study of nonlinear wave equations on the Witten bubble spacetime (also known as the \"bubble of nothing\"), which is an $\\mathrm{SO}(3,1)\\times \\mathrm{U}(1)$-symmetric solution to the Einstein vacuum equations in $(4 + 1)$ dimensions. This spacetime was introduced by Witten to model the semiclassical instability of the Kaluza--Klein spacetime $\\mathbf{R}^{3+1}\\times S^1$ (which is classically stable by work of Huneau--Stingo--Wyatt). We prove a small-data global existence result without symmetry assumptions and an improved decay result for $\\mathrm{U}(1)$-symmetric solutions to a class of semilinear equations satisfying a version of the null condition. Key to the proof are novel estimates for the linear wave equation, which has been studied in the physics literature by Bhawal and Vishveshwara and in the mathematics literature by Bachelot.", "id": "Paper/67532", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67532"}, {"title": " Hypersurface Restrictions of Linear Series Through Hilbert Functions in Nonstandard Graded Algebras ", "webprogram_exclude": "0", "session_ids": ["Session/18347"], "source_sha256": "cb382f2ff8cc49175ad089bac1f2f03ec46a2048fb87b7db5155ae6dc4aa9dce", "withdrawn": "", "abstract": "Theorems of Macaulay and Gotzmann give bounds for the growth of Hilbert functions of standard graded algebras, and a theorem of Green gives bounds after restriction to a general hyperplane. We discuss extensions of these results to nonstandard gradings through generalized Macaulay representations.", "id": "Paper/67535", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67535"}, {"title": " Bridging the Gap Between Stable Marriage and Stable Roommates: A Parameterized Algorithm for Optimal Stable Matchings ", "webprogram_exclude": "0", "session_ids": ["Session/18106"], "source_sha256": "828fceeabe43e70d502d0d97befda814d3489e9cf8d89cc42a65da7546b10923", "withdrawn": "", "abstract": "An instance of the Stable Roommates (SR) problem consists of\n$2n$ agents, each with a preference list that linearly orders the other agents. The goal is to find a perfect matching that is stable — one with no pair of agents who mutually prefer each other to their assigned partners. In this talk, we consider the problem of finding an optimal stable matching. \nEfficient algorithms exist for Stable Marriage (SM) instances, but the problem is NP-hard for SR instances. We sketch a solution showing how an optimal stable matching for an SR instance can be obtained by \"covering\" it with SM instances. In particular, the closer the SR instance is to an SM instance, the more efficient the resulting solution.", "id": "Paper/67536", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67536"}, {"title": " Shallow Weights, Deep Thoughts ", "webprogram_exclude": "0", "session_ids": ["Session/17705"], "source_sha256": "3803b1f8ef16a22cadab198994e549e95be1b590386be0538a9de024e0965818", "withdrawn": "", "abstract": "Despite the success of modern neural networks, the mathematical foundations of their reasoning ability remain poorly understood. Looped transformers provide a tractable setting for studying how iterative computation can produce complex reasoning behavior. We investigate these architectures from a mathematical perspective, drawing on ideas from dynamical systems, fixed-point theory, approximation theory, and related areas. Our results suggest that computational depth need not require many distinct layers, it can instead emerge from the repeated application of a single carefully structured map.", "id": "Paper/67537", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67537"}, {"title": " Distance Geometry of the Convex Code Problem ", "webprogram_exclude": "0", "session_ids": ["Session/18007"], "source_sha256": "c4b357b3dbad18dfaadf5d808852a809aabd8fa532c6c6e3069835ffdc82f3ab", "withdrawn": "", "abstract": "Hippocampal place cells and orientation-selective cells in visual cortex provide paradigmatic examples of \"receptive field coding\": neuron $i$ has a preferred stimulus $x_i$ in a latent metric space $X$ of all possible stimuli, and its  response to stimulus $x$, $r_i(x)$, decays with the distance from $x$ to $x_i$. In a population of such neurons, pairwise and higher-order moments of the joint activity carry geometric information about $X$. Starting with a motivating example where $r_i$ is the indicator function for a convex subset of $\\mathbb{R}^d$ (the convex code problem), we move on to study this coding scheme in cases where $r_i(x)$ is continuous but has has convex superlevel sets. We present some preliminary results on relationships between pairwise and higher-order moments, their dependence on the dimension of the latent space, and implications for information content in neural codes.", "id": "Paper/67538", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67538"}, {"title": " Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18315"], "source_sha256": "6a04793059517f66dbbab7fb5a0b354971c47520902008352a247b1f277d77cc", "withdrawn": "", "abstract": "Motivated by recent work of Kocurek, Oveis Gharan, and Tjowasi, which gives an efficient sampling algorithm for the hard-core model on random regular bipartite graphs by decomposing into fixed-size slices, we study the worst-case tractability of approximate counting and sampling of  fixed-size slices for bipartite independent set problems.\n\nLet \\(G=(L\\sqcup R,E)\\) be a bipartite graph  with \\(|L|=|R|=n\\) and maximum degree $\\Delta$. The fixed-slice problem asks to sample uniformly from independent sets satisfying \\(|I\\cap L|=\\alpha_L n\\) and \\(|I\\cap R|=\\alpha_R n\\). We show that if the overall density $\\alpha$ lies in the interval $(\\frac{1}{\\Delta}, \\tfrac{1}{2})$, and the densities on the two sides are more balanced than the typical phase densities of a random $\\Delta$-regular bipartite graph, then there is no FPRAS or efficient sampling scheme unless $\\mathbf{NP}=\\mathbf{RP}$. \n\nWe then study a related fugacity model in which the  densities are not fixed,\nbut the independent set is required to be balanced between the two sides of the bipartition. For \\(\\lambda>0\\), the balanced hard-core model is the ordinary hard-core model with fugacity \\(\\lambda\\), conditioned on the event \\(|I\\cap L|=|I\\cap R|\\). We prove that this model has the same computational threshold as the  hard-core model on general bounded-degree graphs. That is, for every fixed \\(\\Delta\\ge 3\\), if \\(\\lambda<\\lambda_c(\\Delta)\\), then the balanced partition function admits an FPTAS and the balanced hard-core distribution admits an efficient sampling scheme. Conversely, if \\(\\lambda>\\lambda_c(\\Delta)\\), then no FPRAS or efficient sampler exists on this graph class unless $\\mathbf{NP}=\\mathbf{RP}$.", "id": "Paper/67539", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67539"}, {"title": " MacWilliams Identities over infinite rings ", "webprogram_exclude": "0", "session_ids": ["Session/18388"], "source_sha256": "607aee9fa7dc2d3560880409c90781bb313dfa49db535deb6c9cca7303da5220", "withdrawn": "", "abstract": "In this talk, we show new foundations for the theory of linear codes over local Artinian commutative rings. We use algebraic invariants such as the socle, type, length, and minimal number of generators to measure the size of codes. We introduce a conceptually different version of the weight enumerator polynomial. This enumerator is meaningful\neven in the case of infinite rings and yields new applications in the finite setting. Using this polynomial, we prove a MacWilliams identity that holds over Frobenius rings, not necessarily finite.", "id": "Paper/67541", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67541"}, {"title": " Rhythm Generation and Control in Insect Locomotion ", "webprogram_exclude": "0", "session_ids": ["Session/18257"], "source_sha256": "cca9f675a5190b035c20832366fe5198ddc7302b31c41e707f61b64e5a7649bf", "withdrawn": "", "abstract": "Animal locomotion emerges from interactions among neural control, musculoskeletal dynamics, and environmental forces, and can be viewed as a network of coupled nonlinear systems producing coordinated rhythmic activity. Although stable rhythmic patterns can arise intrinsically within neural circuits, sensory feedback is essential for enhancing their robustness and stability. In this talk, I use locomotion in the stick insect as a case study to examine how stepping rhythms arise and are stabilized across feedforward and closed-loop settings. I first consider a biologically grounded model of central pattern generator (CPG) networks for the metathoracic segment, formulated as an 18-dimensional system of synaptically coupled ordinary differential equations. Using tools from nonlinear dynamical systems, particularly fast–slow decomposition, we identify mechanisms underlying the generation and control of stable, robust, and flexible multi-phase stepping rhythms. I then extend the analysis to a closed-loop setting by incorporating sensory feedback and biomechanics, investigating how interactions between neural circuitry and mechanical dynamics shape and stabilize single-leg stepping patterns. Together, these results illustrate how dynamical-systems approaches can connect mechanisms of intrinsic rhythm generation with the feedback processes required for robust locomotion.", "id": "Paper/67551", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67551"}, {"title": " Student Generative AI Usage for Exam Preparation in First-Year Calculus ", "webprogram_exclude": "0", "session_ids": ["Session/18346"], "source_sha256": "a370a80a91b7bb4724467425d37abb4bd63f0bd27b782427fb8e9ccfdcbd28ba", "withdrawn": "", "abstract": "While college students increasingly turn to generative AI tools for exam preparation, research remains limited regarding how students engage with AI and how distinct strategies of using AI for exam preparation impact exam outcomes.\n\nBuilding on a study in an introductory psychology course - which found that higher-performing students more often used AI to request explanations, generate examples, and verify their understanding, whereas lower-performing students more often used AI for summarization and practice testing - this project extends the investigation to introductory mathematics courses. The researchers collected post-exam data across two Calculus 1 courses and two Calculus 2 courses to better understand students’ AI use to prepare for exams. Through qualitative coding of post-exam survey responses detailing general exam preparation and AI usage, the researchers examine how AI is incorporated into exam preparation in introductory calculus, and how strategies involving AI use differ between psychology and calculus contexts. \n\nThis project represents one phase of a larger multi-disciplinary study investigating cross-field patterns of student AI engagement in higher education. The results reported are preliminary.", "id": "Paper/67563", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67563"}, {"title": " From Andrews’ Conjectures to Almost Alternating Sign Patterns ", "webprogram_exclude": "0", "session_ids": ["Session/18333"], "source_sha256": "af0b879583a5ebc0ebf4fa9210ce2d57b921e92ed941bf37501ece20f0fbcf83", "withdrawn": "", "abstract": "In 1986, Andrews studied five mysterious $q$-series from Ramanujan's Lost Notebook and made six conjectures about the growth and sign behavior of their coefficients. \nThe first two conjectures are on the $q$-series $\\sigma(q)$, and their resolution by Andrews--Dyson--Hickerson marked the beginning of a celebrated story, continued through the work of Cohen, Zwegers, Zagier, and others. \nThe next four conjectures concern the $q$-series $v_1(q),v_2(q),v_3(q),$ and $v_4(q)$.\nRecent independent work by Folsom--Males--Rolen--Storzer and Bachraoui resolved the conjectures for $v_1(q)$. In this talk, we will discuss the cases for $v_2(q),v_3(q)$, and $v_4(q)$, completing the resolution of all of Andrews' conjectures and their analogs for these five $q$-series.\n\nWe first explain how an adapted version of Wright's circle method yields precise asymptotic expansions for the coefficients, revealing an interplay between exponential growth and oscillatory behavior. \nThese asymptotics are then used to show that the coefficients are alternating in sign outside a density-zero exceptional set, establishing an \\emph{almost alternating sign pattern}. \nWe then discuss how a finer analysis of the oscillatory behavior reveals that this exceptional set is highly structured. \nFinally, we introduce a new family of $q$-series whose coefficients appear to exhibit similar sign phenomena, suggesting a broader underlying theory.\n\nThe talk will emphasize the main ideas behind the proofs.\n\n\\noindent\nRelated papers:\n\\begin{itemize}\n    \\item \\emph{On a conjecture of Andrews and almost alternating sign patterns}, arXiv:2607.01210\n    \\item \\emph{On $v_2(q),v_3(q),v_4(q)$, and Andrews' Conjectures 5 and 6}, arXiv:2607.20858\n\\end{itemize}", "id": "Paper/67564", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67564"}, {"title": " No Detour Required: A Scaffolded Differential Calculus Pilot for Students Below the ALEKS Cutoff ", "webprogram_exclude": "0", "session_ids": ["Session/18091"], "source_sha256": "e9bd841e1c76db412050b995797b2e5859f7f6429b8e17aa75ed586a40870ea0", "withdrawn": "", "abstract": "Students who place below the standard ALEKS cutoff for calculus readiness face a familiar bind: delay graduation by repeating coursework, or attempt calculus underprepared and risk failing a high-stakes gatekeeping course. In response, the LSU Department of Mathematics piloted a supported section of differential calculus paired with corequisite support in College Algebra and Trigonometry, aimed at keeping these students on track to graduate on time. The pilot's central design goal was student engagement: daily scaffolded handouts followed a concrete-to-abstract, \"I do → we do → you do\" structure, building new material from problems students could reason through informally before formal notation appeared. Since this particular section was largely composed of pre-health and life-sciences majors, several of these problems were framed around biology and health-science contexts to motivate the material for that audience. This talk discusses how that design created an inclusive, engaging classroom, and traces the initiative's impact across levels: students who succeeded in a course they were expected to struggle with, a department that adopted the pilot permanently, and an institution rethinking corequisite support as a tool for equity and retention.", "id": "Paper/67567", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67567"}, {"title": " Arithmetic Discrete Operators over Imaginary Quadratic Fields ", "webprogram_exclude": "0", "session_ids": ["Session/18277"], "source_sha256": "3f68b7c5c2cb3525ac3b12984502cd42385c12e5242f45b16552bacf653b4b88", "withdrawn": "", "abstract": "We establish a criterion for weighted pointwise ergodic theorems over the rings of integers of imaginary quadratic fields. The criterion is based on quantitative exponential-sum estimates at rational frequencies and their angular twists. Under these hypotheses, we obtain pointwise convergence, scale-free improving estimates, and sparse bounds for the associated discrete operators. We apply the criterion to several classical arithmetic weights, highlighting a common operator-theoretic framework for these averaging problems.", "id": "Paper/67568", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67568"}, {"title": " Supercritical mean field limits ", "webprogram_exclude": "0", "session_ids": ["Session/18331"], "source_sha256": "cc2e3e5a9d0abd65b32352f47b4d9bbcbe0a27794cc89affa6f0d83d2b749d23", "withdrawn": "", "abstract": "The supercritical mean-field limit aims to establish a derivation of a fluid equation (compressible or incompressible) from many body dynamics. As such, it can be viewed as a combined mean-field hydrodynamical limit. The supercritical mean-field limit is intimately linked with the quasi-neutral limit, which offers a derivation of fluid equations from kinetic PDEs of Vlasov type. The pioneering commutator estimates proved by Serfaty in 2020 and the proceeding work of Iacobelli-Han Kwan have shed light on the problem of rigorously deriving fluid equations from Newtonian dynamics with a supercritical scaling. I will review recent developments in supercritical mean-field limits, with a view towards contemporary and future research directions.", "id": "Paper/67569", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67569"}, {"title": " Integrating Longitudinal Survival Analysis with a Physical Activity-Stratified Compartmental Model of Cardiovascular Disease and Mortality ", "webprogram_exclude": "0", "session_ids": ["Session/19359"], "source_sha256": "7a54873d569b158366269496a6b7c6eeb8d202fb5402372559e38b9e6aac86b9", "withdrawn": "", "abstract": "Cardiovascular disease and physical activity both change over time, making it important to account for their longitudinal relationship when studying mortality. In this work, we combine survival analysis with a compartmental mathematical model to study cardiovascular disease, physical activity, and all-cause mortality among older adults. Using repeated observations from the Health and Retirement Study, we construct counting-process survival data and fit Cox proportional hazards and extended Cox models with time-varying covariates. The analysis is used to examine the association of cardiovascular disease and physical activity with mortality while accounting for other health and demographic factors. We then develop a compartmental model in which individuals are grouped by cardiovascular disease status and physical activity level. A key feature of the model is that mortality information from the survival analysis is used to inform the death rates in the corresponding compartments. This creates a direct link between individual-level longitudinal data and a population-level dynamical system. The mathematical analysis focuses on properties of the model such as positivity, boundedness, and long-term behavior. Numerical simulations will be used to study how changes in physical activity, cardiovascular disease progression, and mortality rates affect population outcomes. This framework provides a way to combine observed health data with mathematical modeling for the study of chronic disease dynamics.", "id": "Paper/67570", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67570"}, {"title": " A counterexample to Fermi isospectral rigidity for two dimensional discrete periodic Schrödinger operators ", "webprogram_exclude": "0", "session_ids": ["Session/18292"], "source_sha256": "ac11b7f3c8f57639ee04058b4f208a25fe72c858c3773badcf3d12fc03cd1ea1", "withdrawn": "", "abstract": "Using numerical certification, we prove the existence of a nontrivial real-valued two dimensional periodic potential whose associated discrete Schrodinger operator is Fermi isospectral to the zero potential.", "id": "Paper/67576", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67576"}, {"title": " Infinite-Time Recursive Mean Field Games with Heterogenous Major-Minor Agents ", "webprogram_exclude": "0", "session_ids": ["Session/17781"], "source_sha256": "74570b0c6323ee228c7b48e8e7e26bf270b60a513d3677482c34605c7e272671", "withdrawn": "", "abstract": "This paper investigates a class of infinite-horizon mean field games with one major agent and numerous heterogeneous minor agents, where the agents’ cost functionals are recursive and admit representations via nonlinear backward stochastic differential equations. We refer to such games as recursive major-minor (RMM) problems. Our RMM formulation is fairly general: empirical state–control averages define weak couplings in both the cost functionals and dynamics of all agents, irrespective of their status as major or minor. We construct an auxiliary limiting problem for the RMM through a novel unified structural scheme that combines bilateral perturbation and mixed hierarchical re-composition. This scheme is of independent interest and can accommodate coupling structures more sophisticated than those considered in existing RMM frameworks. We then derive the associated consistency condition and characterize asymptotic RMM equilibria. Additionally, we study the RMM problem within specific infinite-horizon linear-quadratic settings for illustrative purposes via algebra Riccati equations.", "id": "Paper/67579", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67579"}, {"title": " Reconstruction of caterpillars under two models ", "webprogram_exclude": "0", "session_ids": ["Session/18141"], "source_sha256": "71384ecca6d446cca0d9722cc4a762aeea593daaba0eab0fd36d41213f2d5917", "withdrawn": "", "abstract": "A {\\it card} of a graph $G$ is a subgraph obtained by deleting one vertex.  The Reconstruction Conjecture of Kelly and Ulam states that every graph with at least three vertices is determined by its multiset of cards.  A {\\it caterpillar} is a tree in which the nonleaf vertices form a path.  We consider reconstruction of caterpillars under two refined models.\n\nThe {\\it reconstruction number} ${\\rm rn}(G)$ is the least number of cards that determine $G$.  When given only some cards, the degree of the missing vertex is not apparent.  A {\\it dacard} specifies that vertex degree along with the card.  The {\\it degree-associated reconstruction number} ${\\rm drn}(G)$ is the minimum number of dacards that determine $G$.  We review results of Barrus and West on ${\\rm drn}(G)$.  In particular, ${\\rm drn}(G)=2$ for all caterpillars except stars and one $6$-vertex example.  It remains conjectured that ${\\rm drn}(G)\\le 2$ for all but finitely many trees.\n\nAnother model consider subgraphs with fewer vertices.  The {\\it $k$-deck} of an $n$-vertex graph $G$ is its multiset of subgraphs induced by $k$ vertices.  Always the $k$-deck determines the $(k-1)$-deck, so an enhanced version of the reconstruction problem is to seek the smallest $k$ such that the $k$-deck determines $G$.  Manvel conjectured that for each $\\ell$ there is a threshold $M_\\ell$ such that when $n\\ge M_{\\ell}$ every $n$-vertex graph is determined by its $(n-\\ell)$-deck; the classical Reconstruction Conjecture is $M_1=3$.  We will describe known results on reconstruction from smaller cards.\n\nOf particular interest is the threshold on $n$ to guarantee reconstructibility of $n$-vertex trees from the $(n-\\ell)$-deck.  It is known that $n\\ge6\\ell+11$ suffices, and it is conjectured that $n\\ge2\\ell+1$ suffices, with small exceptions.  We will present several ideas from a recent proof that the conjectured threshold suffices for caterpillars and is best possible.  The result on caterpillars is joint work with Alexandr V. Kostochka, Zishen Qu, and Maddy Ritter.", "id": "Paper/67580", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67580"}, {"title": " THE GEOMETRY OF JOINT NUMERICAL RANGES FOR REAL DIAGONAL MATRICES ", "webprogram_exclude": "0", "session_ids": ["Session/18229"], "source_sha256": "6f2e0b068025b1ea467c143f1ee910fdcd5490347e796b0b937a2bf9a5179e05", "withdrawn": "", "abstract": "The joint numerical range of $n\\times n$ real diagonal matrices $A,B,C$ is defined by\n\t\t\\[ W(A,B,C)=\\{(\\text{tr}(QA),\\text{tr}(QB),\\text{tr}(QC)) \\in \\mathbb{R}^3 : Q=xx^*, x \\in \\mathbb{C}^n, x^*x=1 \\}.\\]\n\t\t\n\t\tMotivated by Embry's result on the multiplicity of points in the numerical range, we introduce the notion of projection multiplicity $p(u)$ of a point $u \\in W(A,B,C)$. Specifically, $p(u)$ is the maximal number of linearly independent rank-one orthogonal projection matrices $Q$ satisfying\n\t\t\\[ u=(\\text{tr}(QA),\\text{tr}(QB),\\text{tr}(QC)). \\]\n\t\t\n\t\tWe show that $W(A,B,C)$ is a convex polyhedron in $\\mathbb{R}^3.$\tFor an interior point $u \\in W(A,B,C)$, $p(u)$ depends on the affine dimension of $W(A,B,C)$. We also determine the projection multiplicity $p(u)$ of extreme points from the entries of $A,B,C$.", "id": "Paper/67582", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67582"}, {"title": " Factored Sparse Approximate Inverse Preconditioning via Spectral Optimization ", "webprogram_exclude": "0", "session_ids": ["Session/18282"], "source_sha256": "528878bdb01d0c37c05704a9b0ce845461d6fba838f8681900fcd1ffded9abeb", "withdrawn": "", "abstract": "In this talk, we study value selection for fixed-pattern factorized sparse approximate inverse preconditioners.  Given a prescribed sparsity pattern for a factor \\(G\\), we choose its admissible entries by optimizing spectral objectives of the congruent preconditioned operator \\(P(G)=GAG^\\top\\).  This differs from classical sparse approximate inverse and FSAI constructions, which choose entries through algebraic Frobenius-residual criteria.  For symmetric positive definite systems, the spectral target is a cluster near \\(+1\\).  For symmetric indefinite systems, where congruence preserves inertia, we introduce a bimodal loss that drives positive and negative eigenvalues toward separated clusters near \\(+1\\) and \\(-1\\), while penalizing eigenvalues near zero. To make these objectives practical for large sparse matrices, we derive projected Krylov support-gradients.  Lanczos runs provide both a stochastic trace estimate of the spectral objective and a Ritz approximation to the exact gradient.  We implement the resulting gradient through a detached Rayleigh surrogate: the Lanczos data are computed without gradient tracking and held fixed, while the backward pass differentiates only recomputed Rayleigh quotients with respect to the admissible entries of \\(G\\).  This avoids differentiating through the Lanczos recurrence while returning a matrix-free gradient on the prescribed support. Experiments on finite-element test problems show that spectral value selection improves fixed-support preconditioners, especially for symmetric indefinite saddle-point systems. We further demonstrate a graph neural network model for predicting admissible factor entries across related matrices.", "id": "Paper/67583", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67583"}, {"title": " Multi-level, multi-color mathematical graph neural networks for molecular property prediction ", "webprogram_exclude": "0", "session_ids": ["Session/17970"], "source_sha256": "97407d3108c99d9b0e2c7bf8985c22d7b9b032f4597504d8080ad504c8c1fb70", "withdrawn": "", "abstract": "Graph Neural Networks (GNNs) have demonstrated significant potential in molecular property prediction. However, current GNN architectures mostly rely on standard node or edge features that overlook the complex, multi-scale interactions between atoms in small molecules. This research introduces a mathematics-driven approach that integrates concepts from Geometric Graph Learning (GGL) and Algebraic Graph Learning to enhance molecular representations. Drawing upon GGL principles, we construct multi-color molecular graphs where nodes represent atoms and edges are weighted based on both spatial distances and local geometric features, such as curvatures derived from differential geometry applied to atomic interactions. Furthermore, we encode high-dimensional atomic interactions through the spectral properties of algebraic subgraphs, such as the Laplacian and adjacency matrices derived from these geometric graphs. The construction of these multi-level graphs and their connectivity follows the principles of Persistent Spectral Graph Theory, where a filtration process generates a family of graphs across different scales, capturing both topological persistence and geometric evolution of atomic relationships. This integrated approach enables reliable and robust molecular representations by incorporating both short- and long-range dependencies, thereby surpassing the limitations of conventional GNNs. Our approach significantly improves predictive performance in molecular property prediction tasks and provides a reliable framework to advance drug discovery and materials science applications.", "id": "Paper/67584", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67584"}, {"title": " Coarse Structures on Homogeneous Spaces ", "webprogram_exclude": "0", "session_ids": ["Session/18213"], "source_sha256": "576f4b1e04b6e85e1083febf020dc5347f4ac3d1ccb0cb00821515667ee8ad2f", "withdrawn": "", "abstract": "We begin with a brief introduction to the coarse geometry of topological groups, following the framework developed by Christian Rosendal. In particular, we introduce coarse structures and the relevant left-coarse structures on topological groups.\n\nNext, we present joint work with Rosendal in which, given a short exact sequence of Polish groups, we characterize when the metrizability of the respective left-coarse structures of the kernel group and the quotient group implies the metrizability of the left-coarse structure of the middle group. The characterization is presented in terms of the coarse structure that the middle group induces on the quotient group when the latter is viewed as a homogeneous space under the canonical action from the former.\n\nWe illustrate the characterization with both positive and negative examples regarding the metrizability of the left-coarse structure of the middle group. Finally, we compare our analysis of left-coarse structures with the analogous situation for left-uniform structures on topological groups.\n\nWe will also comment on how these ideas allow us to do geometric group theory on topological groups, while highlighting connections to descriptive set theory.", "id": "Paper/67589", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67589"}, {"title": " A general strong property for IEP-<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.827ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 786.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">G</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-47\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q492 659 471 656T418 643T357 615T294 567T236 496T189 394T158 260Q156 242 156 221Q156 173 170 136T206 79T256 45T308 28T353 24Q407 24 452 47T514 106Q517 114 529 161T541 214Q541 222 528 224T468 227H431Q425 233 425 235T427 254Q431 267 437 273H454Q494 271 594 271Q634 271 659 271T695 272T707 272Q721 272 721 263Q721 261 719 249Q714 230 709 228Q706 227 694 227Q674 227 653 224Q646 221 643 215T629 164Q620 131 614 108Q589 6 586 3Q584 1 581 1Q571 1 553 21T530 52Q530 53 528 52T522 47Q448 -22 322 -22Q201 -22 126 55T50 252Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-47\" x=\"0\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/17911"], "source_sha256": "5dac2a17a58be4533d34abedf0c25e3bd8000f0d3c1ff1aa59f9467828b5f2bb", "withdrawn": "", "abstract": "The Inverse Eigenvalue Problem for a Graph (IEP-$G$) asks for the possible spectra of a real symmetric matrix when only its off-diagonal zero / nonzero pattern, as described by a graph $G$, is known.\nThree matrix properties, collectively called the ``strong properties'', have become prominent in the study of this problem, due in part to their good behavior with respect to graph minors.\nThe three properties differ in what eigenvalue data is preserved:\n\\begin{itemize}\n\\item For the Strong Arnold Property (SAP), a single multiplicity.\n\\item For the Strong Multiplicity Property (SMP), all multiplicities.\n\\item For the Strong Spectral Property (SSP), all multiplicities and locations.\n\\end{itemize}\n\nIn most cases, a question that calls for a strong property will be served well by one of these three perspectives.\nThere does, however, exist a more general perspective that contains each of these as a special case, here introduced as the General Strong Property (GSP), for which any chosen subset of eigenvalue multiplicities can be preserved, whose locations can be allowed to vary locally subject to linear or smooth constraints.\nPattern manifolds more general than just zero / nonzero are also possible.\nThe usual strong property consequences are obtained:\n\\begin{itemize}\n\\item an algebraic definition equivalent to the manifold definition,\n\\item a verification matrix,\n\\item superpatterns and other manifold inclusions,\n\\item augmentation,\n\\item edge decontraction, generalized to \\emph{clique decontraction,}\n\\item matrix liberation,\n\\item and a refined Bifurcation Lemma, giving stronger results for SAP and SMP.\n\\end{itemize}\n\nIn addition, the null space characterization of SAP given by H. van der Holst is extended to an eigenspace characterization of GSP, including the special cases of SMP and SSP, whose eigenspace characterizations have not appeared in the literature.", "id": "Paper/67596", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67596"}, {"title": " Region-Based Validation and Uncertainty Mapping for Hyperspectral Classification with Sparse Labels ", "webprogram_exclude": "0", "session_ids": ["Session/19345"], "source_sha256": "c6c43f8da641f374bf6c838585f602e5439ac9f35d1c7823018864d97afc66ea", "withdrawn": "", "abstract": "Spatial dependence creates a validation problem in hyperspectral image classification when labels are available only in a few small regions. Nearby pixels often have similar spectra, so random pixel splits can overestimate performance on a new region. We study this problem in a selected region of a nondestructive hyperspectral scan of meteorite material. Four separated patches contain the labels. Because the material types represented by the four patches have not yet been confirmed, we compare different ways of grouping the patches into two temporary classes rather than assigning material names to them.\nAfter spectral preprocessing, Gaussian spatial smoothing is used to incorporate local information. We fit linear support vector machines, with nearest-neighbor, principal-component, and sparse optimal scoring methods as baselines. To measure spatial transfer rather than performance on randomly selected pixels, we compare random splits with balanced patch-pair tests and leave-one-patch-out validation, where complete patches are held out during fitting.\nThe results show that generalization depends strongly on label grouping. Under one proposed grouping, a linear classifier using locally smoothed spectra performs well on held-out patches, whereas an alternative grouping does not generalize reliably. This difference shows why the label structure must be confirmed before physical meaning is assigned to predicted classes.\nWe also apply the fitted models across the full image region and map estimated class probabilities and normalized entropy. These maps show where the model gives stronger or weaker support to its predictions, but they do not directly measure material composition. Overall, this work shows that spatial sampling, label interpretation, and independent validation are central to hyperspectral classification with sparse labels.", "id": "Paper/67599", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67599"}, {"title": " Improvements on the schemes VOX and QR UOV When minus is a plus ", "webprogram_exclude": "0", "session_ids": ["Session/18073"], "source_sha256": "d156a9f68e027e4900b57b28ca315f937c5c374f4b463e430f92a43a18c33772", "withdrawn": "", "abstract": "I present here an improvement for QR UOV and a reparation of VOX. Both candidates to the NIST Post-Quantum Cryptography: Additional Digital Signature Schemes.\n\n    Thanks to the use of the perturbation minus we are able to fully exploit the parameters in order to reduce the public key. It also helps us to repair the scheme VOX. With QR UOV- we are able to significantly reduce the size of the public key at the cost of a small increase of the signature size. We show that VOX does not bring significant advantage in terms of sizes compared to QR but gives a double security aspect.\n    We also show that the use of minus perturbation is very useful with schemes that use the QR (Quotient ring perturbation).", "id": "Paper/67601", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67601"}, {"title": " Harnack inequality for singular or degenerate parabolic equations in non-divergence form ", "webprogram_exclude": "0", "session_ids": ["Session/17947"], "source_sha256": "190f23c49330d6c9a3ccbc98edd154cec866e040c985611f1b027b30e448bb3a", "withdrawn": "", "abstract": "In this talk, we explore the behavior of solutions to a class of linear parabolic equations in non-divergence form, featuring measurable leading coefficients that can be either singular or degenerate. The degree of singularity or degeneracy is governed by weights belonging to the Muckenhoupt $A_{1+\\frac{1}{n}}$ class. We will discuss how to establish a Krylov-Safonov Harnack inequality for these equations under a smallness assumption on the weighted mean oscillation of the weight. We will also examine some immediate consequences of these results, including H\\\"{o}lder regularity estimates with respect to an underlying quasi-distance, a new Liouville-type theorem, and a related $W^{2,\\epsilon}$ Lin-type estimate. To prove these results, we introduce a novel framework of generic weighted parabolic cylinders, establish key growth lemmas, and employ a perturbation method combined with a parabolic Aleksandrov-Bakelman-Pucci (ABP) maximum principle applied to carefully constructed barrier functions.", "id": "Paper/67602", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67602"}, {"title": " Stochastic Control with Temporally Correlated Noise ", "webprogram_exclude": "0", "session_ids": ["Session/18293"], "source_sha256": "4b891be893f9ed5e201f1a76f584db35afb903ec42ec1af5247fa1cd3c588546", "withdrawn": "", "abstract": "We study discrete-time stochastic control problems where the noise driving the state dynamics is a stationary infinite-order chain rather than an i.i.d. sequence. We formulate the problem as a controlled Markov process by enlarging the state space to include the posterior distribution of the noise given the state-action history. Assuming that the sensitivity of the noise transition kernel to past noise values decays exponentially, we show that the expected total variation distance between the full-history and finite-memory noise filters decays at rate $\\sqrt{N}\\rho^{\\sqrt{N}}$ for some $\\rho<1$. We use this result to construct finite-memory control models and establish near-optimality bounds for their policies. Finally, under suitable ergodicity conditions, we show that Q-learning converges to the optimal solution of the approximate model, so the same performance bounds apply to the learned policies.", "id": "Paper/67603", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67603"}, {"title": " Mean-Field Control with a Common Hidden State under Decentralized Observations ", "webprogram_exclude": "0", "session_ids": ["Session/18274"], "source_sha256": "7fcf3dce0faf850e79979aa17f8d1f1e2a06aecc7c202700ef224658bfa0f05b", "withdrawn": "", "abstract": "We study optimal control of a system with multiple decision makers who share a common hidden state and receive fully decentralized observations through identical channels. The dynamics of the hidden state and the cost received by the agents depend on the agents' actions only through their empirical distribution. In the limit problem with infinitely many agents, the problem reduces to a single agent control problem where the agent affects the hidden state dynamics via the conditional law of the actions\ngiven the past values of the hidden state process. We formulate this problem as a deterministic measure valued control problem over the space of policies.\nWe show that the optimal symmetric policies designed for the infinite population problem are near optimal for the finite population problem with bounds on the loss of performance.", "id": "Paper/67604", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67604"}, {"title": " On the regularity of minimizing fractional harmonic maps ", "webprogram_exclude": "0", "session_ids": ["Session/17883"], "source_sha256": "a9b79aef5a641549e8cfcf7fd847934a397adea72819e8d760b271a9757cf8d9", "withdrawn": "", "abstract": "We discuss the regularity of minimizing fractional harmonic maps and analyze the dimension of their singular sets. These are mappings $u\\in \\dot{W}^{s,p}(\\mathbb{R}^n,\\mathcal{N})$ into manifolds $\\mathcal{N}$ with sufficiently simple topology that minimize the nonlocal energy\n$$\\int_{\\mathbb{R}^n}\\int_{\\mathbb{R}^n}\\frac{|u(x)-u(y)|^p}{|x-y|^{n+sp}} \\;dx\\;dy.$$\nWe prove that these minimizers are locally H\\\"older continuous in a bounded domain $\\Omega$ outside a singular set $\\Sigma $ with Hausdorff dimension strictly smaller than $n-sp.$ We avoid the use of a monotonicity formula, which is unknown when $p \\neq 2$, by using a blow-up argument instead.", "id": "Paper/67606", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67606"}, {"title": " Automating Mathematics Assessment: Lessons from Educational Practice in Kenya and Italy ", "webprogram_exclude": "0", "session_ids": ["Session/18092"], "source_sha256": "460bcf88771d2a17ca3a86af7a640ab0338f8249b7c3d99ff9b0c43429df76b9", "withdrawn": "", "abstract": "There is no doubt that teaching, learning, and assessment are undergoing an increasing shift towards automation. Mathematics presents a particularly interesting case because assessment often requires students to construct and communicate mathematical expressions rather than simply select an answer.\nIn this talk, I will share findings from my doctoral research, reflecting on two case studies, Kenya and Italy, which involve institutions using STACK (System for Teaching and Assessment using a Computer Algebra Kernel), an open-source system for automated mathematics assessment. Drawing on studies with students, lecturers, and institutional implementations, the talk will examine what happens when automated mathematics assessment moves from a technological possibility into educational practice. I will discuss both the opportunities and challenges, including student engagement, communicating mathematics to a computer, automated feedback, assessment design, learning analytics, and implementation at scale.", "id": "Paper/67607", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67607"}, {"title": " Bergman Kernel Asymptotics: From Complex to Cauchy–Riemann Geometry ", "webprogram_exclude": "0", "session_ids": ["Session/18295"], "source_sha256": "edb178f673ba98be2d94cbc30abc32b8a2be90c7f07f6a46ee809c125f53b810", "withdrawn": "", "abstract": "The asymptotic expansion of Bergman kernels for high tensor powers of positive holomorphic line bundles encodes geometric information of the underlying complex manifold. In this talk, we revisit this expansion and describe its geometric consequences, in particular for the approximation of K\\\"ahler metrics. We then turn to the CR setting, where the absence of ellipticity introduces new analytic features, and discuss how analogous asymptotic phenomena emerge despite these structural differences.", "id": "Paper/67608", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67608"}, {"title": " Almost free modules relative to <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"8.117ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 3495 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\textrm {Add}(X)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-41\" d=\"M255 0Q240 3 140 3Q48 3 39 0H32V46H47Q119 49 139 88Q140 91 192 245T295 553T348 708Q351 716 366 716H376Q396 715 400 709Q402 707 508 390L617 67Q624 54 636 51T687 46H717V0H708Q699 3 581 3Q458 3 437 0H427V46H440Q510 46 510 64Q510 66 486 138L462 209H229L209 150Q189 91 189 85Q189 72 209 59T259 46H264V0H255ZM447 255L345 557L244 256Q244 255 345 255H447Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-64\" d=\"M376 495Q376 511 376 535T377 568Q377 613 367 624T316 637H298V660Q298 683 300 683L310 684Q320 685 339 686T376 688Q393 689 413 690T443 693T454 694H457V390Q457 84 458 81Q461 61 472 55T517 46H535V0Q533 0 459 -5T380 -11H373V44L365 37Q307 -11 235 -11Q158 -11 96 50T34 215Q34 315 97 378T244 442Q319 442 376 393V495ZM373 342Q328 405 260 405Q211 405 173 369Q146 341 139 305T131 211Q131 155 138 120T173 59Q203 26 251 26Q322 26 373 103V342Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-58\" d=\"M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-41\"></use>\n <use xlink:href=\"#E1-MJMAIN-64\" x=\"750\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-64\" x=\"1307\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"1863\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-58\" x=\"2253\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"3105\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18371"], "source_sha256": "7ce2119866232b4980b7fe736c62e905541ea1d3402d7c8f9fe9c6cb95c2a918", "withdrawn": "", "abstract": "Almost free abelian groups are those abelian groups that have many free subgroups but, in principle, they are not free. Among these notions of almost freeness we have the $\\kappa$-free, strongly $\\kappa$-free, and $\\kappa$-free in the weak sense for $\\kappa$ an infinite cardinal. There has been a significant amount of research trying to find which cardinals $\\kappa$ satisfy that every almost free module related to $\\kappa$ is free. Usually, the answer of this question depends on the set-theoretic assumption used.\n\nLet $R$ be any ring. In the category if right $R$-modules we can consider natural extensions of these notions replacing the class of all free modules with another class of modules $\\mathcal X$. We are interested in the case where $\\mathcal X=\\textrm{Add}(X)$ for a fixed module $X$, that is, in almost free modules relative to $\\textrm{Add}(X)$.\n\nIn the talk, we will discuss several notions of almost freeness relative to $\\textrm{Add}(X)$ and see how some classical constructions of almost free abelian groups can be extended to this setting. Moreover, we will relate these constructions to several problems in module theory: Enochs' conjecture on covering classes of modules and the condition for the module $X$ to have a perfect decomposition.", "id": "Paper/67609", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67609"}, {"title": " On some lower bounds for Call-Silverman canonical heights of polynomials ", "webprogram_exclude": "0", "session_ids": ["Session/17755"], "source_sha256": "0234bc6a2843ab86c7f89efc2dbf05fa351c3bda84a01b03a6e219700fd2fe6e", "withdrawn": "", "abstract": "We report on some new lower bounds for the canonical height associated with polynomial maps over number fields, including classes of non-hyperbolic polynomials and those that are not conjugate to powers or Tchebychev maps.", "id": "Paper/67610", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67610"}, {"title": " Mutation-equivalence in Tree-triangle Quivers ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "f07dc398191161eceea59d65163aebe431ef128e323b5d4a462d88fb15e66fd8", "withdrawn": "", "abstract": "Cluster algebras were first introduced by Fomin and Zelevinsky in 2001 to understand total positivity in semisimple groups by quiver mutation. Fomin poses the question of developing an algorithm that determines if two quivers are mutation-equivalent. In this paper, we build on prior research into quivers with the same underlying tree by extending the algorithm to handle graphs with 3-cycles, or triangles. We define four types of quiver triangles that determine mutation-equivalence based on their position in the tree. This algorithm provides a framework for answering Fomin’s problem for certain families of graphs.", "id": "Paper/67611", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67611"}, {"title": " Mathematical modeling in medicine: applications to glaucoma and heart transplantation ", "webprogram_exclude": "0", "session_ids": ["Session/18275"], "source_sha256": "7c19bfcb15a7ac3392f9e5f1e7d968cd09bac18c432638b1c9d2a28fda93f756", "withdrawn": "", "abstract": "Mathematical models are indispensable tools that provide a more complete understanding of biological interactions and causal relationships across spatial, temporal, and organizational scales.  The development of such mathematical models has catalyzed major progress in medicine and science.  Here, the role of math in medicine will be exemplified in two clinical applications:  glaucoma and heart transplantation.  First, impairments in retinal blood flow and oxygenation have been shown to contribute to the progression of glaucoma.  A theoretical model of the retinal vasculature is used to show that reduced capillary density, increased intraocular pressure, or impaired blood flow regulation can cause decreased tissue oxygenation. The model demonstrated that the metabolic effects of reduced vessel density reductions were exacerbated when combined with other vascular impairments.  The model framework allows for comparisons to sectorial-specific clinical data to help assess the potential role of impaired retinal blood flow in ocular disease.  Second, organ transplantation is a lifesaving procedure that is still met with serious risks, including organ rejection, infection, and a compromised immune system.  A mathematical model is used to identify combination therapeutic strategies that could yield transplant acceptance while reducing the reliance on immunosuppression.  The model combines the effect of immunosuppression and adoptive transfer of regulatory T cells with a goal of determining which immune mechanisms should be targeted by immunosuppression to optimize the benefit of adoptive transfer and reduce the required levels of immunosuppression.  The study shows the utility of mathematical modeling in guiding future experimental studies of new therapeutic strategies in transplant immunology.", "id": "Paper/67615", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67615"}, {"title": " A Unifying Complex Time Representation Framework: From Dirac Operators to Kimesurfaces and AI Modeling ", "webprogram_exclude": "0", "session_ids": ["Session/18272"], "source_sha256": "9471dac3cdfc935ec05a70c08cb4014807e6b558e3cc8f6344db007b861c3203", "withdrawn": "", "abstract": "Complex time (kime), $\\kappa = t\\,e^{i\\theta}$, unifies two disjoint problems: quantum mechanics in multi-time spacetimes and repeated-measurement longitudinal data. We formulate the Dirac equation on $(3{+}2)$-dimensional flat spacetime, signature $(-,-,-,+,+)$, with a compactified second time dimension. The kime-magnitude $t\\geq 0$ is a deterministic classical time preserving macroscopic causality; the compactified kime-phase $\\theta$ is an internal stochastic degree of freedom governed by Fokker-Planck dynamics. We prove no chirality operator exists in $D=5$ (eliminating Weyl spinors), construct the $\\mathrm{Cl}(3,2)$ Clifford algebra with signature-consistent gamma matrices, and derive the 5D Dirac operator in kime coordinates with $1/t$ scaling and spin-connection terms. A naïve Kaluza-Klein reduction yields tachyonic instabilities in the $n \\neq 0$ sectors. The stochastic projection $\\Phi_n(t) = e^{-Dn^2t}$, a low-pass filter, exponentially suppresses them while preserving the stable $n=0$ sector with standard relativistic dispersion, consistent with unitarity and causality.\n\nComplex-time geometry aids data representation and AI inference: generalizing event order from the positive reals to the complex plane transforms time-series into two-dimensional manifolds (kimesurfaces) via a bijective Laplace-transform correspondence; the kime-phase encodes repeated-observation fluctuations, the kime-magnitude the longitudinal dynamics. We develop a tensor-regression linear model on these manifolds, validated on functional MRI data, extending classical protocols for multivariate longitudinal inference, prediction, classification, and regression. The filter $e^{-Dn^2t}$ stabilizes multi-time physics and mirrors diffusion regularization in manifold learning, while the stochastic kime-phase captures quantum-fluctuation and repeated-measurement uncertainty.", "id": "Paper/67616", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67616"}, {"title": " What Should Digital Assessment Make Visible to Mathematics Teachers? ", "webprogram_exclude": "0", "session_ids": ["Session/18092"], "source_sha256": "822d10615a1e86cce24374bbdd0b6f2940584949332b5f6ed87d332cf0dd123d", "withdrawn": "", "abstract": "As digital assessment grows, teachers have access to more data, but more data does not always mean better teaching decisions. The key question is: what information should digital assessment systems show teachers so that the data are actually useful within the time frame it is intended for?\nIn this talk, we use a project developed in Moodle, an online learning platform, and STACK, a tool for automatically assessing mathematical answers and uses algebraic reasoning. We ask four simple questions: What should teachers look for in the data? What should they investigate? How should they interpret the data? And what should they do with that information?\nAlthough our case is based on STACK, the problem applies to any digital assessment system. We aim to share what we have learned and also hear from the audience about what information they would find useful in their own teaching. Suppose they would be using a tool like STACK.", "id": "Paper/67617", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67617"}, {"title": " Rigidity and Graph Coloring ", "webprogram_exclude": "0", "session_ids": ["Session/18238"], "source_sha256": "80f4f59756679c53003daaca50b517f5766690ad30cb5b015916f4d631f87769", "withdrawn": "", "abstract": "In 2019, Georg Grasegger, Jan Legerský, and Josef Schicho published “Graphs with Flexible Labelings” in which they found that a connected graph G has a flexible realization in $\\mathbb{R}^2$ if and only if there exists a NAC-coloring of its edges. An edge-coloring $\\delta: E \\rightarrow \\{Blue, Red\\}$ is considered a NAC-coloring if it is surjective and no cycle of G is almost monochromatic (i.e., for every cycle in G, either all edges are the same color, or there are at least two blue and two red edges in each cycle). In this work, I will investigate the relationship between a given NAC-coloring and the flexes of the resulting framework in $\\mathbb{R}^2$.", "id": "Paper/67621", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67621"}, {"title": " Orthodontia and Lascoux Positivity ", "webprogram_exclude": "0", "session_ids": ["Session/18308"], "source_sha256": "625bedf14fa354c160fe3ee85ca64564ca29d68ae566687ecc7024a7bb694d10", "withdrawn": "", "abstract": "Schubert polynomials appear in representation theory as the characters of reducible $B$-modules, the flagged Schur modules. A formula of Magyar gives a Demazure-like character formula for Schubert polynomials through a combinatorial algorithm, in the process giving a short proof of their key positivity. We study Grothendieck polynomials, $K$-theoretic analogues of Schubert polynomias, and describe several generalizations of Magyar's formula. We explain a Lascoux-positivity result arising from the extensions. This talk is based on joint work with Karola M\\'esz\\'aros and Linus Setiabrata.", "id": "Paper/67624", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67624"}, {"title": " Accessibility in Math Courses in Higher Education ", "webprogram_exclude": "0", "session_ids": ["Session/17471"], "source_sha256": "d8332e7f6b1173f01c0184d1b8660cbe6274dad0ebd6852ff0fab240844c04be", "withdrawn": "", "abstract": "Starting in April 2027, institutions of higher education will need to make their course content compliant with Web Content Accessibility Guidelines (WCAG) 2.1AA. This is to comply with Title II of the Americans with Disabilities Act. Mathematics courses provide unique accessibility challenges. In this talk, I will present publicly available tools which I have used over the last four years to make my courses accessible. \n\nAbout me: I have C.P.A.C.C. (Certified Professional in Accessibility Core Competencies) and A.D.S. (Accessible Document Specialist) credentials from the I.A.A.P. (International Association of Accessibility Professionals).", "id": "Paper/67625", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67625"}, {"title": " On degenerate reaction-diffusion epidemic models with mass action or standard incidence mechanism ", "webprogram_exclude": "0", "session_ids": ["Session/17688"], "source_sha256": "8b0fc8331f4f2d7d10c980d7d3733846c4d32a841959cb14e5301f275315da17", "withdrawn": "", "abstract": "We consider  reaction-diffusion epidemic models with mass action or standard incidence mechanism and study the impact of limiting population movement on disease transmissions. We set either the dispersal rate of the susceptible or infected people  to zero and study  the corresponding degenerate reaction-diffusion model.  Our main approach to study the global dynamics of these models is to construct  delicate Lyapunov functions.   Our results show that the consequences of limiting the movement of susceptible or infected people depend on transmission mechanisms, model parameters, and population size.", "id": "Paper/67630", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67630"}, {"title": " The Gray product via lax grids ", "webprogram_exclude": "0", "session_ids": ["Session/18000"], "source_sha256": "cc30635bfc8a8204902f5a7469dd8dec8b6ce1cfc15cc407aaa348153e896055", "withdrawn": "", "abstract": "The Gray product is a fundamental operation on higher categories that is often difficult to construct explicitly. A productive approach uses cubical models of higher categories, whose basic cells are lax cubes. In joint work with Shai Keidar, we introduce a new model for (\\infty,n)-categories (n\\le \\infty) as Segal sheaves on lax grids, which are pasting diagrams of lax cubes.\nThis model allows for a construction of the Gray product via Day convolution. I will present this model and discuss future applications to cobordism categories.", "id": "Paper/67636", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67636"}, {"title": " The Value of Duplicate Measurements When Decoding Second-Order Reed-Muller Codes ", "webprogram_exclude": "0", "session_ids": ["Session/18020"], "source_sha256": "d13cfe69f2f55d509c521c6ae48fe3905c0b59cd1414db6be8d4ec1e38a41758", "withdrawn": "", "abstract": "We compare the performance of the RPA and CHIRRUP decoding algorithms for second-order Reed-Muller codes. The RPA algorithm recovers a binary quadratic form associated with a skew-symmetric matrix $M$, whereas CHIRRUP recovers a $\\mathbb{Z}_4$-valued quadratic form associated with a symmetric matrix $P$. We describe how the Gray map connects the evaluation vectors of these forms, inducing a rank-preserving correspondence between $M$ and $P$. We analyze how Euclidean distance between evaluation vectors is governed by matrix rank differences using Delsarte-Goethals sets $DG(m, r)$. We demonstrate that CHIRRUP uses repeated measurements more effectively than RPA on these ensembles. While a kernel-aware variant of RPA improves performance on singular quadratic forms by aggregating projection directions across cosets of $\\ker M$, CHIRRUP's tree search combines multiple row estimates more efficiently on $DG(m, r)$ when $r < \\frac{m-1}{2}$, outperforming vanilla RPA.", "id": "Paper/67639", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67639"}, {"title": " Visualizing Large Graphs to Understand Cluster Algebras ", "webprogram_exclude": "0", "session_ids": ["Session/18100"], "source_sha256": "73be4f4e6c7d6aa2bccf8c428daecc34d3d9d959e07c180b793e4d0384a3600c", "withdrawn": "", "abstract": "Cluster algebras provide a rich combinatorial structure on many interesting algebras including the coordinate ring of a Grassmannian and the Teichm\\\"uller space of decorated hyperbolic structures on a surface. It provides an associated \\emph{cluster complex} which is a large (usually infinite) graph which encodes good sets of generators of the algebra and there relations. By finding realizations of these graphs in the plane we not only produce compelling mathematical illustrations but are able to observe the structure of a cluster algebra that is hidden in the technical combinatorial definition.", "id": "Paper/67640", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67640"}, {"title": " Impact of network connectivity on metapopulation growth rate and total biomass ", "webprogram_exclude": "0", "session_ids": ["Session/18275"], "source_sha256": "2dd54bd53e5e0010eab7e57935872a46757c6031dc7846f749d5e5dc5f7cabd8", "withdrawn": "", "abstract": "We consider the impact of network connectivity on the dynamics of a population in a\nstream environment. The population is modeled using a graph theoretical framework,\nwith habitats represented by isolated patches. We introduce a change in connectivity into the model through the addition of a bi-directional or one-directional edge\nbetween two patches and examine the impact of this edge modification on the metapopulation growth rate and the network biomass. Our main results indicate that adding\na bi-directional edge often decreases both measures, while the effect of adding one-directional edge is more intricate and dependent on the model parameters. We establish\ncomplete analytical results for stream networks of three patches, and provide some\ngeneralizations and conjectures for more general stream networks of n patches. These\nconjectures are supported with numerical simulations.", "id": "Paper/67641", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67641"}, {"title": " Hilbert-Schmidt Hankel operators with harmonic symbols on the Bergman space of strongly pseudoconvex domains in <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.897ex\" height=\"2.343ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -863.1 1247.1 1008.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbb {C}^n</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJAMS-43\" d=\"M684 131Q684 125 672 109T633 71T573 29T489 -5T386 -19Q330 -19 276 -3T174 46T91 134T44 261Q39 283 39 341T44 421Q66 538 143 611T341 699Q344 699 364 700T395 701Q449 698 503 677T585 655Q603 655 611 662T620 678T625 694T639 702Q650 702 657 690V481L653 474Q640 467 628 472Q624 476 618 496T595 541Q562 587 507 625T390 663H381Q337 663 299 625Q212 547 212 336Q212 249 233 179Q274 30 405 30Q533 30 641 130Q658 147 666 147Q671 147 677 143T684 131ZM250 625Q264 643 261 643Q238 635 214 620T161 579T110 510T79 414Q74 384 74 341T79 268Q89 213 113 169T164 101T217 61T260 39L277 34Q270 41 264 48Q199 111 181 254Q178 281 178 344T181 434Q200 559 250 625ZM621 565V625Q617 623 613 623Q603 619 590 619H575L588 605Q608 583 610 579L621 565Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJAMS-43\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-6E\" x=\"1021\" y=\"608\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/19362"], "source_sha256": "9ceb754581873e7ca88c0188a38bf28375a39450cda9251e566d8fb88a07b832", "withdrawn": "", "abstract": "We characterize Hilbert-Schmidt Hankel operators on the Bergman space of smoothly bounded strongly pseudoconvex domains in $\\mathbb{C}^n$ for $n\\geq 2$.  The symbols we consider are harmonic on the domain and smooth up to the closure of the domain.  We use the boundary geometry of the domain, $\\overline{\\partial}$ estimates for $L^2$, and the $L^2$ regularity of the Berezin transform in a significant way.", "id": "Paper/67642", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67642"}, {"title": " A Cut Finite Element Framework for Multiphase Flow Problems ", "webprogram_exclude": "0", "session_ids": ["Session/19344"], "source_sha256": "b6a3d5115c83b95d630f7a16a6dbc37d8eb07cc05c9e473490c4d86c5200ac36", "withdrawn": "", "abstract": "This work extends a stabilized Nitsche-type Cut Finite Element Method (CutFEM) from two-phase to multiphase flow problems involving complex, implicitly defined interfaces. The presence of multiple interacting phases introduces additional challenges due to discontinuous material properties across several interfaces and the possibility of complex interface configurations. The proposed formulation employs Nitsche’s method to weakly enforce interface conditions, together with Continuous Interior Penalty (CIP) stabilization and Ghost Penalty (GP) terms to maintain stability independently of how the interfaces intersect the background mesh. Building on the two-phase framework, the method is generalized to accommodate multiple subdomains with distinct physical properties and interface coupling conditions. Using an Oseen-type formulation, we investigate the stability of the resulting multiphase CutFEM formulation and establish a priori error estimates under appropriate assumptions. This theoretical framework provides a foundation for unfitted finite element approximations of multiphase flow problems with complex and evolving interface geometries.", "id": "Paper/67644", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67644"}, {"title": " The lattice of abstract elementary classes of modules ", "webprogram_exclude": "0", "session_ids": ["Session/18371"], "source_sha256": "50c255ff63a55126ff780af237dfd081ad1ce031942e17e651e76f96c393dfed", "withdrawn": "", "abstract": "Abstract elementary classes constitute the prominent model-theoretic framework used to study non-elementary classes of structures. We will introduce abstract elementary classes in the context of module theory and focus on understanding the lattice of abstract elementary classes whose underlying class is the class of all $R$-modules for a fixed ring $R$ and whose strong submodel relation lies between the submodule and direct summand relations, with the order given by reverse inclusion. We will show that the structure of the lattice depends heavily on the properties of the ring $R$ and showcase some of its properties when $R = \\mathbb{Z}$.", "id": "Paper/67645", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67645"}, {"title": " Localization of Roots For Trinomial Families ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "53470d9c441a334d6a8ed90ddded81d09a3fcd432b4f95c3d95ad634ace5592a", "withdrawn": "", "abstract": "For $n \\ge 2$, we analyze the root distribution of the trinomial family $\\mathcal{F}_n = \\{z^n + z^k - 1 : 1 \\le k \\le n-1\\}$ in the complex plane. While the roots of $z^n - 1$ lie entirely on the unit circle, the lower-order term $z^k$ disrupts this symmetry, distributing roots across the interior, exterior, and boundary of the unit circle in the complex plane. To geometrically localize the roots, we find $n$ disjoint Rouch\\'e sectors centered at the $n^{\\text{th}}$ roots of unity each containing $n-1$ family roots (counting multiplicity). Furthermore, we use Rouch\\'e's theorem to show that all roots are tightly bounded within an annulus $1/r \\le \\vert{}z\\vert{} \\le r$, depending on $n$. Intersecting the Rouch\\'e sectors with the annular bands constructs polar rectangular regions confining all roots, whose area shrink to the unit circle as $n \\to \\infty$.", "id": "Paper/67648", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67648"}, {"title": " Mathematics and the New Black Humanism: Frank Chapman’s  Science and Africa  ", "webprogram_exclude": "0", "session_ids": ["Session/18374"], "source_sha256": "bfecc081257b19f191c4687f3961d4da74f0dfd96b91c5e6c9c3acd4d3d83e6e", "withdrawn": "", "abstract": "In 1973, Polish American Claudia Zaslavsky (1917-2006) published \\textit{Africa Counts: Number and Pattern in African Cultures}, one of the first mainstream monograph to focus on mathematics in Africa. Zaslavsky made no mystery that her writing was influenced by the never published \\textit{Science and Africa: Essays on the Part Which People of Color Have Played in the Development of the Natural Sciences and Mathematics}, written by a young imprisoned African American man in his twenties: Frank E. Chapman Jr.\n\nFrom an unedited manuscript of \\textit{Science and Africa}, this talk analyses the place that Chapman gave to science, and in particular mathematics in the history of mankind and how he tied this history to Black Liberation during the Civil Rights Movement. By blending influences and putting in conversation historians of science, like George Sarton and David Eugene Smith with Black scholars like W.E.B Dubois and Frantz Fanon, Chapman reframed the stakes of history of mathematics as a struggle for the acknowledgement of one’s humanity. In addition, drawing on his engagement with Marxism, he hoped that his history of mathematics could help start a revolution. \n\nProviding an entry point to mathematics being a path to political liberation, Chapman’s work invites us to question how neutral and apolitical a work of history of mathematics can be.", "id": "Paper/67649", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67649"}, {"title": " Scattering theory of quantum Klein–Gordon fields in asymptotically flat spacetimes ", "webprogram_exclude": "0", "session_ids": ["Session/18326"], "source_sha256": "09383c89595105f42d38e0d318e73eac6825cec2b57ad9035bc9eff983b061c2", "withdrawn": "", "abstract": "I will describe how microlocal analysis can be used to define distinguished incoming and outgoing vacuum states in the quantum theory of massive Klein--Gordon fields in asymptotically flat spacetimes. The vacuum states satisfy the Hadamard condition, and the particle representations they define are unitarily equivalent, or in other words the quantum S-matrix is well-defined. An essential ingredient of the construction are distinguished retarded, advanced, Feynman and anti-Feynman propagators, whose existence, uniqueness, and microlocal properties (established in this setting in joint work with Andr{\\'a}s Vasy) give rise to natural incoming and outgoing single-particle structures.", "id": "Paper/67650", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67650"}, {"title": " Understanding Course Coordinators’ Interactions Within Coordinated Systems of Undergraduate Gateway Mathematics Courses ", "webprogram_exclude": "0", "session_ids": ["Session/18250"], "source_sha256": "b8eb861ecfc44f245a73ba6e7a688f4c53b6bcf2044beee719b0b9cccce411a6", "withdrawn": "", "abstract": "Course coordination has been identified as a promising approach for improving consistency and supporting instruction across multiple sections of undergraduate gateway mathematics courses (e.g., Adeyemi et al., 2023). Course coordinators play a particularly important role within these systems, mediating among departmental contexts and structures, instructors of coordinated courses, and students enrolled in these courses (e.g., Smith et al., 2021). However, little is known about how coordinators interact with these different components of the coordinated system and how this might differ across institutions (Carney et al., 2025).\n\nThis study examines how course coordinators of undergraduate gateway mathematics courses describe and make sense of their interactions within their coordinated system, including their interactions with departmental contexts and structures, instructors of coordinated courses, and students enrolled in these courses. As part of a larger explanatory sequential mixed-methods study, a national survey of course coordinators examines coordinators’ perceptions of their role and their interactions. This presentation will report findings from the national survey with a focus on answering the following research question: How do course coordinators of undergraduate gateway mathematics courses describe and make sense of their interactions with others in the coordinated system (i.e. departmental context and structures, coordinated instructors, and students in coordinated courses)? The results will provide a broad picture of how course coordination is structured and enacted across institutions and identify patterns in coordinators’ roles and interactions within coordinated systems. Furthermore, results may help departments better understand the course coordinator role and inform decisions about how coordinators are positioned and supported within undergraduate gateway mathematics programs.", "id": "Paper/67652", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67652"}, {"title": " Practical Advice and Resources for Course Coordination of Large Enrollment Courses ", "webprogram_exclude": "0", "session_ids": ["Session/18250"], "source_sha256": "4eb26d05bd6b2b51319573f807e43965e24d151f376a057273d68f80ac8fd520", "withdrawn": "", "abstract": "At the University of Tennessee, Knoxville, course coordination of lower-division courses is designed to promote consistency across sections, facilitate student success, and provide support and resources for instructors while, at the same time, allowing instructors autonomy and freedom in their classes. As student enrollment and the number of instructors increase, course coordination becomes more challenging. \n\nIn this session, we will discuss practical advice for managing the workload of course coordination, particularly in large-enrollment courses with many instructors. Jack Ryan will share his experience as the Course Coordinator for Math 123: Finite Mathematics, a lower-division course with a typical semester enrollment of 1300-1900 students taught by 25-35 instructors. The emphasis will be on providing attendees with practical advice for course coordination, including sharing various template documents, spreadsheets, and forms that minimize workload and promote efficiency while maintaining effectiveness.", "id": "Paper/67653", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67653"}, {"title": " Elliptic discrete KP and BKP hierarchies ", "webprogram_exclude": "0", "session_ids": ["Session/19363"], "source_sha256": "14e25f0cb550311affce1b149ae130c4f370a7e23ff8753faf91057475e2abbe", "withdrawn": "", "abstract": "In this talk, the generalizations of discrete Kadomtsev--Petviashvili (dKP) and discrete BKP (dBKP) hierarchies of elliptic type are proposed. The determinant and pfaffian solutions (tau functions) to the fundamental discrete KP and BKP equations of elliptic type are derived by using the Darboux and Moutard transformations, respectively. Furthermore, based on above tau functions, the discrete KP and BKP hierarchies are constructed by the determinant or pfaffian identities. \nThrough the Miwa transformation, the continuous KP and BKP hierarchies of elliptic type can be generated, which paves a way for constructing various soliton solutions with elliptic background to many integrable PDEs such as the nonlinear Schr\\\"odinger (NLS) equation, (modified) KdV equation, (modified) Camassa–Holm equation, and the massive Thirring (MT) model.", "id": "Paper/67657", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67657"}, {"title": " Double Averaging Schemes for Fixed Points of Nonlinear Mappings ", "webprogram_exclude": "0", "session_ids": ["Session/18363"], "source_sha256": "773312f628a502bedab0436d0a51a1fb4d44049770bb20e92d0df008060dcb80", "withdrawn": "", "abstract": "We discuss iterative schemes for fixed points of nonlinear mappings in Hilbert spaces that combine two averaging mechanisms, a cumulative mean of all previous iterates and a damped application of the mapping. This double averaging yields strong convergence for a broad class of pseudocontractive mappings, and a simple residual criterion determines when the limit is a fixed point. We also present a relaxed variant of the scheme that converges to a fixed point in all cases.", "id": "Paper/67659", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67659"}, {"title": " A General Risk-Limiting Audit Framework for STV Elections ", "webprogram_exclude": "0", "session_ids": ["Session/18097"], "source_sha256": "5af73bd373184ae7996dd3937bf677bad5d8905494c8d22302b251c7f6634d94", "withdrawn": "", "abstract": "We present the first fully general framework to design non-trivial Risk-Limiting Audits (RLAs) for arbitrary Single Transferable Vote (STV) elections using the assertion-based method. An election RLA is a statistical test which compares a random sample of paper ballots against the reported tabulation and either confirms the reported outcome or escalates to a full hand count, with a guaranteed bound on the risk that a wrong outcome is confirmed. To be assertion-based, this statistical test must be made up of a set of simple null hypotheses whose simultaneous rejection would suffice to verify the election outcome. We introduce Audit Graphs as a tool to generate such a set of null hypotheses for arbitrary election profiles, with empirically high success rates on real-world data. Along the way, we share some insights into how NP-hard problems in Computational Social Choice can be wrangled into computational tractability for real-world applications.", "id": "Paper/67662", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67662"}, {"title": " The topology of the moduli space of dilation surfaces ", "webprogram_exclude": "0", "session_ids": ["Session/18269"], "source_sha256": "4aabcf4f312c0f404388e9711e56c13cf0fd03bb8b3cab6d6692f35fd2d8caf1", "withdrawn": "", "abstract": "Translation surfaces are geometric objects that can be defined as a collection of polygons with sides identified in parallel opposite pairs by translation. If we generalize slightly and allow for polygons with sides identified by both translation and dilation, we get a new family of objects called dilation surfaces. While translation surfaces are well-studied, much less is known about dynamics on dilation surfaces and their moduli spaces. In this talk, we will survey recent progress in understanding the topology of moduli spaces of dilation surfaces. We will do this by seeing the moduli space of dilation surfaces as a covering space of the moduli space of Riemann surfaces.", "id": "Paper/67665", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67665"}, {"title": " A novel introduction to the teaching of abstract algebra ", "webprogram_exclude": "0", "session_ids": ["Session/19341"], "source_sha256": "6617223ec020ea79b7ce9183ec56a7d77c66eaa50a682ec616a72e356cd38b02", "withdrawn": "", "abstract": "Abstract algebra presents a steep learning challenge.  Early examples are unfamiliar and carry little intuitive meaning.  Permutation groups and geometric symmetries are founded on function composition, which is computationally complex. Axiomatic reasoning of abstract algebra has little curricular precursor, and does not answer immediate intellectual need or provide motivation. Beyond new knowledge gain, new intuitions must be constructed. Direct immersion in this world can feel at first like an austere exercise without clear purpose. Common approaches to teaching abstract algebra ignore and so fail to exploit what its students bring: they have taken calculus and likely had some exposure to linear algebra.  Thus, they have an intuitive sense of the real number line, R, with its three interacting structures: algebraic (+, –, ×, ÷); order (x < y); and metric (dist(x, y) = |x – y|). \nMy proposed introduction is to revisit the real number line with a group theoretic lens. The cornerstone is real division with remainder, DwR(a, b) a = qb + r: a, b are real numbers, b > 0, q is an integer, and 0 ≤ r < b.  The introduction is a study of real additive groups (RAGs), defined to be non-empty sets of real numbers closed under addition and subtraction.  First examples: Za (any real a), Q, R, and the set Per(f) of periods of a function of a real variable. Call a RAG A discrete if, for some r > 0, |a| ≥ r for all a ≠ 0 in A.  The students are then supported to discover and prove three theorems: (I) A RAG is either discrete or dense in R. (II) If A is discrete, then A = Za for a unique a ≥ 0.  (III) Za + Zb is discrete <==> a, b are commensurable (a/b ∈ Q).  In this case, Za + Zb = Zd, Za ∩ Zb  =  Zm, and we define gcd(a, b) = d and lcm(a, b) = m.  Among their now expanded meanings and properties are:  gcd(a/b, c/d)  =  gcd(a, c)/lcm(b, d) for reduced fractions, and  gcd(a1, a2, ..., an)•lcm(1/a1, 1/a2, ..., 1/an) = 1. There is no space to explain the advantages of this approach.", "id": "Paper/67667", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67667"}, {"title": " Thin incompressible surfaces in cusped arithmetic hyperbolic manifolds ", "webprogram_exclude": "0", "session_ids": ["Session/17904"], "source_sha256": "cb95ccb34fd60acf5d90796c2e9b00825d2a78f4ff4bff6958084ab85733ee9c", "withdrawn": "", "abstract": "The existence of (closed) surface subgroups in fundamental groups of hyperbolic manifolds has been investigated over many decades, even just in dimension $3$, for its deep implications about the topology of the underlying locally symmetric space. For compact hyperbolic manifolds, our understanding of this question is essentially complete but for non-compact, finite-volume ones, this question is still open in full generality. For such manifolds which are arithmetic, its easy to use elementary number-theoretic constructions to show surface subgroups exist, but these examples are always totally geodesic. Whether surface subgroups exist which are \\textit{thin}, in turn, makes this question nontrivial again. In joint work with Sara Edelman-Mu\\~noz, we show that such subgroups always exist. I'll give an overview of different geometric contexts in which thin matrix groups arise, outline our construction and, time permitting, discuss some additional geometric properties one may impose on these surface subgroups.", "id": "Paper/67669", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67669"}, {"title": " EL-Labeling the Shifted Lower Bruhat Intervals ", "webprogram_exclude": "0", "session_ids": ["Session/18138"], "source_sha256": "062b154c7f414ed297f55264318d4ca3ea51168523977841c99132d23764042b", "withdrawn": "", "abstract": "For $w,x$ in a Coxeter group $W$, the shifted lower Bruhat interval $[e,w]\\,x^{-1} = \\{vx^{-1} : v \\le w\\}$ is ordered by the Bruhat order of $W$. It is known that Bruhat intervals, and their tiled or twisted counterparts, are EL-shellable. That is, one can label their cover relations in a fashion that is compatible the maximal chains. These shifted lower intervals are neither twisted nor tilted Bruhat intervals. This talk shows that all shifted lower intervals are nonetheless EL-shellable for every Coxeter group.", "id": "Paper/67670", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67670"}, {"title": " Manifold topological deep learning for biomedical data ", "webprogram_exclude": "0", "session_ids": ["Session/18554"], "source_sha256": "2ef707b3d1c8c23fcad5aab422c25c221fb9cc14ea65fc84e8497d2483e4472c", "withdrawn": "", "abstract": "In this talk, I will introduce a Manifold Topological Deep Learning (MTDL) framework that extends topological deep learning from point-cloud data to differentiable-manifold data, including biomedical images. The key idea is to model images as smooth manifolds equipped with vector fields and to use Hodge theory to decompose these fields into orthogonal components. These components are then concatenated and incorporated into a streamlined convolutional neural network architecture. I will demonstrate the effectiveness of MTDL on the MedMNIST v2 benchmark, which contains 717,287 biomedical images from eleven 2D and six 3D datasets. The results show that MTDL significantly outperforms competing methods, highlighting its potential as a principled framework for extending topological deep learning to smooth-manifold data.", "id": "Paper/67672", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67672"}, {"title": " DTDL: Dual Topological Deep Learning for Drug Discovery ", "webprogram_exclude": "0", "session_ids": ["Session/17970"], "source_sha256": "955674b2aa740b2168813bbfc8fe9bae1aee340f122f3e09bb670d3949cb2ddb", "withdrawn": "", "abstract": "Despite great progress in artificial intelligence (AI) in the past decade, drug discovery remains a challenge. Although topological deep learning (TDL) offers a viable solution to this challenge, existing\nTDL methods are limited to either topological featurization or topological neural networks. This work pioneers a dual topological deep learning (DTDL) architecture that takes advantage of algebraic topology in both featurization and neural structure. Our approach integrates a topological spectral representation of three-dimensional (3D) protein-ligand structures and a copresheaf topological neural network (CTNN) to encode geometric, topology, and element-specific interaction patterns in protein–ligand complexes. We pretrain DTDL with a masked reconstruction objective on large collections of unlabeled structural complexes, enabling the model to learn reusable biomolecular interaction priors,latent physical constraints, and multiscale structural regularities. We further develop a low-rank copresheaf mechanism that preserves expressive directional transport across local feature spaces while improving scalability. After pretraining, the resulting DTDL is effectively transferred to downstream\ndrug discovery tasks. Empirically, DTDL achieved outstanding performance in binding affinity scoring and docking benchmarks, outperforming competing methods across diverse datasets. DTDL can be directly applied to address challenging problems in science, engineering, and technology.", "id": "Paper/67673", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67673"}, {"title": " Nonlocal three-phase energies without the triangle inequality ", "webprogram_exclude": "0", "session_ids": ["Session/18377"], "source_sha256": "0f163001d199be924dd2ac2bf945f73903f38d9b6f1c5996e2e01f1433c11e80", "withdrawn": "", "abstract": "In multi-phase systems, the so-called ``triangle inequality'' is a structural condition on the interfacial energy coefficients that ensures a direct interface between any two phases is more favorable than transitioning between an intermediate phase. \nWe consider the nonlocal setting in which the triangle inequality does not hold. \nWe will show that the energy still favors intermediate phase transitions, but assigns only a small energy to thin, intermediate layers. \nMoreover, we prove that the nonlocal energies $\\Gamma$-converge to the classical local energy with relaxed coefficients. This work is joint with Serena Dipierro (University of Western Australia) and Enrico Valdinoci (University of Western Australia).", "id": "Paper/67674", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67674"}, {"title": " Distributionally Robust Portfolio Optimization with Monge–Kantorovich Metrics ", "webprogram_exclude": "0", "session_ids": ["Session/18328"], "source_sha256": "1d846f8014dbe2d7743637bc440dc02bf8d0e83b4ae468adc980452ddd91e4e1", "withdrawn": "", "abstract": "This work develops a distributionally robust framework for portfolio optimization using Monge--Kantorovich probability metrics. Rather than relying on a single estimated return distribution, the approach considers an ambiguity set of probability measures within a prescribed transport-metric distance from a reference distribution, providing a systematic way to account for distributional uncertainty in financial decision-making. The framework connects classical Monge and Kantorovich mass-transference formulations with the Kantorovich--Rubinstein--Kemperman interpretation, multi-marginal transportation, and Fortet--Mourier-type probability metrics. These connections provide a flexible mathematical foundation for constructing portfolios that are less sensitive to distributional misspecification and for studying the role of transportation-based ambiguity in portfolio risk and allocation decisions.", "id": "Paper/67675", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67675"}, {"title": " Instability of invariant manifolds for iterated function systems ", "webprogram_exclude": "0", "session_ids": ["Session/17960"], "source_sha256": "b6cdd61f18f98ae68f8433e341d20283d883f495c7b525a6c69bf71192281125", "withdrawn": "", "abstract": "Invariant manifolds play a pivotal role in a variety of models of practical interest, e.g., those coming from physics for which the stabilizer set of a given symmetry subgroup is invariant. In parallel with the stability theory of equilibria and periodic orbits in ODEs and discrete-time systems, it is natural to seek stability criteria for invariant sets based on linearizations along the invariant set. On the other hand, simple examples (e.g., Bowen's figure-eight attractor) illustrate that linearization criteria alone cannot decide whether \"persistent\" dynamics occurs off the invariant set -- without further \"global\" information, it is possible for nonlinear structures to direct trajectories back to a linearly unstable invariant set. \n\nIn this talk I will discuss how the analogous problem for random dynamical systems (e.g., those coming from iterated function systems in discrete time or stochastic flows of stochastic differential equations) actually does, under mild natural conditions, reduce to a purely linearized criterion. I will discuss my own joint work with Jacob Bedrossian and Sam Punshon-Smith, as well as other recent works from the past few years using the same body of ideas.", "id": "Paper/67681", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67681"}, {"title": " Lyapunov exponents and chaos for random dynamical systems with mixed phase spaces ", "webprogram_exclude": "0", "session_ids": ["Session/18348"], "source_sha256": "ca66d4c35736920882f0bd6f8f3ad7f2676d635c402043bfcd2ca82751c63ae2", "withdrawn": "", "abstract": "Despite the existence of a comprehensive abstract theory of nonuniform hyperbolicity, it remains a notoriously challenging problem to rigorously verify persistent chaotic dynamics for dynamical systems with a \"mixed phase space\", blending hyperbolic expansion and elliptic-type behavior. These challenges remain insurmountable even for low-dimensional toy models, including the Chirikov standard map, alternating (Pierrehumbert) shear flows, and certain dynamical billiard systems including the \"lemon\" and \"moon\" tables. \n\nRemarkably, the problem of rigorously verifying chaotic behavior, e.g., sensitive dependence w.r.t. initial data, becomes considerably more tractable in the presence of small noisy perturbations applied to the system. From the perspective of applications this is extremely natural since noiseless, purely time-autonomous systems rarely occur in nature. The purpose of this talk will be to introduce the relevant ideas to a broad audience, and to document some of the results from the last few years on this subject, including those of myself and others, including joint work with Jinxin Xue, Lai-Sang Young, Yun Yang, Jacob Bedrossian, and Sam Punshon-Smith. Discussion will include applying some of these ideas to systems coming from fluid mechanics.", "id": "Paper/67684", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67684"}, {"title": " The Size of Minimal Zero Forcing Sets Relative to Graph Order: From REUF to Undergraduate Research ", "webprogram_exclude": "0", "session_ids": ["Session/17921"], "source_sha256": "f8754825c69a3bebbf13db3cb720e4b10639b7f3373dad4ee5aa0885aa7d23af", "withdrawn": "", "abstract": "This talk will focus on results from an undergraduate research project inspired by my experience with REUF. Zero Forcing is a color-change rule on the vertices of a graph. We start by selecting a set S of colored vertices. If any of these vertices is adjacent to exactly one uncolored vertex, it colors that vertex. After repeating this process, if all of the vertices of the graph are colored, we say S is a zero-forcing set, or Z-set. We consider the difference between minimal Z-sets of maximum and minimum size. Specifically, we find an upper bound on this difference relative to graph order and show this bound is sharp for an infinite family of graphs. A similar result is also found on the difference in propagation times for minimum Z-sets. I will also briefly discuss how my experience with REUF helped me develop the research agenda for my undergraduate research students this summer.", "id": "Paper/67686", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67686"}, {"title": " An equivariant transgression theorem ", "webprogram_exclude": "0", "session_ids": ["Session/17701"], "source_sha256": "74af8b7a2cb1ec1ed285fb4877244b74b423d2d5803558849360d8674762283a", "withdrawn": "", "abstract": "Kudo’s description of how differentials in the Serre spectral sequence interact with power operations vastly increased the effectiveness of the Serre spectral sequence as a computational tool. For example, this was a key input to Serre’s computation of the cohomology of Eilenberg–MacLane spaces and Cohen–May’s calculation of the homology of iterated loop spaces. My thesis and recent joint work with Bhattacharya, Zeng, and Zou constructs G-equivariant power operations and Steenrod operations for any finite group G, providing the exact analogues to those used in these classical computations. In this talk, I will outline an equivariant transgression theorem showing how these operations interact with the differentials of Hill–Hopkins–Ravenel’s slice spectral sequence. Time permitting, I will discuss applications to studying slice differentials for BP_{R} and its norms.", "id": "Paper/67690", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67690"}, {"title": " The Free Functional Calculus in General ", "webprogram_exclude": "0", "session_ids": ["Session/17377"], "source_sha256": "5cbde26efd5f07928d9c592e73543c0b65cbecd17b4c0c5f4d9db8eb218c3a6b", "withdrawn": "", "abstract": "The free functional calculus generalizes the notion of noncommutative polynomials and rational functions to great effect, providing a powerful noncommutative analogue of complex analysis. However, it is not equipped to deal properly with the Schur complement and similar functions of non-square matrices. \n\nThis difficulty is dealt with using a natural categorial object which we call a free map, a functor between functor categories which commutes with natural transformations. This gives a concrete and efficient way to discuss a free analysis as a ``morphism functional calculus” in the same terms as the classical nc functions, expanding to both general infinite dimensional spaces and non-square maps in such a way that natural proofs in classical free analysis can be naturally  lifted to the general case. \n\nAs an example of where the general theory expands the classical theory, it is sometimes possible to faithfully represent a category of topological spaces and continuous maps as linear maps between reproducing kernel Hilbert spaces. This allows us to analyse the dynamics of such spaces using the functional calculus, which in a special case gives insight into the beneficial overfitting phenomenon in neural nets.", "id": "Paper/67691", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67691"}, {"title": " A Mapping Approach for Examining the Role of Calculus in Computer Science and Mechanical Engineering ", "webprogram_exclude": "0", "session_ids": ["Session/18236"], "source_sha256": "32e553949b6f72fbd1545720fc55b0524c13add941f5ef12246fa0bdec60b133", "withdrawn": "", "abstract": "Undergraduate calculus often serves as a gateway to STEM degree programs, yet its conventional scope may not align with the mathematics students use in advanced disciplinary coursework. This study develops a degree-mapping approach to make the relationships between calculus and disciplinary learning more explicit. We identified 65 Calculus I and II topics through syllabus and textbook analyses, documented prerequisite relationships, and mapped them to four computer science course concentrations. Connections were represented through mapping matrices and explanatory rationales refined through iterative expert review. \n\nFindings indicate that calculus relevance to computer science is concentrated in a limited set of topics including differentiation rules, optimization, and mathematical modeling, while topics such as trigonometric substitution, integration by partial fractions, and polar coordinates appear less frequently connected. These findings challenge the assumption that prerequisite completion alone is sufficient for understanding how mathematical ideas support learning across computing pathways. \n\nTo examine whether these patterns are discipline-specific, we are extending the approach to mechanical engineering. For undergraduate mathematics education, degree mapping offers a method for examining how calculus concepts are used and extended in later disciplinary coursework. Rather than prescribing discipline-specific calculus curricula, the approach can help mathematics and disciplinary faculty make cross-course connections more explicit. By making relationships among concepts visible across disciplines, degree mapping provides a foundation for more coherent learning pathways and a stronger understanding of why particular mathematical ideas matter within STEM fields. The resulting mappings and visualizations provide practical resources for exploring how STEM disciplines draw upon calculus topics, thereby supporting conversations about curricular coherence and transfer.", "id": "Paper/67693", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67693"}, {"title": " A membrane-conforming tetrahedral mesh generation scheme for ion channel finite element calculation ", "webprogram_exclude": "0", "session_ids": ["Session/17970"], "source_sha256": "0924865a2d1fcc98ab39d4a47cfeacad7f609461875a208d6cda06f23765d69b", "withdrawn": "", "abstract": "Finite element solutions of ion channel dielectric continuum mod-\nels, such as the Poisson-Boltzmann and Poisson-Nernst-Planck equations, re-\nquire an unstructured mesh of a simulation box that is fitted to the interfaces\nbetween the protein, membrane, and solvent regions. In our previous package\n(ICMPv2), the membrane and solvent meshes were extracted from a solvent\nmesh by ray tests, which resolved the two membrane planes only approximately\nand failed silently for complicated proteins. In this paper we make the mem-\nbrane planes explicit facets of the piecewise linear complex handed to TetGen.\nThe protein surface mesh is traced on the Gaussian molecular surface by either\nof two interchangeable routes — a built-in marching cubes route, which is the\ndefault and needs no external program, or the TMSmesh2 program used by\nICMPv2 — and is then optimized: it is isotropically remeshed, every vertex\nis projected onto the exact Gaussian molecular surface, and the few remaining\npoorly shaped triangles are repaired locally, which removes the degenerate tri-\nangles of the traced surface and most of the sliver tetrahedra they cause. The\ntwo routes are shown to give tetrahedral meshes of the same quality. Internal\ncavities are filled automatically and a pore radius profile sets an adaptive mesh\nsize in the channel pore. The schemes are implemented in a new pure-Python\npackage, icmesh (ICMPv3), which writes meshes with cell and facet tags for\nFEniCSx. Numerical results on several ion channel proteins, including the\nthree-pore OmpF porin, show that all the meshes are generated efficiently and\nwithout manual adjustment, including a sliver removal pass and the mapping\nof the atomic charges onto the mesh.", "id": "Paper/67694", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67694"}, {"title": " Recent progress on graphs with <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"5.33ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 2295.1 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">q=2</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-71\" d=\"M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-71\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-3D\" x=\"738\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-32\" x=\"1794\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18207"], "source_sha256": "796ac97901cdfa609bb69cef880efcc0de6418cb25fe1f9e413ca8c334ff9b05", "withdrawn": "", "abstract": "We discuss recent progress on trying to understand graphs that admit 2 distinct eigenvalues. Let $\\mathcal{S}(G)$ be the set of symmetric matrices with the same zero/nonzero pattern as the graph $G$ (with the diagonals free). Define $q(G)$ to be the minimum number of distinct eigenvalues that a matrix in $\\mathcal{S}(G)$ may have. Understanding for which graphs $q(G) = 2$ is an impossibly hard problem. We study graphs which are very dense and develop a variety of techniques to give upper bounds on $q(G)$ in this regime. This is joint work with Wayne Barrett, Shaun Fallat, Vera Furst, Shahla Nasserasr, and Brendan Rooney.", "id": "Paper/67700", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67700"}, {"title": " The Weighted <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.642ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 1137.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">L^p</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4C\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-70\" d=\"M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-4C\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-70\" x=\"963\" y=\"513\"></use>\n</g>\n</svg> Minkowski Problem ", "webprogram_exclude": "0", "session_ids": ["Session/18265"], "source_sha256": "2aa0d44bda50a971b976c8c0aaf5f0298c0ebed537426434679a936967a1083c", "withdrawn": "", "abstract": "The Minkowski problem asks when a given Borel measure on the unit sphere arises, up to normalization, as a surface area measure of a convex body. Two important modern variants are the $L^p$ Minkowski problem and the weighted Minkowski problem, the latter including the extensively studied Gaussian Minkowski problem. In this talk, I will discuss a weighted $L^p$ Minkowski problem for rotationally invariant measures, extending the theory beyond the Gaussian setting. We establish existence results for all $p\\in\\mathbb R$ (with symmetry assumptions in some cases), uniqueness for $p\\geq 1$ under a concavity assumption, and existence results in the small-mass regime using degree theory.", "id": "Paper/67703", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67703"}, {"title": " Connectivity of Distance-Regular Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "f8fdce3970cc1f53f4f938d7b70790b9b3f918e31c512fced9d91599b1037300", "withdrawn": "", "abstract": "In 1985, Brouwer and Mesner proved that the vertex-connectivity of a strongly regular graph equals its valency and the only disconnecting sets of this size are point neighborhoods. In 2009, Brouwer and Koolen generalized this result to distance-regular graphs. \n\nIn 1996, Brouwer conjectured that the minimum size of a disconnecting set of vertices whose removal disconnects a connected strongly regular graph into non-singleton components equals the size of the neighborhood of an edge. In 2014, Cioaba, Kim, and Koolen disproved Brouwer's conjecture, but also showed that the conjecture is true for many families of strongly regular graphs. \n    \nIn their 2016 survey, van Dam, Koolen, and Tanaka asked whether Brouwer's conjecture is true for distance-regular graphs with diameter at least three. In this talk, I will describe our progress regarding this restricted vertex-connectivity of distance-regular graphs.", "id": "Paper/67704", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67704"}, {"title": " Higher-Order Affine Isoperimetric Inequalities ", "webprogram_exclude": "0", "session_ids": ["Session/18442"], "source_sha256": "84ca98cb4f9b92cc54c78db6c87ce207ab1b3981408c5759babcf537850fe545", "withdrawn": "", "abstract": "A classical theme in convex geometry is to associate new convex bodies to a given convex body and study the resulting affine isoperimetric inequalities. Motivated by Schneider's higher-order covariogram and higher-order difference bodies, we introduce higher-order analogues of the polar projection body and centroid body. These constructions connect higher-order covariograms, mixed volumes, and random simplices, and lead to higher-order versions of several classical affine inequalities. In particular, we obtain extensions of Zhang's projection inequality, Petty's projection inequality, and the Busemann–Petty centroid inequality, together with corresponding equality characterizations. I will also discuss how radial mean bodies provide a natural bridge between the higher-order Rogers–Shephard and Zhang inequalities.", "id": "Paper/67707", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67707"}, {"title": " Dynamical Systems Modeling to Determine the Role of Crosstalk in Shaping STAT Signaling Profiles ", "webprogram_exclude": "0", "session_ids": ["Session/18220"], "source_sha256": "2305a83d2876c6020a8e67c79b15ae74ba2ef1b664d3343d54092235173e79cb", "withdrawn": "", "abstract": "Macrophages use the JAK/STAT signaling pathway to integrate cytokine cues into context-specific functional decisions. Understanding the mechanisms underlying this process is complicated by the observation that the same JAK kinases and STAT transcription factors can direct a range of gene expression programs depending on the activating cytokine. The high degree of regulatory symmetry in this pathway led us to hypothesize that the cytokine-environment controls the relative contribution of parallel network arms and that asymmetric kinetics determine its capacity to appropriately discriminate stimuli. \n\nOur group previously developed a computational workflow that links features of cytokine-induced STAT phosphorylation profiles to downstream gene expression. While the ODE model is able to recapitulate experimental observations and correctly predict the impact of JAK2 variation on gene expression, many of the 40+ model parameters are poorly constrained by the available data. Thus, our ability to understand how context-specific variation impacts signal transduction is limited. Here we present work toward optimizing parameter estimation and predicting data necessary to constrain individual model parameters. We also discuss the role of cross-talk and kinetic asymmetries in shaping cytokine-specific STAT phosphorylation profiles. Our aim is to predict the impact of network component perturbations on phospho-STAT trajectories and ultimately downstream gene expression profiles.", "id": "Paper/67708", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67708"}, {"title": " Mapper and risks to interpretability: best practices and traps ", "webprogram_exclude": "0", "session_ids": ["Session/18114"], "source_sha256": "a11d0ce318770fb6f4a0ae1c7726e65dcfee052d1a74dfb9b896721bd40601bc", "withdrawn": "", "abstract": "The Mapper construction produces a simplicial complex representing an arbitrary dataset as viewed through a \\emph{lens function}. The algorithm works by clustering within fibers of the lens function and then building a nerve complex to combine the fibers to a view of the entire dataset. Since its introduction in 2008, the method has found broad applicability and become a cornerstone of topological data analysis. However, there are choices to be made for using the Mapper method. Some choices that seem to fall naturally for practitioners have drastic impact on the resulting simplicial complex, contributing possibly arbitrary edits to the topology of the complex and without much warning to a user of the methods. Some of these possible choices that have the potential to harm the structure of the resulting complex even come recommended from prominent open source software libraries and tutorials. In this talk, we will describe work on formulating best practices and potential traps when using Mapper for data analysis, discussing both the critical roles of identifying a good cover in the sense of the nerve lemma and of picking an adaptive approach to the clustering within fibers step.", "id": "Paper/67715", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67715"}, {"title": " Understanding Population Structure and Local Adaptation in California Current Brown Rockfish ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "55478b85b33c4acf461e740910a7aa4f2dc60c0a9b6a1801effe0e5d16fc1cac", "withdrawn": "", "abstract": "Low-coverage whole-genome sequencing (lcWGS) is an increasingly common, but statistically demanding approach in population genetics. Low coverage sequencing data possesses statistical uncertainties when calling genotypes and variants. By applying genotype-likelihood frameworks (PCAngsd & NGSAdmix) to our lcWGS data from 39 brown rockfish (Sebastes auriculatus), we take these statistical uncertainties into account. Sampling across three sites, Newport, Oregon (OR), Duxbury Reef, California (CA), and El Rosario, Baja California Norte (BCN), this project focuses on revealing and understanding adaptive differences in brown rockfish, a widely distributed and heavily exploited fish in the California Current Large Marine Ecosystem. Estimating population structure and pairwise genetic differentiation (FST) across this range of hundreds of miles, we observed clear genetic differences among the BCN samples, with a significant weighted FST value between BCN and OR/CA of 0.5, and no evidence of genetic structure between OR and CA samples, with a weighted FST of 0.1. Next, accounting for population structure, we used Latent Factor Mixed Modeling (LFMM) and Redundancy Analysis (RDA), statistical analyses which model linear relationships among environmental variables and genomic variation, while identifying the allele frequency associated with environmental variables. We identified specific candidate loci associated with sea surface temperature and chlorophyll levels. The LFMM and RDA resulted in the identification of 14 and 7 candidate loci, respectively, with no overlapping loci from our two analyses. This study demonstrates how likelihood-based and ordination methods can uncover genetic structure and environmental association with sparse, uneven genomic data. These results can contribute to the formulation of an efficient fishery management plan designed to avoid overharvesting of demographically independent or adaptively unique stocks of this species.", "id": "Paper/67716", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67716"}, {"title": " Quantitative comparison of closed- and open-loop linear–quadratic <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.064ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 888.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">N</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4E\" d=\"M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-4E\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-player differential games ", "webprogram_exclude": "0", "session_ids": ["Session/18124"], "source_sha256": "67bae24f8242e2d58384ac831c7aaa70cdd01b9c822a7b0ffa7e0dbf5ad0a952", "withdrawn": "", "abstract": "We compare closed-loop and open-loop Nash equilibria in a finite-horizon stochastic linear--quadratic $N$-player game with decoupled state dynamics and interaction through the state costs. We introduce a block-diagonal reference game and a nearby perturbed game, and study each under both information structures. The closed-loop and open-loop problems lead to different Riccati systems, but for the reference game their induced equilibrium state and control processes coincide exactly. We then prove solvability and stability under weak perturbations of the state costs, yielding quantitative bounds between the corresponding equilibria. In particular, when the perturbation decreases sufficiently fast with the population size, the closed-loop and open-loop equilibria of the perturbed game become asymptotically equivalent. The comparison is carried out directly at the finite-player level, without requiring exchangeability or a mean-field limit.", "id": "Paper/67718", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67718"}, {"title": " Two-Player Pebbling Games ", "webprogram_exclude": "0", "session_ids": ["Session/18338"], "source_sha256": "6eb4a35d23d75b168fa1e04217373b2b8913bee0b2987003c717899535ddc52e", "withdrawn": "", "abstract": "We introduce a two-player game graph pebbling game. Based on classical graph pebbling, players take turns removing two pebbles from a vertex and placing a single pebble on an adjacent vertex. Mover wins if a pebble is placed on a specified root and Defender wins if the root is not reached and no pebbling moves remain. Previous work has demonstrated a successful strategy for the Defender when the graph is a 4x4 grid or larger. We examine configurations, the initial placement of pebbles, for which each player wins on certain small grids as well as Complete Multipartite graphs.", "id": "Paper/67742", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67742"}, {"title": " Incomplete Open Platonic Solids ", "webprogram_exclude": "0", "session_ids": ["Session/18232"], "source_sha256": "222cc792380cdaaf924989cbddaa5c4b9fd2ef49b1a4dfdb6faa9a2c34f56610", "withdrawn": "", "abstract": "Sol LeWitt famously enumerated all the incomplete open cubes, finding 122 of these connected, non-planar subsets of the edges of the cube.\n    Since then, while several projects have revisited the cube enumeration, no such enumeration has been published for any other interesting solid.\n    In this talk we present work on enumerating all the incomplete open platonic solids, finding 6 tetrahedra, 122 cubes (just like LeWitt), 185 octahedra, 2\\,423\\,206 dodecahedra and 16\\,096\\,166 icosahedra. For the enumeration, we draw on group actions, subset representations by bitmasks, and embarrassingly parallel reformulations of the computational problem.", "id": "Paper/67746", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67746"}, {"title": " Boundary Growth and Gradient Estimates for <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.488ex\" height=\"1.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -576.1 640.5 721.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\alpha</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-3B1\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Harmonic Equations in the Unit Ball ", "webprogram_exclude": "0", "session_ids": ["Session/19336"], "source_sha256": "973540a524b38366ee5bc12bd02cea897ff53f54b031ac57227a491d352167fb", "withdrawn": "", "abstract": "We investigate boundary growth and differential estimates for solutions associated with the family of elliptic operators $\\Delta_\\alpha$ on the unit ball $\\mathbb{B}^n$, where $\\alpha>-1$ and $n\\ge3$. For the nonhomogeneous problem $\\Delta_\\alpha u=g$, we obtain quantitative Schwarz-type bounds under the decay assumption $|g(x)|\\le M(1-|x|^2)^\\beta$.\nThe resulting boundary behavior exhibits a transition at the threshold $\\beta=\\alpha+1$. For positive $\\alpha$-harmonic functions, we establish a sharp derivative estimate at the origin and use it to derive global gradient bounds, Harnack-type inequalities, and Lipschitz estimates with respect to the hyperbolic metric. We also obtain a boundary Schwarz principle for $\\alpha\\in(-1,0]\\cup[n-2,\\infty)$. In the hyperbolic case, this yields an explicit nonconstant harmonic example with identically vanishing outward normal derivative on the sphere, despite having a unique boundary maximum. These results provide a unified view of Euclidean and hyperbolic boundary phenomena within the $\\alpha$-harmonic framework.", "id": "Paper/67748", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67748"}, {"title": " Fence Posets, Good Gradings and Frobenius Maximal Parabolics ", "webprogram_exclude": "0", "session_ids": ["Session/18278"], "source_sha256": "e195dd2a9c0ee270ad9b6d1deeb00f0f8b839b04053c19c465e3950c50261e2b", "withdrawn": "", "abstract": "Let $\\mathfrak L$ be a Frobenius maximal parabolic subalgebra of $\\mathfrak{sl}_n$. For any\n$F\\in\\mathfrak L^*$ for which the Kirillov form\n$B_F(x,y)=F([x,y])$ is non-degenerate, let $\\widehat F$ denote the\nassociated principal element. We prove that the multiplicities of the\neigenvalues of $\\operatorname{ad}_{\\widehat F}$ on $\\mathfrak L$ form a\nunimodal sequence symmetric about $\\frac12$. We also prove that the multiplicities of the\neigenvalues of $\\operatorname{ad}_{\\widehat F}$ on $\\mathfrak{gl}_n$ form a\nunimodal sequence symmetric about $0$. The proof relates the ranked meander associated to $\\mathfrak L$ to the order ideals of a related fence poset through Panyushev reduction. The known unimodality of the rank polynomial of the fence poset implies that of the meander, which in turn determines a good grading of $\\mathfrak{gl}_n$ in the sense of Elashvili and Kac. We prove that this grading coincides with that induced by the principal element and that the pyramid associated to this grading may be filled in such a way that its good element $e$ lies in $\\mathfrak L$. The two unimodality results then follow from the injectivity properties of $\\operatorname{ad}_e$ coming from the good grading and the duality induced by the bilinear form $B_F$.", "id": "Paper/67749", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67749"}, {"title": " Translation Surfaces arising from Right Regular Prisms ", "webprogram_exclude": "0", "session_ids": ["Session/18269"], "source_sha256": "fa95708e9e04a71a114b71ec8eb8d047eb0451a0ef9e9a4f308008a3d64ce204", "withdrawn": "", "abstract": "The class of right regular $n$-prisms is one of two infinite families of uniform\npolyhedra. We study flat metrics arising from right regular $n$-prisms by viewing them as $n$-differentials and analyzing their associated translation unfoldings. We show that the unfolding of a right regular $n$-prism is never a lattice surface unless $n = 4$, in contrast with the case of Platonic solids. The lack of the lattice property significantly complicates their study. Despite this, we prove that these surfaces admit translation coverings to hyperelliptic surfaces, allowing us to determine their $GL(2, \\mathbb{R})$-orbit closures using the classification of hyperelliptic components of strata.\n\nAs a consequence, we obtain exact quadratic asymptotics for a certain average of the\nnumber of saddle connections on the base surfaces, their unfoldings, and the original\nprisms, including their Siegel–Veech constants. This provides a natural infinite family\nof non-lattice surfaces for which orbit closures and counting problems can be computed\nexplicitly.", "id": "Paper/67752", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67752"}, {"title": " Long-time behavior and turnpike properties of linear-quadratic graphon mean field control problems ", "webprogram_exclude": "0", "session_ids": ["Session/17800"], "source_sha256": "f58133a718bd6d74056b62fbc42c937242428e3352729060ef4c7ca8d19df7ae", "withdrawn": "", "abstract": "We investigate the asymptotic behavior and turnpike properties of graphon mean field control (GMFC) problems in the linear-quadratic setting. We consider both a finite-horizon GMFC problem and its associated ergodic counterpart, in which the controlled dynamics are governed by a graphon mean field stochastic differential equation with heterogeneous interactions. The optimal controls and state trajectories for both problems are characterized by systems of Riccati equations together with systems of generalized differential and algebraic equations on suitable Hilbert spaces. Under a stabilizability condition and appropriate positivity assumptions on the graphon-induced operators, we establish the unique solvability of the ergodic control problem and derive exponential convergence estimates for the finite-horizon system to its stationary limit. As a consequence, we establish an exponential turnpike property for the optimal pair and prove the convergence of the time-averaged value function for the finite-horizon GMFC problem.", "id": "Paper/67753", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67753"}, {"title": " Adapting Specifications Grading for a Large Enrolment Pass/Fail Class: Process and Lessons Learned ", "webprogram_exclude": "0", "session_ids": ["Session/18081"], "source_sha256": "efd1a1b86ab481e3e1c75de30c427629993673c2642ab66f03e2506507812348", "withdrawn": "", "abstract": "During the fall semester of 2025, the Department of Mathematics & Statistics at the University of Calgary implemented specifications-based grading into one of three large, multi-section (1000+ annual enrolment) first-year calculus courses to support the transition to a credit/non-credit final transcript record. In this talk, I will give an account of the backwards design process used by the team responsible for implementing these changes. The talk will focus on the design choices made to ensure that alternative grading methods would be appropriate for a large-scale, coordinated course. I will also report on adjustments made along the way in response to student feedback and observations from instructors.", "id": "Paper/67754", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67754"}, {"title": " Almost-Orthogonality in <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.642ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 1137.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">L^p</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4C\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-70\" d=\"M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-4C\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-70\" x=\"963\" y=\"513\"></use>\n</g>\n</svg> spaces ", "webprogram_exclude": "0", "session_ids": ["Session/17815"], "source_sha256": "f341db3fcf1ffe2f2e482f9f320f034f36028411592cd694e9e0b142e08d0625", "withdrawn": "", "abstract": "Disjointly supported functions satisfy an exact $L^p$ summation identity, while arbitrary sums are controlled by the triangle inequality. We will discuss sharpened triangle inequalities that quantify the intermediate regime through pairwise overlap. Motivated by questions of Carbery, we identify the optimal overlap exponent $p'=p/(p-1)$ and establish an almost-orthogonality inequality for every real $p\\ge2$, both for functions and for arbitrary operators in the Schatten–von Neumann classes. This talk is based on joint work with Jaume de Dios Pont and Paata Ivanisvili.", "id": "Paper/67761", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67761"}, {"title": " Machine Learning Driven Adaptive Mesh Refinement for Ocean Modeling ", "webprogram_exclude": "0", "session_ids": ["Session/18272"], "source_sha256": "92c6ab3fb97ddf7d42ed2eef7909fd67168226e4c1105ad0f227e969cac1cf0e", "withdrawn": "", "abstract": "Adaptive mesh refinement (AMR) can substantially reduce the computational cost of ocean simulations by concentrating resolution in regions with dynamically important features. However, designing refinement criteria that are both reliable and broadly applicable remains challenging. In this talk, we present preliminary results on using machine learning to guide AMR for the shallow water equations discretized with a high-order discontinuous Galerkin method. Our approach trains a model to identify regions where increased spatial resolution is likely to improve the numerical solution, using information derived from the evolving flow. We will discuss the integration of the learned refinement strategy with the high-order solver and compare its behavior with conventional refinement indicators. This work is an initial step toward adaptive ocean models that use data-driven methods to allocate computational resources more effectively.", "id": "Paper/67762", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67762"}, {"title": " A family of second order, linear, unconditionally stable methods for the Cahn-Hilliard-Navier-Stokes equations ", "webprogram_exclude": "0", "session_ids": ["Session/18258"], "source_sha256": "cf9db125a1f2b774b02d6c85b946238fc345082b61c7f29c4a83e370ae36daa0", "withdrawn": "", "abstract": "The Cahn–Hilliard–Navier–Stokes (CHNS) equations provide a diffuse-interface model for incompressible two-phase flows, but their nonlinear coupling and energy structure pose challenges for accurate and stable numerical approximation. In this talk, we present a family of second-order, linear implicit–explicit (IMEX) schemes for the matched-density CHNS system. Although the scheme is unconditionally stable, numerical experiments show that the choices of the time-stepping parameter (\\theta) and the stabilization parameter (\\epsilon) can significantly affect their computational robustness. We demonstrate these effects and validate the scheme through several numerical benchmarks.", "id": "Paper/67764", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67764"}, {"title": " Heights and measures in stochastic arithmetic dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/18259"], "source_sha256": "2956792727d6a614bc29a281aab8c97d3c721ec443a2d7d73d34167640357482", "withdrawn": "", "abstract": "Associated to a rational function $\\varphi$ defined over a number field $K$ is an {\\it adelic} canonical measure---a choice of invariant measure at each place of $K$. These measures allow us to define Julia sets at each place as well as to recover the Call-Silverman canonical height function associated to $\\varphi$. Kawaguchi and Healey-Hindes have extended the construction of canonical heights to the context of {\\it stochastic} dynamical systems, generated not by a single function (as in the classical setting), but by a set $S$ of rational functions defined over $K$ together with a probability measure $\\nu$ on $S$. We construct an adelic canonical measure for such systems $(S,\\nu)$ defined over $\\overline{\\mathbb Q}$ (but not necessarily over a single number field), compare the resulting height function with that of Kawaguchi and Healey-Hindes, and describe equidistribution results, including equidistribution of random backward orbits.", "id": "Paper/67765", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67765"}, {"title": " A Mathematical Model of Protein Homeostasis: Time-Dependent Dynamics and Stability Analysis ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "3a698b405c25e13ac9840975c2c8e35c0d58abacf1c9b466e1762aaaac7b3a66", "withdrawn": "", "abstract": "This research investigates the dynamic interplay between energy metabolism and protein homeostasis (proteostasis) under conditions of energetic stress. We present a two state kinetic model that tracks how proteins transition between unfolded and native conformations through synthesis, folding, unfolding, and degradation. This framework captures both transient and steady state behavior of the protein pool, allowing us to identify biologically realistic parameter ranges to establish baseline mechanisms and parameter bounds. We explore different kinetic assumptions, such as linear, nonlinear, and Michaelis–Menten forms to determine how they affect stability, with a key focus on identifying conditions under which the system becomes unstable, as an overload of unfolded proteins is expected to drive proteostatic collapse. We will also discuss how we are extending this preliminary model by introducing an aggregation state to better reflect the proteostasis mechanisms. Comparing the two and three state models will enable us to evaluate whether aggregation acts as a stabilizing or destabilizing force. We first establish proteostasis baselines before adding energetics, revealing whether instability arises internally or from energy limits. Together, these results define theoretical boundaries between resilience and collapse, providing mechanistic insight into stress responses across molecular and cellular scales.", "id": "Paper/67766", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67766"}, {"title": " On the representation ring of a poset and connections with persistent homology ", "webprogram_exclude": "0", "session_ids": ["Session/17949"], "source_sha256": "1653f90071b3d84c1b9c33e22c66a5d9991b9e60f6ece45c4d3943c0ef4720fe", "withdrawn": "", "abstract": "This talk will present joint work in progress and a conjecture.  The (split) representation ring of a quiver has a Z-basis of its indecomposable representations and multiplication from pointwise tensor product; this descends to subcategories of representations satisfying commutativity relations, for example representations of posets.  \n\nIn the case of rooted tree quivers, the presenting author's 2009 PhD dissertation identified a class of \"reduced representations\" which form a basis for the representation ring modulo its nilradical. Perhaps surprisingly, a given rooted tree quiver admits only finitely many reduced representations even when it is wild representation type.\n\nKey constructions of this 2009 dissertation have been rediscovered and extended several times since then in the context of persistent homology theory, such the \"rank of a quiver representation\" (a.k.a. \"generalized rank invariant\").   Most relevant to this talk is the natural appearance of the reduced representations mentioned above in work of Bindua, Br\\\"ustle, Scoccola on decomposing zero-dimensional persistent homology over rooted tree quivers and associated finiteness implications in that setting.\n\nIt is natural to wonder to what degree the concept of reduced representations, their associated generalized rank functions, and the finiteness results extend to other finite posets.  This talk will cover work in progress related to the first-named author's 2027 PhD dissertation, including a conjecture related to breakdown of the finiteness property already for a specific poset with 8 elements.", "id": "Paper/67767", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67767"}, {"title": " On the Converse of Freedman’s Theorem on Functionally Commutative Matrices ", "webprogram_exclude": "0", "session_ids": ["Session/19350"], "source_sha256": "9a867e564fe0ddf71cd3e034962c36dc8681da545ba426661a7780d8bcebeada", "withdrawn": "", "abstract": "In 1975, H.~I.~Freedman proved that if a one-parameter matrix \\(A(t)\\), \n\\(t\\in\\mathbb{R}\\), is functionally commutative,\n\\[\nA(t)A(s)=A(s)A(t) \\qquad \\text{for all } s,t\\in\\mathbb{R},\n\\]\nand its minimal polynomial equals its characteristic polynomial, then \n\\(A(t)\\) has constant eigenvectors. The converse, however, is false. \nNamely, a one-parameter matrix may have constant eigenvectors and equal \nminimal and characteristic polynomials without being functionally \ncommutative. Using explicit counterexamples, we investigate what additional \nconditions, together with constant eigenvectors and equality of the minimal \nand characteristic polynomials, are sufficient to guarantee functional \ncommutativity.\n\n\\end{document}", "id": "Paper/67768", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67768"}, {"title": " An Integrated Surface Growth and Reaction–Diffusion Mathematical Model for Morphogenesis and Pattern Formation Problems ", "webprogram_exclude": "0", "session_ids": ["Session/19371"], "source_sha256": "4275e4ea3d16bfeb876b9dd8d89645ddb5fdef58cf8ccb6a2c5b5d6d501cc074", "withdrawn": "", "abstract": "Biological surfaces often develop complex shapes and spatial patterns simultaneously. In this work, we conducted numerical studies of biological geometries using a coupled model of local curve evolution following Moulton-Goriely’s framework, with Gierer–Meinhardt-type reaction–diffusion kinetics for surface pattern formation, to simulate the concurrent formation of surfaces and patterns.\nSurface growth is modeled by evolving a generating curve using Darboux-frame kinematics. These equations can generate different types of surfaces used in evolutionary biology modeling. At each time step, a two-component Gierer–Meinhardt reaction–diffusion PDE model, formulated as an activator–inhibitor or activator–substrate system, is solved along the growing curve to determine the spatial distribution of pattern-forming chemical species. The PDE model is numerically solved with spectral methods for high accuracy, while a standard fourth-order Runge-Kutta advances the Darboux equation over time.\nThe model is applied to several biological geometries, such as the nautilus seashell, to understand how growth parameters, reaction kinetics, and diffusion coefficients affect the final morphology and surface pattern. Numerical results will be presented.", "id": "Paper/67769", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67769"}, {"title": " Inequalities for Complex Polynomials in an Elliptic Domain ", "webprogram_exclude": "0", "session_ids": ["Session/19368"], "source_sha256": "c3c53c2a5d16a6ac813248f6340b2e7a57d4c692ec9418f0c6d17d33920fe5f4", "withdrawn": "", "abstract": "An inequality of fundamental importance for complex polynomials was established by Rivlin [T. J. Rivlin, On the maximum modulus of polynomials, {\\it Amer. Math. Monthly}, {67(3)} (1960), 251-253].  It states that for a polynomial \\( P(z) \\) of degree \\( n \\) having no zeros in the region  \\( |z|<1 \\), the following inequality is valid:  \n$$\n\\max_{|z|=r}|P(z)|\\geq \\left(\\frac{1+r}{2}\\right)^n\\max_{|z|=1}|P(z)|, \n$$\nfor \\( 0\\leq r\\leq 1 \\). In the present work, we establish an analogous inequality in an elliptic setting, considering two concentric ellipses and relating the maximum moduli of $P(z)$ on these ellipses.", "id": "Paper/67772", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67772"}, {"title": " Creative Exploration with Curve Stitching ", "webprogram_exclude": "0", "session_ids": ["Session/18216"], "source_sha256": "398025c845974bdae4396a787f418bba3eb87bdf3155b56adff35977197f6b66", "withdrawn": "", "abstract": "A  \\emph{modular stitch graph} is produced with a simple rule. Take $m$ points equally spaced around the circle, choose an integer multiplier $a$, and draw a chord from point $p$ to $a p \\mod m$. The choice of integers $m$ and $a$,  produces a wide range of intricate designs. These objects are a favorite in recreational mathematics for their mysterious patterns and connection with planetary orbits and epicycloids. Constructing these designs with string around a circular frame is a common educational activity.\n\nIn this talk, I will discuss my own line of mathematical inquiry with modular stitch graphs and how a perspective from dynamics and topology completely reveals which design appears from a choice of $m$ and $a$. Then, I will introduce some hands-on activities and virtual educational tools based on these objects. With little prerequisite knowledge required, I propose modular stitch graphs as a creative first encounter with mathematical exploration.", "id": "Paper/67775", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67775"}, {"title": " A stochastic approach to multiscale problems in heat transfer and fluid dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/18305"], "source_sha256": "4094662eb4e734ffd13af70a07b0457069d3c633b44f3e3304064e8990e09e82", "withdrawn": "", "abstract": "Multiscale problems arise naturally in heat transfer and fluid dynamics, where fine-scale structures can strongly influence large-scale behavior. In this talk, I will present stochastic approaches for capturing these effects without resolving all underlying scales, using stochastic representations of the governing PDEs together with neural network approximations. I will first discuss a neural network approach to homogenization based on stochastic walkers. The method learns an effective description of multiscale PDEs without explicitly computing homogenized coefficients or solving cell problems, and its computational cost can remain independent of the underlying microscale periodic structure. I will then extend this stochastic perspective to incompressible turbulent flows, where local flow dynamics are incorporated into the stochastic formulation. This provides a non-intrusive multiscale approach for capturing macroscopic flow behavior without explicitly coupling coarse- and fine-scale models.", "id": "Paper/67776", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67776"}, {"title": " The Response of Molecular Motors in Flagella to Changes in Fluid Viscosity ", "webprogram_exclude": "0", "session_ids": ["Session/18220"], "source_sha256": "c871360fa27ab316282d713998060781c7dba7795f80054263c366914d712fb0", "withdrawn": "", "abstract": "Many microswimmers propel themselves using flagella, which are thin, threadlike filaments that beat in a periodic wavelike motion. The flagellar beat emerges from the coupled interactions between the surrounding fluid and the active and passive responses of the flagellum. It is thought that this spatiotemporal coordination among motors is due to mechanical feedback on dynein motors. However, the mechanisms of mechanochemical feedback are not well understood, since the motor forces cannot be measured directly. We develop a computational model for the microorganism \\textit{Chlamydomonas reinhardtii} that couples a molecular motor model with a nonlinear swimming simulation to examine how motor forces respond to external loading. Although these motor models have been shown to qualitatively reproduce the \\textit{Chlamydomonas reinhardtii} waveform, we find that they do not reproduce the beat frequency or beat asymmetry observed in our dataset.", "id": "Paper/67777", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67777"}, {"title": " Curve Stitching and Dancing Planets ", "webprogram_exclude": "0", "session_ids": ["Session/18365"], "source_sha256": "da0a9d874bc0f7eb220ea187f41cbb871f48f15dd12a3adaf841c13c0eb48893", "withdrawn": "", "abstract": "Curve stitching is a classic educational activity where one constructs elegant curves from a family of straight lines. We perform curve stitching around a circle to make a \\emph{modular stitch graph}. Take $m$ points equally spaced around a circle, choose an integer multiplier $a$, and draw a chord from point $p$ to $a p \\mod m$. Depending on the choice of integers $m$ and $a$, a wide range of intricate patterns appear. We connect these discrete objects to a continuous-time dynamical system and apply a topological perspective to understand what design is produced from $m$ and $a$.", "id": "Paper/67780", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67780"}, {"title": " The Flat Singular and Flat Virtual Singular Braid Monoids and Their Connections with Knot Theory ", "webprogram_exclude": "0", "session_ids": ["Session/18384"], "source_sha256": "099d9125e31b267d54e80c34b0f217cd6f8d718e34c469f15061f5e1bea814b8", "withdrawn": "", "abstract": "We introduce and study the flat singular braid monoid and the flat virtual singular braid monoid via generators and relations. Our interest in these algebraic structures stems from their connections with the classical braid group and the singular braid monoid, as well as their role in the study of invariants of flat singular knots and flat virtual singular knots.", "id": "Paper/67781", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67781"}, {"title": " L1 Norms of Gabor Dual Windows ", "webprogram_exclude": "0", "session_ids": ["Session/17945"], "source_sha256": "de232f5177930734a2d4bae9427f4bb382ed632289c7dcede526a308518a2891", "withdrawn": "", "abstract": "Given a suitable Gabor frame, we address the problem of finding dual windows with minimal L1-norm.  We achieve a full characterization in special cases.  Motivated by compressed sensing, where minimizing the L1-norm often coincides with minimizing the L0-norm, we also investigate the support properties of Gabor dual windows that achieve minimal L1-norm.", "id": "Paper/67782", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67782"}, {"title": " The Asymmetric Index of Forests ", "webprogram_exclude": "0", "session_ids": ["Session/19366"], "source_sha256": "4dc7e3c1d73d6adc2769af24c62618f5bac13f97fbb79e48caadbefcb95917ab", "withdrawn": "", "abstract": "A graph $G$ is \\textit{asymmetric} if its automorphism group is trivial. Asymmetric graphs were introduced by Erd\\H{o}s and R\\'{e}nyi (1963). They suggested the problem of starting with an asymmetric graph and removing some number $r$ of edges and/or adding some number $s$ of edges so that the resulting graph is non-asymmetric. Erd\\H{o}s and R\\'{e}nyi defined the \\textit{degree of asymmetry} of a graph to be the minimum value of $r+s$. Castano et al. defined the asymmetric index of a graph which measures how close a given non-asymmetric graph is to being asymmetric. The \\textit{asymmetric index} of a graph $G$, denoted $\\ai(G)$, is the minimum of $r+s$ so that the resulting graph $G$ is asymmetric. We investigate the asymmetric index of disjoint unions of trees.", "id": "Paper/67783", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67783"}, {"title": " Model identifiability and indistinguishability for sparse model discovery with unobserved dynamical states ", "webprogram_exclude": "0", "session_ids": ["Session/18319"], "source_sha256": "61e0b6150b3006f36b3919af60d188629a05ce7c423308c6b79125b2aa068369", "withdrawn": "", "abstract": "Despite rapid advances in experimental imaging and sensor technology, many real-world systems from physics and biology to weather and robotics remain measurable in only a subset of their dynamically relevant variables. Discovering predictive nonlinear dynamical models and their parameters directly from noisy experimental observations with unobserved dynamical variables is essential for understanding such systems. Sparse model discovery under partial observations, however, is ill-posed, limiting its applicability. By combining concepts from sparse regression, dynamical systems, control, and identifiability, we provide a theoretical framework for understanding this ill-posedness. We show that under partial observations, equivalent models lie on continuous manifolds in parameter space, leading to multiple indistinguishable model structures. Furthermore, we show how these manifolds are constrained by the phase-plane behavior of the dynamical system, improving our understanding of the ill-posedness of model selection with unobserved variables and providing practical rules of thumb for overcoming this ill-conditioning.", "id": "Paper/67784", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67784"}, {"title": " Convolution Identities for Mock Modular Forms via Holomorphic Projection ", "webprogram_exclude": "0", "session_ids": ["Session/17450"], "source_sha256": "31b9260d9c2347f371b61c169e10a43e11034abe3db7f21dfa4a337158808743", "withdrawn": "", "abstract": "Convolution identities for modular forms have a long history, with classical examples arising from relations among Eisenstein series. Such identities for mock modular forms are subtler because one must account for the nonholomorphic terms in their modular completions. In this talk, I will present new convolution-type $q$-series identities involving Ramanujan’s third-order mock theta functions, including an identity conjectured by Garvan. The identities are obtained by applying weight-$2$ holomorphic projection to the tensor product of a vector-valued harmonic Maass form and a vector-valued cusp form. A decomposition of the resulting tensor-product representation, together with a general projection formula, converts the nonholomorphic contributions into indefinite double sums connected with generalized Pell equations. This method produces eighteen component identities, which reduce to five distinct identities through classical relations among the mock theta functions.\n\n\\bigskip\nRelated paper:\n\\begin{itemize}\n    \\item \\emph{Some convolution identities for mock modular forms arising from the theory of holomorphic projection},\\\\ arXiv:2608.13324 \n\\end{itemize}", "id": "Paper/67785", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67785"}, {"title": " Signed compositions and the representation theory of the Mantaci–Reutenauer algebra ", "webprogram_exclude": "0", "session_ids": ["Session/18134"], "source_sha256": "e8d5c6661d59687bb572087d3ee0ddc8dbb08c9a1170ead5226619316e86312c", "withdrawn": "", "abstract": "The Mantaci–Reutenauer algebra is a type B analogue of Solomon's descent algebra arising naturally in algebraic combinatorics, and dual to Poirier's Hopf algebra of signed quasisymmetric functions. In this talk, we study the representation theory of the Mantaci–Reutenauer algebra through the combinatorics of signed compositions and signed partitions. In particular, we give a new combinatorial interpretation of the characters of the simple modules and completely determine its Cartan invariants. We also present a conjectural description of its Ext-quiver. Assuming this description, we determine the representation type of the algebra. This is ongoing joint work with Alice Dell'Arciprete.", "id": "Paper/67786", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67786"}, {"title": " Academic Partnerships, Fellowships, and Collaborative Research with the Department of War ", "webprogram_exclude": "0", "session_ids": ["Session/18024"], "source_sha256": "0701eb36a3ab47fa42d4782054c6008c0d53a59a86f13fb83178fe7a92a807cf", "withdrawn": "", "abstract": "Navigating federal research opportunities can often appear daunting to academic departments, yet the demand for mathematical talent within the defense science and technology enterprise is at an all-time high. The Air Force Research Laboratory (AFRL), alongside sister service laboratories (ARL, DEVCOM,NRL, ONR, NIWC), actively maintains robust partnerships with university faculty, postdoctoral researchers, and students to advance foundational science.\nThis presentation provides an overview of collaborative mechanisms available to the mathematical community. Key programs highlighted include the SMART Scholarship-for-Service Program—which offers full tuition, stipends, and guaranteed civilian research placement—as well as regional research hub partnerships and competitive basic research grant programs through AFOSR, ARO, and ONR. By reviewing the historical legacy of university-defense partnerships and charting practical steps for engagement, this talk equips educators, researchers, and students with actionable resources to support their academic and scientific endeavors.", "id": "Paper/67787", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67787"}, {"title": " The Kingman Bound Basically Holds in the <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"9.717ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 4183.5 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">GI/GI/n</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-47\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q492 659 471 656T418 643T357 615T294 567T236 496T189 394T158 260Q156 242 156 221Q156 173 170 136T206 79T256 45T308 28T353 24Q407 24 452 47T514 106Q517 114 529 161T541 214Q541 222 528 224T468 227H431Q425 233 425 235T427 254Q431 267 437 273H454Q494 271 594 271Q634 271 659 271T695 272T707 272Q721 272 721 263Q721 261 719 249Q714 230 709 228Q706 227 694 227Q674 227 653 224Q646 221 643 215T629 164Q620 131 614 108Q589 6 586 3Q584 1 581 1Q571 1 553 21T530 52Q530 53 528 52T522 47Q448 -22 322 -22Q201 -22 126 55T50 252Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-49\" d=\"M43 1Q26 1 26 10Q26 12 29 24Q34 43 39 45Q42 46 54 46H60Q120 46 136 53Q137 53 138 54Q143 56 149 77T198 273Q210 318 216 344Q286 624 286 626Q284 630 284 631Q274 637 213 637H193Q184 643 189 662Q193 677 195 680T209 683H213Q285 681 359 681Q481 681 487 683H497Q504 676 504 672T501 655T494 639Q491 637 471 637Q440 637 407 634Q393 631 388 623Q381 609 337 432Q326 385 315 341Q245 65 245 59Q245 52 255 50T307 46H339Q345 38 345 37T342 19Q338 6 332 0H316Q279 2 179 2Q143 2 113 2T65 2T43 1Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-47\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-49\" x=\"786\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2F\" x=\"1291\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-47\" x=\"1791\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-49\" x=\"2578\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2F\" x=\"3082\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-6E\" x=\"3583\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/17976"], "source_sha256": "7ae73f9977ea742c060173319f6d25b3373c508e64590538b6cadf67b6ddce39", "withdrawn": "", "abstract": "I will define the GI/GI/n queue and introduce Kingman’s classical bound on the mean number of waiting jobs in a first-come, first-served single-server queue. We will then present a new, very similar result that holds for any number of servers. The talk will also discuss some of the history behind this result and introduce some of the key new ideas that make the bound possible.", "id": "Paper/67792", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67792"}, {"title": " Levi subgroup posets and Steinberg modules ", "webprogram_exclude": "0", "session_ids": ["Session/18264"], "source_sha256": "c523073bc07728899c6b85ec1d2a03a57f780a3dd8554f63f2daecedd4bb4a88", "withdrawn": "", "abstract": "In his study of the rank filtration of algebraic K-theory, Rognes introduced the common basis complex for $\\mathrm{GL}_n(F)$, whose simplices are collections of proper subspaces that can be simultaneously spanned by subsets of a single basis. By work of Miller, Patzt, and Wilson, its reduced homology is concentrated in a single degree and, in that degree, is the stable Steinberg module for $\\mathrm{GL}_n(F)$. This module appears naturally in algebraic K-theory and as a coefficient module in the homology of $\\mathrm{GL}_n(F)$. This motivates asking whether these constructions, and the resulting representation modules, extend beyond type A. Using the geometry of apartments and opposition, we construct equivariant analogues for arbitrary spherical buildings. When the building comes from a connected reductive group, one construction is the poset of proper rational Levi subgroups, while the common-basis analogue is homotopy equivalent to a poset built from rational parabolic and Levi subgroups. We prove that both spaces have reduced homology concentrated in a single degree, yielding natural modules for groups of Lie type and extending the type-A picture. This is joint work with J. Shareshian and V. Welker.", "id": "Paper/67794", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67794"}, {"title": " Exceptional Sign Pairs in Oscillatory Asymptotics ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "e19f48f13ce4017379bb265221c7e02c9a8b66db44a4819cd5785c2339f74926", "withdrawn": "", "abstract": "Oscillatory asymptotic formulas often govern subtle sign patterns in the coefficients of $q$-series. This poster presents an exceptional sign pair phenomenon for a broad class of integer sequences with exponentially growing oscillatory asymptotics. We establish general conditions under which such a sequence contains infinitely many pairs of consecutive terms having the same sign, with the magnitude of at least one term in each pair forming a local minimum. The poster illustrates how these exceptional pairs arise from sign changes near the zeros of the oscillatory factor in the dominant asymptotic term. The main ideas and the resulting sign phenomena will be illustrated through well-known examples.", "id": "Paper/67795", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67795"}, {"title": " Fast Algorithms for Counting Stamp Foldings ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "75e0f0b1fcb21fdd51b032714d00fa22cd2c3132581be8050d515d04c7c606a6", "withdrawn": "", "abstract": "The labeled stamp folding problem asks how many distinct ways there are to fold a strip of stamps so that the stamps are stacked on top of each other. Somewhat surprisingly, the problem does not have a known formula (if such a formula exists). We present improvements upon known algorithmic methods for determining the number of unique foldings by merging combinatorial theory with algorithm design.", "id": "Paper/67797", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67797"}, {"title": " Exploring the LMFDB visually ", "webprogram_exclude": "0", "session_ids": ["Session/18366"], "source_sha256": "eddb21f98ad6b3f39ade8ec8442df3b558113ac7c040e99c39a8b17e05ab4db1", "withdrawn": "", "abstract": "The L-functions and Modular Forms Database (LMFDB) contains a vast collection of objects and invariants of interest to number theorists (and other mathematicians).\nRecently, the LMFDB introduced a new way to explore the many objects in the database: interactive two-dimensional scatter plots, which sometimes reveal beautiful patterns in the data.\n\nI will discuss some of the technical challenges and design decisions underlying this new feature, including efficiently handling large datasets in the browser and setting sensible and informative defaults.", "id": "Paper/67800", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67800"}, {"title": " Coordination as a Tool for Training and Team Building ", "webprogram_exclude": "0", "session_ids": ["Session/17971"], "source_sha256": "624a12566e77b92d2e0d7963f721ba85efc73e23d804c9956bf2bb355029aade", "withdrawn": "", "abstract": "While course coordination is traditionally designed to ensure consistency across multiple class sections, it also serves as a powerful mechanism for instructor training, pedagogical exchange, and team building. This presentation shares the author’s experience initiating and leading the coordination of Multivariable Calculus at a large state university over a three-year period. It highlights the strategies used to foster collaborative best practices, navigate departmental dynamics, and ultimately achieve the institutional goal of implementing a unified common examination.", "id": "Paper/67802", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67802"}, {"title": " Automated Verification of Survey Logic ", "webprogram_exclude": "0", "session_ids": ["Session/18240"], "source_sha256": "a4bf96fcb04d082df314a0f42a22484e3ad1efe8e9e79aa778badbc7bd3b0951", "withdrawn": "", "abstract": "Companies design surveys to analyze consumer behavior and market trends. These complex surveys can be modeled as branching logical systems in which each response imposes constraints on the possible paths through the survey. As surveys grow in complexity, the number of possible answer paths can increase exponentially with the number of questions and branching conditions, making properties such as reachability, branching behavior, and quota feasibility increasingly difficult to verify manually. We develop a formal verification pipeline that reduces these properties to Satisfiability Modulo Theories (SMT) problems. Our method translates survey specifications written in a domain-specific language (DSL) into logical constraints that represent the behavior of individual DSL operations. The resulting formulas encode the semantics of survey operations using Boolean and arithmetic expressions, together with axioms that define the behavior of more complex operations, allowing survey properties to be expressed as satisfiability queries. To automate the verification of these queries, we parse the DSL expressions into Abstract Syntax Trees (ASTs) and traverse the ASTs to construct the corresponding SMT constraints. We present a generalized solver architecture capable of handling all 42 DSL operations. Finally, we validate the pipeline on a real survey involving 25 distinct DSL operations, verifying both a termination query and a quota query within 45 seconds. These results demonstrate that survey properties can be verified by composing the logical constraints of individual DSL operations.", "id": "Paper/67812", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67812"}, {"title": " Geometric Realizations of Embeddings of High-Dimensional Spheres ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "c32b74b71a479a9879f983e82d73bbb5aa0d794874da71e5d1f5504a53d9d77d", "withdrawn": "", "abstract": "Let $r$, $m$, and $p_1,\\ldots, p_r$ be positive integers with $p_i < m-2$ for all $1\\leq i \\leq r$. Consider the set of embeddings of $S^{p_1}\\sqcup\\ldots\\sqcup S^{p_r}$ into $S^m$ up to isotopy. We call this set $\\text{E}(\\sqcup_{i=1}^r S^{p_i}, S^m)$. This is an abelian group under componentwise connect sum, and has a subgroup of embeddings with only unknotted components (denoted with $\\text{E}_U$) and a subgroup of Br\\\"unnian embeddings (denoted with $\\text{E}_B$). \n\nHaefliger showed that the group of unknotted embeddings $\\text{E}_U(\\sqcup_{i=1}^r S^{p_i}, S^m)$ fits into a long exact sequence with homotopy groups of wedges of spheres, and used this sequence to show that they are finitely generated abelian groups and to compute the ranks in some special cases. More recent work by Crowley, Ferry, and Skopenkov determined the rationalizations $\\text{E}_B\\otimes\\mathbb{Q}$ and $\\text{E}_U\\otimes\\mathbb{Q}$. These rationalizations can be expressed in terms of free Lie algebras with generators corresponding to the embedded spheres $S^{p_1},\\ldots,S^{p_r}$. \n\nWe realize all of these embeddings explicitly, through a construction of an embedded commutator. In order to establish our generating set, we first find algebraic generating sets for $\\text{E}_B\\otimes\\mathbb{Q}$ and $\\text{E}_U\\otimes\\mathbb{Q}$. After we construct our generators, we apply the theory of Hopf invariants to show they are of full rank.", "id": "Paper/67816", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67816"}, {"title": " Bicrossed Products of Fusion Categories and Their Functors ", "webprogram_exclude": "0", "session_ids": ["Session/17907"], "source_sha256": "dc73e20e46b2271dec86ff40c4197c72723d7f43881e12374fe274640981b2ca", "withdrawn": "", "abstract": "Fusion categories are categories equipped with many ”nice” algebraic structures that generalize the structures present in the categories of representations of finite groups and finite dimensional\nHopf algebras. These categories have proven to provide a useful language for the study of a variety of topics in mathematics and physics including quantum groups, operator algebras, conformal field theory, knot and link invariants, and topological quantum field theories.\n\n\nThe study of fusion categories is young and a problem at the forefront of the field is to develop a robust catalog of examples on which to test our intuition. In 2024, M. Müller, J. Plavnik, and H. Peña Polastri introduced a construction of fusion categories called the bicrossed product which\ncategorifies the notion of the bicrossed product of groups. A common perspective among category theorists is that understanding a mathematical object’s relationship to other objects is critical to understanding the object itself. As such, in this talk, we will define this construction and aim to better understand it by characterizing the functors out of bicrossed products of fusion categories. This talk is based on ongoing joint work with Monique Müller, Héctor Peña Polastri, and Julia Plavnik.", "id": "Paper/67818", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67818"}, {"title": " Analytic Properties of Maximal Proper Divisor Sets ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "69da27d9e4da0d18fd7b3c6ef4ab86c2128266a78b06b0bca203a417bef284a5", "withdrawn": "", "abstract": "A maximal proper divisor of a positive integer $n$ is a proper divisor that does not divide any other proper divisor of $n$. Letting $\\mathcal{M}(n)$ denote the set of maximal proper divisors of $n$, we prove that every such divisor has the form $n/p$, where the prime $p|n$, establishing $\\vert{}\\mathcal{M}(n)\\vert{} = \\omega(n)$, where $\\omega(n)$ is the number of distinct prime divisors of $n$. We show that $\\mathcal{M}(n)$ contains no 3-term arithmetic progressions and can be uniquely reconstructed from any two of its elements. Since $\\mathcal{M}(n)$ is a {\\it primitive set}; that is, a set whose elements do not divide each other, we examine the reciprocal logarithmic sum $f(\\mathcal{M}(n)) = \\sum_{m \\in \\mathcal{M}(n)} \\frac{1}{m \\log m}$, and obtain the sharp upper bound $\\frac{1}{2 \\log 2} + \\frac{1}{(n/2)\\log(n/2)}$, with equality iff $n = 2p$. We also establish a local analog to the Banks-Martin conjecture: the sequence of local maximums $M_k = \\max_{\\Omega(n)=k+1} f(\\mathcal{M}(n))$ is strictly monotonically decreasing and maximized at $n = 3 \\cdot 2^k$, where $\\Omega(n)$ is the number of prime factors of $n$ counted with multiplicity. Finally, we prove that $f(\\mathcal{M}(n))$ has an asymptotic average order of $O(1 / \\log n)$.", "id": "Paper/67823", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67823"}, {"title": " Computing the Minimal Euclidean Function on the Gaussian Integers, and the Sizes of its Pre-Images ", "webprogram_exclude": "0", "session_ids": ["Session/19355"], "source_sha256": "52805629443341a694430b0090e40648f3ce3f148d5677eb40a09a1009b2e234", "withdrawn": "", "abstract": "A domain is Euclidean if and only if it has a Euclidean function.  In 1948, Motzkin showed that the pointwise minimum of the Euclidean functions on a domain $R$ is itself a Euclidean function, called the minimal Euclidean function on $R$ and denoted by $\\phi_R$.  Motzkin found the minimal Euclidean function on the integers, $\\mathbb{Z}$, but there were no other explicit formulas for minimal Euclidean functions on (non-trivial) number fields until 2023.  Instead, the mathematics community computed sizes of the preimages of the minimal Euclidean functions for imaginary quadratic fields. This talk presents the first formula to compute the minimal Euclidean function on the Gaussian integers, $\\mathbb{Z}[i]$,  a proof of the formula for the size of the pre-image $|\\phi_{\\mathbb{Z}[i]}^{-1}([0,n])$, and the geometric constructions that let us perform these computations.", "id": "Paper/67824", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67824"}, {"title": " Equivariant fundamental classes in Bredon cohomology for cyclic groups ", "webprogram_exclude": "0", "session_ids": ["Session/17843"], "source_sha256": "5bbb13137f7cce0fc3e6dcd4075b0ce3b61cddaa887cdfa0bd637f15e9c04770", "withdrawn": "", "abstract": "Let $G$ be a finite group. Given a manifold with a $G$-action, we can consider its equivariant Bredon $RO(G)$-graded cohomology. In this talk, we give an introduction to Bredon cohomology for cyclic groups. We then show how a version of the Thom isomorphism theorem in $RO(C_2)$-graded cohomology can be used to develop a theory of fundamental classes for equivariant submanifolds (here $C_2$ denotes the cyclic group of order two). We end by discussing recent work to generalize these techniques to other cyclic groups.", "id": "Paper/67826", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67826"}, {"title": " Quasi-Gorenstein morphisms of DG-rings and exact sequences ", "webprogram_exclude": "0", "session_ids": ["Session/18025"], "source_sha256": "ce2000f2dc97b5c7f764dfd246cf60260d9f99ebdc13e25d9d74614e382bb5b2", "withdrawn": "", "abstract": "A quasi-Gorenstein homomorphism of commutative noetherian local rings, as first defined by Avramov and Foxby, naturally characterizes the Gorenstein property in commutative algebra. In particular, the canonical surjection of a noetherian local ring $R$ onto its residue field is quasi-Gorenstein if and only if $R$ is Gorenstein, and if a local homomorphism $R \\to S$ is quasi-Gorenstein, then $R$ is Gorenstein if and only if $S$ is Gorenstein. Extending the classical definition of a quasi-Gorenstein homomorphism, we introduce quasi-Gorenstein morphisms between DG-rings (which are special DG-algebras that behave similarly to noetherian local rings). We will then demonstrate that a sequence of elements in a local ring is exact if and only if certain maps between Koszul complexes formed with respect to the sequence are quasi-Gorenstein (as DG-rings). This result generalizes a previous theorem on exact sequences by Avramov, Henriques, and \\c{S}ega. This presentation is based on joint work with Andrew Soto Levins and Ryan Watson.", "id": "Paper/67827", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67827"}, {"title": " Nonexistence of Approximate Dual Frames via Weighted Composition Operators ", "webprogram_exclude": "0", "session_ids": ["Session/17377"], "source_sha256": "ba573a43dc9aab0b5774de868cb2188e48252c67ca9dd37b462b038a4e374f4f", "withdrawn": "", "abstract": "Reconstruction from the coefficients of a frame often requires a dual frame, and the canonical dual is obtained by inverting the frame operator, which is rarely available in a closed form.  It is therefore natural to ask whether the duality can instead be implemented by an operator of prescribed form. We study this problem in the context of weighted composition operators on Hardy and Bargmann-Fock spaces. We first characterize those weighted composition operators which carry a frame together with a dual of it to another such pair.  We then prove that if the image of a frame under a weighted composition operator is itself a dual frame, then such an operator is a positive scalar multiple of the identity and the frame is tight on both Hardy and Bargmann-Fock spaces. Relaxing duality to approximate duality, we show that on the Hardy space, composition is still forced to be the identity under mild regularity for the weight function. Approximate tightness, however, fails completely.  On the Bargmann-Fock space, the situation is rigid: such an approximate dual exists precisely when the ratio of the optimal frame bounds does not exceed an explicit sharp threshold determined by the prescribed error.", "id": "Paper/67828", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67828"}, {"title": " Factorizations in Hecke algebras: the q-Harer-Zagier formula ", "webprogram_exclude": "0", "session_ids": ["Session/18376"], "source_sha256": "03cdc52ef9af4566074ce3a86ea67af74005e501454efe899ece6cf61f5acb2c", "withdrawn": "", "abstract": "The celebrated Harer-Zagier formula enumerates many intriguing quantities, such as the number of unicellular maps on a surface of genus g and the orbifold Euler characteristic of the moduli space of curves.  In this talk, I will discuss a generalization of this formula to the Hecke algebra, which involves studying its center. \n\nJoint work with Jose Bastidas, Alejandro Morales, GaYee Park and Franco Saliola.", "id": "Paper/67829", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67829"}, {"title": " A Novel Computational Framework to Discover Isospectral Polygons in Planar Domains ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "cf4e92d25f15476782da181436d46068b690335a3c116db4e2345272e7bc156f", "withdrawn": "", "abstract": "In his influential 1966 paper Can One Hear the Shape of a Drum, Mark Kac asked whether two geometrically different shapes could have exactly the same spectrum, or set of eigenvalues. Although isospectral examples are known, finding them systematically remains difficult, especially in the plane. We introduce a new exhaustive and scalable computational framework to search for non-congruent Dirichlet-isospectral polygons. We start by grouping polygons into finite classes $(m,n)$ of side count $m$ and maximum edge displacement $n$. We then describe a program that uses computational methods to enumerate and filter polygons within each class. The framework rediscovered the classic Gordon--Webb--Wolpert pair in class $(8,2)$ and recovered larger isospectral non-congruent pairs in classes $(15,1)$ and $(13,2)$. Using the method of transplantation, we derive explicit matrices to prove isospectrality. This framework offers a scalable way to explore larger lattice polygon classes where isospectrality is not clearly understood.", "id": "Paper/67830", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67830"}, {"title": " Steklov Rigidity of Euclidean Balls ", "webprogram_exclude": "0", "session_ids": ["Session/17965"], "source_sha256": "f7d627cb999254582cb6ded12fea5af2159ca818d434376c56c809d9c94a8ea8", "withdrawn": "", "abstract": "Let $\\Omega\\subset\\mathbb{R}^n$, $n\\geq 3$, be a bounded domain with smooth boundary. In this talk, we will show that if the Steklov spectrum of $\\Omega$ tends to that of a ball at a sufficiently fast rate, then $\\Omega$ must itself be a ball. In particular, in any dimension and among all bounded domains with smooth and possibly disconnected boundary, Euclidean balls are uniquely determined by their Steklov spectrum. We will go through an overview of the proof, which combines periodicity of the boundary geodesic flow with Steklov heat invariants, and then will briefly discuss how AI was employed in the development of this result.", "id": "Paper/67831", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67831"}, {"title": " The Circle in the Doily ", "webprogram_exclude": "0", "session_ids": ["Session/18365"], "source_sha256": "9c56887ba895b89f2e7dc0a104a8385b147124a1084ed03714c0fb4ac56d9d44", "withdrawn": "", "abstract": "Gauss used the norm function to show that the ring $\\mathbb{Z}[i]$ is Euclidean, which is why we now call the ring the Gaussian integers.  The norm, however, is not the only Euclidean function on the Gaussians.  In 2023, the author found a formula for $\\phi_{\\mathbb{Z}[i]}$, the minimal Euclidean function on $\\mathbb{Z}[i]$, and gave an explicit geometric description the pre-images of the interval $[0,n]$, denoted by $\\phi_{\\mathbb{Z}[i]}^{-1}([0,n])$.  Plots of the pre-images in the complex plane form pierced octagons that look like paper doilies.  Illustrations of the norm's pre-images reveal they form the doilies' solid centers, creating a surprising and beautiful bridge between classical and modern mathematics.", "id": "Paper/67833", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67833"}, {"title": " Generating Functions of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.07ex\" height=\"2.009ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -576.1 460.5 865.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">q</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-71\" d=\"M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-71\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-chromatic Polynomials ", "webprogram_exclude": "0", "session_ids": ["Session/18359"], "source_sha256": "19ab5f36f5eb8488ffbc920bcd2d0ccc64fa5682bde71fccb277322a288ac08c", "withdrawn": "", "abstract": "Given a graph $G=(V,E)$ and a linear form $\\lambda \\in \\mathbb{Z}_{ > 0 }^V$, Bajo et al.~(2025) introduced the $q$-chromatic polynomial $\\chi_G^\\lambda(q,n) := \\sum q^{\\sum_{v \\in V} \\lambda_v c(v)}$ where the sum is over all proper colorings $c: V \\to [n] := \\{ 1, 2, \\dots, n \\}$; they showed that $\\chi_G^\\lambda(q,n)$ is a polynomial in $[n]_q := 1 + q + \\dots + q^{ n-1 } $ with coefficients in $\\mathbb{Z}(q)$. For $d \\in \\mathbb{Z}_{>0}$ and the linear form given by $(d,d^2,\\ldots,d^d)$, we show that the $q$-chromatic polynomial distinguishes labeled graphs with vertex set $[d]$. Using permutation statistics introduced by Chung--Graham (1995), called $G$-statistics, and polyhedral geometry, we give the multivariate integer point transform for the region of proper colorings of a given graph~$G$. This integer point transform allows us to find the generating function for the $q$-chromatic polynomial with respect to any linear form. We further specialize these results to the linear form $(1, 1, \\dots, 1)$, which allows us to write the $q$-chromatic polynomial in the $q$-binomial basis, clarifying expressions found by Bajo et al. Moreover, we show that $G$-statistics are compatible with the theory of order polytopes used by Bajo et al.\\ and Chow (1999). This yields further properties for the generating function of $q$-chromatic polynomial with linear form $(1,1,\\ldots,1)$, where certain coefficients of the numerator polynomial are palindromic polynomials in $q$.", "id": "Paper/67834", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67834"}, {"title": " Weak Lefschetz Properties for Monomial Complete Intersections in Positive Characteristic ", "webprogram_exclude": "0", "session_ids": ["Session/18030"], "source_sha256": "b2d711aa94d14c80078abb61a2b38beb123b3203b5d3ad0059568fb44b02b073", "withdrawn": "", "abstract": "The Weak Lefschetz Property (WLP) asks whether multiplication by a general linear form has maximal rank in every degree of a graded Artinian algebra. Over fields of characteristic zero, it is well known that every monomial complete intersection satisfies this property.\n\nIn positive characteristic, however, this result no longer holds: the Weak Lefschetz Property may fail, depending on the field characteristic and the degrees of the monomial generators.\n\nIn joint work with C. Raicu, A. Kyomuhangi, and E. Reed, we provide a complete classification of the WLP. Our proof is based on the connection between the WLP and the cohomology of line bundles on the incidence correspondence - the partial flag variety parametrizing pairs consisting of a point in projective space and a hyperplane containing it.", "id": "Paper/67838", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67838"}, {"title": " Comparative Evaluation of Machine Learning and Deep Learning Models for Tropical Cyclone Track and Intensity Forecasting in the North Atlantic Basin ", "webprogram_exclude": "0", "session_ids": ["Session/19322"], "source_sha256": "e1bf3ce73cb642310739abd32afccd7b933218d7d60d50ca692571d0c540a68a", "withdrawn": "", "abstract": "Accurate forecasts of tropical cyclone (TC) track and intensity with a sufficient lead time are critical for disaster preparedness and risk mitigation. Traditional numerical weather prediction models, while fundamental to operational forecasting, often exhibit systematic errors due to limitations in observations, physical parameterizations, and model resolution. In recent years, machine learning (ML) and deep learning (DL) approaches have emerged as promising data-driven alternatives for improving TC forecasts. This study presents a comparative evaluation of six ML and DL models—Random Forest (RF), Extreme Gradient Boosting (XGBoost), Light Gradient Boosting Machine (LightGBM), Categorical Boosting (CatBoost), Artificial Neural Network (ANN), and Convolutional Neural Network (CNN)—for forecasting TC track and intensity in the North Atlantic basin.The models are trained using the National Hurricane Center’s (NHC) HURDAT2 best-track dataset for storms from 1990 to 2019 and evaluated on an independent test set from the 2020 season. Model performance is compared across all models and benchmarked against the 2020 mean Decay-SHIFOR5 intensity error, CLIPER5 track errors, and the NHC official forecast (OFCL) errors. Forecast skill is assessed using mean absolute error (MAE) with 95\\% bootstrap confidence intervals and the coefficient of determination ($R^2$) across lead times of 6, 12, 18, 24, 48, and 72 h. The results show that: (1) several ML and DL models achieve intensity forecast performance that is broadly comparable in magnitude to the 2020 mean OFCL benchmarks, with an average error reduction of 5–11\\% at the 24 h lead time; (2) among the ML models, XGBoost and CatBoost slightly outperform LightGBM and RF in accuracy, while LightGBM demonstrates the highest computational efficiency; and (3) among the DL models, CNNs outperform ANNs in predictive accuracy and intensity forecasting efficiency, while ANNs exhibit lower computational cost for track forecast. Bootstrap confidence intervals indicate relatively low variability in model errors, supporting the statistical stability of the results within the 2020 season. Overall, the findings demonstrate the potential of ML/DL-based approaches to enhance TC track and intensity forecasting in the North Atlantic basin.", "id": "Paper/67840", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67840"}, {"title": " Duality of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"4.258ex\" height=\"3.176ex\" style=\"vertical-align: -1.005ex;\" viewBox=\"0 -934.9 1833.5 1367.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">F_{\\alpha ,\\omega }^p</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-46\" d=\"M48 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H742Q749 676 749 669Q749 664 736 557T722 447Q720 440 702 440H690Q683 445 683 453Q683 454 686 477T689 530Q689 560 682 579T663 610T626 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y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/19368"], "source_sha256": "b04fafc3ce0c4f647c51ee2fd049ba08621b0435e90e7b98b02f6900974c67c0", "withdrawn": "", "abstract": "Given a weight $\\omega$ (i.e., a positive a.e. measurable function)  on $\\mathbb{C}$, the weighted  Fock space $F_{\\alpha, \\omega} ^p$ is the space of entire functions $f$ on the complex plane such that $f(\\cdot) e^{-\\frac{\\alpha}{2} |\\cdot|^2} \\in L^p(\\mathbb{C}, \\omega \\, dA)$ where $dA$ is the ordinary area measure. I will discuss how duality can hold for weighted Fock spaces with weight functions satisfying the Muckenhoupt $\\mathbb{A}_p$ condition over all unit squares in the case of $1 < p < \\infty.$ \n\nNamely, for such weights, we will prove that if $\\alpha, \\beta > 0,$ $\\gamma = \\sqrt{\\alpha \\beta},$ $\\frac{1}{p} + \\frac{1}{q} = 1,$ and $\\omega'$ is the scaled dual weight function $\\omega'(z) = \\omega^{-\\frac{q}{p}} \\left(\\sqrt{\\frac{\\beta}{\\alpha}}z\\right)$, then  $ (F_{\\alpha, \\omega}^p)^* = F ^q _{\\beta, \\omega'}$  under the integral pairing \n\\[ F_\\gamma (f,g) = \\lim_{R \\to \\infty} \\int_{|z| < R} f(z)\\overline{g(z)}  e^{-\\gamma |z|^2} \\, dA(z).\\]", "id": "Paper/67841", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67841"}, {"title": " Weighted Veronese Rings via Convex Semigroups ", "webprogram_exclude": "0", "session_ids": ["Session/18253"], "source_sha256": "508708ac6196da01120d31d7429fa5f39ce261065c07e72bcae20dd49bd70979", "withdrawn": "", "abstract": "For a standard-graded polynomial ring R, the d-Veronese subring is generated as a k-algebra by degree d monomials. It is Koszul, and its defining ideal is quadratic, binomial, and determinantal. In this talk, I will discuss what happens if we instead start with a non-standard graded polynomial ring.\n\nIn joint work with A. Seceleanu, L. Fiorindo, B. Chase, T. de Holleben, S. Singh, and T. Nguyen, we determine properties of two-dimensional weighted Veronese rings and, more generally, normal affine semigroup rings, including determinantal presentation, Gröbner basis, graded Hilbert series and graded Betti numbers, and their Koszul property. \n\nIn contrast, in three or more variables, these properties no longer hold in general. We provide explicit examples where the ring fails to be determinantal and Koszul.", "id": "Paper/67843", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67843"}, {"title": " Personalizing Cancer Models under Data Scarcity via Parameter Decomposition ", "webprogram_exclude": "0", "session_ids": ["Session/17970"], "source_sha256": "effc5f055d602aac118e8e392c7111b30fa41fd74d9fe03d2bcdca694cfa48c4", "withdrawn": "", "abstract": "A medical digital twin (MDT) is a virtual representation of disease which is continuously updated in real time using longitudinal patient data. Effective MDTs may be used in a clinical setting to predict disease outcomes and make treatment decisions. Such models rely on robust and efficient parameter calibration under data scarcity. In this work, we develop novel methods to recover and personalize parameters of models relevant to MDTs under limited test data. We decompose selected model parameters into a common component, shared across patients and a personalized component, which is patient-specific and is continuously updated with new patient data. The common component represents a commonality between patients and is estimated once, while the personalized component represents each patient’s deviation from the common component. We decompose parameters by formulating and solving an optimization problem.  We demonstrate the utility of this decomposition by applying our techniques to synthetic data generated by canonical dynamical systems, such as cancer models with treatment intervention. Our results show accurate and rapid parameter personalization, even in limited data regimes.", "id": "Paper/67845", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67845"}, {"title": " Students’ Perceptions of Generative AI Before and After AI-Integrated Tasks in Calculus I ", "webprogram_exclude": "0", "session_ids": ["Session/18346"], "source_sha256": "98879301c4afe8199b080fe32fad5e835197ff066cb5abd8b8f06eb694fc41a8", "withdrawn": "", "abstract": "As generative artificial intelligence (GenAI) becomes more prominent in higher education, questions remain about how students’ perceptions of these tools and approaches to using them evolve through guided classroom experiences. This study explored shifts in students’ understanding and perceptions of GenAI in Calculus I courses, where students participated in specially designed tasks that integrated GenAI into mathematical problem solving. Working with two experienced instructors, the research team developed tasks in which students identified mathematical errors, used GenAI to generate calculus problems based on those errors, solved the problems, and evaluated AI-generated explanations and solutions. The tasks encouraged students to question and verify AI output rather than accept it without careful evaluation. Data collection included anonymous pre- and post-surveys as well as one-on-one interviews, providing both quantitative and qualitative insights. Results indicated that while students already possessed a foundational awareness of GenAI’s strengths and limitations, the guided tasks led to reduced concerns about its academic risks, such as dishonesty and overdependence. Interview participants described how evaluating AI output helped them recognize concerns about accuracy and reliability. They also reported developing more responsible strategies including checking AI-generated solutions, comparing approaches, and using GenAI to learn mathematical concepts rather than merely obtain answers. The study suggests that thoughtfully structured classroom experiences can help bridge the gap between technological advances and educational practices.", "id": "Paper/67847", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67847"}, {"title": " A geometric approach to data-driven modeling of dynamical systems ", "webprogram_exclude": "0", "session_ids": ["Session/18357"], "source_sha256": "46a49f777aeea6571d3209032fb18f65dd165fef66e1d8b3c9d747bab9f6a499", "withdrawn": "", "abstract": "We present a novel framework for data-driven modeling of dynamical systems that builds geometric multiscale descriptions based in classical dynamical systems theory. To address complexity of real-world problems which are difficult to describe in a single global model, we will construct phase-portraits by identifying and fitting local geometric features---such as fixed points, limit cycles, manifolds, and separatrices---directly from time-series data. These interpretable features will be assembled into a coherent global phase portrait, enabling modular and adaptable description of complex nonlinear dynamics.", "id": "Paper/67850", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67850"}, {"title": " Exact Total Variation Minimizers via differential inclusions as Non-Oscillatory Limiters in High-Order Methods for Conservation Laws ", "webprogram_exclude": "0", "session_ids": ["Session/17703"], "source_sha256": "25bad53aed4feb7ec83a461a6c624aa43747c317b39f4a30a285512b2e2e6010", "withdrawn": "", "abstract": "High-order numerical methods for conservation laws can generate spurious oscillations near discontinuities. We propose to suppress these oscillations by post-processing the numerical solution with a total variation (TV) denoising step that reduces the total variation of the nodal values. For a general analysis operator, the resulting discrete minimization problem need not satisfy the submodularity property that existing exact max-flow algorithms require, so we instead compute the TV minimizer exactly using a differential inclusion algorithm. In one dimension, the differential inclusion algorithm computes the TV minimizer in finitely many steps, requires no tuning of algorithmic parameters, and preserves the total mass. In two dimensions, we apply the 1D algorithm dimension by dimension. We test the method as a post-processing limiter for Fourier pseudospectral methods and a fifth-order finite difference scheme applied to scalar conservation laws, compressible Euler equations, and the two-dimensional incompressible Euler equations.", "id": "Paper/67851", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67851"}, {"title": " The scramble number of outerplanar graphs ", "webprogram_exclude": "0", "session_ids": ["Session/19366"], "source_sha256": "9c51cbd20a3d0833cb4c3e5dd25307c7938461cc1d1ecbfd1c65cf7369ab56c5", "withdrawn": "", "abstract": "For planar graphs, it is known that their treewidth is bounded by $O(\\sqrt{n})$, where $n$ is the number of vertices of the graph. A related invariant to treewidth, is the scramble number of graphs. Recently, Connor et. al proved that planar graphs of bounded maximal degree have scramble number bounded by $O(\\sqrt{n})$. An open question is whether the scramble number of any planar graph follows this same bound. We give a definitive answer with an explicit bound for a subset of planar graphs, the simple outerplanar graphs and the simple near outerplanar graphs.", "id": "Paper/67852", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67852"}, {"title": " Wave decay on extremal Kerr-Newman black holes with slow rotation ", "webprogram_exclude": "0", "session_ids": ["Session/18148"], "source_sha256": "4af843c4f54b2b1ebbb5a3667ba66ffb24134566f762f083f9feb193506265e3", "withdrawn": "", "abstract": "In this talk, I will discuss the decay of solutions to the wave equation on slowly-rotating extremal Kerr-Newman black holes. The behavior of waves on extremal spherically symmetric black holes and axisymmetric waves on rotational extremal black holes has seen remarkable recent developments. I will discuss how these developments can be extended to the case of slowly-rotating extremal Kerr-Newman, highlighting the similarities between the structure of the wave operator at null infinity and the structure of the wave operator at the extremal horizon. This is joint work with Allen Fang and Jingbo Wan.", "id": "Paper/67854", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67854"}, {"title": " The Large-<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.064ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 888.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">N</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4E\" d=\"M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-4E\" x=\"0\" y=\"0\"></use>\n</g>\n</svg> Limit of Ricci curvature in the Zeitlin Model on the Torus ", "webprogram_exclude": "0", "session_ids": ["Session/19358"], "source_sha256": "079fcd0151fb0812eea9e776ca61504ebd5b9b60628d102fb397d67b318369da", "withdrawn": "", "abstract": "The incompressible Euler equations of hydrodynamics may be interpreted as a geodesic flow on the infinite-dimensional group of its volume-preserving diffeomorphisms, as first described by Arnold. \nOn the torus, the associated Poisson algebra of stream functions admits a geometric quantization, producing the Zeitlin model: a sequence of Lie algebras isomorphic to $\\mathfrak{su}(N)$ that approximates the Lie algebra of divergence free vector fields on the torus as $N\\to\\infty.$ We introduce a notion of averaged Ricci curvature in these finite-dimensional approximations and prove convergence in the limit, thereby obtaining a natural candidate for Ricci curvature on the diffeomorphism group.", "id": "Paper/67855", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67855"}, {"title": " Investigation of Impacts of COVID-19 on Real-Estate Market ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "b06132e21c96894697e055fccafba1431fca8b657fd39a16fd647d00f4bea531", "withdrawn": "", "abstract": "We investigate how the real estate market changes after the hit of COVID-19. As\nmajor, long-term financial commitments, housing markets are highly sensitive to macroeconomic and socioeconomic fluctuations. COVID-19 had major impacts on housing prices,\nand it was assumed that the property prices would go lower during and after the pandemic, but we observed the opposite of our assumptions. Utilizing a panel data framework with fixed-effects models, this paper quantifies the specific impacts of the pandemic\nshock on local housing dynamics. The results indicate that shifts in buyers’ behavioral\npreferences—coupled with evolving socioeconomic structures such as remote work adaptation and shifting interest rates—counteracted downward pressures and instead accelerated\nprice appreciation.", "id": "Paper/67858", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67858"}, {"title": " Meromorphic Open-String Vertex Algebras and Courant algebroids ", "webprogram_exclude": "0", "session_ids": ["Session/18270"], "source_sha256": "ab32e5b8e4a5c550b36554632b2a7aa12ad9592f997184594a07fb6e25331d67", "withdrawn": "", "abstract": "Motivated by supersymmetric nonlinear sigma models, I will describe a construction of meromorphic open-string vertex algebras and their canonically twisted modules from transitive Courant algebroids. Using a generalized metric, a compatible torsion-free connection, and suitable spinor data, the construction couples bosonic covariant differentiation with fermionic Clifford action. Distinguished vertex-operator components act on embedded spinor ground states as the canonical Dirac generating operator, its formal adjoint, and the generalized Hodge operator. For the standard untwisted exact Courant algebroid, these operators become the de Rham differential, its adjoint, and the Hodge Laplacian. This is joint work with Fei Qi.", "id": "Paper/67860", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67860"}, {"title": " Neural Network Approximation of Continuous Functions in High Dimensions ", "webprogram_exclude": "0", "session_ids": ["Session/18190"], "source_sha256": "fa96929488200e7e35b0e7efcafbd6f74be5d54b5f5545ab8124ba1ea3d4c65e", "withdrawn": "", "abstract": "The remarkable successes of neural networks in a huge variety of inverse problems has fueled their adoption in disciplines ranging from medical imaging to seismic analysis over the past decade. However, the high dimensionality of such inverse problems has simultaneously left current theory, which predicts that networks should scale exponentially in the dimension of the problem, unable to explain why the seemingly small networks used in these settings work as well as they do in practice. To reduce this gap between theory and practice, we will discuss a general method for bounding the complexity required for a neural network to approximate a Holder continuous function (as well as uniformly continuous functions that admit a specified modulus of continuity) defined on a high-dimensional set with a low-complexity structure.", "id": "Paper/67863", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67863"}, {"title": " Infinitesimal Homeostasis and Circadian Rhythms via Hopf Bifurcation ", "webprogram_exclude": "0", "session_ids": ["Session/18257"], "source_sha256": "f48b6389be82e07478fa04097e6df93548efb10c50a76141328f79ad5d7e1985", "withdrawn": "", "abstract": "Homeostasis is a biological phenomenon in which a function of the state of a system remains approximately constant as an input parameter varies. Golubitsky and collaborators developed a mathematical theory of homeostasis that is based on methods from singularity theory. In this theory, the state is a steady state, and the function is often a coordinate of the steady state. The weaker requirement that a function of the state remain approximately constant is replaced by the requirement that the derivative of the function with respect to the input parameter vanishes at an isolated point. This notion of a zero derivative has the name infinitesimal homeostasis. Homeostasis can also apply to many oscillatory biological processes. For example, the period of circadian rhythms remains approximately constant as parameters such as ambient temperature and gene expression levels vary. The objective of this talk is to develop a theory of homeostasis for periodic phenomena. We call this notion infinitesimal period homeostasis. A common way for periodic solutions to arise in models, such as the circadian rhythm models mentioned above, is by Hopf bifurcation. We limit ourselves to analyzing models that undergo nondegenerate Hopf bifurcation. Our main result in this setup is that singularity theory can be used to find infinitesimal period homeostasis. This result is illustrated using numerical simulations of a simple model of the mammalian circadian clock that was proposed by Kim and Forger.  Our theoretical results are based on having two parameters (a bifurcation parameter and an input parameter) and the circle symmetry of Hopf normal form.", "id": "Paper/67864", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67864"}, {"title": " The Life and Legacy of James P. Keener ", "webprogram_exclude": "0", "session_ids": ["Session/17988"], "source_sha256": "28cda760d4d480778184a126f5d44a810b77aca3185ab3de7be1ddec75790cf2", "withdrawn": "", "abstract": "James P. Keener made a big impact in mathematical biology and applied mathematics over many years. With more than 50 mentored PhD students, 200 publications, three benchmark textbooks, and many friends and colleagues, his influence expands in a self-perpetuating spiral. In this talk, I will provide a brief overview of his work, his passions, and his accomplishments shared through the lens of friends, colleagues, and students.", "id": "Paper/67866", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67866"}, {"title": " Outcomes from the  Generative AI and Mathematics Education Convening  ", "webprogram_exclude": "0", "session_ids": ["Session/18199"], "source_sha256": "457c0cfc7ac6e33a817a52d33227d167fb6df344a762a5ba3a4a579a2c574c1b", "withdrawn": "", "abstract": "We report on outcomes from the {\\it Generative AI and Mathematics Education Convening} held over two days in June 2026. Thirty participants broke into teams focused on the themes: \n\n\\begin{itemize}\n\\item\\cdot Generative AI in teaching mathematics\n\\item\\cdot Generative AI in learning mathematics\n\\item\\cdot Generative AI in assessing mathematical knowledge\n\\item\\cdot Curriculum modifications and/or updates necessary due to Generative AI\n\\end{itemize}\n\nThis convening was motivated by the important questions raised by undergraduate mathematics educators in light of the remarkable capabilities of generative artificial intelligence. As happened with slide rules, handheld calculators, and computer algebra systems, we must ask how to balance the ease of technology-assisted mathematical work with the need to have mental intuition for fundamental ideas. Generative AI simultaneously complicates how we teach and assess our students, while offering myriad tools to use in teaching and assessment. And how do we guide our students to use generative AI in a way that supports their learning rather than detracting from it?\n\nRelying on our collective experience with such questions, as well literature reviews, convening participants drafted recommendations regarding generative AI and their focal theme. The recently released {\\it MAA Statement on AI in Higher Education} grew from this draft. We will discuss these recommendations as well as other projects that have come from the convening.\n\nThis work was supported by the National Science Foundation Award #2617959. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.", "id": "Paper/67867", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67867"}, {"title": " A Fredholm framework for the wave operator on the Clifton-Pohl torus ", "webprogram_exclude": "0", "session_ids": ["Session/17999"], "source_sha256": "0607ed471b202f1ce0cbbb95ecfd237688e9bac4e397bc46efa98615c2d8c3c8", "withdrawn": "", "abstract": "The Clifton-Pohl torus is a classical example of a compact Lorentzian manifold with\nincomplete null geodesics. We prove Fredholm estimates for the wave operator on this\nmanifold acting between suitable variable-order Sobolev spaces. The proof uses the source-sink dynamics of the projectivized null-geodesic flow to rule out the existence of non-trivial\nmicrolocal defect measures.", "id": "Paper/67868", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67868"}, {"title": " Plethysm coefficients and the uniform block permutation algebra ", "webprogram_exclude": "0", "session_ids": ["Session/18375"], "source_sha256": "9843cf860026d24bb68dc13e8b44e0aea3dbf70a26cab2447578bd27bdbf43d0", "withdrawn": "", "abstract": "The monoid of uniform block permutations $\\mathcal{U}_k$, also known as the party algebra, contains the symmetric group $\\mathfrak{S}_k$ as a submonoid. The multiplicities in the restriction of an irreducible $\\mathcal{U}_k$-module to $\\mathfrak{S}_k$ are plethysm coefficients of Schur functions, which makes $\\mathcal{U}_k$ a natural algebraic setting in which to attack the problem of computing them combinatorially.\n\nThe submonoids of $\\mathcal{U}_k$ containing $\\mathfrak{S}_k$ are in bijection with the downsets of a certain partial order on partitions of $k$, so the passage from $\\mathcal{U}_k$ down to $\\mathfrak{S}_k$ can be factored into many small steps. I will give a rule for restricting along this lattice: a module either remains irreducible or decomposes with multiplicities again given by plethysm coefficients. Kronecker coefficients appear as well, as multiplicities for restriction to maximal subgroups.\n\nThis is joint work with Rosa Orellana, Anne Schilling, and Mike Zabrocki.", "id": "Paper/67873", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67873"}, {"title": " Modeling Multidrug Therapy and Antibiotic Resistance in Cystic Fibrosis Infections ", "webprogram_exclude": "0", "session_ids": ["Session/18275"], "source_sha256": "4d872c22897742683ca9098b67f2d414ba3002cf1f81bff91bba9690356aabf4", "withdrawn": "", "abstract": "Chronic pulmonary infections are a major contributor to disease progression and mortality in individuals with cystic fibrosis (CF). These infections often require prolonged antibiotic treatment, which can promote the emergence and persistence of antibiotic-resistant bacteria, further complicating treatment decisions. We develop an ordinary differential equation model to investigate susceptible and resistant bacterial populations under a two-drug treatment regimen. Unlike models that represent resistance acquisition through a single generalized mutation process, our model incorporates distinct mechanisms of resistance development, including spontaneous and division-associated mutation, conjugation, and transformation, as well as reversion, fitness costs associated with resistance, and drug-specific effects. Model parameters are estimated using experimental growth and mutation frequency data for \\textit{Staphylococcus aureus} and \\textit{Pseudomonas aeruginosa}, two clinically relevant bacterial species. Results suggest that accounting for these resistance mechanisms and differential antibiotic effects is important for reproducing observed bacterial dynamics. We use the calibrated model to compare candidate treatment schedules and evaluate their ability to limit the emergence of antibiotic resistance in polymicrobial CF infections.", "id": "Paper/67874", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67874"}, {"title": " Hyperelliptic Shimura Curves ", "webprogram_exclude": "0", "session_ids": ["Session/17903"], "source_sha256": "3c64235ae68b73043727293f320f75ffaf08d4ee8a1cfc8c50c3860bfb695d54", "withdrawn": "", "abstract": "We work towards completely classifying all hyperelliptic Atkin--Lehner quotients of Shimura curves $X_0(D,N)/W$ with level $N$ coprime to $D$ and $W \\le W_0(D,N)$, extending, on the one hand, a result of Ogg that provided such a classification for the trivial quotients (the case $W = 1$), and on the other hand, results of Furumoto and Hasegawa that provided such a classification for modular curves (the case $D = 1$). As a byproduct of our methods, building on the works of Guo and Yang, we also obtain models for some quotients of genus at most two, answering some questions of Padurariu and Saia.", "id": "Paper/67876", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67876"}, {"title": " Application of Zigzag Persistence in Machine Learning ", "webprogram_exclude": "0", "session_ids": ["Session/18354"], "source_sha256": "93f8de38fe0be493deb292cd861458fd6af2284ebd89f56a013b6544c80ae7c2", "withdrawn": "", "abstract": "Zigzag persistence enhances the capability of standard persistence by allowing deletions along with insertions in filtrations. We give two examples where zigzag persistence is used in machine learning. \nIn the first one, we present Quasi Zigzag Persistent Homology (QZPH) as a framework for analyzing time-varying data by integrating multiparameter persistence and zigzag persistence. To this end, we introduce a stable topological invariant that captures both static and dynamic features at different scales. We show that it enhances the machine learning models when applied to tasks such as sleep-stage detection, demonstrating its effectiveness in capturing the evolving patterns in time-evolving datasets. In the second example, we introduce a new paradigm for hallucination detection in LLM by analyzing the dynamic topology of the evolution of model's layer-wise attention. We model the sequence of attention matrices as a zigzag graph filtration and use zigzag persistence to extract a topological signature. We validate our framework, HalluZig, on multiple benchmarks, demonstrating that it outperforms strong baselines. Furthermore, our analysis reveals that these topological signatures are generalizable across different models and hallucination detection is possible only using structural signatures from partial network depth.\n\nThis is a joint work with S. Samaga and G. Gonzalez-Arroyo", "id": "Paper/67877", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67877"}, {"title": " Extension of CR functions from CR singular manifolds ", "webprogram_exclude": "0", "session_ids": ["Session/18295"], "source_sha256": "374a967eb251333bee48528a9b0ad59ddb9b6b65c5508e402bec4053d74b6cc8", "withdrawn": "", "abstract": "We study the conditions under which a real-analytic function on a real-analytic CR singular submanifold that is CR at CR points extends to a holomorphic function.  In particular, we are interested in conditions on nonextension.  One such condition is being a CR image of a CR submanifold.  A particular set of examples we are interested in are the perturbations of \\(w = \\bar{z}_1 z_2\\).", "id": "Paper/67879", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67879"}, {"title": " Explorations with Extended Springer Fibers ", "webprogram_exclude": "0", "session_ids": ["Session/18278"], "source_sha256": "3d182889c3b1e0533ae34b2fa7b034eccfccf19728073dd89b30030a466bd858", "withdrawn": "", "abstract": "The extended Springer resolution is a map first defined by William Graham that factors through the Springer resolution and has connections to Lusztig’s generalized Springer correspondence. The study of this map has been rich with combinatorial and geometric methods, and it has led to new insights into Lusztig's correspondence.  This talk will focus on this perspective, giving highlights of these techniques and also a big picture of results relating to the extended Springer resolution in all types.", "id": "Paper/67880", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67880"}, {"title": " The Bias Conjecture for One-Parameter Families of Elliptic Curves with Non-Constant <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"0.985ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex; margin-left: -0.027ex;\" viewBox=\"-11.5 -791.3 424 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">j</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6A\" d=\"M297 596Q297 627 318 644T361 661Q378 661 389 651T403 623Q403 595 384 576T340 557Q322 557 310 567T297 596ZM288 376Q288 405 262 405Q240 405 220 393T185 362T161 325T144 293L137 279Q135 278 121 278H107Q101 284 101 286T105 299Q126 348 164 391T252 441Q253 441 260 441T272 442Q296 441 316 432Q341 418 354 401T367 348V332L318 133Q267 -67 264 -75Q246 -125 194 -164T75 -204Q25 -204 7 -183T-12 -137Q-12 -110 7 -91T53 -71Q70 -71 82 -81T95 -112Q95 -148 63 -167Q69 -168 77 -168Q111 -168 139 -140T182 -74L193 -32Q204 11 219 72T251 197T278 308T289 365Q289 372 288 376Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-6A\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Invariant ", "webprogram_exclude": "0", "session_ids": ["Session/18076"], "source_sha256": "ccc2faf2b4a0f0f33cfa81267572e1aaa0d95a6e412560c5e4306f9377a88c4e", "withdrawn": "", "abstract": "We investigate Miller's bias conjecture for general one-parameter families of elliptic curves over $\\mathbb{Q}$ with non-constant $j$-invariants. Utilizing methods developed by Michel, we view the second moment as the sum of distinct cohomological components: a main $p^2$ term, a $p^{3/2}$ term arising from the first cohomology over the projective line, and terms of order $p$ or lower corresponding to singular fibers. By assuming the generalized Sato-Tate conjecture, we employ representation and motive theory to demonstrate that the coefficient of the $p^{3/2}$ term averages to zero in the limit. We then independently analyze the lower-order contributions without assuming Sato-Tate. By applying the Chebotarev density theorem and analyzing Galois representations, we show that the contributions to the order $p$ term from additive singular fibers also average to zero. Consequently, the only remaining average contribution to the $p$ term is $-B_pp$, where $B_p$ denotes the number of \"bad\" points where the discriminant vanishes. Because $B_p$ averages to a strictly positive value, the overall coefficient of the $p$ term averages to a strictly negative value in the limit, thereby establishing the bias conjecture for these elliptic curves families.", "id": "Paper/67881", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67881"}, {"title": " Pirogov-Sinai Theory for the Hard-Core model and <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.55ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 667.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbb {Z}</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJAMS-5A\" d=\"M39 -1Q29 9 29 12Q29 23 60 77T219 337L410 648H364Q261 648 210 628Q168 612 142 588T109 545T97 509T88 490Q85 489 80 489Q72 489 61 503L70 588Q72 607 75 628T79 662T81 675Q84 677 88 681Q90 683 341 683H592Q604 673 604 666Q604 662 412 348L221 37Q221 35 301 35Q406 35 446 48Q504 68 543 111T597 212Q602 239 617 239Q624 239 629 234T635 223Q635 215 621 113T604 8L597 1Q595 -1 317 -1H39ZM148 637L166 648H112V632Q111 629 110 622T108 612Q108 608 110 608T116 612T129 623T148 637ZM552 646Q552 648 504 648Q452 648 450 643Q448 639 266 343T77 37Q77 35 128 35H179L366 339L552 646ZM572 35Q581 89 581 97L561 77Q542 59 526 48L508 37L539 35H572Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJAMS-5A\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Homomorphisms ", "webprogram_exclude": "0", "session_ids": ["Session/18315"], "source_sha256": "982fa891a5e788c9d74c368da3e01ed6c334e3ab314ba6bd0b351d9df9a785a4", "withdrawn": "", "abstract": "We use Pirogov--Sinai theory together with known container-type results to prove that the infinite-volume pressure for the hard-core model on $\\mathbb{Z}^d$ is analytic when $\\lambda \\geq \\frac{C\\log^2 d}{d^{1/3}}$ and $d\\geq d_0$. Our approach also yields efficient approximate sampling and counting algorithms on finite regions of $\\mathbb{Z}^d$ with prescribed boundary conditions. With substantial adaptations, we apply the same general framework to obtain efficient approximate sampling and counting algorithms for $\\mathbb{Z}$-homomorphisms and, via reductions, for 3-colorings and Lipschitz functions.", "id": "Paper/67882", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67882"}, {"title": " Bounding the number of zeros near the central point in families of cuspidal newforms ", "webprogram_exclude": "0", "session_ids": ["Session/18276"], "source_sha256": "503d91f6e991d50bd31b5a76d1e11619cb3581002fc71fd987f10a682525d6c6", "withdrawn": "", "abstract": "We study low-lying zeros in families of even holomorphic cuspidal newforms of fixed weight and prime level, with particular emphasis on the number of forms having a zero in a prescribed normalized window about the central point and on the distribution of the number of such zeros among the forms. We quantify the number of forms having at least one zero in the window and study the distribution of the number of zeros in that window among the forms. Assuming the Generalized Riemann Hypothesis, we obtain new lower bounds for the number of forms having a low-lying zero. We first prove that, along an infinite sequence of prime levels $N$, the number of such forms is $\\gg N^{7/8}\\log N$. We then use higher centered moments and an appropriate test function to show that a positive proportion of the family has a zero in a prescribed window. Finally, we obtain polynomial upper-tail bounds for the number of zeros occurring there and show that a positive proportion of forms have a bounded, nonzero number of low-lying zeros.", "id": "Paper/67884", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67884"}, {"title": " Fast Answers, Broken Evidence: What My Student and I Each Got Wrong About AI ", "webprogram_exclude": "0", "session_ids": ["Session/18346"], "source_sha256": "af38dadba5b27541463dc85f98e756907bf88c7e0c280ebbd97be65180a5ad7b", "withdrawn": "", "abstract": "Four years in, many of us are experimenting with AI in our courses,  and our students are experimenting far more, often on their own and without guidance. What happens when they use these tools to study? Does AI-assisted practice produce learning, or just the feeling of it? And what does their AI use mean for the evidence we've always relied on: the homework, the problem sets, the finished proofs? We will look at recent research on student learning and AI, including a case from my own linear algebra course, and consider protocols for student AI use that support learning and fit within a typical mathematics course.", "id": "Paper/67885", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67885"}, {"title": " Atoroidal surface bundles and restrictions on their geometry, II. ", "webprogram_exclude": "0", "session_ids": ["Session/18267"], "source_sha256": "a5bf224178c704e74a389164d6b9d21ca4810970a4aca55c4c015123757b313c", "withdrawn": "", "abstract": "I will (continue to) discuss work with Leininger showing that our atoroidal surface bundles over surfaces are typically not complex surfaces nor hyperbolic manifolds.", "id": "Paper/67886", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67886"}, {"title": " Semilinear parabolic equations in end-point Besov spaces and beyond ", "webprogram_exclude": "0", "session_ids": ["Session/18265"], "source_sha256": "d14f0ab5497c4166164993a6473d132ab207fd8ea9ec097bef728a3b0ccb9276", "withdrawn": "", "abstract": "We address the question of global in time existence for the semilinear parabolic equation\n$ \\partial_tu-\\Delta u=|u|^{q-1}u$ in  $\\mathbb{R}^n\\times (0,\\infty)$, with initial condition\n $u(\\cdot,0)= u_0$ in  $\\mathbb{R}^n$,\nwhere $q> 1+2/n$. We found a space of initial  data, optimal in a certain sense, that guarantees the existence of a global in time solution whenever the norm of the initial datum $u_0$ is small in such a space.\nMoreover, our results contain all of the known results in the literature and imply in particular  that global in time existence does actually hold for end-point Besov and Triebel-Lizorkin spaces. \nThis talk is based on joint work with Gael Y. Diebou.", "id": "Paper/67887", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67887"}, {"title": " Efficient generation of projective modules: a motivic view ", "webprogram_exclude": "0", "session_ids": ["Session/18219"], "source_sha256": "849761dfb257131dc1316bb8478e6d5156a0801784b0a018f92ac2532fdd054d", "withdrawn": "", "abstract": "Assume k is a field and R is a smooth k-algebra of dimension d. If P is a projective module of rank r, the classical Forster--Swan theorem asserts that P can be generated by r+d-elements. Under suitable assumptions on r and d, we investigate obstructions to generation of P by fewer than r+d elements using motivic homotopy theory. For example, we observe that a quadratic enhancement of the classical Segre class obstructs generation by r+d−1 elements, whether or not k is algebraically closed, generalizing old results of M.P. Murthy. Along the way, we also establish efficient generation results for symplectic modules. The techniques used in this project involve motivic homotopy theory, which I will explain in a non-technical way.", "id": "Paper/67889", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67889"}, {"title": " Evolution of Internal Waves in a 2D Perturbed Cylinder ", "webprogram_exclude": "0", "session_ids": ["Session/19363"], "source_sha256": "3efcb7d3f8d673975767ece45da2dad642cccd1754b41e180dae6890dfaab33d", "withdrawn": "", "abstract": "I will discuss the long-time behavior of solutions to the internal wave equation in a 2D perturbed cylinder with flat ends. The long-time profile of such solutions is analyzed via regularity of solutions to the stationary equation. I will show how to obtain a limiting absorption principle for the stationary equation via a propagation of defect measure argument.", "id": "Paper/67890", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67890"}, {"title": " Patterns in the enumeration of complex topological vector bundles on complex projective space ", "webprogram_exclude": "0", "session_ids": ["Session/18217"], "source_sha256": "54356b776384e29117b62ac3b24984aabe44b0e4843b8dac7f63f7a3314222c1", "withdrawn": "", "abstract": "I will discuss my ongoing attempt to understand the enumeration and classification of complex topological vector bundles on complex topological spaces. For a fixed (complex) dimension n and (complex) rank r<n, one can study complex topological vector bundles on CP^n with a given K-theory class. There are always finitely many such bundles, up to isomorphism; but often more than one. Distinguishing non-isomorphic vector bundles that represent the same K-theory class is an interesting and subtle problem, which can be worked out explicitly for n and/or n-r small. I will discuss progress on this question and future directions. These results include work, and work-in-progress, with Hood Chatham and Yang Hu.", "id": "Paper/67892", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67892"}, {"title": " A Numerical and Theoretical Analysis of the Porous Medium Equation with Reaction and its Limit ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "c87a740e433aaecc94e8ccc787d215af278ea585b5c94eefdf796252825198ee", "withdrawn": "", "abstract": "We consider a porous medium partial differential equation (PDE) with parameter $m>1$ that models tissue growth of a tumor,\n\\[ u_t-(u^m)_{xx}=u\\left(\\mu(x)-p\\right), \\]\nwhere $\\mu:\\mathbb{R}\\to\\mathbb{R}$ represents the favorability of the tissue's environment at a point $x$ and the pressure $p$ is given in terms of the density $u$ by $p=\\frac{m}{m-1}u^{m-1}$. Our goal is to find criteria on $\\mu$ that determine whether the tumor grows or shrinks. This issue is well-understood for linear diffusion equations, that is, if $(u^m)_{xx}$ is replaced by $u_{xx}$, but very little is known in the porous medium case.\n\nWe approach this problem from both numerical and analytical perspectives. It is known that in the limit as $m\\to\\infty$, the PDE becomes a free-boundary problem, with $\\overline{p}:=\\lim_{m\\to\\infty}p$ satisfying:\n\\[ \\left\\{\\begin{array}{l} -\\overline{p}_{xx}=\\mu(x)-\\overline{p} \\quad \\text{on } (0,r(t))=\\{x\\in(0,\\infty)\\mid\\overline{p}(x,t)>0\\}, \\\\ \\dot{r}(t)=-\\overline{p}_x(r(t),t), \\\\ r(0)=r_0>0,\\quad \\overline{p}(0,t)=1,\\quad \\overline{p}(r(t),t)=0. \\end{array}\\right. \\]\nWe prove the existence, uniqueness, and non-negativity of solutions to this system. We study how various conditions on $\\mu$ affect the asymptotic behavior of $r(t)$.\n\nTo obtain our numerical results, we model the PDE using an implicit finite-difference method and use our empirical findings to develop conjectures about conditions on $\\mu$ that guarantee either tumor growth or extinction.", "id": "Paper/67896", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67896"}, {"title": " Connecting Microscale Kinetics to Macroscale Structure in Branched Actin Networks ", "webprogram_exclude": "0", "session_ids": ["Session/17988"], "source_sha256": "12cf6831c1907afbf02386e822f6ae6cd11c8961ac1c6c43c5cad1276a8a201a", "withdrawn": "", "abstract": "Actin, the most abundant protein in cells, is involved in key cellular functions including cell motility, cell division, and muscle contraction. Branched actin networks emerge from local molecular events whose collective effect on macroscopic network architecture is not fully understood. This talk presents two complementary approaches, built on a minimal agent-based stochastic model of actin network formation, that connect microscale kinetics to macroscale structure. First, we show how measures extracted from the microscale simulation can be mapped onto the diffusion coefficient and growth rate of a macroscale reaction-diffusion equation, revealing that bulk transport parameters depend nonlinearly on molecular-level rates. Second, we tackle the inverse problem: given only an image of an actin network’s density, can we infer the molecular conditions that produced it? We present a classification pipeline combining convolutional neural networks with supervised learning based on network density and unsupervised learning based on network symmetry that identifies dominant microscale mechanisms with up to 99\\% accuracy. Together, these results illustrate two ways of linking local cytoskeletal dynamics to observable network structure.", "id": "Paper/67898", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67898"}, {"title": " Homogenization and Mean-Field Approximation for Multi-Player Games ", "webprogram_exclude": "0", "session_ids": ["Session/18274"], "source_sha256": "5139d95c438ab03213546c8191cf407c6f401dac22bd1916c06f49e042681229", "withdrawn": "", "abstract": "We establish quantitative approximation guarantees for mean-field games in large heterogeneous populations. Starting from a partition of the player population into groups, we introduce an intermediate finite-player game of mean-field type and show that strategy profiles lifted from the associated multi-population mean-field game have explicitly controlled average exploitability in the original heterogeneous game. The resulting non-asymptotic error bound decomposes into two terms: a finite-population mean-field error, governed by empirical-measure approximation within each group, and a heterogeneity error measuring deviations of individual players’ rewards and transition dynamics from their group-level approximations. Our results hold for compact state and action spaces and allow heterogeneous deterministic initial states within each population. We further characterize the tradeoff between population size and within-group heterogeneity induced by the bound. In a parametrized heterogeneous setting, optimizing the resulting certified bound over population partitions leads to a mixed-integer second-order cone program, and in the large-population regime is closely related to K-means clustering.", "id": "Paper/67900", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67900"}, {"title": " Structured Picard elements and Applicaitons ", "webprogram_exclude": "0", "session_ids": ["Session/18287"], "source_sha256": "62eef4f10c92e8631a1fc366ec205c89bac175c590650f3f9259f5c93d5bdd72", "withdrawn": "", "abstract": "A central object of study in classical algebra is the Picard group of a ring, whose elements are invertible modules over that ring. In the world of homotopical algebra, the invertible modules over a ring spectrum form a space; this space acquires further structure when the ring spectrum does. In this talk I will outlines some such structures and various applications in mathematical physics and chromatic homotopy theory, including a resolution to soms conjectures of Hovey-Ravenel.", "id": "Paper/67902", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67902"}, {"title": " Stability and positivity for plactic monoid centralizers ", "webprogram_exclude": "0", "session_ids": ["Session/18333"], "source_sha256": "f2d1c6e49e9c94041b1eeef36f384142240baa416452c4278eaa10af2d69385e", "withdrawn": "", "abstract": "The plactic monoid is a monoid of words modulo Knuth equivalence, whose elements can be identified with semistandard Young tableaux through the Robinson–Schensted–Knuth correspondence. The centralizer of a word consists of those words that commute with it under Knuth equivalence. In this talk, I will discuss stability and enumerative properties of these centralizers using Young tableau methods. I will present results addressing conjectures of Sagan and Wilson, along with some remaining open questions. This is joint work with Bruce Sagan.", "id": "Paper/67907", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67907"}, {"title": " Quantum Mechanics-Based Multitensor AI/ML Uniquely Able to Discover, Validate and Interpret Predictors of Patient Outcomes and Drug Targets from Small-Cohort, Noisy and High-Dimensional Multiomic Data ", "webprogram_exclude": "0", "session_ids": ["Session/18294"], "source_sha256": "19ce40527519d2dd615033ca429644d0370cc9d658baf836db55c2ac2c62c472", "withdrawn": "", "abstract": "We have mathematically proven that our AI/ML overcomes the challenges of real-world multiomic data [1]. We have computationally shown that our algorithms, known as comparative spectral decompositions, are uniquely able to discover accurate, precise, actionable, and mechanistically interpretable predictors, applicable to the general population, from the multiomes of as few as 18 patients [2]. We have experimentally demonstrated that our predictors consistently validate across laboratories and sometimes across indications, in federated and imbalanced studies and over time, and outperform all other indicators where they exist [3].\n\nReferences:\n[1] Alter, AWS Education Research Webinar (2000);\nhttps://youtu.be/s4ezu0OHKAs\n[2] Alter et al., ASCO (2026);\nhttps://ascopubs.org/doi/10.1200/JCO.2026.44.16\\textunderscore suppl.3019\n[3] Alter et al., APL Quantum (2026);\nhttps://doi.org/10.1063/5.0305656", "id": "Paper/67910", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67910"}, {"title": " From Marginalization to Rights of Multilingual Undergraduate Mathematics Students ", "webprogram_exclude": "0", "session_ids": ["Session/18068"], "source_sha256": "95257f9dbb4a9cb4bed46d63dc21d2a7b954760929375692ec68579caae024b8", "withdrawn": "", "abstract": "This study uses the counterstory of a multilingual international undergraduate student enrolled in an inquiry-oriented linear algebra course at a U.S. university to illuminate rights of multilingual mathematics learners. An inductive analysis of student interview data examined experiences in which linguistic and culturally situated communicative conditions marginalized the student’s mathematical participation, positioning, and meaning-making. The analysis illuminates rights to safely draw on one’s full linguistic repertoire, have mathematical contributions valorized across communicative modes, participate mathematically without conforming to dominant linguistic norms, and have one’s cultural ways of communicating and participating considered. These rights articulate safeguards against forms of marginalization made salient through the student’s counterstory. The presentation will discuss implications for honoring these rights in undergraduate mathematics instruction.", "id": "Paper/67912", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67912"}, {"title": " Dissipative Evolutions in Metric Spaces ", "webprogram_exclude": "0", "session_ids": ["Session/17991"], "source_sha256": "e596abf0e7c12c3045f1227a41c2f2cc41909a0c353e440ccbda156c1e19ba3b", "withdrawn": "", "abstract": "Motivated by the setting of minimax and multispecies coupled gradient flows, we study a novel class of evolution variational inequalities (EVI) driven by \nbifunctions $b:D \\times D \\to \\mathbb{R}$ defined on a subset $D$ of a metric space $(X,d)$ and satisfying a natural dissipativity condition\n$b(x,y)+b(y,x)\\le \\eta d^2(x,y).$ We provide general conditions for existence,  \nstability, regularity, approximation and asymptotic behavior of solutions, \n by proposing a metric framework that generalizes the classical \nstructure of evolutions driven by monotone operators in Hilbert spaces.\nTo construct solutions, we introduce a variational movement scheme (VMS), a time discretization scheme in which each update is a saddle point of a metrically  \npenalized bifunction, generalizing the classical minimizing movement/ JKO scheme for single species gradient descent. In the coupled multispecies case, the VMS reduces to a Nash equilibrium problem. We prove existence of discrete solutions to the VMS via \na general approach which combines dissipativity of $b$ with a new notion of \nconvexity along suitable \\textit{barycentric interpolations} (which is inspired by \nconvexity along generalized geodesics, a crucial notion for gradient flows).\nTogether, these conditions provide a zeroth-order notion of game-theoretic monotonicity applicable to general metric spaces without linear structure. This is joint work with Franca Hoffmann and Giuseppe Savar\\'e.", "id": "Paper/67916", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67916"}, {"title": " TAPS: Target-Aware Permanent Sampling for Graph Diffusion ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "731c5a67501512f936c204b495f9928820057e2a0877e8cdbbf6256d666f3a79", "withdrawn": "", "abstract": "Permanent air-quality networks are costly to install and maintain, yet many \ndecisions depend on one future regional exposure rather than reconstruction \nof the complete pollution field. We introduce Target-Aware Permanent Sampling \n(TAPS), a graph-diffusion framework for selecting permanent locations that \nare observed repeatedly over time. We formulate the resulting permanent \nspace-time sampling problem, prove that exact recovery of a prescribed target \ncan occur before full-state identification, and derive a greedy placement rule \nwhose marginal gain factors into target response and conditional retention. \n\nIn California, ten TAPS locations recover the Bay Area target while the \nretained state remains underdetermined, and increasing repeated observations \nreduces the greedy exact-target requirement from 33 permanent locations to seven. \nIn England, the population-weighted South East target is exact at ten locations, \nwhereas full-state rank requires 22. We also study a greenfield setting in which candidate sites have no prior \nground-monitor $\\text{PM}_{2.5}$ histories. Across 100 blind prospective California \nhistories built only from exogenous environmental information, TAPS has the \nlowest tested ten-location model risk in 92; matching TAPS-10 requires median \nbudgets of 15 target-weight or 17 raw-response locations, corresponding to \n33.3\\% and 41.2\\% fewer permanent monitors. In the eight-window regime, TAPS \noutperforms the stronger practical baseline in all 25 histories and removes \na median 65.7\\% of its excess risk above the 2025-only oracle. \n \nHeld-out experiments show that the preferred network and the balance between spatial \ncoverage and repeated readings depend on the downstream estimator. TAPS \ntherefore separates target recovery from full-field reconstruction and provides \na framework for designing permanent monitoring infrastructure around the \nfuture quantity of interest, including before deployment.", "id": "Paper/67918", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67918"}, {"title": " Course Coordination as a Tool to Provide Professional Development and Promote Effective Pedagogy ", "webprogram_exclude": "0", "session_ids": ["Session/17971"], "source_sha256": "8b0327dd95dca7314fa0ba98ec15afdb099cbf2f0a1c4e3ec8bb3e5cea0ba91d", "withdrawn": "", "abstract": "Course coordination can be one of the most effective tools available to provide ongoing, in-depth professional development for instructors and support sustained implementation of effective pedagogies such as active learning, flipped classrooms, authentic assessment and alternative grading practices.\n\nIn 2018, the Chancellor of the California State University system presented Executive Order 1110 which removed mathematics remediation from the system and introduced the requirements of providing multiple pathways for students to meet their general education quantitative reasoning requirement. The Chancellor's office also invested in course coordination as a tool to redesign and support these pathways. In response to this Executive Order, Cal State LA developed three pathways and used course coordination to support the pathways in providing a path to success for all entering students, regardless of their preparation level for collegiate level mathematics. \n\nIn this talk, we will share lessons learned from over 8 years of experience with the course designed for a statistics pathway: a highly-coordinated, multi-section general education Introductory Statistics course. With over 9,000 students having gone through this program since 2018 and over 30 instructors having taught in the course during that time, we will share the tools and methods employed to engage instructors, get buy-in for teaching practices, and provide critical support to make lasting changes in instruction and instructor attitudes. Topics will include: structuring and running weekly meetings, providing course materials, creating collaborate team spaces, and holding difficult discussions amongst instructors.", "id": "Paper/67920", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67920"}, {"title": " Transport twistor spaces, blowdown maps and X-ray transforms ", "webprogram_exclude": "0", "session_ids": ["Session/17859"], "source_sha256": "6bd3289f85fa378681ca6ba4fbf40e8c77d196dea3b00a1bd7795507e5a61284", "withdrawn": "", "abstract": "Some problems of integral geometry are concerned with the recovery of functions from their integrals along families of curves on a manifold (their X-ray transform). On Riemannian surfaces where integration is done along a geodesic or magnetic flow, the resolution of these problems has passed through important notions (so-called “fiberwise holomorphicity”) which were hinting at an underlying complex-geometric picture, although this link was only clarified a few years ago by Jan Bohr and Gabriel Paternain through the notion of transport twistor (TT) space. \n\nGiven a Riemannian surface $(M,g)$ with a fixed admissible flow of integration $\\varphi_t$, the TT space of $(M,g,\\varphi_t)$ is a complex surface containing the unit tangent bundle $SM$ as a boundary component, and whose complex structure degenerates the flow $\\varphi_t$ at $SM$. Such a construction has allowed to build correspondences between “fiberwise holomorphic” invariant distributions on $SM$, and genuine holomorphic functions on twistor space. This viewpoint has already served as a helpful conceptual tool to reframe and approach geometric inverse problems questions, and leaves many open questions regarding the properties, classification, and rigidity of transport twistor spaces, and their further use in inverse problems, notably for reconstruction purposes.\n\nIn this talk, I will report on recent works on the above topics, notably on the existence of \"good\" coordinates on these twistor spaces (namely, maps with \"holomorphic blowdown structure\"), and a partial understanding of how they serve the inversion of an X-ray transform. \n\nJoint works with Bohr-Paternain and Qi.", "id": "Paper/67921", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67921"}, {"title": " <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.732ex\" height=\"2.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -1006.6 1176.4 1152.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbb {A}^1</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJAMS-41\" d=\"M130 -1H63Q34 -1 26 2T17 17Q17 24 22 29T35 35Q49 35 64 44T88 66Q101 93 210 383Q331 693 335 697T346 701T357 697Q358 696 493 399Q621 104 633 83Q656 35 686 35Q693 35 698 30T703 17Q703 5 693 2T643 -1H541Q388 -1 386 1Q378 6 378 16Q378 24 383 29T397 35Q412 35 434 45T456 65Q456 93 428 170L419 197H197L195 179Q184 134 184 97Q184 82 186 71T190 55T198 45T205 39T214 36L219 35Q241 31 241 17Q241 5 233 2T196 -1H130ZM493 68Q493 51 481 35H619Q604 56 515 256Q486 321 468 361L348 637Q347 637 330 592T313 543Q313 538 358 436T448 219T493 68ZM404 235Q404 239 355 355T295 488L275 430Q241 348 208 232H306Q404 232 404 235ZM155 48Q151 55 148 88V117L135 86Q118 47 117 46L110 37L135 35H159Q157 41 155 48Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJAMS-41\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-31\" x=\"1021\" y=\"606\"></use>\n</g>\n</svg>-Milnor numbers ", "webprogram_exclude": "0", "session_ids": ["Session/18095"], "source_sha256": "0590609b96fc76ed029638a4aa28462e5e675057712c54194e264013f3abe1c5", "withdrawn": "", "abstract": "The $\\mathbb{A}^1$-Milnor number of a polynomial is an invariant that generalizes the classical Milnor number. It takes values that are symmetric bilinear forms, and the classical Milnor number can be recovered as the rank of these forms. This generalization also enables the definition of Milnor numbers over arbitrary fields. As shown by Kass and Wickelgren (2019), the $\\mathbb{A}^1$-Milnor number coincides with a form previously studied by Eisenbud--Levine (1977) and Khimshiashvili (1977) that is now known as an EKL form. This result made computing $\\mathbb{A}^1$-Milnor numbers accessible. We study which symmetric bilinear forms arise as $\\mathbb{A}^1$-Milnor numbers, develop SageMath tools for their computation, and investigate how $\\mathbb{A}^1$-Milnor numbers change under deformations of the polynomial.", "id": "Paper/67923", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67923"}, {"title": " Coinvariant Divisors for Pointed Vertex Operator Algebras on the Moduli Space of Curves ", "webprogram_exclude": "0", "session_ids": ["Session/19350"], "source_sha256": "16318ccca846d25019b4e9d03c1aa0ea818886ac37e2fd0ab3525ac6eccbd705", "withdrawn": "", "abstract": "Vertex operator algebra (VOA) is a generalization of associative algebra and Lie algebra. Given a vertex operator algebra, along with $n$-tuple of modules, we may define a sheaf the on the moduli stack of curves $\\overline{\\mathcal{M}}_{g,n}$. Under some mild conditions, they form a vector bundle, and it is called the \\emph{vector bundle of coinvariants}, and its dual sheaf is called the \\emph{vector bundle of conformal blocks}. \n\nHistorically, the rank formula of such vector bundle has been of wide interest, and is typically referred to as the \\emph{Verlinde formula} or \\emph{generalized Verlinde formula}. One of the classical methods to compute the rank is through the famous Factorization Theorem, which was first proved for affine VOAs by Tsuchiya, Ueno, and Yamada, and later generalized by Damiolini, Gibney, and Tarasca. However, the factorization theorem is recursive in nature.\n\nHere, we introduce a non-recursive way to compute the Verlinde formula. We introduce \\emph{FA-matrices} for computing ranks of vector bundles of coinvariants and conformal blocks associated with modules over vertex operator algebras on the moduli space of stable pointed curves. The FA-matrices unify the notions of \\emph{fusion matrix} and \\emph{averaging matrices}. We show that the usual matrix operations on FA-matrices admit natural geometric interpretations, thereby allowing us to generalize Ueno’s work on the generalized Verlinde formula. We compute ranks of vector bundles determined by pointed VOAs (i.e., all irreducible modules are invertible under fusion) and the tensor product of certain VOAs. \n\nAs an application, we analyze the positivity properties of the first Chern classes of certain vector bundles of coinvariants, also known as \\emph{coinvariant divisors}. We provide the first non-trivial example of a VOA (actually infinitely many) whose coinvariant divisors on $\\overline{\\mathcal{M}}_{g,n}$ are all nef, for all $g\\ge 0$ and for all $n\\ge 0$, where $2g-2+n> 0$.", "id": "Paper/67927", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67927"}, {"title": " An Interface-Coupled Reaction-Diffusion-Advection Model for Population Persistence ", "webprogram_exclude": "0", "session_ids": ["Session/18325"], "source_sha256": "d8f7166e6e8a376021cd51020f2dc068a62d187cb795064ffa7b26fa694d01f8", "withdrawn": "", "abstract": "We develop a mathematical and computational framework for an interface-coupled reaction-diffusion-advection model describing population movement in a heterogeneous one-dimensional habitat. The domain is divided into two adjacent patches: one governed by diffusion with directional bias toward the interface, and the other governed by pure diffusion. The patches are coupled through a nonlinear interface condition that models density-dependent migration across the interface. We establish a weak formulation and a sub- and supersolution framework for proving the existence of positive steady states. We implement a finite element method to study how advection strength, patch size, and migration probability at the interface influence population persistence for a single species.", "id": "Paper/67930", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67930"}, {"title": " Mathematics of the 2026 Bundibugyo Virus Disease Outbreak in a Conflict Setting ", "webprogram_exclude": "0", "session_ids": ["Session/17688"], "source_sha256": "3187fe2f56dc18927c26096cf2e6335cca7897263c0e8edb3d5c85e6859d0e23", "withdrawn": "", "abstract": "Bundibugyo virus disease, a severe viral haemorrhagic fever caused by an ebolavirus for which no vaccine or therapeutic has been licensed, has caused a large outbreak in the eastern Democratic Republic of the Congo (DRC) since May 2026 (with 6,757 confirmed cases and 3,267 confirmed deaths reported by 7 September 2026). The outbreak is unfolding in a region of protracted armed conflict, where insecurity restricts access to affected communities, disrupts contact tracing, isolation, and safe and dignified burial, and displaces populations across international borders. A further complication is that the early symptoms of the disease are readily mistaken for other common diseases, such as malaria or typhoid fever (thereby delaying diagnosis and the timely isolation of cases). In this talk, I will present a new mathematical model, in the form of a deterministic system of nonlinear differential equations, for assessing the combined population-level impact of conflict-related disruption, diagnostic misclassification, and cross-border spread on the transmission dynamics and control of the disease.  The epidemic model has a continuum of disease-free equilibria which is globally asymptotically stable whenever the associated control reproduction number is less than unity. Simulations of the model, which is calibrated using the reported daily case data for the DRC, show that community transmission accounts for approximately 70\\% of the overall transmission potential, with unsafe burial accounting for a further 25\\%. The model also identifies a critical level of conflict-related disruption below which the baseline public health response suffices to eliminate the disease, and above which the level of every intervention needed for elimination increases with the severity of the conflict.", "id": "Paper/67931", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67931"}, {"title": " Dynamic Downside-Risk Optimization and Option-Based Portfolio Insurance for Listed Real Estate Securities ", "webprogram_exclude": "0", "session_ids": ["Session/19365"], "source_sha256": "d1d8d0096aea60db03e30f5bf3456febb03f8d73ad879f94529112632b4fd1ee", "withdrawn": "", "abstract": "This study investigates whether dynamic downside-risk optimization and index-proxy option insurance improve risk management of listed real-estate portfolios after accounting for constraints, trading costs, and option-market liquidity. Using daily returns for 29 real-estate-related securities from 2021 through 2024, we compare historical portfolios with portfolios based on one-step-ahead ARMA--GARCH forecasts linked through a Student-$t$ copula. The out-of-sample analysis covers 529 trading days and six mean--variance and CVaR objectives under long-only and constrained long--short specifications.\n\nThe dynamic model materially improves intermediate-tail risk calibration. Across 42 configurations, the Kupiec test rejects 36 historical 95\\% value-at-risk forecasts but none of the dynamic forecasts. However, Diebold--Mariano tests do not establish significant superiority in joint VaR--expected-shortfall predictive accuracy. Tight turnover constraints limit differences between historical and dynamic allocations, while relaxing them produces objective-dependent differences.\n\nFor downside protection, each optimized portfolio is cross-hedged with monthly IYR puts using rolling IYR betas. We use 25 contracts, with purchases at ask prices and liquidations at bid prices. Across 84 implementations, the overlay reduces volatility, 95\\% and 99\\% expected shortfall, maximum drawdown, and losses on IYR stress days. These improvements involve a material cost: terminal wealth declines by 3.57--8.77 units from an initial value of 100 relative to uninsured portfolios. A midpoint-execution counterfactual and spread screens show that option-market liquidity accounts for much of this cost. Overall, dynamic optimization and protective puts provide complementary risk management, but the option overlay is costly risk transfer rather than return enhancement.", "id": "Paper/67932", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67932"}, {"title": " Interactive Dynamics of Compressible Fluid-Plate Interaction Coupled PDEs ", "webprogram_exclude": "0", "session_ids": ["Session/18351"], "source_sha256": "b0360ff4ed4e7b175257ea1eb1db24665b5a9d85a937060a80a83d3e64646331", "withdrawn": "", "abstract": "We consider an FSI PDE model for which the coupled system describes the interaction between an elastic plate and a flow of compressible barotropic, viscous fluid. Such interactive dynamics arise in the design of many engineering systems (e.g., aircraft, engines, and bridges). The study of compressible flows (gas dynamics) itself has implications to high-speed aircraft, jet engines, rocket motors, hyperloops, high-speed entry into a planetary atmosphere, gas pipelines, commercial applications (such as abrasive blasting), and many other fields. We address well-posedness of the system in the presence of the von Karman/Berger plate nonlinearity. In addition, we analyze the stability properties of the solutions to this coupled system.", "id": "Paper/67933", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67933"}, {"title": " Interpolation of Hopf monoids ", "webprogram_exclude": "0", "session_ids": ["Session/18134"], "source_sha256": "47951cafa3c336f4ade5a048df6fb022e4afb0970c0e24413f998051e037330a", "withdrawn": "", "abstract": "In this talk we lift the theory of $r$-quasisymmetric functions to the theory of Hopf monoids. We provide a general method of interpolating between two Hopf monoids, one being the free monoid on a positive comonoid and the other being the free commutative monoid on a positive comonoid. We then apply this interpolation to a few examples including planar rooted forests and parking functions.", "id": "Paper/67934", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67934"}, {"title": " Solution of general LQ problem for systems with delays in state vectors and control ", "webprogram_exclude": "0", "session_ids": ["Session/19337"], "source_sha256": "d04d9cfe1152b6ff57f3e89c459f029bca03fa40dc8e32790b0d34acd0a87a49", "withdrawn": "", "abstract": "We study linear time-invariant control systems with discrete and continuous delays in state vector and control. Such system appears in different models of biological systems such as Hemostat models or ecological models. A generalization of the Cauchy formula (classical for delay-free systems) is established for the solution, expressed in terms of the fundamental matrix of the homogeneous system and an associated kernel derived from the control channel. We consider the classical LQ(Linear Qudratic) control problem with Infinite horizon and general quadratic form of state vector and control without delays. Under a coercivity assumption on the cost functional with respect to the control, we prove that the optimal control admits a feedback representation consisting of a constant gain acting on the current state together with an $L^2$ operator acting on a delay-line functional of the past trajectory. The closed-loop system reduces to a renewal (Volterra) integral equation; a Laplace-transform stability criterion, together with Datko's theorem, is then used to construct a symmetric two-variable kernel representing the optimal cost-to-go. A dynamic-programming argument yields a coupled system of generalized algebraic and partial integro-differential equations, extending the classical Riccati equation known for finite-dimensional LQ problem to systems with mixed discrete and distributed delays. We establish an equivalence theorem linking the Riccati system to optimality, an explicit formula for optimal control, and a cost decomposition identity. The resulting framework unifies the treatment of distributed and discrete delays within a single Riccati-based synthesis procedure and lays the groundwork for extensions to $H_\\infty$ robust control of time-delay systems.", "id": "Paper/67935", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67935"}, {"title": " Solving nonlinear multiscale PDEs using learned local solutions ", "webprogram_exclude": "0", "session_ids": ["Session/17926"], "source_sha256": "5574020b631c30d5b257e483c15458f89d1d5f9c1806257d0fe29b9f143ab5c2", "withdrawn": "", "abstract": "We study a local–global finite element method for strongly monotone quasilinear elliptic problems. A fine-grid finite element problem is condensed to its interface trace. A single parameterized model approximates the local Dirichlet maps while preserving prescribed boundary values exactly. The global trace equation is assembled by pulling local nodal finite element residuals back through derivatives of the learned maps.\n\nIn the matched Cartesian setting, we prove that the ideal trace equation is equivalent to the original fine-grid Galerkin problem. Strong monotonicity yields a conditional energy estimate with three error groups: finite element discretization, local reconstruction, and global residual error. The global group comprises quadrature consistency, the discrepancy between learned and ideal trace residuals, and algebraic solve error. The estimate holds at any differentiability point satisfying the algebraic residual test; the nonalgebraic error quantities require comparison with ideal or exact solutions.\n\nNumerical experiments for two-dimensional potential problems assess the three error groups and the predicted refinement behavior. Comparisons with exact condensation and global finite elements examine the effects of local approximation and algebraic solution. Further experiments examine model reuse under varying boundary data at fixed local physics and across a scalar coefficient family with fixed source and flux form.\n\nThe work is partially supported by Hong Kong RGC General Research Fund (Projects: 14305624, 14305423, 14304525).", "id": "Paper/67937", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67937"}, {"title": " Non-Kähler Ricci flows from singular Kähler initial metrics ", "webprogram_exclude": "0", "session_ids": ["Session/17871"], "source_sha256": "2ed6c0e7adc0ca503ec00c69026f80a844005aa8038fa0d0e6ac720b8be1d137", "withdrawn": "", "abstract": "The Ricci flow preserves many geometric properties when it starts from smooth initial data, including positive scalar curvature, isometry groups, and K\\\"{a}hlerity. We show that the last property may not be preserved when starting from singular initial data: there exist non-K\\\"{a}hler--Ricci flows emanating from certain K\\\"{a}hler cones. These are moreover self-similar flows which come from expanding Ricci solitons.", "id": "Paper/67938", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67938"}, {"title": " Dynamics and Memorization in Noise-Blind Diffusion Models ", "webprogram_exclude": "0", "session_ids": ["Session/17705"], "source_sha256": "2a13561b60135bf70016a1cfb226267e38757bda49850dfd69fe8321f7964356", "withdrawn": "", "abstract": "Diffusion models have emerged as a powerful class of generative models capable of producing high-quality synthetic data across a variety of domains. Given their empirical success, it is imperative to gain a better understanding of the dynamical mechanisms underlying the generative process and how these mechanisms relate to data memorization and generalization. In this work, we investigate diffusion-based generative models through the lens of dynamical systems theory. By interpreting the reverse diffusion process as a learned dynamical system, we analyze the fixed points, local stability properties, and long-term behavior induced by the learned score field.\nParticular attention is given to noise-blind diffusion models, in which the score network depends only on the state variable and not explicitly on time or noise as input. This simplification permits the application of classical dynamical systems tools, including linear stability analysis and attractor characterization. We propose several quantitative metrics for measuring convergence toward training samples and underlying data manifolds, allowing us to distinguish memorization from geometric learning. Experiments on both low-dimensional toy datasets and higher-dimensional image datasets reveal the emergence of attracting structures that influence sample generation.", "id": "Paper/67940", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67940"}, {"title": " Localizing the source of an SI infection in a tree network ", "webprogram_exclude": "0", "session_ids": ["Session/18343"], "source_sha256": "6d35f2ac8e773971fe99e794ba6c922ae6aacb0b22cc7d160830e7cfbecc513f", "withdrawn": "", "abstract": "In this talk, I will address the problem of localizing the infection source in an undirected, tree-structured network under a susceptible-infected (SI) outbreak model. The infection propagates with independent random time increments (i.e., edge delays) between neighboring nodes, but the infection times of only a subset of nodes are observed. We identify the nodes that are sufficient to estimate the source and propose an estimator based on the Laplace transforms of their infection times. Time permitting, we will also discuss lower-complexity approaches for estimating the source.\n\nThis work is in collaboration with Graham Kesler O'Connor, Julia M. Jess, Devlin Costello, and Levi Barksdale.", "id": "Paper/67944", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67944"}, {"title": " The infinitude of solvable degree <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.162ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 500.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">5</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-35\" x=\"0\" y=\"0\"></use>\n</g>\n</svg> points on curves ", "webprogram_exclude": "0", "session_ids": ["Session/18214"], "source_sha256": "e31bcd6213cdb04580089de1f375fdb9a4d6797487756e52e54d6d265f3bc8ea", "withdrawn": "", "abstract": "Let $X$ be a nice curve over a number field. We show that if the genus of $X$ is at least $12,$ then $X$ contains infinitely many degree $5$ solvable points if and only if there is a degree $5$ solvable morphism $X \\to Y$ parameterizing them. Heuristically, for curves of genus at least $12,$ there are infinitely many degree $5$ solvable points if and only if there is a geometric reason behind their existence. In this talk, we will discuss the main ingredients of the proof, the sharpness of the genus bound, and possible generalizations to higher degrees.", "id": "Paper/67948", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67948"}, {"title": " Packing Steiner Forests in Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18386"], "source_sha256": "60a185a6f5cda5943ba06e32680ca570dd7f3ee58fb1731f3eb8ace913888004", "withdrawn": "", "abstract": "We consider the problem of packing edge-disjoint Steiner forests in a graph. The input consists of a multi-graph $G=(V,E)$ and a collection of $t$ vertex subsets $S={S_1,S_2,...,S_t}$. A Steiner forest for $S$, also called an $S$-forest, is a forest of $G$ in which each $S_i$ is connected. In the case where $t=1$, this is the Steiner tree packing problem. Kriesell's conjecture postulates that $2k$-edge-connectivity of $S_1$ is sufficient to find $k$ edge-disjoint $S_1$-trees, which if true serves as a generalization to the Tutte-Nash-Williams Theorem. Lau showed that $24k$-edge-connectivity suffices for the Steiner tree packing problem, which was improved to $6.5k$ by West and Wu and $5k+4$ by Devos, McDonald and Pivotto. Steiner tree and forest packing have natural applications in routing and computer networking problems in Computer Science. \n\nIn his PhD thesis, Lau asserts that for the Steiner forest packing problem, if each $S_i$ is $30k$-edge-connected in $G$, then there exist $k$ edge-disjoint $S$-forests. However, Lau's proof relies on an intermediate theorem called the Extension Theorem, which has a gap in the proof, and is proven false as evidenced by a counterexample we found to this theorem. We will cover the flaw in the inductive proof of the original Extension Theorem, and how we fixed it to obtain the result that $32k$-edge-connectivity of each $S_i$ suffices to pack $k$ $S$-forests.\n\nThis project was done as my undergraduate thesis under the supervision of Chandra Chekuri.", "id": "Paper/67951", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67951"}, {"title": " On Semisymmetric Height and a Multidimensional Generalization of Weighted Catalan Numbers ", "webprogram_exclude": "0", "session_ids": ["Session/19346"], "source_sha256": "e3b027ef731e6518a9fa4acf16c68f95b5f778044dd0278a143af1bb0bea0031", "withdrawn": "", "abstract": "Weighted Catalan numbers are a class of weighted sums over Dyck paths. They are well studied for their arithmetic properties and applications to enumerative combinatorics. Motivated by our recent $k$-dimensional generalization of these numbers, we introduce an alternative generalization: the $k$-dimensional semisymmetric weighted Catalan numbers ($k$-dimensional SSWCNs), which are weighted sums over $k$-dimensional balanced ballot paths, a generalization of Dyck paths. We define them using the notion of semisymmetric height, a new statistic on points in $\\mathbb{Z}^k_{\\geq 0}$ inspired by geometric symmetries of the balanced ballot paths and of the fundamental Weyl chamber of type $A_{k-1}$. We also define a variant, the $k$-dimensional $u$-bounded semisymmetric weighted Catalan numbers ($k$-dimensional $u$-bounded SSWCNs), which are weighted sums over $k$-dimensional balanced ballot paths all of whose points have semisymmetric height at most $u$. We prove eventual periodicity modulo $m$ for the $k$-dimensional $u$-bounded SSWCNs for every $m$, and for the $k$-dimensional SSWCNs under certain conditions on $m$. We also derive explicit formulas for several families of $k$-dimensional $u$-bounded SSWCNs. In addition, we use the semisymmetric height statistic to introduce new analogs of the enumeration of Dyck paths by height and of the Narayana numbers.", "id": "Paper/67953", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67953"}, {"title": " Dense degree <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.162ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 500.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">5</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-35\" x=\"0\" y=\"0\"></use>\n</g>\n</svg> points on the modular curves <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"6.851ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 2949.9 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">X_0(N)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-58\" d=\"M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4E\" d=\"M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-58\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-30\" x=\"1171\" y=\"-213\"></use>\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"1282\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-4E\" x=\"1671\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"2560\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "3a1ff128902275dd299761799463fa0fec6b0405824f0d5947c50b60eb697567", "withdrawn": "", "abstract": "In 2025, Derickx, Hwang, Jeon, and Orlic initiated the classification of which modular curves $X_0(N)/\\mathbb{Q}$ have infinitely many degree $5$ points, leaving $30$ levels $N$ unanswered. We further this classification by determining $16$ of the $30$ open cases, leaving $14$ remaining. In doing so, we study the possible sources of degree $5$ points on an algebraic curve, generalizing results of Kadets and Vogt. In this poster, I will motivate this problem, present the main tools used in our results, and discuss the $14$ remaining cases. The results presented are joint work with Bryan Boehnke and Alexander Galarraga.", "id": "Paper/67954", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67954"}, {"title": " What’s up with Polysymmetric Functions? ", "webprogram_exclude": "0", "session_ids": ["Session/18134"], "source_sha256": "8ff267eca5e47b73da6bc64e8a92528aa7a0d285f31276f27e34194830d5adf9", "withdrawn": "", "abstract": "In this talk, we introduce the audience to the notion of polysymmetric functions, which are tensor products of symmetric functions where the $i$th tensor factor has degrees of variables scaled by $i$. The study of transition matrices between the bases of polysymmetric functions involves wonderful inductive and bijective methods which extend the rich combinatorics found in the theory of symmetric functions. The understanding of the combinatorics of polysymmetric functions is deeply tied to the combinatorial interpretations of plethysms. We will discuss the current state of the algebraic combinatorics of polysymmetric functions and discuss possible future directions.", "id": "Paper/67955", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67955"}, {"title": " Crossing the Epistemic Boundary: Didactic Transposition and Institutional Tensions in the History and Teaching of the Limit ", "webprogram_exclude": "0", "session_ids": ["Session/17853"], "source_sha256": "e3d389e62c99464dda99e68f9a2704c342a32aac9d54c106ac5e0dec6aceb460", "withdrawn": "", "abstract": "Abstract\n\nAlthough the limit is now routinely introduced as a formal definition and set of techniques, its emergence in analysis involved tension between dynamic intuitions of variation and increasingly rigorous accounts of proof. This conceptual paper brings that history into conversation with the Anthropological Theory of the Didactic (ATD). Using didactic transposition as its central lens, it asks how an epistemic problem becomes a school object: What changes when knowledge developed around motion, approximation, and infinitesimal change is reorganized as knowledge to be taught?\n\nThe paper does not treat nineteenth-century formalization as the simple correction of previously defective mathematics. It examines the shift from historically situated practices of reasoning about change to the institutional presentation of the limit as a stable, completed definition. Within ATD, this shift is more than simplification. It selectively reorganizes knowledge, determining which questions, representations, and forms of justification become visible to learners. The boundary between scholarly knowledge and school knowledge can consequently make rigor appear as an authoritative endpoint rather than as a response to epistemic difficulty.\n\nThe paper argues that the opposition between intuition and rigor is not merely inherited from the past; it is continuously managed through curricula, textbook conventions, and classroom expectations. It does not call for school mathematics to reenact the history of analysis. Rather, it uses the history of the limit to reveal what is at stake when institutions decide which mathematical practices count as legitimate understanding. The paper contributes to philosophy of mathematics by treating rigor as an institutional as well as epistemic achievement, and to mathematics education by showing how didactic transposition shapes students' sense of mathematical truth.", "id": "Paper/67957", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67957"}, {"title": " <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"4.136ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 1780.9 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">SL_4</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-53\" d=\"M308 24Q367 24 416 76T466 197Q466 260 414 284Q308 311 278 321T236 341Q176 383 176 462Q176 523 208 573T273 648Q302 673 343 688T407 704H418H425Q521 704 564 640Q565 640 577 653T603 682T623 704Q624 704 627 704T632 705Q645 705 645 698T617 577T585 459T569 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xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\operatorname {Gr}(4,16)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-47\" d=\"M56 342Q56 428 89 500T174 615T283 681T391 705Q394 705 400 705T408 704Q499 704 569 636L582 624L612 663Q639 700 643 704Q644 704 647 704T653 705H657Q660 705 666 699V419L660 413H626Q620 419 619 430Q610 512 571 572T476 651Q457 658 426 658Q401 658 376 654T316 633T254 592T205 519T177 411Q173 369 173 335Q173 259 192 201T238 111T302 58T370 31T431 24Q478 24 513 45T559 100Q562 110 562 160V212Q561 213 557 216T551 220T542 223T526 225T502 226T463 227H437V273H449L609 270Q715 270 727 273H735V227H721Q674 227 668 215Q666 211 666 108V6Q660 0 657 0Q653 0 639 10Q617 25 600 42L587 54Q571 27 524 3T406 -22Q317 -22 238 22T108 151T56 342Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-72\" d=\"M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 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<use xlink:href=\"#E1-MJMAIN-31\"></use>\n <use xlink:href=\"#E1-MJMAIN-36\" x=\"500\" y=\"0\"></use>\n</g>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"3514\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18386"], "source_sha256": "dbc4a59fd2e0a9594aa5b7e198f305ba80fbce09500e1b1750fc626836deb9bb", "withdrawn": "", "abstract": "The Fraser--Lam--Le pairing establishes a duality between tensor invariants via boundary measurements on the Grassmannian $\\operatorname{Gr}(k,n)$. Prior work established that this holds for $SL_2$, $SL_3$, and pairings between $\\operatorname{Gr}(3,12)$ and $\\operatorname{Gr}(4,12)$. A recent breakthrough paper by Gaetz et al. provides growth rules to construct $SL_4$ webs from $4 \\times k$ tableaux, making the self-dual case $\\operatorname{Gr}(4,16)$ the next frontier to explore. Here, rotation-invariant web bases are formed by the 24,024 hourglass plabic graphs, indexed by Yamanouchi words of $4 \\times 4$ standard Young tableaux. We establish local vanishing criteria, including an $SL_r \\times SL_k$ fork lemma and local boundary configurations, to eliminate zero-pairings across the roughly 36.5 million candidate pairs without requiring skein expansions. For surviving pairs, we apply wrench, square, and double-trident moves to expand webs into Pl\\\"ucker monomials and evaluate pairings via edge coloring. Finally, we analyze benzene faces and conjecture relations for transpose duality.", "id": "Paper/67959", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67959"}, {"title": " Uniqueness for a class of strongly singular <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.259ex\" height=\"2.009ex\" style=\"vertical-align: -0.671ex; margin-left: -0.089ex;\" viewBox=\"-38.5 -576.1 542 865.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">p</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-70\" d=\"M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-70\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Laplacian problems ", "webprogram_exclude": "0", "session_ids": ["Session/18103"], "source_sha256": "b2c6f09854431fa5015ab5a66f457ae7ef3c764e94dd320aa2a712989c0bcd8a", "withdrawn": "", "abstract": "We prove uniqueness of positive solutions to the strongly singular\n$p$-Laplacian problem \n\\[\n\\left\\{ \\begin{array}{c}\n-\\Delta_{p}u=\\frac{f(x,u)}{u^{\\delta}}\\ \\ \\text{in }\\Omega,\\\\\nu=0\\text{ on }\\partial\\Omega\n\\end{array}\\right.\n\\]\nwhere $p>1,\\Omega$ is a bounded domain in $\\mathbb{R}^{n}$ with\nsmooth boundary $\\partial\\Omega,\\ 0<\\delta<(2p-1)/(p-1),$ $f:\\bar{\\Omega}\\ \\times\\lbrack0,\\infty)\\rightarrow(0,\\infty)$\nis continuous and $f(x,z)/z^{p-1+\\delta}$ is decreasing on $(0,\\infty)$ for $x\\in\\Omega.$ We also establish a uniqueness result when $p=2$, $0<\\delta<3$, $z^{-\\delta}f(x,z)$ is nonincreasing for $z$ large, and an existence result for all $\\delta>0, p>1.$", "id": "Paper/67966", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67966"}, {"title": " The plethysm problem ", "webprogram_exclude": "0", "session_ids": ["Session/18134"], "source_sha256": "e49fb336ac6b7d49f6c22d571230e5f65257ad5cc8dfccc2c452a51aabb7e3aa", "withdrawn": "", "abstract": "The plethysm problem asks for a combinatorial understanding of the coefficients that arise when a Schur function is substituted into another Schur function:\n\\[\ns_\\lambda[s_\\mu]=\\sum_\\nu a_{\\lambda,\\mu}^{\\nu}s_\\nu.\n\\]\nDespite the fundamental role of plethysm in the representation theory of symmetric and general linear groups, relatively little is known about the coefficients $a_{\\lambda,\\mu}^{\\nu}$, and no general combinatorial rule is known for computing them.\n\nIn this talk, I will focus on recent joint work with Gutiérrez, Saliola, Schilling, and Zabrocki, in which we take a generating function approach to the plethysm problem. We study bivariate generating functions for plethysm coefficients in which the length of the resulting partition is bounded, and show that these generating functions are rational. In the case of partitions of length two, we give a geometric interpretation using $q$-Ehrhart theory and integer-point enumeration. I will describe these results and their connections with symmetric chain decompositions and the combinatorial structure of plethysm coefficients.", "id": "Paper/67968", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67968"}, {"title": " A two variable chromatic polynomial ", "webprogram_exclude": "0", "session_ids": ["Session/18206"], "source_sha256": "e97c25a45fd83e651972511e286c693a578ba6cefe4809f014658c3ef8ba0328", "withdrawn": "", "abstract": "We introduce a two-variable polynomial associated to a graph $G$ by summing over its proper colorings. For any positive integer $n$, let $\\kappa: V \\rightarrow \\{0, 1, 2, \\ldots, n\\}$, then define \n\\[\nZ_{G,n}(q,t)=\\sum_{\\kappa}q^{s(\\kappa)}t^{\\ell(\\kappa)},\n\\]\nwhere $s(\\kappa)$ is the sum of the colors and $\\ell(\\kappa)$ is the number of distinct colors used. This polynomial refines the chromatic polynomial by recording additional information about each coloring. Notice that if we set $q=t=1$ we obtain the number of proper colorings of $G$ with $n$ colors.  Since all trees on the same number of vertices have the same chromatic polynomial, we investigate how much more structure is detected by $Z_{G,n}(q,t)$ for small $n$.\nFor $n=2$, we classify the resulting classes of  all caterpillars that have the same  $Z_{G,2}(q,t)$ polynomial. For $n=3$, we show that the polynomial distinguishes two families: elongated bistars and caterpillars with three internal vertices. We conclude with the conjecture that $Z_{G,4}(q,t)$ distinguishes all trees.\n\nJoint work with A. Bingham, K. Celano, P. Commins, J. Pan, and M. Simone", "id": "Paper/67971", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67971"}, {"title": " Optimal Dosing Strategies in a Differential Equation-Based Model of Bioaugmented Remediation ", "webprogram_exclude": "0", "session_ids": ["Session/18023"], "source_sha256": "cb98895d022803613d5788746a1db95283e0590665eab6fc22f8e391fdebdb2d", "withdrawn": "", "abstract": "Bioaugmented remediation uses pollutant-degrading bacteria to treat contaminated water, offering a low-cost alternative to chemical treatment. However, pollutants such as toluene can be toxic to the bacteria introduced to remove them. In species such as Pseudomonas putida, intoxicated cells may lyse, returning unmetabolized pollutant and a secondary toxin to the environment. We build a five-compartment ordinary differential equation model coupling susceptible, intoxicated, and resistant bacterial populations to pollutant and toxin concentrations. We prove that solutions exist, remain nonnegative, and stay bounded. A basic reproduction number separates pollutant recycling from toxin release and helps identify the feedback pathway responsible for persistent contamination. We then introduce a bounded protective dose that transfers biomass from the susceptible class to a resistant class that remains active in pollutant removal. On a finite horizon, we compare two optimal-control formulations. A quadratic effort cost produces a smooth, front-loaded dosing strategy, while a linear effort cost produces a bang-bang strategy. Pontryagin's Maximum Principle yields the state and adjoint systems, and a forward-backward sweep computes the dosing schedules. Both strategies reduce the remediation objective relative to no intervention and continuous maximum dosing. These findings connect the model's feedback mechanisms to practical decisions about when and how strongly to dose, supporting efficient bioaugmentation strategies aligned with United Nations Sustainable Development Goal 6: Clean Water and Sanitation.", "id": "Paper/67973", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67973"}, {"title": " Simultaneous Decompositions of Quaternion Tensors and Applications ", "webprogram_exclude": "0", "session_ids": ["Session/18229"], "source_sha256": "30bcea330d6b8204ef9c8bd6c790b5fbddb9446be289469bd5e8f3715561ba92", "withdrawn": "", "abstract": "Quaternion tensors provide a natural framework for representing multidimensional color data, but their algebraic structure is more complicated than that of real or complex tensors because of the noncommutativity of quaternion multiplication. In this talk, we establish a simultaneous decomposition for a compatible quaternity of quaternion tensors under the Einstein product. Through invertible tensor transformations, the four tensors are reduced to canonical forms whose entries are only zero and one. We describe the structure of these canonical forms and characterize their block dimensions in terms of ranks of associated quaternion matrix representations. This result extends existing simultaneous decomposition results for quaternion tensor systems. As an application, we combine the decomposition with the discrete wavelet transform to obtain a framework for color-video encryption and decryption that also permits simultaneous compression. Numerical examples illustrating the encryption and reconstruction of color video will be presented.", "id": "Paper/67974", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67974"}, {"title": " Unexpected primes of good reduction in quotients of modular and Shimura curves ", "webprogram_exclude": "0", "session_ids": ["Session/18276"], "source_sha256": "434a13f0e69dc8b04c8439035fedcabab3d31b26f2d9855a501a85000fa13927", "withdrawn": "", "abstract": "We find all zero-dimensional spaces of newforms of weight 2 and squarefree level $N$ with a fixed Atkin--Lehner sign pattern. As an application, we classify unexpected primes of good reduction of Atkin--Lehner quotients of modular and Shimura curves of squarefree levels.", "id": "Paper/67978", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67978"}, {"title": " Two-sided descents and a fundamental basis for two-parameter quasisymmetric functions ", "webprogram_exclude": "0", "session_ids": ["Session/18134"], "source_sha256": "06ad389f33c787cc5d57405e732714d57233ecd8cf45ea0f6236f81255cff366", "withdrawn": "", "abstract": "The two-parameter quasisymmetric functions of Diehl-Schmitz generalize the quasisymmetric functions to formal power series in doubly-indexed variables. We introduce fundamental two-parameter quasisymmetric functions, indexed by matrix compositions, and relate them to two-parameter shuffles. We connect this to notions of descents using an isomorphic Hopf algebra construction on packed matrices studied by Foissy-Malvenuto-Patras, and explore connections to the two-sided Coxeter complex of type A.", "id": "Paper/67979", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67979"}, {"title": " Understanding mathematics and AI ", "webprogram_exclude": "0", "session_ids": ["Session/18190"], "source_sha256": "1eb3c05acd71e267abdffbdf6e5c7841281d4207e07da5f2c8a82a697aa3dac5", "withdrawn": "", "abstract": "The practices and conditions of mathematics is changing rapidly as artificial intelligence systems rapidly improve in capabilities. This talk will focus on questions around working productively with these tools for day to day mathematics research.", "id": "Paper/67987", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67987"}, {"title": " Nash equilibria and A-discriminants ", "webprogram_exclude": "0", "session_ids": ["Session/19321"], "source_sha256": "6429dbfb164689bfd6f6773db55f6cd3f7600f9370e7cf20762c6b422b8e3d04", "withdrawn": "", "abstract": "An $n$-player game in normal form is said to be of format $\\textbf{d} = (d_1, \\dots, d_n)$ if the $i$th player has $d_i$ options for $1 \\le i \\le n$, and is said to be balanced if $d_n - 1 \\le \\sum_{i=1}^{n-1} (d_i - 1)$. The Nash equilibria of the game correspond to solutions of the system of indifference equations for the game, with payoff differences as coefficients and strategy probabilities as variables. As such, the mixed discriminant of this system gives some information about which games could have an unusual number of totally mixed Nash equilibria. This mixed discriminant can be regarded as an $A$-discriminant for some matrix $A$ in the sense of [Gelfand--Kapranov--Zelevinsky 1994], and the convex hull of the columns of $A$ is a polytope, which we call the Nashtope. \n\nWe study this $A$-discriminant for each balanced game with at least three players. This discriminant is a subset of the Nash discriminant variety introduced in [Abo--Portakal--Sodomaco 2026]. We compute the (co)dimension and degree of this discriminant for all balanced games, including those of boundary format, using the Euler obstruction formula in [Matsui--Takeuchi 2011]. Our $A$-discriminant locus corresponds to a special multigraded Hurwitz locus studied in [Pratt–Sodomaco–Sturmfels 2026].", "id": "Paper/67988", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67988"}, {"title": " Flag polytopal spheres arising from ternary graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18339"], "source_sha256": "d07a6813de3ae34fc167aab3eb1a5e0fa11c741f9a634f2ff531f18f6d8c34eb", "withdrawn": "", "abstract": "Flag simplicial spheres are objects of great interest in combinatorial topology. In this talk, we examine such spheres arising as the independence complexes of Gorenstein ternary graphs. In particular, we discuss three desirable combinatorial and geometric properties that they exhibit. First, they are boundaries of vertex-decomposable simplicial polytopes. Second, transformations between these spheres via edge subdivisions and contractions can be modeled by the Hasse diagram of the partition refinement poset. Finally, their $h$-polynomials are real-rooted, and thus they satisfy Gal’s $\\gamma$-positivity conjecture for flag homology spheres. This talk is based on joint work with Margaret Bayer, Richard Danner, Thiago Holleben, and Marie Kramer.", "id": "Paper/67990", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67990"}, {"title": " Selling students on math modeling mindset, worldview, and activities ", "webprogram_exclude": "0", "session_ids": ["Session/19005"], "source_sha256": "630e92d69ae5317356ef260bcc77394db3f0a8cea1ecf686dc07148f68aa29e0", "withdrawn": "", "abstract": "I will share some experiences from the past 25 years of organizing Math Modeling activities at Cornell University. This will include our annual university-wide competition Cornell Mathematical Contest in Modeling (CMCM; see https://e.math.cornell.edu/sites/mcm/) and my junior-level course, for which CMCM is used in lieu of the final exam. I will also try to discuss what I see as the main challenges and opportunities for the mathematical modeling education in the age of rapid AI advances.", "id": "Paper/67996", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67996"}, {"title": " Rectangulation left-right posets ", "webprogram_exclude": "0", "session_ids": ["Session/19340"], "source_sha256": "e26954c36ee55e2c1271b21c219cca10b15acc35b45203f974ff1ab1c1a7c377", "withdrawn": "", "abstract": "A \\emph{rectangulation} $\\mathcal{R}$ is a finite decomposition of a rectangle into smaller rectangles such that no four of them meet at a single corner. A \\emph{segment} in a $\\mathcal{R}$ is a union of sides of one or more rectangles in $\\mathcal{R}$ that form a straight line, is maximal, and is not one of the exterior edges of $\\mathcal{R}$. Rectangle $A$ is a \\emph{left neighbor} of rectangle $B$ in $\\mathcal{R}$ if the right side of $A$ is part of the same segment as the left side of $B$. More generally, we say that $A$ is \\emph{left of} $B$ is there is a sequence of rectangles $A=r_0,r_1,\\dots,r_{n-1},r_n=B$ such that for each $0\\le i \\le n-1$, $r_i$ is a left neighbor of $r_{i+1}$.\n\nIn this work we define the \\emph{left-right poset} $P_\\mathcal{R}$ of a rectangulation $\\mathcal{R}$. The poset $P_{\\mathcal{R}}$ is defined on the rectangles of $\\mathcal{R}$ and has the relation $A<B$ if and only if $A$ is left of $B$ in $\\mathcal{R}$. We prove that an arbitrary poset $P$ is a left-right poset for some rectangulation $\\mathcal{R}$ if and only if it has dimension at most two and is cover-N-free. That is, there are no four elements $a,b,c,d\\in P$ such that the only relations among them are $a \\lessdot b$, $a \\lessdot d$, and $c\\lessdot d$. We also show that given a left-right poset $P_{\\mathcal{R}}$ labeled in such a way that $P_{\\mathcal{R}}$ is the intersection of the identity permutation and a permutation $\\sigma$, then $\\sigma$ is a Baxter permutation and $\\mathcal{R}$ is the image of $\\sigma$ under the map from permutations to rectangulations as defined by Ackerman, Barequet, and Pinter.\r\n\r\nFinally, we can similarly define \\emph{above-below neighbors} and an \\emph{above-below poset} for $\\mathcal{R}$. We show that given a rectangulation $\\mathcal{R}$, its left-right and above-below posets are conjugates and conversely, given a pair of conjugate posets which are both cover-N-free, there is a rectangulation which they correspond to.", "id": "Paper/67997", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/67997"}, {"title": " Completely decomposable Jacobian varieties ", "webprogram_exclude": "0", "session_ids": ["Session/17808"], "source_sha256": "7465e72399937f10a8ff43dd30d893d1bc5c501f10d458066cf95ee24b6f42ac", "withdrawn": "", "abstract": "Thirty years ago, Ekedahl and Serre posed two intriguing questions about the decomposition of Jacobian varieties.  They asked if, for every genus, there is a curve whose Jacobian variety decomposes into only elliptic curves and, barring that, if there is an upper bound to the genera for which such a curve exists.  Using several different techniques they gave examples up to genus 1297 (but still with many unknown genera less than 1297). I will talk about work that has been done since then, mainly computational, to find many more examples.", "id": "Paper/68000", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68000"}, {"title": " Regularity of minimizing fractional harmonic maps and the dimension of their singular sets ", "webprogram_exclude": "0", "session_ids": ["Session/19357"], "source_sha256": "ad2cfad256d1231d33d7516512d312405764e9c9e8837aecc86cb3b7ea60f32c", "withdrawn": "", "abstract": "We discuss the regularity of minimizing fractional harmonic maps and analyze the dimension of their singular sets. These are mappings $u\\in \\dot{W}^{s,p}(\\mathbb{R}^n,\\mathcal{N})$ into manifolds $\\mathcal{N}$ with sufficiently simple topology that minimize the nonlocal energy\n$$\\int_{\\mathbb{R}^n}\\int_{\\mathbb{R}^n}\\frac{|u(x)-u(y)|^p}{|x-y|^{n+sp}} \\;dx\\;dy.$$\nWe prove that these minimizers are locally H\\\"older continuous in a bounded domain $\\Omega$ outside a singular set $\\Sigma $ with Hausdorff dimension strictly smaller than $n-sp.$ We avoid the use of a monotonicity formula, which is unknown when $p \\neq 2$, by using a blow-up argument instead.", "id": "Paper/68007", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68007"}, {"title": " The combinatorics of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.07ex\" height=\"2.009ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -576.1 460.5 865.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">q</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-71\" d=\"M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-71\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Hoggatt numbers ", "webprogram_exclude": "0", "session_ids": ["Session/17968"], "source_sha256": "8531464a62c2112bb365a0eef86b12537d55c13ab34434f13ec4e76a3d100dd2", "withdrawn": "", "abstract": "We prove the nonnegativity and palindromicity of a family of polynomials arising from $q$-Hoggatt numbers. The nonnegativity is derived from Stanley's $(P,\\omega)$-partition theory through a standard Young tableau formula, while the palindromicity is proved by an involution on rectangular standard Young tableaux. Our result confirms a conjecture of Cigler. This is joint work with Wenle Shi.", "id": "Paper/68013", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68013"}, {"title": " Pin, spin and compact symplectic groups as products of Grassmannians ", "webprogram_exclude": "0", "session_ids": ["Session/17942"], "source_sha256": "41fd647ad77b30bbfe5c19f2cd96169c7ed0ec60db8a8ced200dfc170f0f3c10", "withdrawn": "", "abstract": "We describe two curious structures relating classical groups and Grassmannians. \nFirst, we show that $\\text{Pin}(n)$ is a product of the subgroup generated by a fixed unit vector and two oriented Grassmannians, while $\\text{Spin}(n)$ is a product of two oriented Grassmannians. \nHere the oriented Grassmannian $\\widetilde{\\mathbb{G}}(k, \\mathbb{R}^n)$ is realized as $\\widetilde{\\text{Gr}}(k, \\mathbb{R}^n)$, a submanifold of the Clifford algebra. \nWe also discuss the complex analogue $\\widetilde{\\mathbb{G}}(k,\\mathbb{C}^n)$.  \nSecond, we show the compact symplectic group $\\text{Sp}(n) \\cong \\text{U}(n,\\mathbb{H})$ can be expressed as a matrix product of quaternionic Grassmannians realized as quaternionic unitary involution matrices.\n$\\text{Sp}(n)$ is a product of four quaternionic Grassmannians when $n$ is even, and five copies suffice when $n$ is odd. \nThis gives a positive answer to Open Problem~7.1 posed in our earlier work [Lim--Lu--Ye, \\textit{SIAM J. Matrix Anal. Appl.} 47 (2026), 954--975].", "id": "Paper/68014", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68014"}, {"title": " Connectivity of Districting Metagraphs ", "webprogram_exclude": "0", "session_ids": ["Session/18310"], "source_sha256": "db96cab37ed38633e35266d2c93006f9c03d71b015f105db26b36460b7340f36", "withdrawn": "", "abstract": "Markov chain Monte Carlo (MCMC) methods are used for studying districting maps,\ne.g. in outlier analysis. For these MCMC methods to see all possible\ndistricting maps, the related metagraph needs to be connected.\n\nIn this talk, we present connectedness results on such metagraphs. We show that for\ndistricts of size 2, and maps where the underlying dual graph is a triangular\nsubset of the triangular lattice with side length $n \\ge 5$, the associated\nmetagraph is connected. We also show that connectedness is fragile: We construct\nan infinite family of maps for which the corresponding metagraph is\ndisconnected. These maps' underlying dual graph is close to the triangular\nlattice.", "id": "Paper/68015", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68015"}, {"title": " Mackey Embedding for Casselman Algebras ", "webprogram_exclude": "0", "session_ids": ["Session/18381"], "source_sha256": "16621a1875c279d5221135e10ab16e7fd17ae4364d0c455da712c563e9ca7271", "withdrawn": "", "abstract": "The Mackey embedding is an injective C*-homomorphism from the reduced group C*-algebra of a motion group to the reduced group C*-algebra of an associated reductive group. This can be used to characterize the one-to-one correspondence between the tempered dual of the reductive group and the tempered dual of the associated motion group, known as the Mackey bijection. In fact, the embedding can be used to show that the above correspondence is continuous in one direction.\n\t\nThe above characterization uses the fact that there is a one-to-one correspondence between the spectrum of the reduced group C*-algebra and the tempered dual. In this talk, I will show progress on constructing a similar mapping for Casselman algebras, a subalgebra of the C*-algebra, whose spectrum corresponds to a larger class of representations known as admissible representations. There is indeed a Mackey bijection between the two admissible duals but not much else is known about it.\n\t\nThis is based on joint work with Jacob Bradd.", "id": "Paper/68018", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68018"}, {"title": " Mechanistic Ensemble Modeling of Tissue Growth in Scaffold Pore Networks ", "webprogram_exclude": "0", "session_ids": ["Session/17860"], "source_sha256": "5864f86aaa4cb7fac65ab1d69fc3d83a7b4435ea4afe08c0358e86892df26771", "withdrawn": "", "abstract": "Tissue engineering scaffolds are porous, interconnected media that support \\textit{in vitro} tissue growth. Many existing models resolve either scaffold-scale behavior or detailed transport and growth within a single pore, but this separation limits their ability to capture how network connectivity redistributes flow, nutrients, wall shear stress, and tissue accumulation. In this talk, I will present a mechanistic pore-network model of a tissue-engineering scaffold. Vertices represent pore junctions and boundary pores, while edges represent cylindrical channels. Tissue growth is coupled to Hagen--Poiseuille flow, advection--diffusion--reaction nutrient transport, shear-dependent proliferation, and elastic deformation of the scaffold.\n\nTo examine how scaffold architecture influences growth, we perform ensemble simulations over randomly generated scaffold networks under fixed transport and growth parameters. This allows us to compare growth outcomes across many admissible network geometries and identify structural features associated with favorable tissue accumulation. The simulations suggest that networks with more vertices and channels tend to fill faster and produce larger tissue yields. Across the ensemble, higher internal surface area and larger initial void volume are associated with greater total tissue growth and higher filled-volume fraction. These results illustrate how mechanistic and ensemble-based modeling can help evaluate scaffold architectures before experimental fabrication.", "id": "Paper/68024", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68024"}, {"title": " Identities and congruences for Ramanujan’s mock theta functions ", "webprogram_exclude": "0", "session_ids": ["Session/18276"], "source_sha256": "e6c72d3bb42e4f25ba97a9d61d929234e7ed3c56143a63ac53bef244531fbf2d", "withdrawn": "", "abstract": "We survey recent identities and congruences for\nRamanujan's mock theta functions that use holomorphic projection\nand half-integer weight Hecke operators.", "id": "Paper/68030", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68030"}, {"title": " Topological representation of monadic De Morgan monoids ", "webprogram_exclude": "0", "session_ids": ["Session/18589"], "source_sha256": "641c19d88fcce78796960ac3cc19b216d651ba638246504c6c68c59b8cedec93", "withdrawn": "", "abstract": "The algebra of the logic of relevant implication ($\\mathbf R$) is a De Morgan \nmonoid $\\mathbf A_1=\\langle A;\\land,\\lor,{\\sim},\\circ,e\\rangle$ of similarity \ntype $\\langle2,2,1,2,0\\rangle$. A bounded De Morgan monoid also includes a \ngreatest ($\\top$) and a least ($\\bot$) element together with two equations. \nI define \\textit{monadic De Morgan monoids} ($\\mathbf A_2$) by adding a \nquantifier ($\\exists$) together with a couple of new equations to bounded De Morgan \nmonoids. Thus, the class of monadic De Morgan monoids is a finitely based \nvariety. A topological structure for $\\mathbf A_2$ is based on Priestley \ntopology and it extends a topological structure for $\\mathbf A_1$ with a binary \nrelation and several new conditions. I prove \\textit{full duality} between the \ncategory of monadic De Morgan monoids with homomorphisms and the category of \ntopological structures for $\\mathbf A_2$ with frame morphisms.", "id": "Paper/68031", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68031"}, {"title": " Characterizations of Minimal Frobenius Splitting Numbers in Gorenstein Rings ", "webprogram_exclude": "0", "session_ids": ["Session/18347"], "source_sha256": "d4630160a766bd30bec2f57cce548163ba5f8b75437b980bfef2eed7d5257bb4", "withdrawn": "", "abstract": "Let $(R,\\mathfrak m,k)$ be an $F$-finite, $F$-pure, Gorenstein local ring. The Frobenius splitting number $a_e(R)$ is the free rank of $F_*^eR$. In this talk, I will show that $a_e(R)=[k^{1/p^e}:k]$ for some $e$ if and only if this equality holds for every $e$. These conditions are also equivalent to $I_e(R)=\\mathfrak m$ for some (equivalently, every) $e$, and to the splitting prime $\\mathcal{P}(R)$ being the maximal ideal. For hypersurface quotients, I will describe these conditions using colon ideals and discuss their behavior under perturbation of the defining equation.", "id": "Paper/68033", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68033"}, {"title": " From Reflection-Positive Euclidean Kernels to Computable Scattering ", "webprogram_exclude": "0", "session_ids": ["Session/19338"], "source_sha256": "99a6dc21303476d24e086cb794d18179a3bfeb6dd7e2c1d926ee075717f56d96", "withdrawn": "", "abstract": "Reflection positivity provides a route from Euclidean kernels to the physical Hilbert space and dynamics of relativistic quantum systems. We study the computational realization of this framework using an explicit scalar connected four-point kernel from a previously constructed reflection-positive class. A positive spectral representation establishes reflection positivity analytically, while numerical tests examine Gram positivity, Euclidean covariance, transfer-operator contractivity, and clustering.\n\nFor separable two-body benchmark models, we reconstruct the bounded operator (e^{-\\beta H}) directly from Euclidean-time-translated Gram kernels. Combining the Kato-Birman invariance principle with polynomial approximation yields computable scattering approximants. Comparisons with direct matrix evaluations and systematic refinement distinguish polynomial and quadrature errors from finite-parameter effects.", "id": "Paper/68034", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68034"}, {"title": " Optimal resource management on heterogenous spatial domains with multiple managers ", "webprogram_exclude": "0", "session_ids": ["Session/18023"], "source_sha256": "06d5f992937e876bbcfe49ef468fb7bd49bc9ec408736d6de52049617c919fd8", "withdrawn": "", "abstract": "We consider the optimal management of spatially heterogeneous fisheries across a coastal-to-offshore gradient. We extend a model of nonlinear parabolic partial differential equations describing the dynamics of a fish population and its habitat. Spatial heterogeneity is incorporated through habitat quality, harvesting costs, catchability, and habitat sensitivity to harvesting. Using optimal control theory, we investigate multiple management scenarios involving small-scale coastal and industrial fisheries, both independently and when exploiting a shared resource. We derive the corresponding optimality systems and use numerical simulations to examine how spatial heterogeneity, habitat degradation, and differences between fishing sectors influence optimal harvesting strategies. We also consider alternative management objectives and explore the resulting ecological and economic tradeoffs between harvesting and conservation.", "id": "Paper/68035", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68035"}, {"title": " Triangles and topographs ", "webprogram_exclude": "0", "session_ids": ["Session/18100"], "source_sha256": "c68779c8bcb19619ea6dae1dbd07ae247904b5a30c836e1bb4f0168e3b60559c", "withdrawn": "", "abstract": "In the 1990s, Conway introduced the topograph -- a hand-drawable map which can be used to navigate binary quadratic forms.  It allows one to see landmarks in classical number theory, such as reduction theory and finiteness of class number, for definite and indefinite forms.  Illustration turns tedium into play, and like much of Conway's work, magically captures deep connections between arithmetic and geometry.\n\nWhat makes Conway's topograph \"work\" is the fact that $PGL_2({\\mathbb Z})$ is a Coxeter group -- an arithmetic triangle group to be precise.  Such groups were classified and tabulated by Takeuchi in the 1970s.  In joint work with Amethyst Price, we realized that dozens of arithmetic triangle groups offer new topographs, new illustrations displaying results (old and new) in classical number theory.  We present these topographs, with implications for binary and ternary quadratic forms and the arithmetic of quaternion orders.", "id": "Paper/68036", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68036"}, {"title": " Ensemble Modeling of Tissue Growth in Mechanistic Scaffold Pore Networks ", "webprogram_exclude": "0", "session_ids": ["Session/19371"], "source_sha256": "4a1dad36aa3233dfdefea9d5bf4ce95490347a20c488e93719efe5d71f9a0d5b", "withdrawn": "", "abstract": "Tissue engineering scaffolds are porous, interconnected media that support in vitro tissue growth. Many existing models resolve either scaffold-scale behavior or detailed transport and growth within a single pore, but this separation limits their ability to capture how network connectivity redistributes flow, nutrients, wall shear stress, and tissue accumulation. In this talk, I will present a mechanistic pore-network model of a tissue-engineering scaffold. Vertices represent pore junctions and boundary pores, while edges represent cylindrical channels. Tissue growth is coupled to Hagen–Poiseuille flow, advection–diffusion–reaction nutrient transport, shear-dependent proliferation, and elastic deformation of the scaffold.\n\nTo examine how scaffold architecture influences growth, we perform ensemble simulations over randomly generated scaffold networks under fixed transport and growth parameters. This allows us to compare growth outcomes across many admissible network geometries and identify structural features associated with favorable tissue accumulation. The simulations suggest that networks with more vertices and channels tend to fill faster and produce larger tissue yields. Across the ensemble, higher internal surface area and larger initial void volume are associated with greater total tissue growth and higher filled-volume fraction. These results illustrate how mechanistic and ensemble-based modeling can help evaluate scaffold architectures before experimental fabrication.", "id": "Paper/68037", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68037"}, {"title": " Total Bondage Number of Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/19360"], "source_sha256": "918c59849eda99dad646fb6bf0a646754e78a9797cfa686b3c5522229f267fa1", "withdrawn": "", "abstract": "For a finite graph $G$ without isolated vertices, a vertex set $D$ of $G$ is said to be a total dominating set of $G$, if every vertex $v\\in V(G)$ has a neighbor in $D$. Define $\\gamma_t (G)$ to be the minimum cardinality among all total dominating sets of $G$. $B$ is a total bondage edge set if $B\\subset E(G)$ such that $G-B$ does not have isolated vertices and $\\gamma_t(G-B)>\\gamma_t(G)$. The total bondage number of $G$ is denoted by $b_t(G)$, and $b_t(G)=$ min$\\{|B|: B$ is a total bondage edge set of $G\\}$ if $G$ has at least one total bondage edge set. Otherwise, we put $b_t(G)=\\infty$. In this talk, we investigate upper bounds on the total bondage number of graphs. We develop bounds based on local structural properties, including degree conditions and degree sums of vertices associated with small faces. Our results yield improved upper bounds for several classes of graphs, with particular attention to trees and planar graphs. These improvements strengthen previously known results and provide further insight into the relationship between graph structure and the total bondage number.", "id": "Paper/68038", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68038"}, {"title": " Some results on selection problems in mean field games ", "webprogram_exclude": "0", "session_ids": ["Session/17781"], "source_sha256": "d099246735645c261d9b11058e0b5d258f3f69bbae1d47f1fae6d1e0a9edba0d", "withdrawn": "", "abstract": "In mean field games, the existence of multiple Nash equilibria is the rule rather than the exception. Selection from among multiple equilibria is therefore a perennial open question. The master equuation is a nonlinear transport equation on the space of probability measures whose solutions are meant to correspond to Nash equilibria. One way to resolve the existence of multiple solutions to a nonlinear transport equation is through the definition of entropy solutions. In this talk we explore the possibilities and limitations of this approach, give some new results on entropy solutions to nonlinear transport equations on the Wasserstein space, and offer some interpretations in terms of the selection of equilibria.", "id": "Paper/68044", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68044"}, {"title": " When stationary measures fail to be Hölder regular ", "webprogram_exclude": "0", "session_ids": ["Session/18313"], "source_sha256": "cbccf181d0b9ab2918312461694ea3568a138abfe2ce3bd4599691a27520a867", "withdrawn": "", "abstract": "Under mild assumptions, stationary measures of random systems generated by diffeomorphisms are Hölder regular. In this talk, we will show that replacing global invertibility by local invertibility can destroy even the absence of atoms. We construct smooth, locally invertible maps of the circle which have no common invariant probability measure, but whose random iteration admits an atomic stationary measure. This measure also describes the time averages of random trajectories from Lebesgue-almost every initial point.\nThis is joint work with Victor Kleptsyn.", "id": "Paper/68045", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68045"}, {"title": " Nonabelian planar difference sets and music structure ", "webprogram_exclude": "0", "session_ids": ["Session/19340"], "source_sha256": "02fd2be1af68ac312331c0da760f52f3356bc12c3df1c70618a54d86b2b4f14e", "withdrawn": "", "abstract": "Planar difference sets have particular significance for musical structure. A subset $S = ( v, k,\\lambda )$ of size $k$ in a group $G$ of order $v$ is a planar difference set if every element of $G \\backslash \\{ e \\}$ can be expressed as a product $s_{i}^{-1}s_{j}$ of elements $s_{i}, s{j} \\in S$ in exactly $\\lambda = 1$ way. In mathematical music theory, differences such as $s_{i}^{-1}s_{j}$ correspond to intervals between pitches, rhythms, etc. Accordingly, a difference set $S$ is maximally efficient in terms of interval content: it represents the smallest subset of $G$ that contains every interval between its members. When $G$ is abelian, all members of the set of right translations of $S$ by the elements of $G$ have the same intervals as $S$ itself. Similarly, in an abelian group, inverting the elements of $S$ stabilizes the set of intervals. In these cases, translation and inversion correspond to traditional musical operations. In nonabelian groups, however, interval preservation also obtains from other operations in the normalizer of $G$ that have the effect of permuting the elements of $G$.  We examine these operations in terms of their musical relevance.", "id": "Paper/68046", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68046"}, {"title": " SUMMIT-P: A model for interdisciplinary STEM partnerships to support student transfer of mathematical knowledge ", "webprogram_exclude": "0", "session_ids": ["Session/18200"], "source_sha256": "ba246cd2d9651ffe8fb13811b4f738b44bedd3bb9244309e0d2cfccae79d2918", "withdrawn": "", "abstract": "Students enrolled in traditional STEM curricula typically have difficulty applying knowledge from mathematics courses to problem solving in their disciplines. A collaborative integrative STEM curriculum would enable students to directly connect mathematical concepts and methodologies to specific applications. This helps them develop the ability to extrapolate this knowledge to increasingly complex applications. It is vital that faculty can adapt to a classroom that embraces an integrative STEM curriculum, and most institutions have limited support for this critical change. \n\nThe National Consortium for Synergistic Undergraduate Mathematics via Multi-institutional Interdisciplinary Teaching Partnerships (SUMMIT-P) has gained significant experience implementing, studying, and disseminating the use of interdisciplinary faculty partnerships to affect change in mathematics courses, improving the quality and effectiveness of undergraduate education–particularly in STEM fields. An intervention model has been developed for implementation at dozens of institutions, leading to substantive collaborations that have culminated in lasting curricular change in the first two years of mathematics and in the partner disciplines served. The SUMMIT-P model has developed a paradigm for change in faculty practice that can be disseminated, adapted, and implemented at other institutions.\n\nThe interdisciplinary faculty partnership is the cornerstone of the SUMMIT-P model and is key to establishing relevancy in the mathematics course through active learning paradigms co-developed by professors from mathematics and the partner discipline. This helps alleviate the compartmentalization students in introductory mathematics courses often feel, particularly where students do not move mathematical knowledge into their more general toolbox.\n\nA workshop for interdisciplinary faculty teams has been developed and used to introduce more than 30 teams to the implementation of the SUMMIT-P model at their institutions. The next SUMMIT-P workshop is scheduled for Spring 2027 and will include the opportunity for participating teams to apply for seed funding to support changes at their institution. For reports, publications, and specific examples from SUMMIT-P, see www.summitp.org.", "id": "Paper/68048", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68048"}, {"title": " Classification theorems, concentration compactness alternatives and blowup analysis for elliptic equations with nonlocal exponential nonlinearities ", "webprogram_exclude": "0", "session_ids": ["Session/18337"], "source_sha256": "63ae204cf1d18d02fa6fee8f6a9e600110cf1a8a32511da4202714a8a27c4327", "withdrawn": "", "abstract": "This talk concerns conformally invariant elliptic problems on $\\mathbb R^n$ and subdomains thereof having nonlocal exponential nonlinearities. These problems can be viewed as nonlocal generalizations of the prescribed $Q$-curvature problem. In the $n$-dimensional setting, and under suitable growth assumptions at infinity, a classification of the entire solutions to the nonlocal version of the constant $Q$-curvature problem is provided. This classification is heuristically consistent with the classification of the corresponding local problem. Applications of this classification result in the two-dimensional setting will be discussed. Specifically, we establish a concentration-compactness for sequences of energy-bounded solutions and, when blowup occurs in the concentration-compactness alternative, an energy quantization result is established.", "id": "Paper/68050", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68050"}, {"title": " Nonlinear Maxwell for Modeling Surface Plasmons ", "webprogram_exclude": "0", "session_ids": ["Session/19365"], "source_sha256": "f4cc598572dbbf3ed00b30b34f5db0b43d8a67c2c8170575cd5fdc3612c2c34f", "withdrawn": "", "abstract": "Surface plasmons are collective excitations arising from oscillations of conduction electrons at metal–dielectric interfaces, with applications in biosensing and nanophotonics. We consider a model for these excitations based on Maxwell’s equations in dispersive media with cubic nonlinearity. We investigate finite element approximations of polychromatic solutions to the resulting system as a computational framework for studying metamaterial behavior.", "id": "Paper/68051", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68051"}, {"title": " Betti numbers of Koszul algebras ", "webprogram_exclude": "0", "session_ids": ["Session/18285"], "source_sha256": "d40070ccbcb63fb372e3832b3dd0eba35852f2e8677715c89b8e4ab00a9d90e7", "withdrawn": "", "abstract": "Many quadratic rings arising naturally in algebraic geometry and commutative algebra are Koszul, such as Stanley-Reisner rings, the coordinate rings of Grassmannians, or Veronese rings of high enough degree. When R=Q/I is a Koszul algebra with Q a standard graded polynomial ring, a question of Avramov, Conca, and Iyengar suggests an upper bound on the Betti numbers of R over Q depending on the minimal number of generators of the defining ideal I. In joint work with Adam LaClair and Mark Walker, we give new classes of Koszul rings satisfying the conjecture.", "id": "Paper/68052", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68052"}, {"title": " Graphexon mean field games on large networks and decentralized strategies ", "webprogram_exclude": "0", "session_ids": ["Session/17781"], "source_sha256": "23e801593c259ebe73d4e2b95443bee0e1bff9263ccc7e298e71ba6b502d0a5a", "withdrawn": "", "abstract": "Standard mean field games adopt uniform coupling weights when modeling the interaction between the agents. By considering spatially distributed agents, where the interaction strength depends on the network edges, the resulting model allows more flexibility to describe interaction heterogeneity.  \n\nWe consider dynamic games where the agents in each given population interact over an underlying graph. For a sequence of graphs, we define the so-called graphexon measure to describe the edge distribution of the limit graph if it exists. Unlike graphon theory, the above graph limit theory does not require the graph sequence to be dense. Next the graphexon mean field game can be formulated over the network limit where the agents interact through a probability kernel appearing in the product decomposition of the graphexon measure. We analyze existence and uniqueness of a solution to such graphexon mean field games, and the resulting decentralized strategies.", "id": "Paper/68053", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68053"}, {"title": " Graph neural network prediction of molecular Born radii for biomolecular electrostatics ", "webprogram_exclude": "0", "session_ids": ["Session/17970"], "source_sha256": "f17b23310f70f668fea6cacbdf575cd94fc0f15656ffff58ea8f06e3374f8d8b", "withdrawn": "", "abstract": "Abstract: Accurate molecular Born radii are essential for efficient biomolecular electrostatic calculations but can be computationally expensive to obtain from physics-based models. We develop a graph neural network (GNN) to predict atomic Born radii directly from molecular structure by learning local chemical and geometric environments. The proposed model achieves high agreement with reference Born radii while substantially reducing computational cost. Compared with conventional numerical calculations, the GNN provides rapid predictions suitable for large-scale biomolecular applications. These results demonstrate the potential of graph-based learning as an accurate and efficient surrogate for molecular electrostatics.", "id": "Paper/68054", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68054"}, {"title": " Characterizing fMRI brain responses to naturalistic stimuli with TDA Mapper ", "webprogram_exclude": "0", "session_ids": ["Session/18114"], "source_sha256": "af372c1732fc8d19316712533832a9fa93937a4ab6502d760e6a1208576ff5c3", "withdrawn": "", "abstract": "How do brains respond to rich, naturalistic, and evocative stimuli? This is a challenging question for many reasons: both brain data and the stimuli are high dimensional, data collection is expensive (limiting sample sizes), measurement limitations add noise to the data, and substantial individual variability is ubiquitous (i.e., no two people show exactly the same brain responses). We present an exploratory analysis of brain responses (measured by functional Magnetic Resonance Imaging; fMRI) to emotionally evocative films using the Topological Data Analysis (TDA) algorithm Mapper. Mapper was applied to this data to characterize the \"shape\" of the distribution of brain responses across people, film-scene stimulus, and brain regions. That is to say: which scenes evoked the most unique brain responses; which brain regions responded similarly to stimuli; and did any sub-population of participants show distinctive response patterns. Our analysis indicates that responses are continuously distributed, admitting no obvious clusters. However, it highlights several brain regions and film-scenes, which elicit unique response patterns (i.e., “corners”, “tendrils” and “central cores” of the structured distribution). This may shed new light and suggests potential future research avenues on how individual brains are organized, how they respond to complex information unfolding over time, and how this varies across a heterogeneous population, all fundamental questions in cognitive neuroscience. \n\nUsing this analysis as a case study we will explore the life cycle of a Mapper analysis: what tools to use to perform Mapper analyses and visualize their output; how to interpret and communicate the results effectively, especially to domain experts; what Mapper provides that traditional dimension reduction techniques do not; and finally, some techniques to address the stability and statistical robustness of the results.", "id": "Paper/68057", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68057"}, {"title": " Relational Extensions of Fixed-Point Theorem in Vector-Valued Metric Spaces ", "webprogram_exclude": "0", "session_ids": ["Session/18363"], "source_sha256": "4ce08609be525a6147209ba5a993fa866f724383e891e9d75d5183c4fd63e0e8", "withdrawn": "", "abstract": "In this paper, we establish new fixed-point theorems in vector-valued metric spaces equipped with an arbitrary binary relation. We revisit and extend a fixed-point theorem to this generalized relational framework. We also present an example to illustrate the applicability of the main results. These theorems extend and unify several existing fixed-point results, contributing to the development of fixed-point theory in generalized metric spaces.", "id": "Paper/68059", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68059"}, {"title": " When Distant Regions Drive Invasion: Nonlocal Pulling in Heterogeneous Media ", "webprogram_exclude": "0", "session_ids": ["Session/18009"], "source_sha256": "e6cb7d4596aceb8ace037f7394bd48031b0edf335fd24af9b0a33f19c550d209", "withdrawn": "", "abstract": "Motivated by classical conjectures of Shigesada–Kawasaki and recent work on shifting habitats, we study invasion phenomena in competition systems and their connections to scalar KPP-type models.\nWe develop a Hamilton–Jacobi framework, based on viscosity solution methods, to characterize spreading speeds and front dynamics. In particular, we derive a variational formula for the spreading speed and identify regimes of nonlocal pulling, in which the invasion speed is determined by favorable regions far from the invasion front rather than by the local environment near the front.\nFinally, we present recent progress on the fine asymptotics of level sets, including the characterization of logarithmic delays and convergence to traveling wave solutions.", "id": "Paper/68060", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68060"}, {"title": " Bayesian Copula Modeling of Multivariate Climatic Dependence for Predictive Root-Zone Soil Moisture for Paddy ", "webprogram_exclude": "0", "session_ids": ["Session/17972"], "source_sha256": "c03a73d684d61c9ac0bf75c1ef334167d7a5d41a302eef0556e7db23f6a5a126", "withdrawn": "", "abstract": "Climate-driven agricultural drought emerges from the complex dependence between multiple climatic variables and root-zone soil moisture. Because climatic stress is inherently multivariate, identifying and accurately representing its dependence with soil moisture presents a challenging statistical modeling problem. Copula models provide a flexible framework for characterizing dependence beyond marginal distributions; however, constructing an appropriate dependence structure between multiple climatic variables and soil moisture becomes increasingly challenging as the number of possible variable pairs grows. In this work, we develop a Bayesian copula framework for quantifying the multivariate dependence between climatic stress and root-zone soil moisture for paddy, with particular emphasis on dependence under extreme climatic conditions. The proposed framework jointly represents the relevant climatic variables and root zone soil-moisture response while accounting for uncertainty in the dependence structure and model parameters. Through Bayesian inference, the resulting model provides probabilistic predictions of future root-zone soil moisture, rather than a single deterministic drought estimate. This enables the construction of a predictive agricultural drought indicator for paddy that explicitly incorporates uncertainty and extreme dependence, providing an early-warning framework for agricultural water stress.", "id": "Paper/68063", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68063"}, {"title": " A low-rank neural representation for parametrized nonlocal equations ", "webprogram_exclude": "0", "session_ids": ["Session/18377"], "source_sha256": "885521c16f93faa10e88e3f1662900d2fa04ba2b8818c8fc5d0b3e3ef6768df0", "withdrawn": "", "abstract": "Nonlocal models can become computationally expensive in many-query applications, such as uncertainty quantification and design optimization, since the underlying nonlocal problem must be solved repeatedly for different parameter values. We present a data-driven meta-learning approach that trains a single neural network across a family of nonlocal diffusion problems parametrized by the interaction horizon, kernel parameter, and time, on both periodic and bounded domains. The architecture represents the network weights with shared low-rank bases, while a hypernetwork predicts the corresponding parameter-dependent coefficients. We generate training data using a Fourier spectral method for nonlocal equations. The low-rank structure allows the model to efficiently represent a family of nonlocal solutions and to predict solutions for parameter values not used during training. The resulting surrogate enables rapid many-query prediction of nonlocal solutions across the parameter space, reducing the need for repeated numerical simulations.", "id": "Paper/68066", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68066"}, {"title": " Principal Subspace Approximation by Graph Shift-Invariant Spaces ", "webprogram_exclude": "0", "session_ids": ["Session/17908"], "source_sha256": "54886cabfc46eec307f701bb1cad0db0868ddc61469317bf48f8bb2f3354f418", "withdrawn": "", "abstract": "Low-dimensional representations of graph signals are commonly obtained either from the data, as in principal component analysis (PCA), or from the graph spectrum, as in bandlimited signal models. PCA is fully data-adaptive but does not in general preserve the graph structure, while a bandlimited model imposes a prescribed spectral structure that may be unnecessarily restrictive. We study graph shift-invariant spaces as a structured model that combines data adaptation with compatibility with a prescribed graph shift.\n\nFor a normal graph shift $\\mathbf{S}$, we consider the best low-dimensional shift-invariant approximation to a collection of graph signals and characterize the optimal space through the spectral components of the data. In particular, when an eigenvalue has multiplicity greater than one, a graph shift-invariant space can select the data-supported directions within the corresponding eigenspace rather than retaining the entire eigenspace as a bandlimited model would.\n\nWe then consider the finite-order spaces $K_r(V)=V+SV+\\cdots+S^rV$, which replace the full invariant closure by a finite number of graph-shift operations. The order $r$ provides a natural measure of propagation or computational depth and leads to a practical method for learning the initial subspace $V$. For partially observed graph signals, the best subspace for full-data approximation need not be the best subspace for reconstruction. We characterize this approximation-observability tradeoff and use it to learn finite-order graph-structured models directly from incomplete measurements.", "id": "Paper/68067", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68067"}, {"title": " Spectral-contrast breakpoint localization in HDLSS factor models ", "webprogram_exclude": "0", "session_ids": ["Session/19338"], "source_sha256": "67771f7c113525ec3e32fa64fe3383d5c16c2879dd1e10f6df80181bb675a8bb", "withdrawn": "", "abstract": "Title: Spectral-contrast breakpoint localization in HDLSS factor models\n\nHigh-dimensional factor models may undergo structural changes in the orientation of their latent loading spaces even when only a short observation window is available. We study localization of a single such breakpoint in the high-dimension, low-sample-size regime, where the cross-sectional dimension \\(p\\) tends to infinity while the time dimension \\(n\\) remains fixed. A natural estimator compares the leading empirical eigenspaces before and after each candidate split. Although PCA recovery supports this approach when both \\(p\\) and \\(n\\) grow, with fixed \\(n\\) the empirical singular vectors retain nonvanishing random spectral coefficients that can obscure the split contrast.\n\nWe introduce the spectral-contrast angle-chaser, which reweights the empirical eigenspaces using the separation between the leading eigenvalues and the noise bulk, with truncation to suppress unstable directions. We show that this correction removes the leading HDLSS distortion while preserving the geometry of the loading spaces, and we prove almost-sure eventual exact recovery of the breakpoint. To accommodate time-varying idiosyncratic variances, we combine an identifiable low-rank-plus-diagonal minimum-residual decomposition of the dual Gram matrix with Gram padding before applying the corrected score. Under corresponding identifiability and stability conditions, the consistency conclusion transfers to the Gram-padded estimator. Simulations comparing the raw alignment, corrected, Gram-padded, and quasi-maximum likelihood estimators show that the corrected procedures improve as \\(p\\) grows and are particularly effective when the break is primarily directional.", "id": "Paper/68076", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68076"}, {"title": " Finite Element Simulation of Triple-Negative Breast Cancer with Stochastic Dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "d1b8cf51efbddb1752239a7160a7a2b117ad3686d81eb6517dfbf7fc5c84a11c", "withdrawn": "", "abstract": "Recent developments and improvements in breast cancer models have been motivated by the increasing demand for digital-twin-based technology, with the goal of using a digital version of the tumor to simulate how the real tumor will respond to treatment. However, many factors are not accounted for, such as unmeasurable physiological characteristics or ambient biological noise. This may lead to the accumulation of slight discrepancies between the model and the real-life tumor over time. Therefore, we introduce a novel model of breast tumor progression as a stochastic partial differential equation, incorporating temporal randomness to account for these differences. By doing so, we shift the model from a single point prediction to a probabilistic forecast of tumor progression, allowing the model capture variability in the tumor's response to treatment.", "id": "Paper/68077", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68077"}, {"title": " Experiences starting up COMAP at Northwestern in the Industrial Engineering Dept. ", "webprogram_exclude": "0", "session_ids": ["Session/18066"], "source_sha256": "09ec0dd0d48329b808abd2d90bf9fac29a8da6d78af29ae0b61b6c8fc2e6af17", "withdrawn": "", "abstract": "When I joined Northwestern full-time in the fall of 2023, I wanted our students to compete in COMAP. I didn't any teams in Jan of 2024.  By 2025, I wanted just one team and we had that. In 2026, we had six teams competing.  In this talk, I'll cover how we recruited teams (including the failures), how we prepared teams (which was more from a time point of view), student feedback, and plans going forward.", "id": "Paper/68079", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68079"}, {"title": " Towards a unified framework for multiple stable states in ecological systems ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "ea5e288cef8b273882acaa58970c338ec1ca72012f6df973964edb410c6b9e0c", "withdrawn": "", "abstract": "Multiple stable states–the coexistence of two or more distinct ecological configurations under identical environmental conditions–have attracted sustained interest in ecology, yet the field still lacks a unified framework connecting ecological mechanisms and dynamical models. Using perspectives on stability, tipping, hysteresis, and transient dynamics, we work contextualize examples of ecological systems with multiple stable states within a common mathematical framework. Importantly, examining the structure of the Jacobian reveals the importance of positive feedback loops in models of these systems.This allows for further exploration on the relationship between stable and transient dynamics, the roles of spatial and temporal scales in feedback identification, and the implications for ecological restoration and management.", "id": "Paper/68081", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68081"}, {"title": " Slope Gap Distributions for Covers of Translation Surfaces ", "webprogram_exclude": "0", "session_ids": ["Session/17902"], "source_sha256": "4b27386b99088163a64021913173f53d0359793955a667f5800b9fc65f9a05a7", "withdrawn": "", "abstract": "We study the distribution of gaps between slopes of saddle connections on square-tiled surfaces, with an emphasis on how this distribution reflects the geometry of the covering construction. Using the horocycle flow and a suitable Poincar{\\'e} section, we analyze the slope-gap distribution of a particular ten-tile origami and show that, unlike previously computed examples, the resulting distribution cannot be expressed as a finite sum of scaled copies of the Hall distribution (the limiting gap distribution of the square torus). This provides a concrete example showing that slope-gap statistics of a translation surface need not be inherited in a simple way from a base surface under a branched covering. We will discuss the dynamical methods behind this phenomenon and some questions it raises about slope-gap distributions of translation surfaces arising from covering constructions.", "id": "Paper/68087", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68087"}, {"title": " Relaxation to Equilibrium in Voigt-Regularized MHD ", "webprogram_exclude": "0", "session_ids": ["Session/18104"], "source_sha256": "ffb2696e4b92ff70ce01be5ec49939228c9daf3c5804cd708c768418ec99ea4a", "withdrawn": "", "abstract": "Voigt-regularized MHD (VMHD) is investigated as a potential tool for the computation of 3D stellarator equilibria with magnetic islands and stochasticity. VMHD admits modified energy and magnetic helicity which provably prevent the formation of singular structures during relaxation. Numerical results in 2D test problems for forced and spontaneous magnetic reconnection show that VMHD relaxation provides ~40-60-fold speedup compared to ideal relaxation (Phys. Plasmas 32, 062507 (2025)). Asymptotic analysis of linear-phase and nonlinear evolution in the Hahm-Kulsrud-Taylor problem is supported by numerics. Additional dissipation terms provide a modest additional speedup without changing the final equilibrium (https://arxiv.org/abs/2603.02432). Preliminary results in 3D geometry, including helical and toroidal domains, are presented.", "id": "Paper/68094", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68094"}, {"title": " Accelerating Sheaf Laplacian Computations: Classical and Quantum Approaches ", "webprogram_exclude": "0", "session_ids": ["Session/18026"], "source_sha256": "f35a708801a81a9e938f335cfb878c062dcb6b6d29090b357f16e314f458c64b", "withdrawn": "", "abstract": "Sheaf Laplacians generalize graph and simplicial Laplacians by incorporating local data spaces and maps that encode relationships between them. Their potential applications to biological networks and multiscale data analysis motivate the development of efficient computational methods. This talk presents two complementary approaches to efficient computation with sheaf Laplacians. First, we discuss classical spectral sparsification on graphs, which reduces the number of interactions while preserving the associated quadratic energies up to controlled relative error. Second, we introduce a quantum algorithm for estimating normalized persistent Betti numbers with sheaf coefficients through spectral filtering of the persistent sheaf Laplacian. We outline its main ideas and the assumptions governing its computational complexity. Throughout, we emphasize the information preserved or extracted by each approach and the relationship between computational cost and approximation accuracy.", "id": "Paper/68095", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68095"}, {"title": " Coherent BCK-algebras ", "webprogram_exclude": "0", "session_ids": ["Session/17471"], "source_sha256": "5fb23e769b224df1935ff76b6fc604bcd2a973bc5e8cddb0c360fbb8afa46536", "withdrawn": "", "abstract": "Given a commutative ring, the set of prime ideals can be endowed with a topology which yields a so-called spectral space: a compact, sober topological whose compact open subsets are a basis for and a sublattice of the topology. Similar constructions exist for many algebraic structures. In this talk I will focus on the prime spectra of BCK-algebras -- these are algebraic structures related to a non-classical logic. The prime spectrum of a bounded commutative BCK-algebra is known to be a spectral space; removing the hypothesis of boundedness, the prime spectrum may no longer be compact, leaving us with what is known as a generalized spectral space. It is then natural to ask: what happens if we remove the hypothesis of commutativity? In attempting to answer this question, I will define the class of coherent BCK-algebras and discuss the desirable properties that their spectra possess.", "id": "Paper/68098", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68098"}, {"title": " Multi-strain modeling for viral infections ", "webprogram_exclude": "0", "session_ids": ["Session/17860"], "source_sha256": "b754422c8621ba4ff0394c324aabd13c25c0d8095ea7c67778f55cfcfe0e31a8", "withdrawn": "", "abstract": "We describe a few mathematical models to study the transmission and spread of viral infections, with a focus on the interplay between different viral strains at the population level. We discuss how the effects of asymptomatic infection, strain competition, and reinfection shape the disease transmission dynamics. Using COVID-19 as an example, we present numerical simulation and fitting results to validate model outcomes based on SARS-CoV-2 surveillance data from the US.", "id": "Paper/68100", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68100"}, {"title": " Irreducibility in <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"5.356ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 2305.9 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbb {N}_0[x]</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJAMS-4E\" d=\"M20 664Q20 666 31 683H142Q256 683 258 681Q259 680 279 653T342 572T422 468L582 259V425Q582 451 582 490T583 541Q583 611 573 628T522 648Q500 648 493 654Q484 665 493 679L500 683H691Q702 676 702 666Q702 657 698 652Q688 648 680 648Q633 648 627 612Q624 601 624 294V-8Q616 -20 607 -20Q601 -20 596 -15Q593 -13 371 270L156 548L153 319Q153 284 153 234T152 167Q152 103 156 78T172 44T213 34Q236 34 242 28Q253 17 242 3L236 -1H36Q24 6 24 16Q24 34 56 34Q58 35 69 36T86 40T100 50T109 72Q111 83 111 345V603L96 619Q72 643 44 648Q20 648 20 664ZM413 419L240 648H120L136 628Q137 626 361 341T587 54L589 68Q589 78 589 121V192L413 419Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-5B\" d=\"M118 -250V750H255V710H158V-210H255V-250H118Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-78\" d=\"M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-5D\" d=\"M22 710V750H159V-250H22V-210H119V710H22Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJAMS-4E\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-30\" x=\"1021\" y=\"-213\"></use>\n <use xlink:href=\"#E1-MJMAIN-5B\" x=\"1176\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-78\" x=\"1454\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-5D\" x=\"2027\" y=\"0\"></use>\n</g>\n</svg>: Atomic Density and Bounded Distance Problems ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "a9025b922f13fa074249a8e82495e381569613c5bb3ed98fb2a51d3e5c2b0dad", "withdrawn": "", "abstract": "We study the asymptotic and constructive behavior of irreducible polynomials in the semiring \\(\\mathbb{N}_0[x]\\) of polynomials with coefficients in the nonnegative integers. First, we strengthen the iterated-limit formulation of the atomic density of \\(\\mathbb{N}_0[x]\\) by proving a simultaneous two-parameter density result in the uniform-height model. We then study nonuniform coefficient boxes, prescribed-coefficient boxes, and related reducible-count estimates. Finally, we introduce a certification framework for irreducibility criteria in \\(\\mathbb{N}_0[x]\\), report computational coverage data, and prove several support-based and coefficient-based irreducibility criteria suggested by the residual data. We also explore Tur\\'an's problem on the distance to irreducibility, investigating a Tur\\'an-type bounded-distance problem for irreducibility in \\(\\mathbb{N}_0[x]\\).", "id": "Paper/68101", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68101"}, {"title": " Quantitative propagation of chaos and fluctuations for non-exchangeable diffusions ", "webprogram_exclude": "0", "session_ids": ["Session/17800"], "source_sha256": "910e37bcd999ac200f19cd0e70afd966c80a2b6e5993021ea4351d85940dd7c5", "withdrawn": "", "abstract": "We study a system of interacting diffusions with heterogeneous pairwise interactions, so the particle system is non-exchangeable. In the first part of the talk, we develop a quantitative, non-asymptotic approach to mean field approximation by comparing the law of any subcollection of particles with a suitably chosen product measure and proving sharp relative entropy bounds. The proof uses a BBGKY hierarchy adapted to the non-exchangeable setting and an unexpected connection with first-passage percolation.\nIn the second part, we establish a universal central limit theorem for the global fluctuation field around the McKean-Vlasov limit. Under suitable structural and denseness conditions on the interaction matrix, the fluctuations converge to the same Gaussian SPDE as in the classical exchangeable mean field case. For $m_n$-regular graphs, this holds when $m_n/\\sqrt n\\to\\infty$, and a spatial interaction model shows that the $n^{-1/2}$ denseness threshold is sharp. The proof builds on the sharp propagation of chaos estimates developed in the first part, together with functional inequalities and an analysis in negative Sobolev spaces.\n\nBased on joint work with Daniel Lacker and Fuzhong Zhou, and on joint work with Mykhaylo Shkolnikov.", "id": "Paper/68103", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68103"}, {"title": " Monochromatic triangles in measurable colorings ", "webprogram_exclude": "0", "session_ids": ["Session/18359"], "source_sha256": "d0d9c329b0f051e8c679878a48969a91e028efa59fd2d05beb5afa3be4f41f70", "withdrawn": "", "abstract": "In 1973, Erd\\H{o}s, Graham, Montgomery, Rothschild, Spencer, and Straus conjectured that every 2-coloring of the plane contains a monochromatic copy of every non-equilateral triangle. We prove this conjecture for Lebesgue-measurable colorings.", "id": "Paper/68104", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68104"}, {"title": " Anscombe’s Quartet and the Structural Constraints of Principal Component Analysis ", "webprogram_exclude": "0", "session_ids": ["Session/18330"], "source_sha256": "a35b2779d72a724ad477176eb7a41ee73125aad6607e05331eb8ebabc20a2c15", "withdrawn": "", "abstract": "Principal component analysis for standardized data relies entirely on the eigen-decomposition of the sample correlation matrix. For two variables, this input is a symmetric $2\\times2$ matrix defined by unit diagonal entries and a single off-diagonal parameter $r$. We prove that the eigenvectors of this matrix are invariant regardless of the value of $r$. This structural invariance forces the principal component directions to remain fixed for all possible data geometries in two dimensions. Consequently, PCA cannot distinguish between arbitrary point configurations that share a correlation coefficient because it projects data onto structurally predetermined axes. We verify this result numerically using Anscombe's quartet. The four datasets are geometrically distinct but share a common correlation structure to three decimal places. Our results show identical principal component directions and nearly exact explained-variance ratios across all four cases. These findings demonstrate how rigid constraints on input matrices lead to algorithmic blindness in dimensionality reduction. The natural open question is how far this blindness extends: which correlation structures in three or more dimensions force similar eigenvector degeneracy, and what classes of geometrically distinct datasets can be constructed to expose it.", "id": "Paper/68105", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68105"}, {"title": " Obstructions to Hydrodynamic Implosions in Kinetic Theory ", "webprogram_exclude": "0", "session_ids": ["Session/18331"], "source_sha256": "42982ff00c4359a80f0b6603b91ee65c806c807e61f290829c670b797f4e6eb4", "withdrawn": "", "abstract": "At the macroscopic level, gas dynamics is modeled by the compressible Euler equations, which admit a broad range of finite-time singularity formation scenarios, including implosions. At the mesoscopic level, gas dynamics is described by kinetic theory, with the Boltzmann and Landau equations as two of its most fundamental models. A natural and widely open question is whether the implosion singularities seen in Euler also occur in kinetic models, or whether some feature of the kinetic description prevents their formation.\n\nI will discuss recent continuation criteria for the Boltzmann and Landau equations that require less control than the corresponding macroscopic quantities. As a consequence, we obtain restrictions on when a given Euler blow-up profile could be used to construct singularities in kinetic models. In particular, throughout the physical parameter range of the Boltzmann and Landau equations, no known Euler singularity profile can yield such a construction; for the Landau-Coulomb model, this approach to blow-up is ruled out entirely.", "id": "Paper/68106", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68106"}, {"title": " Optimal Vaccination Strategies and Cost–Efficacy Thresholds in a Two-Class SVIR Model with Heterogeneous Transmission Rates ", "webprogram_exclude": "0", "session_ids": ["Session/19359"], "source_sha256": "d0ef408a153f9658170ea7f1e2d4422d05d4a49cc691ccfcad1dbdba50e1b521", "withdrawn": "", "abstract": "Vaccination programs must balance the epidemiological benefits of reducing infection against the economic costs associated with vaccine deployment. In this study, we develop a two-class susceptible–vaccinated–infectious–recovered (SVIR) epidemic model with heterogeneous transmission rates to investigate optimal vaccination strategies under varying vaccine efficacy and infection costs, with vaccination costs proportional to efficacy. Numerical simulations and heatmaps examine cumulative vaccination, cumulative infection, and optimal control effort, with Pontryagin’s Maximum Principle used to characterize the optimal vaccination policy and highlight the trade-off between infection and vaccination costs for two cost formulations: a purely quadratic and an extended quadratic–linear control cost.\nThe results demonstrate a clear economic trade-off between vaccination effort and infection burden. As the cost of infection increases, the optimal vaccination strategy shifts toward greater vaccination effort and lower cumulative infection burden. This trade-off is more pronounced in the higher-transmission population. Threshold-like regions reveal distinct vaccination scenarios under different combinations of infection cost and vaccine efficacy.\nThe quadratic–linear formulation preserves the overall qualitative structure of the quadratic optimal control policy but shifts the transition toward intensive vaccination to higher infection-cost levels and narrows the region in which widespread vaccination is economically optimal, reflecting the additional per-unit acquisition and deployment costs. These findings demonstrate how vaccine efficacy and economic constraints jointly shape optimal vaccination policies and provide insight into cost-effective vaccination strategies for populations with differing levels of disease transmission.", "id": "Paper/68107", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68107"}, {"title": " Sidon and sum-free subgroups associated with APN and Planar exponents ", "webprogram_exclude": "0", "session_ids": ["Session/18073"], "source_sha256": "336e00911570fdedd6b06196ccf4dc3015851a427fbd95db0e5d886924c885d6", "withdrawn": "", "abstract": "Almost perfect nonlinear (APN) functions attain optimal differential uniformity in characteristic two, making them of interest in the design of block cipher components resistant to differential cryptanalysis. Planar functions attain the corresponding optimum in odd characteristic. We study APN and planar power functions through the additive structure of associated multiplicative subgroups. For a power function $x^d$ over $\\mathbb{F}_{p^n}$, we consider subgroups of orders $e_j=\\gcd(d-p^j,p^n-1)$, where $0\\le j<n$. Building on the known connection for APN power functions, we show that planarity forces each of these subgroups to be both Sidon and sum-free. We characterize these additive properties using cyclotomic numbers. In characteristic two, we relate them to codewords of weights three and four in associated binary cyclic codes; the simultaneous Sidon and sum-free conditions are equivalent to minimum distance at least five. We discuss how these connections bring together differential uniformity, additive combinatorics, and coding theory.", "id": "Paper/68110", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68110"}, {"title": " Local Data and Course Coordination: A Self-Reinforcing Cycle ", "webprogram_exclude": "0", "session_ids": ["Session/18250"], "source_sha256": "c3569767915ded88f6193d5d976996e27311c115bdb90c1b678f39f258afabc1", "withdrawn": "", "abstract": "This talk describes the 10-year process of coordinating Calculus I in a math department at a small, public, research university. \n\nLocal data was the catalyst triggering the initial experiment in course coordination. The high-quality data obtained from coordination has since been leveraged to refine the course and measure the impact of the changes. The relationship proved self-reinforcing: coordination made it possible to collect uniform data across sections and years, and that data in turn justified and shaped further coordination.\n\nWe emphasize two embedded measures that proved especially useful: one of student content knowledge and one of student behavior, both collected in the first three weeks of Calculus I and maintained since 2016. We describe the baseline data; the statistical models and departmental structures used to translate it into pedagogical and structural reforms; measures of the impact of those reforms; and the continuing value to the department of sustaining both the coordination and the measures that support it.\n\nThe approach may interest anyone concerned with starting, maintaining, or expanding course coordination. Because the measures and interventions operate at the departmental level, they offer a model for departments seeking to formulate evidence-based strategies of their own. That autonomy is precisely what lets a department generate data to test hypotheses, calibrate interventions, or measure long-term trends.", "id": "Paper/68114", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68114"}, {"title": " Quasi Optimal Recovery of the Poisson Equation with missing boundary information: the noisy measurement case ", "webprogram_exclude": "0", "session_ids": ["Session/18258"], "source_sha256": "87ac5a119d417baad2a65ad575fcb895b8372b16944c3967b5c04ce6e190ada2", "withdrawn": "", "abstract": "We consider the problem of numerically approximating the solutions to a\n  partial differential equation (PDE) when there is insufficient information\n  to determine a unique solution. Our main example is the Poisson boundary\n  value problem, when the boundary data is unknown and instead one\n  observes finitely many linear\n  measurements of the solution, polluted by Gaussian noise. We view this\n  setting as a minimax recovery problem and develop theory and numerical\n  algorithms for its solution. The main vehicle employed is a semidefinite\n  program, built from the Riesz representers of these functionals with\n  respect to relevant Hilbert spaces of harmonic functions, whose value\n  determines the optimal recovery error up to a logarithmic factor. Since\n  these representers are not available in closed form, we implement the\n  recovery algorithm with finite element method approximations, and show\n  that the recovery so obtained remains quasi-optimal in the noisy setting.", "id": "Paper/68118", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68118"}, {"title": " Semilinear Elliptic Systems with Nonlocal Homogeneous Critical Nonlinearities ", "webprogram_exclude": "0", "session_ids": ["Session/18337"], "source_sha256": "a52d8697b7bf2ac73a52cc914e95b4e739e5c051c2f4458c2a1d77b2efb06c38", "withdrawn": "", "abstract": "This paper concerns a variational system of nonlinear elliptic equations that generalizes the classical Brezis--Nirenberg problem. In addition to considering vector-valued unknown functions in place of scalar-valued unknown functions, the problem under consideration generalizes the Brezis--Nirenberg problem in two directions. First, the nonlinearity is the sum of two homogeneous functions of suitable homogeneity degrees. Second, the Sobolev-critical term in the nonlinearity is nonlocal. We establish conditions under which a nontrivial solution to the system under consideration is guaranteed to exist and conditions under which the system under consideration admits only the trivial solution.", "id": "Paper/68120", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68120"}, {"title": " Here Be Dragons: A Fantasy Cartography of Mathematics ", "webprogram_exclude": "0", "session_ids": ["Session/18062"], "source_sha256": "8b10f87e0945ab5f3be8477e66a9bfd2c2da5d7e0ddb4afcfd5e1f925c8da83b", "withdrawn": "", "abstract": "The Mapth (https://codesmith512.github.io/mapth) reimagines the landscape of mathematics as a fantasy world map, designed to inspire an intuitition for the use of mathematics as a generalist. Fields of mathematics appear as cities, positioned so that related fields sit near one another. Roads between cities describe the relationships between them. Unsolved problems are marked as dragons and monsters prowling the edges of the known world.\n\nEach city is accompanied by an in-world guidebook, conveying not just the primitives of the field, but also how practitioners of that field see the world, with notes about practical applications disguised as commentary on the local economy. It also remains cross-referenced to authoritative formal sources (Mathlib, Lean4) for readers who want rigor underneath the narrative. Roads between cities describe the relationships between fields of math, teaching readers to interpret the \"road signs\" of category theory.\n\nThe project sits at the intersection of expository writing, worldbuilding, and formal mathematics, aimed at giving everyone an idea for \\textit{when} math is useful, and making it approachable by showing how it is interconnected to what they already know, even when they don't (yet) have the technical skills to see those relationships directly. This talk walks through how the Mapth's design choices (geography, fantasy framing, and gentle rigor) come together to create a more approachable and investigative view of pure and applied mathematics, and invites feedback from the community on where the Mapth should grow next.", "id": "Paper/68122", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68122"}, {"title": " Decay in Countable Groups and Amalgamated Free Products ", "webprogram_exclude": "0", "session_ids": ["Session/17756"], "source_sha256": "95abe588d69163e0b5248f84ba677c2fcb29027ca22f0a189a11d10dd22a2390", "withdrawn": "", "abstract": "In this talk, I will discuss joint work with Kunnawalkam Elayavalli and Patchell, where we introduce the notion of subexponential decay (SD) for countable groups with respect to a length function, a generalization of Haagerup-Jolissaint's rapid decay property. I will also discuss a new permanence result for decay in amalgamated free products, and demonstrate that it is, in a sense, optimal. The talk will include a few key examples of interest and applications to $C^*-$algebras.", "id": "Paper/68123", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68123"}, {"title": " Spiral Endgame for Computing Singular Solutions ", "webprogram_exclude": "0", "session_ids": ["Session/18042"], "source_sha256": "aa850c77250465afa65c8aa55f5956c778e82ad2fdb3aa3dcaa6fddc55e64083", "withdrawn": "", "abstract": "When numerically computing solutions to polynomial systems using homotopy continuation, numerical ill-conditioning arises as a homotopy path approaches a singular solution.  Rather than track to a singular endpoint, endgames are employed in numerical algebraic geometry to approximate the endpoint using extrapolation.  Two well-known endgame methods are the Cauchy endgame and Power Series endgame.  This talk will summarize existing endgame methods and describe a new endgame.  Several examples will be used to demonstrate the computational efficiency.", "id": "Paper/68124", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68124"}, {"title": " On the category <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.85ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 796.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathcal {O}</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJCAL-4F\" d=\"M308 428Q289 428 289 438Q289 457 318 508T378 593Q417 638 475 671T599 705Q688 705 732 643T777 483Q777 380 733 285T620 123T464 18T293 -22Q188 -22 123 51T58 245Q58 327 87 403T159 533T249 626T333 685T388 705Q404 705 404 693Q404 674 363 649Q333 632 304 606T239 537T181 429T158 290Q158 179 214 114T364 48Q489 48 583 165T677 438Q677 473 670 505T648 568T601 617T528 636Q518 636 513 635Q486 629 460 600T419 544T392 490Q383 470 372 459Q341 430 308 428Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJCAL-4F\" x=\"0\" y=\"0\"></use>\n</g>\n</svg> for Generalized Weyl algebras ", "webprogram_exclude": "0", "session_ids": ["Session/18372"], "source_sha256": "918062e6428c0c76b912aaea0e5c68a5345dc0c4ffeef090f9f14126e1c5deec", "withdrawn": "", "abstract": "Motivated by Kashiwara's theorem and its positive-characteristic analogue due to Shiho, we study the category $\\mathcal{O}$ (modules with locally nilpotent $x$-action) over generalized Weyl algebras $H(R,\\phi,z)$.\n\nAssume there exists a nilpotent central element $b\\in Z(R)$ fixed by $\\phi$, such that $(z,\\phi^i(z))=Z(R)$ for all $0<i<l$, and $\\phi^l(z)\\equiv z \\pmod b$. We prove that $\\mathcal{O}(H(R,\\phi,z))$ is equivalent to $\\mathcal{O}(H(R,\\phi^l,z))$, its $l$-th twist. The equivalence is realized by the functor $M\\mapsto M^{z^\\infty}$.\r\n\r\nThis result significantly generalizes the known equivalence for the Weyl algebra over $\\mathbb{Z}/p^n\\mathbb{Z}$, and applies naturally to quantized Weyl algebras and classical generalized Weyl algebras (noncommutative deformations of type A Kleinian singularities).", "id": "Paper/68128", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68128"}, {"title": " Linearity of Quantum Ternary Functionals on <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"3.562ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 1533.7 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">W^*</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-57\" d=\"M436 683Q450 683 486 682T553 680Q604 680 638 681T677 682Q695 682 695 674Q695 670 692 659Q687 641 683 639T661 637Q636 636 621 632T600 624T597 615Q597 603 613 377T629 138L631 141Q633 144 637 151T649 170T666 200T690 241T720 295T759 362Q863 546 877 572T892 604Q892 619 873 628T831 637Q817 637 817 647Q817 650 819 660Q823 676 825 679T839 682Q842 682 856 682T895 682T949 681Q1015 681 1034 683Q1048 683 1048 672Q1048 666 1045 655T1038 640T1028 637Q1006 637 988 631T958 617T939 600T927 584L923 578L754 282Q586 -14 585 -15Q579 -22 561 -22Q546 -22 542 -17Q539 -14 523 229T506 480L494 462Q472 425 366 239Q222 -13 220 -15T215 -19Q210 -22 197 -22Q178 -22 176 -15Q176 -12 154 304T131 622Q129 631 121 633T82 637H58Q51 644 51 648Q52 671 64 683H76Q118 680 176 680Q301 680 313 683H323Q329 677 329 674T327 656Q322 641 318 637H297Q236 634 232 620Q262 160 266 136L501 550L499 587Q496 629 489 632Q483 636 447 637Q428 637 422 639T416 648Q416 650 418 660Q419 664 420 669T421 676T424 680T428 682T436 683Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2217\" d=\"M229 286Q216 420 216 436Q216 454 240 464Q241 464 245 464T251 465Q263 464 273 456T283 436Q283 419 277 356T270 286L328 328Q384 369 389 372T399 375Q412 375 423 365T435 338Q435 325 425 315Q420 312 357 282T289 250L355 219L425 184Q434 175 434 161Q434 146 425 136T401 125Q393 125 383 131T328 171L270 213Q283 79 283 63Q283 53 276 44T250 35Q231 35 224 44T216 63Q216 80 222 143T229 213L171 171Q115 130 110 127Q106 124 100 124Q87 124 76 134T64 161Q64 166 64 169T67 175T72 181T81 188T94 195T113 204T138 215T170 230T210 250L74 315Q65 324 65 338Q65 353 74 363T98 374Q106 374 116 368T171 328L229 286Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-57\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-2217\" x=\"1526\" y=\"513\"></use>\n</g>\n</svg>-TROs ", "webprogram_exclude": "0", "session_ids": ["Session/17834"], "source_sha256": "7c126aa620eb6a59a94f6a633470805c56aa3cf3d1c12eaa3f85fbedee7f5e92", "withdrawn": "", "abstract": "A quantum ternary functional on a $W^*$-TRO $V$ is a complex-valued function that is bounded on the closed unit ball of $V$ and linear on every singly generated subTRO of $V$. It is shown that every quantum ternary functional on a von Neumann algebra is linear, including on type $I_2$ von Neumann algebras. More generally, every quantum ternary functional on a $W^*$-TRO $V$ is linear if and only if $V$ admits no surjective ternary homomorphism onto a Hilbert TRO of dimension greater than one. This talk is based on the paper ``A Ternary Mackey-Gleason Theorem'' by L. Bunce, R. Pluta, B. Russo, and J. Virtanen.", "id": "Paper/68132", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68132"}, {"title": " The Explicit Hypergeometric Modularity Method ", "webprogram_exclude": "0", "session_ids": ["Session/18276"], "source_sha256": "f9d364fe1e1abdf878902493df68740723382b97c51c20e11bd7dbafdf1f88a0", "withdrawn": "", "abstract": "In the recent joint works with Allen, Grove, Long, and Rosen, we develop and explore an explicit “Hypergeometric-Modularity\" method for associating a modular form to a given hypergeometric datum, and confirm the modularity of several hypergeometric representations, including conjectures of Rodriguez-Villegas on Calabi-Yau manifolds and conjectures of Dawsey and McCarthy.   Our method utilizes Ramanujan's theory of elliptic functions to alternative bases, commutative formal group laws, and supercongruences.   As a byproduct, we give collections of certain hypergeometric type modular forms.  \n\nIn this talk, I will discuss some special families of such \"hypergeometric modular forms\" and their applications.", "id": "Paper/68133", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68133"}, {"title": " The first moment of the central values of Artin <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.583ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 681.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">L</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4C\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-4C\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-functions of cubic fields ", "webprogram_exclude": "0", "session_ids": ["Session/18010"], "source_sha256": "4e0999d2054a2dc6c016cf066f2e22fd3590cd4d1fd5573a256e2763563ffd5b", "withdrawn": "", "abstract": "Let $K$ be a cubic field and let $L(s,\\rho_K)$ denote the Artin $L$-function associated with $K$, defined as the quotient of the Dedekind zeta function of $K$ by the Riemann zeta function. In joint work with Arul Shankar and Nicolas Templier, motivated by the non-vanishing problem for Dedekind zeta functions of cubic fields at the central point, we studied the first moment of the central values $L(1/2,\\rho_K)$. While we determined the expected main term, our methods yielded an asymptotic formula only under a strong subconvexity assumption or a positivity assumption. In this talk, I will discuss this work together with ongoing work with Chantal David, Fatemehzahra Janbazi, and Arul Shankar aimed at establishing such an asymptotic formula unconditionally.", "id": "Paper/68135", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68135"}, {"title": " Interlace Polynomials of Certain Triangulated Hamiltonian Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18206"], "source_sha256": "75ea9a9a8c3c01c451c225befd165c7f13f0faa27f22eaaef6090ef3409fcd89", "withdrawn": "", "abstract": "In this research, we study interlace polynomials of certain coded cycle graphs which are also triangulated. Recursive formula for the polynomials are produced which can help to identify properties of the polynomials. We give a formula for the degree of such a polynomial in terms of its order.  We show that the leading coefficient of the polynomials follow a mod-3 scheme that involve certain Lucas numbers. Other coefficient patterns and special values of the polynomials are also recognized.", "id": "Paper/68137", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68137"}, {"title": " Near-minimal expanding generating sets ", "webprogram_exclude": "0", "session_ids": ["Session/18361"], "source_sha256": "0ba66aceb54a639570ce391427656e487e6f94ed43d564dd2ec92740a57851ac", "withdrawn": "", "abstract": "For a given prime $p$ and integer $n_0>2$, it is well known that the minimum number of generators of $G_N:={\\rm SL}_{n_0}(\\mathbb{F}_p)^N$ is at least $C_{n_0,p} \\log N$ where $C_{n_0,p}$ is a positive constant depending only on $n_0$ and $p$. In this talk, I will present a recent joint result with Haoyu Li, in which we prove the existence of a generating set $S_N$ of $G_N$ such that $|S_N|\\leq C'_{n_0,p} \\log N$ and the family of Cayley graphs ${\\rm Cay}(G_N;S_N)$ forms an expander family. Roughly speaking, an expander graph is a highly connected sparse graph. Alternatively, this result implies that a random element of $G_N$ can be generated by multiplying randomly chosen elements of $S_N$ about $N$ times. This answers a question of Alex Lubotzky.", "id": "Paper/68138", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68138"}, {"title": " From AI Solutions to Mathematical Inquiry: Five Classroom Designs for Secondary Mathematics ", "webprogram_exclude": "0", "session_ids": ["Session/17461"], "source_sha256": "4b1747ce03c1c2cce7987df2ac44873597e43cff3ec305f557361df53f18b136", "withdrawn": "", "abstract": "Abstract\n\nGenerative AI can produce polished mathematical solutions in seconds, leading many classroom responses to focus on prohibition, detection, or the requirement that students work independently before consulting AI. This practice-based presentation proposes a different stance: an AI-generated solution can be designed as an object of mathematical inquiry rather than treated as an answer to copy. The aim is not to make AI the solver for students, but to make students responsible for interpreting, challenging, and improving what AI produces.\n\nFive reusable classroom designs illustrate the approach in secondary mathematics. Students (1) compare a textbook solution with an AI-proposed alternative and justify which route best fits the task; (2) audit a flawed AI calculus solution to identify invalid inferences about monotonicity and extrema; (3) reconstruct a contextual linear-programming problem from an AI-produced mathematical model; (4) use an AI-generated reflection argument to connect algebraic optimization with geometric representation; and (5) stress-test an AI statistical conclusion by changing assumptions or introducing an outlier. Across the designs, AI outputs may be correct, incomplete, overly cumbersome, or wrong. In every case, students must supply the mathematical warrant.\n\nThe presentation identifies teacher moves that preserve intellectual ownership: selecting and verifying AI outputs in advance, asking students to name the claim being evaluated, requiring evidence from definitions, representations, or conditions, and treating revision as a normal part of reasoning. It also addresses responsible use by separating assistance with generating possibilities from delegation of mathematical judgment. Participants will leave with a practical framework compare, audit, reconstruct, extend, and stress-test for turning AI solutions into material for mathematical reasoning, communication, modeling, and critical AI literacy.", "id": "Paper/68142", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68142"}, {"title": " Marked Magnetic Action Rigidity ", "webprogram_exclude": "0", "session_ids": ["Session/17960"], "source_sha256": "b60042697e111f5d5f7879b085fc3fd1b7440ce401a41e9154813f1ed6c93f73", "withdrawn": "", "abstract": "After the breakthrough of Guillarmou and Lefeuvre in 2019 on the marked length spectrum via microlocal techniques, several rigidity results have appear in the last few years.  In this talk I will discuss a magnetic analog of this problem. An exact magnetic system over a closed manifold $M$ consists of a pair $(g,\\alpha)$, where $g$ is a Riemannian metric and $\\alpha$ is a 1-form (the magnetic part). As in the Riemannian case, in every free homotopy class there is a unique magnetic geodesic. The action of such curve encodes both its lenght and a magnetic term. A generalization of the marked length rigidity conjecture is the following: does the marked magnetic action spectrum of magnetic systems with Anosov magnetic flow determine the metric and the 1-form, up to a natural obstruction? I will present answers to this question in two settings: 1) locally for systems with close metrics and 1-forms, and 2) for metrics in the same conformal class. The proof involve techniques from dynamics, geometry, and microlocal analysis.", "id": "Paper/68156", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68156"}, {"title": " Some rigidity results for the Steklov inverse problem ", "webprogram_exclude": "0", "session_ids": ["Session/17965"], "source_sha256": "7d3870e0ca0c4912295eaf0e9045e0102be858917c43a82e29b7452c01b4be89", "withdrawn": "", "abstract": "The Steklov spectrum of a smooth compact Riemannian manifold with boundary is the set of eigenvalues, counted with multiplicities, of its Dirichlet to Neumann map. The Steklov inverse spectral problem asks if it is possible to recover the metric from its Steklov spectrum, up to a natural gauge. In this talk, I will present some recent positive results addressing this question under certain dynamical assumptions on the boundary of the manifold. We use methods from dynamics, geometry, and microlocal analysis.", "id": "Paper/68157", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68157"}, {"title": " Identifiability-Aware Bayesian Physics-Informed Inference of Dynamical Regimes in a Threshold-Driven Tumor-Immune Model ", "webprogram_exclude": "0", "session_ids": ["Session/19365"], "source_sha256": "26230862ebb2b846dc9bd554af05d86098c6dfe97b7d1489423b2964c9d754ab", "withdrawn": "", "abstract": "We develop a Bayesian physics-informed neural network (BPINN) that couples closed-form identifiability analysis with posterior regime classification for a hyper-Allee tumor-immune model whose bifurcation structure organizes four regimes --- suppression, persistence, oscillatory decay, and near-bifurcation transition --- around a degenerate Bogdanov--Takens point. Fisher information analysis shows that a growth-rate parameter cluster is practically unidentifiable; we derive its compensation relation directly from the governing vector field, explaining the degeneracy mechanistically rather than only numerically. The deterministic system exhibits bistability, with a saddle-node treatment threshold below which tumor elimination depends on immune priming rather than dose alone. A deterministic PINN recovers point estimates; NUTS Hamiltonian Monte Carlo then samples the posterior, projected onto the bifurcation structure to classify regime and forecast trajectories. Benchmarked against nonlinear least squares and an exact-physics Bayesian ODE fit under identical priors, the BPINN matches baseline accuracy and calibrates measurably better on the two hardest-to-identify parameters; least squares trails both. Applied to real B16F10 mouse melanoma data with both tumor and immune-effector channels observed, the pipeline fits untreated and treated cohorts separately, and a Hill--Emax dose-response fit translates dose into predicted tumor response. These results show that parameter non-identifiability does not imply dynamical non-identifiability: a tumor-immune system can remain scientifically interpretable even when its rate constants cannot be uniquely determined.", "id": "Paper/68158", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68158"}, {"title": " Mapping Class Groups, Drinfel’d Doubles, and Group Cohomology ", "webprogram_exclude": "0", "session_ids": ["Session/17949"], "source_sha256": "209b5bbaada6f57399384a6b26204af358e427984aa124b3c2d810ee432ee74b", "withdrawn": "", "abstract": "In axiomatic versions of conformal and topological field theory, the so-called spaces of conformal blocks are represented by spaces of homomorphisms in certain categories. In relatively recent work of the authors, these block spaces were generalized to the so-called derived block spaces by inserting a projective resolution at an additional puncture of the surface under consideration. In the present talk, we will report on the sequel to this work, in which these derived block spaces were explicitly computed in the case of the representation category of the Drinfel'd double of a finite group. In this case, the derived block spaces can be expressed in terms of group cohomology.", "id": "Paper/68159", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68159"}, {"title": " Redundancy-Aware Tensor Compression of M2L Operators for <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"3.018ex\" height=\"2.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -1006.6 1299.4 1152.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathcal {H}^2</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJCAL-48\" d=\"M18 487Q18 496 29 517T67 566T127 621T216 665T330 683Q359 683 376 669T397 643T400 622Q400 584 382 488T348 343Q348 342 467 342H587L594 366Q615 440 648 534T690 641Q701 656 723 669T764 683Q783 683 783 672L750 578Q716 485 677 346T625 101Q624 92 623 82T622 65T621 56Q621 20 658 20Q666 20 701 25Q709 52 736 69T785 87Q803 87 803 75T791 44T754 3T685 -33T588 -48Q568 -48 562 -46Q522 -31 522 13V23Q531 129 562 250L569 281L565 280Q561 278 556 277T549 274L438 273H328L321 249Q307 202 275 107T232 0Q219 -16 196 -28T155 -41Q149 -41 145 -39T140 -34T139 -29Q139 -24 148 -3T181 86T233 247Q240 270 240 272Q240 273 194 273H169Q139 273 139 285Q139 295 153 308T187 332Q206 341 236 342L260 343L264 359Q278 414 289 482T300 578Q300 613 260 613H254Q198 613 169 592Q148 578 127 544T104 508Q72 478 37 475Q18 475 18 487Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJCAL-48\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-32\" x=\"1195\" y=\"581\"></use>\n</g>\n</svg>-Matrix Fast Multiplication ", "webprogram_exclude": "0", "session_ids": ["Session/18032"], "source_sha256": "14fa15ab33c3078d918ec51d8961c12e73e13e6d73fb49c98e7f5f245eec9f9e", "withdrawn": "", "abstract": "Hierarchical ($\\mathcal{H}^2$) matrix representations of kernel matrices reduce storage and matrix-vector multiplication cost to $\\mathcal{O}(n)$, but the multipole-to-local (M2L) coupling operators that encode far-field interactions remain a dominant storage bottleneck, particularly as accuracy requirements increase. Existing methods, including the black-box fast multipole method (BBFMM), compress each M2L operator independently via the SVD, leaving redundancy across operators at the same tree level unexploited. We instead stack the M2L operators at each level into a single higher-order tensor and compress it jointly using Tucker and tensor-train (TT) decompositions. We show that the coupling tensor has two structurally distinct types of modes — smooth, highly compressible interpolation modes, and a single combinatorial transfer-vector mode — and that recognizing this distinction, rather than the choice of decomposition, is what governs compression performance: compressing the interpolation modes preferentially yields substantially better compression ratios across all schemes tested, and this also explains why TT compression is most effective when the transfer-vector mode is ordered first or last among the TT cores. We further show that the TT-compressed coupling tensor can be contracted directly against a vector inside the $\\mathcal{H}^2$ matrix-vector product without ever forming the dense M2L operator, reducing per-block cost and storage from cubic to linear in the number of Chebyshev interpolation nodes. Across a suite of eleven kernels spanning PDE, radial-basis-function, and Gaussian-process applications, we compare Tucker and TT variants against BBFMM in terms of compression ratio, decomposition time, and multiplication error, and identify which method is preferable in which accuracy regime. We also present a preliminary extension of the framework to nonhomogeneous kernels via an additional scaling mode.", "id": "Paper/68164", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68164"}, {"title": " The Fishbone Structure: From Parametric Models to Artistic Representations ", "webprogram_exclude": "0", "session_ids": ["Session/18232"], "source_sha256": "519cbc05551dc0ed91871b4cea84039f9caced8d0b6db07dd679c046f0050280", "withdrawn": "", "abstract": "This research is inspired by summers I spent in the historic town of Korčula on the island of Korčula, whose urban plan Croatia’s UNESCO Tentative List describes as a “fish bone pattern,” sharing this schema with the Venetian town of Chioggia: a dominant spine crossed by shorter lateral streets. The same schema admits several mathematical descriptions. I model it as a parametric spine curve with paired rib vectors along the unit normal at sampled points; as a tree graph, where a spine of n vertices with m paired ribs has |V|=n+2m and |E|=|V|-1; and, in its herringbone form, as a periodic pattern that can exhibit pgg wallpaper symmetry. What carries into the arts is not the fish-skeleton silhouette but the relation itself: an organizing axis with repeated lateral structure. Hedi Kyle’s Fishbone Fold transforms a flat sheet through cutting and pleating into a cascading display. Fishbone stitch, made from alternating diagonal stitches, is documented in two 14th-century Florentine ecclesiastical embroideries and in traditional Jordanian, Syrian, and Palestinian embroidery. Related herringbone structures occur in textiles as broken-twill weaves and in quilting. Steven Haulenbeek’s Fishbone Sculptures translate the structure into cast bronze, using a curved central element to support thin skeletal forms. In art history, the contested “fishbone perspective,” associated by Panofsky with works including the Boscoreale wall painting and Duccio’s Last Supper, raises a different question: whether apparent convergence reflects perspective or pictorial symmetry. I use these examples to ask what remains invariant when the fishbone moves between urban form, graph theory, parametric geometry, periodic pattern, textile, book arts, sculpture, and pictorial space. I conclude by presenting my own artwork developed from this structural investigation.", "id": "Paper/68165", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68165"}, {"title": " Nonlocal Approximation of Slow and Fast Diffusion ", "webprogram_exclude": "0", "session_ids": ["Session/18331"], "source_sha256": "f95cac366516c11b5e5a8bbdc452a85e5f2298bf544d05bcea87ac5a63cef2f4", "withdrawn": "", "abstract": "Motivated by recent work on approximation of diffusion equations by deterministic interacting particle systems, we develop a nonlocal approximation for a range of linear and nonlinear\ndiffusion equations and prove convergence of the method in the slow, linear, and fast diffusion regimes. A key ingredient of our approach is a novel technique for using the 2-Wasserstein and dual Sobolev gradient flow structures of the diffusion equations to recover the duality relation\ncharacterizing the pressure in the nonlocal-to-local limit. Due to the general class of internal energy densities that our method is able to handle, a byproduct of our result is a novel particle method for sampling a wide range of probability measures, which extends classical approaches\nbased on the Fokker-Planck equation beyond the log-concave setting.", "id": "Paper/68169", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68169"}, {"title": " Realization of Cohomology Classes in Orthogonal Grassmannians ", "webprogram_exclude": "0", "session_ids": ["Session/18368"], "source_sha256": "dfae4e5c431430db60cbf43113e9e4e0b605d8274532fc52ea79a88d394e6759", "withdrawn": "", "abstract": "Building on the work of Coskun and Ross, we investigate which cohomology classes of the orthogonal Grassmannian $OG(k,n)$ can be realized as irreducible subvarieties of $OG(k,n)$. We give a criterion for when the realizable classes in the orthogonal Grassmannian agree with those in the Grassmannian. We give a characterization for realizability in low dimension and codimension and give necessary conditions for realizability in certain orthogonal Grassmannians. This is ongoing work.", "id": "Paper/68171", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68171"}, {"title": " Higher <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.741ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 749.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">F</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-46\" d=\"M48 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H742Q749 676 749 669Q749 664 736 557T722 447Q720 440 702 440H690Q683 445 683 453Q683 454 686 477T689 530Q689 560 682 579T663 610T626 626T575 633T503 634H480Q398 633 393 631Q388 629 386 623Q385 622 352 492L320 363H375Q378 363 398 363T426 364T448 367T472 374T489 386Q502 398 511 419T524 457T529 475Q532 480 548 480H560Q567 475 567 470Q567 467 536 339T502 207Q500 200 482 200H470Q463 206 463 212Q463 215 468 234T473 274Q473 303 453 310T364 317H309L277 190Q245 66 245 60Q245 46 334 46H359Q365 40 365 39T363 19Q359 6 353 0H336Q295 2 185 2Q120 2 86 2T48 1Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-46\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-splittings ", "webprogram_exclude": "0", "session_ids": ["Session/17929"], "source_sha256": "b6b67d67d5d76cd4350f5fb94b0309523004274edac14344c95d179240b280a0", "withdrawn": "", "abstract": "We propose a definition for higher $F$-splitting, generalizing the usual notion of $F$-splitting. This concept is a strengthening of Kawakami and Witaszek's higher $F$-injectivity, which we propose in analogy with the relationship between usual $F$-split and $F$-injective singularities. This is work in progress.", "id": "Paper/68174", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68174"}, {"title": " Random permutons using GEPP ", "webprogram_exclude": "0", "session_ids": ["Session/18230"], "source_sha256": "5acbff633112cc9bf8c5a843ff38a3267883693bad61833f9b14788c8806b07a", "withdrawn": "", "abstract": "Gaussian elimination with partial pivoting remains the most widely used solver for dense linear systems, $A \\mathbf x = \\mathbf b$ for $A \\in \\mathbb C^{N \\times N}$. GEPP results in the factorization $PA = LU$ for $P = P_\\pi$ a permutation matrix, with $\\pi \\in \\operatorname{Sym}(N)$ a permutation. We are interested in studying random butterfly permutons that arise as limits of induced permutations (which form a $2$-Sylow subgroup of $\\operatorname{Sym}(N)$ contained in the separable permutations) from applying GEPP to structured random matrices called butterfly matrices of order $N=2^n$. Random butterfly permutons comprise random fractal measures with Hausdorff dimension $1$, whose intensity measure is a nonuniform fractal measure with Hausdorff dimension $H(q) = 1-(q\\log q + (1-q)\\log(1-q))/\\log 2 \\in [1,2]$ for a bias parameter $q \\in [0,1]$.", "id": "Paper/68176", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68176"}, {"title": " Tverberg cores and Kalai’s cascade conjecture ", "webprogram_exclude": "0", "session_ids": ["Session/18352"], "source_sha256": "fab413b93b5adf5ffae49ae95982c88f50af810ffadf8c42e052504e0db9e1f4", "withdrawn": "", "abstract": "In this talk, we present topological analogues of Kalai's cascade conjecture.  The cascade conjecture is a generalization of Tverberg's theorem, which remains since the 70's.  Given a set $S$ of points in $\\mathbb{R}^d$ and a positive integer $r$, the set of $r$-Tverberg points are those that are contained in the convex hulls of $r$ disjoint sets of $S$.  We show how bounding the dimension of the set of $r$-Tverberg points of a set has interesting additional consequences on the intersection structure of its subsets.  Since the methods we use are topological, our results generalize to continuous functions from high-dimensional simplices to $\\mathbb{R}^d$.", "id": "Paper/68177", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68177"}, {"title": " On Matroids and Complete Flag Arrangements ", "webprogram_exclude": "0", "session_ids": ["Session/18339"], "source_sha256": "bd1244b8a4b2b7243adbc1a3afb0d48d89e8548076da2160c73a8436bd206ef5", "withdrawn": "", "abstract": "In their paper ``Flag arrangements and triangulations of products of simplices,\" Ardila and Billey define a useful family of matroids that connects spread-out arrangements of lattice points in a dilated simplex to the dependence relations in the line arrangements created from intersecting complete flags in $\\mathbb{C}^{n}$. Studying this family of matroids has led to better insight into multiple questions in combinatorics and algebraic geometry, such as the connectivity of classes of products of simplices, new characterizations of triangulations of root polytopes, the study of lozenge tilings, and the non-realizability of some tropical ideals. This talk will share our group’s current progress in studying the properties of this family of matroids.", "id": "Paper/68178", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68178"}, {"title": " Homomorphisms of Borsuk Graphs and Chromatic Numbers ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "4bbe2fe9bfa6b6eb924670d8ee30d8d95255c1b5cfbdafd3b308fcb008ddcad5", "withdrawn": "", "abstract": "Vietoris--Rips complexes connect data points that are sufficiently close, while anti-Vietoris--Rips complexes reverse this perspective and connect points whose dissimilarity exceeds a prescribed threshold. On the sphere $S^k$, with geodesic metric, the Borsuk graph $\\mathrm{Bor}[S^k;r]$ is the $1$-skeleton of the anti-Vietoris--Rips complex at scale $r$. Meaning that, vertex set is $S^k$ and the edges are between two vertices when they are at least $r$ distance apart. Thus, it can be viewed as a dissimilarity graph on the sphere at a threshold. We study for $k>n$, when does a graph homomorphism $f\\colon \\mathrm{Bor}[S^k;r] \\to \\mathrm{Bor}[S^n;t]$ exist? In earlier joint work with Henry Adams, Alex Elchesen, and Michael Moy, the topology of anti-Vietoris--Rips metric thickenings provides an obstruction that for $k>n$, no such graph homomorphism exists when $r<\\pi$ and $t> 2\\pi/3$. In particular, this obstruction is related to the fact that the anti-Vietoris--Rips metric thickening of $S^n$ has the homotopy type of $\\mathbb{RP}^n$ for scales between $2\\pi/3$ and $\\pi$. In ongoing joint work with Henry Adams, we give further bounds when $n=1$ (using chromatic numbers of graphs) or when $f$ is measurable (using independence ratios of graphs). Dually, we produce explicit graph homomorphisms $f$ when $r$ is large and $t$ is small compared to sphere coverings and packings. Further, we investigate how many points need to be uniformly sampled from a sphere until the chromatic number of the resulting random Borsuk graph reaches a certain threshold.", "id": "Paper/68179", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68179"}, {"title": " The third power of a Hamilton cycle in randomly perturbed graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18011"], "source_sha256": "16bdc83c064ddc7b4fc47efead662cd096c3184d5b5118bb002513aa274fecd8", "withdrawn": "", "abstract": "Answering a question of B\\\"ottcher, Parczyk, Sgueglia, and Skokan, we fully determine the randomly perturbed threshold for the containment of the third power of a Hamilton cycle. This provides the first example of a randomly perturbed threshold exhibiting continuous change.", "id": "Paper/68180", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68180"}, {"title": " Modeling Physical Systems with Finite Differences: A Student‑Centered Ungrading Approach ", "webprogram_exclude": "0", "session_ids": ["Session/18081"], "source_sha256": "b9b56f2508993ef728d04e6713f03234fc0009f95f0b628eabd290ce88dba8ea", "withdrawn": "", "abstract": "This presentation describes a student‑centered ungrading framework implemented in a special topics course on finite‑difference methods for modeling physical systems governed by ODEs and PDEs. Drawing on students’ reflective writing and commentary, the presentation will highlight how the course’s assessment structures shape their learning experiences, mathematical autonomy, and engagement with applied modeling. Students participate in homework presentations where they share their work, receive peer and instructor feedback, and reflect on both mathematical ideas and their learning processes; computational projects are ungraded but revisited in midterm and final portfolios, allowing students to articulate conceptual development, methodological reasoning, and refinements to their numerical modeling. These practices replace point‑based grading with structured cycles of revision, reflection, and portfolio‑based assessment. I will also outline the PreTeXt‑Plus version of the course under development, which integrates interactive examples and embedded opportunities for metacognitive support, and discuss pedagogical insights relevant to implementing ungrading in applied mathematics courses.", "id": "Paper/68181", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68181"}, {"title": " Backward-Propagating Jamitons in Second-Order PDE Traffic Models: Structural Conditions and Instability Bounds ", "webprogram_exclude": "0", "session_ids": ["Session/19369"], "source_sha256": "1c059eee0108143fd77b4a39532a32def9b76532b3216dff82d22389439caf9c", "withdrawn": "", "abstract": "Stop-and-go waves are a fundamental feature of congested traffic. Macroscopically, they can be modeled as traveling-wave solutions of hyperbolic PDE models. While first-order hyperbolic traffic models do not admit nontrivial travelling wave solutions, second-order models support families of travelling wave solutions known as jamitons. These waves arise when the sub-characteristic condition (SCC) is violated, and perturbations grow into nonlinear traveling waves. The inspection of traffic data reveals that real waves are predominantly propagated backward along the road, whereas many jamiton constructions presented in the literature chiefly admit forward-propagating waves. \n \nIn this talk, we investigate the structural properties of second-order models required to reproduce qualitative and quantitative properties of nonlinear traveling waves as observed in real traffic. First, we present conditions on model functions of the Aw-Rascle-Zhang (ARZ) model that yield backward propagating stop-and-go waves and construct an admissible hesitation function for which the resulting  family of jamitons  propagates exclusively backwards. Second, we prove a structural limitation on the ARZ framework: under physically desirable conditions on the model, the region of SCC violation is restricted. Motivated by this restriction, we generalize the ARZ framework and study how the generalized ARZ (GARZ) model can preserve the physically desirable structure, while reproducing backward propagating travelling waves over a broader range of congested densities.", "id": "Paper/68184", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68184"}, {"title": " The Nuclear Dimension of Extensions and Graph C*-algebras ", "webprogram_exclude": "0", "session_ids": ["Session/18382"], "source_sha256": "0abef41e56165b2a7cca51be747311aacc3579ef798acb0ae4164eba09866846", "withdrawn": "", "abstract": "Nuclear dimension is a noncommutative analogue of topological covering dimension introduced by Winter and Zacharias. The nuclear dimension of an extension is bounded by an expression involving the nuclear dimensions of the ideal and quotient, but the precise value is not known in general. Many existing results require the extension to be full in order to access absorption of the extension. Using Szab\\'{o}'s KK-Uniqueness Theorem, we construct nuclear dimension approximations that recover many of the existing results about the nuclear dimension of extensions. Furthermore, our techniques apply to extensions whose Busby maps are full modulo their kernels. As a consequence, we prove that all graph C*-algebras have nuclear dimension at most 2; in the real rank zero case, this bound may be reduced to 1. This work is joint with Samuel Evington and Christopher Schafhauser.", "id": "Paper/68187", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68187"}, {"title": " On Counting Independent Sets in Regular Hypergraphs ", "webprogram_exclude": "0", "session_ids": ["Session/18312"], "source_sha256": "70f33f04f496ca6ad8e6021920ba6c4415e2c43cadea52eb0fba3eaae8728822", "withdrawn": "", "abstract": "Balogh, Bollob\\'as and Narayanan conjectured that among all finite simple \\(r\\)-uniform \\(d\\)-regular hypergraphs, the number of weak independent sets is maximized by a natural quasi-bipartite construction \\(H_{r,d}\\).  We give three types of evidence for this conjecture.  For every fixed \\(r\\), we prove the conjectured asymptotic exponential rate whenever the twin quotient has maximum pair codegree \\(o(d)\\).  The proof uses the hypergraph container method.  For hypergraphs with no cross-edges, the occupancy method gives the sharper error bound \\(O_r(\\log d/d)\\). We show that a stronger version of the conjecture in terms of the so-called occupancy fraction is {\\em not true}, by providing a counterexample, for every $r\\ge 3$.  We also prove exact cases of the conjecture when the hypergraph is $2$-regular. Using an entropy decomposition in the dual edge-cover problem, we settle every odd \\(r\\) and the case \\((r,d)=(4,2)\\). Parts of the proof used AI tools, which the speaker will accordingly clarify during the talk.", "id": "Paper/68192", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68192"}, {"title": " Equi-M sets for evolving and learning networks ", "webprogram_exclude": "0", "session_ids": ["Session/19368"], "source_sha256": "8d2b6ca0ee36b41f9c21467285832d75ce7b66842ce1521a4ad1a08cf7fdeb36", "withdrawn": "", "abstract": "Equi-M sets were introduced as a generalization of the Mandelbrot set to networks of coupled quadratic maps, providing a geometric lens on how network structure shapes emerging dynamics. By examining the critical orbit across architectures, equi-M sets capture how topological features such as cusp orientation and connectivity encode the influence of coupling patterns, including the presence of inhibitory (negative) edges. This construction offers a way to compare networks of different architectures within a unified parameter space.\n\nWe now extend this framework beyond fixed architectures to networks that evolve in time. First, we consider externally driven evolution, illustrated in the context of the social board game Resistance, where networks are constructed from the percentages of time players look at each other during gameplay. These time-varying connections provide a natural testbed for examining how transient social interactions reshape equi-M geometry. Second, we examine networks in which connections self-adjust as a function of node states, introducing feedback between activity and architecture. Examples include learning networks in neuroscience and artificial intelligence, where synaptic or weight updates reflect ongoing adaptation. In this setting, equi-M sets no longer represent static measures but dynamic objects, the geometry of which reflects the co-evolution of states and couplings. These extensions highlight the diagnostic power of equi-M sets for adaptive systems, bridging fractal geometry and time-varying network dynamics.", "id": "Paper/68196", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68196"}, {"title": " Thompson’s Group <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.787ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 769.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">V</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-56\" d=\"M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-56\" x=\"0\" y=\"0\"></use>\n</g>\n</svg> and Virtual Link Theory ", "webprogram_exclude": "0", "session_ids": ["Session/18082"], "source_sha256": "38b995b09fb8b873839f1ad34fa995dbb8cf35c0f1275d8a6a193e1768156f9c", "withdrawn": "", "abstract": "Thompson’s groups $F\\subset T \\subset V$ were introduced in 1965 and have since found widespread application in diverse fields. In 2014, Vaughan Jones constructed unitary representations of $F$, factoring through a surjection from $F$ to isotopy classes of links in the 3-sphere. Louisa Liles extended Jones’ surjection to $T$, thereby constructing all isotopy classes of checkerboard colorable (CC) links in the thickened annulus. In this talk, I will discuss how we complete this program for $V$, defining a surjection from $V$ to virtual equivalence classes of CC links in thickened compact oriented surfaces. This construction yields a new oriented subgroup containing Jones’ oriented subgroups of $F$ and $T$. Further, this new oriented subgroup realizes all oriented almost classical virtual links. I will then discuss how to construct unitary representations of $V$ and its oriented subgroup from kei and operator quandle coloring invariants, respectively. This talk is based on joint work with Micah Chrisman and Louisa Liles.", "id": "Paper/68197", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68197"}, {"title": " The Fourier Ratio on Resistance Spaces and Applications to Electrical Networks ", "webprogram_exclude": "0", "session_ids": ["Session/19336"], "source_sha256": "ca34fdba8ce28239cdef6a1a9c9624a931eaec82ba838f68ad33fa071d46024b", "withdrawn": "", "abstract": "We study the Fourier Ratio for spectral expansions of nonnegative self-adjoint operators and show that eigenvalue growth can be converted into quantitative sampling guarantees. Weyl's law is a fundamental link between geometry and spectral growth and we prove that Weyl-type counting estimates control the Fourier Ratio of spectrally regular functions. Since a small Fourier Ratio corresponds to approximate sparsity of the spectral coefficient vector, these bounds yield stable reconstruction from random point samples through $\\ell^1$ minimization. On compact measured resistance spaces, we obtain a stronger geometric principle which is that the full reciprocal eigenvalue sum is exactly one half of the average resistance distance. Consequently, every compact measured resistance space admits a Fourier Ratio bound independent of the spectral cutoff, with constants controlled explicitly by resistance geometry and energy. This same identity forces sublinear eigenvalue counting and, under the usual modified Weyl law, spectral dimension strictly below two. We apply these results to the Sierpinski gasket and other self-similar fractals, obtaining corresponding reconstruction and sensor-stability theorems. We also prove an equidistribution theorem for Fourier Ratios of finite families.", "id": "Paper/68198", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68198"}, {"title": " Integrating Mechanistic Models and Neural Networks to Study Environmental Effects on Honey Bee Colony Dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/18275"], "source_sha256": "b3d40fd6c90d361a23850257ecbf8db12a189d92fe6bbeed0e8403f61f8a6f0b", "withdrawn": "", "abstract": "Honey bee colony dynamics are shaped by interactions among demography, seasonality, and weather conditions. Mechanistic models provide an interpretable description of colony development, but weather effects can be nonlinear, time-dependent, and difficult to specify explicitly.\n\nWe develop a hybrid framework that integrates a mechanistic model of honey bee population dynamics with a neural network. Rather than replacing the biological model, the neural network is used to learn unresolved weather-dependent effects from colony, temperature, and seasonal information while retaining the structure of the underlying population model. We apply the framework to longitudinal data from honey bee colonies monitored in Arizona to examine colony dynamics under varying weather conditions.\n\nWe further explore how weather, seasonal, and colony-level variables contribute to the learned dynamics through feature-attribution and sensitivity analyses. This framework provides a flexible approach for combining mechanistic ecological modeling with data-driven learning and for investigating how weather variability may influence colony growth and survival.", "id": "Paper/68201", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68201"}, {"title": " Sharp Functional Inequalities on Half-Spaces and Orthants: Optimizers and Stability ", "webprogram_exclude": "0", "session_ids": ["Session/17749"], "source_sha256": "383448c9a185bc12fbd77a08d7fed7bc577967c54cb2fc6064c023976d3a33a1", "withdrawn": "", "abstract": "Motivated by the work of Dan Su and Qiao-Hua Yang on sharp Hardy inequalities in orthants, we study several classical functional inequalities on half-spaces and orthants whose boundaries contain the origin. We establish sharp versions of the Heisenberg uncertainty principle and the L^2 Caffarelli-Kohn-Nirenberg inequalities, explicitly determining the optimal constants and characterizing all extremizers. We also obtain sharp weighted Poincare inequalities naturally associated with these problems. In addition, we establish quantitative stability estimates for these inequalities. Our proofs combine a dimension-lifting method, spherical harmonic decompositions, and weighted identities adapted to the geometry of orthants. This talk is based on joint work with Nguyen Lam, Guozhen Lu, and Ambar N. Sengupta.", "id": "Paper/68202", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68202"}, {"title": " The poset of hyperbolic structures for groups ", "webprogram_exclude": "0", "session_ids": ["Session/19362"], "source_sha256": "78614b0133a1b29629dc7d11a94917b51264ff3480592df4a2b90ccf6d5fa84d", "withdrawn": "", "abstract": "Given any group $G$, one can define the poset of hyperbolic structures on $G$; denoted $\\mathcal{H}(G)$. This poset contains equivalence classes of cobounded actions of $G$ on some hyperbolic space. Studying the structure of this poset allows us to study all such actions of a given group and their relations to one another, giving us much more algebraic and geometric information about the group as opposed to focusing on a single action. \\\\\n\nIn this talk will explain how this poset is defined and cover some general results known about its structure. I will then talk about a special subposet $\\mathcal{AH}(G) \\subseteq \\mathcal{H}(G)$, which restricts to \\emph{acylindrical} actions, and cover results its structure as well. Lastly, I will talk about results that showcase how studying this poset leads to strong algebraic and geometric results about many classes of groups that arise naturally in geometry and topology. \\\\\n\nThis is based on joint work with C. Abbott and D. Osin. \\\\", "id": "Paper/68207", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68207"}, {"title": " Real- and Complex-Valued Polynomial and Analytic Solutions of the Eikonal Equation in Two and Three Dimensions ", "webprogram_exclude": "0", "session_ids": ["Session/18240"], "source_sha256": "253a2ee65b3fc1903df115607523f8316cfa543ab10c521384930cc0601c24bc", "withdrawn": "", "abstract": "\\begin{abstract}\n    \\noindent We investigate rigidity and classification properties of polynomial solutions to the eikonal equation\n    \\[|\\nabla u|^2 = 1.\\]\n    Motivated by the applications in geometric optics, evanescent waves, Gaussian beams, and wave propagation, we study how the algebraic structure of solutions changes when the domain and range are allowed to be complex. We first establish affine rigidity for one-dimensional solutions and for real-valued polynomial solutions on $\\mathbb{R}^2$, and discuss the corresponding rigidity result for entire solutions on $\\mathbb{C}^2$. We then examine higher-degree polynomial solutions in $\\mathbb{R}^3\\to\\mathbb{C}$. For quadratic solutions, we show that the highest-degree homogeneous component must be the square of the linear form. For cubic solutions, we investigate the corresponding homogeneous constraint and obtain the structure of cubes of complex linear forms. A key factor in the three-dimensional analysis is the geometry of null vectors with respect to the complex bilinear form. In three dimensions, orthogonal null vectors must be parallel, whereas in four dimensions, nonparallel orthogonal null vectors exist. This dimension-dependent behavior provides a natural obstruction to extending the three-dimensional rigidity arguments to higher dimensions and suggests a broader connection between the algebraic structure of complex eikonal solutions and the geometry of complex null directions.\n\\end{abstract}", "id": "Paper/68215", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68215"}, {"title": " <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.066ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 889.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">K</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-4B\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-theory of Amalgamated free product of twisted \\’etale groupoid <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.852ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 1228 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">C^*</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-43\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2217\" d=\"M229 286Q216 420 216 436Q216 454 240 464Q241 464 245 464T251 465Q263 464 273 456T283 436Q283 419 277 356T270 286L328 328Q384 369 389 372T399 375Q412 375 423 365T435 338Q435 325 425 315Q420 312 357 282T289 250L355 219L425 184Q434 175 434 161Q434 146 425 136T401 125Q393 125 383 131T328 171L270 213Q283 79 283 63Q283 53 276 44T250 35Q231 35 224 44T216 63Q216 80 222 143T229 213L171 171Q115 130 110 127Q106 124 100 124Q87 124 76 134T64 161Q64 166 64 169T67 175T72 181T81 188T94 195T113 204T138 215T170 230T210 250L74 315Q65 324 65 338Q65 353 74 363T98 374Q106 374 116 368T171 328L229 286Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-43\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-2217\" x=\"1094\" y=\"513\"></use>\n</g>\n</svg>-algebras ", "webprogram_exclude": "0", "session_ids": ["Session/18381"], "source_sha256": "1598f195bb1d48351fd6c608eb07283c5769072f0002e24f08d39e121898777b", "withdrawn": "", "abstract": "In this talk, we introduce a concrete construction of amalgamated free products of twisted \\’etale groupoids and establish the corresponding identifications of their groupoid \\(C^*\\)-algebras with suitable amalgamated free products of \\(C^*\\)-algebras.\nIn the second part, we investigate the permanence of approximation properties under amalgamated free products in the category of \\’etale groupoids, with particular emphasis on the Haagerup property. We then discuss applications of these permanence results to the Baum–Connes conjecture with coefficients.\nFinally, we explain how this framework can be used to study \\(KK\\)-theoretic Mayer–Vietoris phenomena for twisted groupoid \\(C^*\\)-algebras, and its potential connection with Cuntz’s conjectural six-term exact sequence for amalgamated free products.", "id": "Paper/68216", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68216"}, {"title": " Designing Quantum LDPC Codes Through Classical Coding Theory ", "webprogram_exclude": "0", "session_ids": ["Session/18020"], "source_sha256": "234a0d31187f9e77bfd18b18a4619b3fc63cd48e9fc84f15a852ac9a7252b791", "withdrawn": "", "abstract": "Classical coding theory provides powerful principles for designing sparse codes with large minimum distance and effective iterative decoding. Adapting these principles to quantum error correction requires satisfying additional orthogonality constraints. In this talk, I will present quantum LDPC constructions, including Kasai codes and pair-partition (PP) codes, that bring classical code-design principles into the quantum setting. I will explain how their algebraic and combinatorial structures reconcile these constraints with favorable graph properties and large minimum distance. The emphasis will be on the underlying design ideas and their role in developing quantum codes with a useful balance of rate, distance, and decoding performance.", "id": "Paper/68217", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68217"}, {"title": " Optimal Predictive Modeling of Non-Linear Voting Behavior in “Dancing With the Stars” and Retrospective Insights from the 2025 Mathematical Contest in Modeling competition ", "webprogram_exclude": "0", "session_ids": ["Session/19005"], "source_sha256": "f6f7a2e8d2b091a1ff187a999af8f2e651250242703fb09b981ae515f4996c7d", "withdrawn": "", "abstract": "Our high school team constructed a solution for the 2025 Mathematical Contest in Modeling, Prompt C. Speakers will share experiences before, during, and after the contest from student and faculty perspectives, such as prior research and the day-by-day model building process. \n\nFirst, we built a Bradley-Terry (BT) model to estimate fan votes obtained by each contestant for each week they competed in Dancing with the Stars (DWTS). Assessing the consistency of estimated fan votes versus actual eliminated-result confidence intervals, we found that all predictions were consistent or inconclusive due to high variability in voter preferences. Then we built a Bayesian model to estimate the fan votes using percentages and concluded that percentage-based scoring controls high values of popularity and estimated fan votes, providing fairer competition.\n\nNext, we built an Ordered Logistic Regression (OLR) model to examine the impact of celebrity attributes on rankings, and two Ordinary Least Squares (OLS) models to examine their impact on average judge scores and estimated fan votes. We found that in seasons using percentage-based scoring, scores were lower depending on the celebrity’s industry, and in seasons using rank-based scoring, final rank and fan votes were significantly lower based on region.\n\nFinally, we proposed revisions. The first revision includes expanding the percentage-based scoring system as used in Seasons 3-27 by factoring in deviation between contestant performance and expected performance in weeks 1-5 of each season. We proposed incorporating judges’ scores and fan votes only for weeks 6-11, since the weight of this \"power-up\" increases each week. The second revision includes reviving the \"bottom-two rule\" (Seasons 28-31) where fans vote for one of the bottom two contestants to remain in the competition each week.  Obtaining at least 90\\% of the fans' vote vetoes the judges' vote, upholding the value of exceptional fan support in DWTS without undermining judges' decisions.", "id": "Paper/68218", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68218"}, {"title": " Study of nonlocal Monge-Ampere Operator ", "webprogram_exclude": "0", "session_ids": ["Session/18377"], "source_sha256": "ed28418b5e4299b53d6a7ff9629f0461148b39647f99d2aa3f1a84002c512c0f", "withdrawn": "", "abstract": "In this talk, we will discuss a nonlocal version of the Monge-Amp\\~ere operator studied by Luis Caffarelli and Luis Silvestre. In their paper, they posed several open problems involving this operator. In our work, we proposed solutions to few of those open problems. This is a joint work with Pablo Ra\\'ul Stinga.", "id": "Paper/68219", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68219"}, {"title": " From Mathematical Theory to Computational Investigation in Undergraduate Numerical Linear Algebra ", "webprogram_exclude": "0", "session_ids": ["Session/18225"], "source_sha256": "c4e81b2555317fa842e46b099009e008e2902a475797e0ef4f47e7b22c8726db", "withdrawn": "", "abstract": "The central ideas in numerical linear algebra offer rich opportunities for students to engage with mathematical theory and algorithmic analysis, investigate numerical phenomena through computation, and apply mathematics to real-world problems at meaningful scales.\nIn this talk, I describe the design and teaching of a newly developed undergraduate Numerical Linear Algebra course in which mathematical theory provided the foundation for a series of labs that extended ideas developed in class through computational investigations using MATLAB. Students also had access to MATLAB Copilot to support aspects of their computational work.\nThe presentation will consider how computational experiences can be deliberately aligned with mathematical theory to deepen students’ mathematical understanding. Examples of student work and survey responses will be presented to illustrate students’ experiences with this approach.\nThis work is in collaboration with Jon Loftin and Mike Michailidis.", "id": "Paper/68220", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68220"}, {"title": " CODEE: Building on a Tradition, Expanding Our Reach, and Envisioning the Future ", "webprogram_exclude": "0", "session_ids": ["Session/17765"], "source_sha256": "d996585e692f06a5c2ff38de68fe1d859043d0b03658a42ddc3e52b788e82847", "withdrawn": "", "abstract": "The Community of Differential Equations Educators (CODEE) is a network dedicated to enhancing the teaching and learning of differential equations through collaboration, innovation, and resource sharing. At the heart of this community is the CODEE Journal, an open-access, peer-reviewed publication that provides high-quality materials for educators and students.\nIn this talk we will showcase CODEE’s activities and presence throughout the past year and introduce new and continuing initiatives. We will share experiences from the JMM 2027 Professional Enhancement Program From Data to Differential Equations: A Hands-On Introduction to SINDy for Teaching and Modeling; highlight papers from the CODEE Journal special issue Using Differential Equations to Engage Students in Data-Driven Modeling and Analysis, and papers published in the journal’s most recent regular issue.\nLooking ahead, we will announce a forthcoming special issue devoted to the teaching and learning of partial differential equations at the undergraduate level and invite participants to contribute innovative, classroom-tested activities, projects, and pedagogical approaches. The talk will also present the many ways educators can become involved with CODEE, including authorship, peer review, editorial service, and participation in future professional-development activities. Together, these initiatives demonstrate how the CODEE Journal serves as a platform for sharing creative approaches, building professional connections, strengthening the teaching and learning of differential equations, and broadening access to meaningful mathematics education.", "id": "Paper/68221", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68221"}, {"title": " Open Cases of the Colmez Conjecture ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "fbe2279144a5d58951193767f0128761905682e1541bd981a03c9489c51abc2d", "withdrawn": "", "abstract": "The Colmez conjecture equates the Faltings height of a complex multiplication (CM) abelian variety with logarithmic derivatives of Artin $L$-functions. CM abelian varieties are determined by CM fields paired with a choice of CM type; the conjecture is known when the CM field has an abelian Galois group, as well as on average over all CM types of a given signature. Every other result in the literature follows directly from these two, together with the linearity of both sides. In particular, any linear combination of class functions where the Colmez conjecture has been verified is itself verified, so the verified class functions form a subspace. Via induction and inflation, we compute this subspace for all $651$ Galois groups up to degree $15$ and all $455$ of prime degree up to $199$. For $592$ and $215$ of these, respectively, the conjecture can be deduced for all CM types of corresponding CM fields purely from the two known results and linear algebra. For the groups that remain, we characterize the codimension of the verified subspace for both prime degree groups and dihedral groups under their natural action. This result motivates our proof of the Colmez conjecture for two-homogeneous Galois groups, a newly discovered infinite family.", "id": "Paper/68222", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68222"}, {"title": " Hybrid Rank-Metric Codes ", "webprogram_exclude": "0", "session_ids": ["Session/18387"], "source_sha256": "ce7380ee846105383c25a306930944922b89f7357e57507c62679d12627da807", "withdrawn": "", "abstract": "We introduce a new family of rank-metric codes characterized by the property that each codeword's row is a vector of a Maximum Distance Separable (MDS) linear code under the Hamming metric. We prove a Singleton-like bound for this family of codes, and show that it achieves such bound with equality, namely these new codes are optimal. We then investigate the practical relevance of these new rank-metric codes comparing them with classical Maximum Rank Distance (MRD) codes, focusing on performance under crisscross erasures, rate reliability, locality properties and behavior in network coding scenarios.", "id": "Paper/68223", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68223"}, {"title": " Infection History Shapes Co-Epidemic Dynamics: A Transmission Source–Pathway Decomposition for COVID-19 and Influenza ", "webprogram_exclude": "0", "session_ids": ["Session/19359"], "source_sha256": "d55d6cda7fc2d29556489307b0bea2192d0da747e11693d92b836150c98a4c43", "withdrawn": "", "abstract": "The concurrent circulation of SARS-CoV-2 and influenza presents a complex epidemiological landscape where infection history alters host susceptibility and transmissibility. Conventional co-infection models frequently aggregate co-infected individuals into single compartments, obscuring how sequence-dependent interactions shape population-level dynamics. In this talk, we present a deterministic, multi-strain ODE framework that explicitly distinguishes between single, concurrent, and sequential infections. Our primary methodological contribution is a transmission source–pathway decomposition framework that mathematically attributes rates of new infections to specific transmission sources (singly, co-infected, or sequentially infected classes) and receiving pathways (susceptible, active co-infection, or post-recovery classes). Model analysis reveals a striking, sequence-driven asymmetry in transmission dynamics: in a baseline co-epidemic scenario, individuals who contract COVID-19 after recovering from influenza generate over 70 $\\%$ of new COVID-19 cases, whereas influenza transmission remains driven primarily by singly infected hosts. This sequence-driven transmission engine remains robust across variations in relative virus transmissibility and latent period inclusion. Finally, we discuss how pathway-aware interventions (e.g., targeted vaccination) alter these transmission engines.", "id": "Paper/68229", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68229"}, {"title": " Likelihood-Based Estimation and Inference for the Power Spherical Distribution on the Unit Hypersphere ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "d42998a4292ea5befa6b37a7691e0389b4d79aa8103d5fb636fc992e2021c61b", "withdrawn": "", "abstract": "Directional data arise naturally when observations are constrained to lie on a unit hypersphere, with applications in directional statistics, shape analysis, and modern high-dimensional data analysis. The Power Spherical distribution provides a computationally efficient model for such data, but likelihood-based estimation and inferential procedures for its parameters remain underdeveloped. We develop a likelihood-based framework for estimation and inference for the Power Spherical distribution, parameterized by a central direction on the unit hypersphere and a concentration parameter. Maximum likelihood estimation is carried out using a constrained fixed-point procedure for the central direction, together with Newton--Raphson estimation of the concentration parameter. Building on these estimators, we construct likelihood ratio tests for hypotheses involving the central direction, concentration parameter, and their joint specification, and derive the corresponding asymptotic chi-square reference distributions. Through extensive simulation studies, we investigate the finite-sample behavior of these tests across varying dimensions, sample sizes, and concentration levels. The asymptotic approximation provides reliable inference when the sample size is sufficiently large relative to the dimension, while noticeable departures occur in high-dimensional, low-concentration settings. A parametric bootstrap procedure improves calibration in these challenging regimes. These results provide a practical likelihood-based framework for estimation and inference for directional data modeled by the Power Spherical distribution.", "id": "Paper/68231", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68231"}, {"title": " Delta-matroids and toric degenerations in the maximal orthogonal Grassmannian OG(n,2n+1) ", "webprogram_exclude": "0", "session_ids": ["Session/18219"], "source_sha256": "f760aa140dec5973bb130bf0bdfb128b02da87b0e133637ca11d97ee81b25ea2", "withdrawn": "", "abstract": "Let Z be a general point of the Grassmannian Gr(k,n), which has an action by $T = (C^*)^n$.  Berget and Fink proved a formula via equivariant localization that expresses the cohomology class of the torus orbit closure of Z as a sum of products of Schubert classes, indexed by partitions. In a previous work, Lian gave a new proof of the formula by constructing an explicit toric degeneration of the general orbit closure in Gr(k,n) into a union of Richardson varieties, whose moment map images form a polyhedral decomposition of that of the general orbit closure. With C. Lian, we apply this strategy to deduce a formula in the case of the maximal orthogonal Grassmannian OG(n,2n+1). I will explain the general strategy, focusing on the case of Gr(k,n), and highlight the additional difficulties in its application to OG(n,2n+1).", "id": "Paper/68233", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68233"}, {"title": " Sample Path Properties of Certain Stochastic Volatility Processes ", "webprogram_exclude": "0", "session_ids": ["Session/18124"], "source_sha256": "f356a4531b4745302aa499d3fa1f7adedf5211595463362f3c37fe4a5547a99e", "withdrawn": "", "abstract": "In this talk, we consider Markovian stochastic volatility processes and (non-Markovian) stochastic Volterra models driven by Brownian motion \nor fractional Brownian motion, and present some results on the roughness and fractal properties of these processes. In particular, we study the Hausdorff dimension of the trajectories and the regularity of their local times.", "id": "Paper/68234", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68234"}, {"title": " Low-energy solutions of singular Neumann problems in exterior domains ", "webprogram_exclude": "0", "session_ids": ["Session/18441"], "source_sha256": "c5609dbddcfe54b37c72d927b9591b431d5f2348cd2395e5464187f4db29800b", "withdrawn": "", "abstract": "Using P.-L. Lions' concentration-compactness principle, we study the weak lower semicontinuity of a class of functionals involving a Hardy-type potential and two critical Sobolev terms on an exterior domain $U\\varsubsetneq\\mathbb{R}^N$, $N\\geq3$, with compact boundary $\\partial U$. This analysis yields a bifurcation result for a nonlinear PDE in $U$ subject to a nonlinear Neumann boundary condition on $\\partial U$. As a further consequence, we obtain a coupled eigenvalue problem involving the Hardy-type potential and a homogeneous boundary condition, whose spectrum contains a continuous family of eigenvalues lying in prescribed ranges.", "id": "Paper/68236", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68236"}, {"title": " Idempotents and Tridempotents in <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.769ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 1192.1 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbb {Z}_n</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJAMS-5A\" d=\"M39 -1Q29 9 29 12Q29 23 60 77T219 337L410 648H364Q261 648 210 628Q168 612 142 588T109 545T97 509T88 490Q85 489 80 489Q72 489 61 503L70 588Q72 607 75 628T79 662T81 675Q84 677 88 681Q90 683 341 683H592Q604 673 604 666Q604 662 412 348L221 37Q221 35 301 35Q406 35 446 48Q504 68 543 111T597 212Q602 239 617 239Q624 239 629 234T635 223Q635 215 621 113T604 8L597 1Q595 -1 317 -1H39ZM148 637L166 648H112V632Q111 629 110 622T108 612Q108 608 110 608T116 612T129 623T148 637ZM552 646Q552 648 504 648Q452 648 450 643Q448 639 266 343T77 37Q77 35 128 35H179L366 339L552 646ZM572 35Q581 89 581 97L561 77Q542 59 526 48L508 37L539 35H572Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 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transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-6E\" x=\"943\" y=\"-213\"></use>\n <use xlink:href=\"#E1-MJMAIN-5B\" x=\"1192\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-69\" x=\"1470\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-5D\" x=\"1816\" y=\"0\"></use>\n</g>\n</svg>, and <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"5.508ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 2371.6 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbb {Z}_n[\\omega ]</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJAMS-5A\" d=\"M39 -1Q29 9 29 12Q29 23 60 77T219 337L410 648H364Q261 648 210 628Q168 612 142 588T109 545T97 509T88 490Q85 489 80 489Q72 489 61 503L70 588Q72 607 75 628T79 662T81 675Q84 677 88 681Q90 683 341 683H592Q604 673 604 666Q604 662 412 348L221 37Q221 35 301 35Q406 35 446 48Q504 68 543 111T597 212Q602 239 617 239Q624 239 629 234T635 223Q635 215 621 113T604 8L597 1Q595 -1 317 -1H39ZM148 637L166 648H112V632Q111 629 110 622T108 612Q108 608 110 608T116 612T129 623T148 637ZM552 646Q552 648 504 648Q452 648 450 643Q448 639 266 343T77 37Q77 35 128 35H179L366 339L552 646ZM572 35Q581 89 581 97L561 77Q542 59 526 48L508 37L539 35H572Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-5B\" d=\"M118 -250V750H255V710H158V-210H255V-250H118Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-3C9\" d=\"M495 384Q495 406 514 424T555 443Q574 443 589 425T604 364Q604 334 592 278T555 155T483 38T377 -11Q297 -11 267 66Q266 68 260 61Q201 -11 125 -11Q15 -11 15 139Q15 230 56 325T123 434Q135 441 147 436Q160 429 160 418Q160 406 140 379T94 306T62 208Q61 202 61 187Q61 124 85 100T143 76Q201 76 245 129L253 137V156Q258 297 317 297Q348 297 348 261Q348 243 338 213T318 158L308 135Q309 133 310 129T318 115T334 97T358 83T393 76Q456 76 501 148T546 274Q546 305 533 325T508 357T495 384Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-5D\" d=\"M22 710V750H159V-250H22V-210H119V710H22Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJAMS-5A\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-6E\" x=\"943\" y=\"-213\"></use>\n <use xlink:href=\"#E1-MJMAIN-5B\" x=\"1192\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-3C9\" x=\"1470\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-5D\" x=\"2093\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/19355"], "source_sha256": "8d07e5b4a98173acf42d5581979780afcf5048883fab9acffe2b856fe7d65652", "withdrawn": "", "abstract": "We determine the number and the exact form of the involutions ($a^2 = 1$), idempotents ($a^2 = a$), and tridempotents ($a^3 = a$)  in $\\mathbb{Z}_n$, in the ring of Gaussian integers modulo $n$, $\\mathbb{Z}_n[i]$, and in the ring of Eisenstein integers modulo $n$, $\\mathbb{Z}_n[\\omega]$, where $\\omega$ is a primitive cube root of unity.  We also provide two useful characterizations of tridempotents.", "id": "Paper/68237", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68237"}, {"title": " THE INTEGRABILITY OF A KNIFE-EDGE BILLIARD IN A DISK ", "webprogram_exclude": "0", "session_ids": ["Session/19363"], "source_sha256": "b39733154f8167757794a83beb0677d75eb8002c725f6097ea3097cf68edc969", "withdrawn": "", "abstract": "Nonholonomic billiards combine smooth dynamics subject to nonholonomic constraints with discontinuous dynamics produced by impacts. In this talk, I will discuss a nonholonomic billiard defined by a knife-edge moving inside a disk. After introducing a formula for elastic nonholonomic impacts, I will describe the impact space using coordinates adapted to the rotational symmetry of the system. Exploiting this symmetry together with elementary Euclidean geometry, we construct a map on the space of post-impact states that completely determines the billiard dynamics. This allows us to prove that the system is integrable and to obtain an explicit description of its long-term behavior. I will also discuss a family of generalized caustics for the knife-edge billiard and some directions for extending these ideas to other nonholonomic billiard systems.", "id": "Paper/68242", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68242"}, {"title": " Leaky Zero Forcing on Unicyclic Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17911"], "source_sha256": "7996335fbf7b47694622e5a20f70b601680601f62099040e13dc6aea2c62130d", "withdrawn": "", "abstract": "Zero forcing is a coloring process on a graph that consists of finding a set of vertices (initially colored blue) that can color the entire graph by following this propagation rule: a vertex can color a white neighbor blue if all other neighbors are blue. The goal is to find the zero forcing number for a graph (the minimum number of initially colored blue vertices needed to color the whole graph by repeatedly applying the propagation rule).\nLeaky forcing is a fault-tolerant variation of zero forcing where certain nodes (not necessarily initially colored blue) cannot force. The goal with leaky forcing is to find the leaky zero forcing number for a graph (the minimum number of initially colored blue vertices needed to observe the whole graph regardless of which small number of vertices can’t force). \nIn this talk, we present a complete characterization of leaky forcing numbers for unicyclic graphs.\nThis is a joint work with Drs. Beth Bjorkman (Wright-Patterson Air Force Base, OH); Lei Cao (Nova Southeastern University, FL); Franklin Kenter (United States Naval Academy, MD), Ryan Moruzzi (California State University, East Bay, CA); Carolyn Reinhart (Swarthmore College, PA), and is part of the AIM Mathematical Research Communities.", "id": "Paper/68243", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68243"}, {"title": " Computing jet differentials and the Green–Griffiths–Lang Conjecture for complements of smooth plane curves ", "webprogram_exclude": "0", "session_ids": ["Session/19356"], "source_sha256": "b546ba2e5a0d3de782cd49a76955e618349e9bb1dbb7122a4fc4cb62fd8d6321", "withdrawn": "", "abstract": "We study the Green--Griffiths--Lang Conjecture for complements of smooth plane curves. We develop an effective method for computing a family of negatively twisted invariant logarithmic 2-jet differentials. By realizing the first logarithmic jet space as a hypersurface in $\\mathbb{P}^2 \\times \\mathbb{P}^2$, we encode these jet differentials in a finitely generated bigraded module that can be computed explicitly. We use this description to give a computational criterion for the Green--Griffiths--Lang Conjecture and verify it for several families of smooth plane curves. In examples with sufficiently many independent jet differentials, we determine the exceptional locus explicitly.", "id": "Paper/68244", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68244"}, {"title": " A Nonlocal Monge-Ampère with an Integrable Kernel ", "webprogram_exclude": "0", "session_ids": ["Session/17883"], "source_sha256": "ad4b86b44ace4ef13b4ee58285af90ee1b1b7cb5dff1160fe38c8ae8fe47ac50", "withdrawn": "", "abstract": "In this manuscript, we study a variant of classical nonlocal version of Monge-Ampere operator introduced by Caffarelli and Silvestre by taking an infimum over kernels having the same distribution as $|y|^{-d-s}$ for $s \\in (1,2)$. In particular, we replace the singular kernel by a bounded, compactly supported kernel\n\\[K_0(y)= e^{-|y|^2}\\textbf{1}_{B_1(0)}(y).\\] We identify which operator properties survive in our setting, and use them to treat several related problems.", "id": "Paper/68248", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68248"}, {"title": " Conformal eigenvalues on Tori ", "webprogram_exclude": "0", "session_ids": ["Session/19352"], "source_sha256": "4feb38d52bf8d8d6f8400f5ba442b87080fd1774046c383df828527aaf0eaa4e", "withdrawn": "", "abstract": "In this talk, I will discuss extremal problems for Laplace–Beltrami eigenvalues of unit-area metrics on tori. I will first review Berger’s isoperimetric problem for the first eigenvalue and present a new proof of its solution using conformal area and Bryant’s results on tori. I will then turn to the second eigenvalue. Building on general bounds for surfaces due to Karpukhin–Stern and Eddaoudi–Girouard, I will present an improved upper bound for the second eigenvalue within a fixed conformal class. This result narrows the range of conformal classes for which the Kao–Lai–Osting conjecture remains to be proved.", "id": "Paper/68264", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68264"}, {"title": " Modeling the effects of trait–mediated dispersal on coexistence of two species: Competition and non–consumptive predator–prey ", "webprogram_exclude": "0", "session_ids": ["Session/18325"], "source_sha256": "9903943834fa6749906991a2b3e3445e4a624c5e89f7e1237fb7f96ccba19834", "withdrawn": "", "abstract": "\\noindent Trait-mediated effects can often have a more significant impact on population persistence and community structure than density-mediated effects. We analyze positive solutions $(u,v)$ to the following reaction-diffusion system, which holds density-mediated effects constant, while measuring trait-mediated effects via density-dependent dispersal:\n\n$$\n\\begin{align*} \n    \\left\\lbrace \\begin{matrix}-\\Delta u=\\lambda u (1-u)  ;~\\Omega\\\\[1ex]\n    -\\Delta v =\\lambda r v (1-v)  ;~\\Omega\\\\[1ex]\n    \\frac{\\partial u}{\\partial \\eta}+ \\sqrt{\\lambda} g(v)u = 0; ~\\partial \\Omega\\\\[1ex]\n    \\frac{\\partial v}{\\partial \\eta}+\\sqrt{\\lambda}h(u)v =0; ~\\partial \\Omega\\\\\n    \\end{matrix} \\right.\n\\end{align*}\n$$\n\n\\noindent Here $\\Omega$ is a bounded domain (patch) in $\\mathbb{R}^N$ of unit length, area, or volume; $N \\in \\{1, 2, 3\\}$ with smooth boundary $\\partial \\Omega$, $ \\lambda > 0$ is a parameter proportional to the square of patch size, and $(u,v)$ represents the normalized densities of two species exhibiting logistic growth inside the patch, which is surrounded by a hostile matrix. We explore the consequences of fragmentation and trait-mediated dispersal on the coexistence of these two species in two cases (competition and nonconsumptive predator-prey) and establish coexistence results analytically via coupled sub-supersolutions.", "id": "Paper/68268", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68268"}, {"title": " Geometry Problems at Two Scales: Knitted Structures and Panel Layout in Digital Fashion ", "webprogram_exclude": "0", "session_ids": ["Session/17370"], "source_sha256": "0ef8bdf592b1e312b23aa82f52b8fde2f969ffed57216c750c091264f3287f2f", "withdrawn": "", "abstract": "Garment production presents geometry problems at different scales, from individual stitches to fabric panels. Yet these disparate scales share a common thread: a discrete structure specified in the plane dictates a three-dimensional form. In this talk, I will describe two such problems, one at each scale, drawn from collaborative research at CLO Virtual Fashion.\n\nAt the stitch scale, knitted structures are designed in the plane through discrete stitch operations such as knit, purl, cable, and tuck. Their three-dimensional form emerges under physical relaxation: knit-purl ribbing buckles out of plane, cables introduce volumetric crossings, tucks contract the fabric locally. We represent such a structure as a graph of these operations, from which the yarn geometry is recovered directly. This construction is complicated by the diversity of local topologies it must accommodate, and by the requirement that it depend only on the graph's current configuration, so that geometry can be generated even for deforming states. I will discuss how our approach meets these demands at interactive rates.\n\nAt the panel scale, flat pieces are shaped so that the sewn assembly achieves a desired three-dimensional form. These shapes are typically settled in design, before the question of how to cut them arises: panel geometry is determined by the target form, not by material efficiency. The layout problem we address asks how to arrange these irregular pieces on a roll of fabric with minimal waste — an irregular packing problem, further constrained by grain direction and print placement, for which an exact tiling generally does not exist.\n\nNo background in textiles will be assumed.", "id": "Paper/68275", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68275"}, {"title": " <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.678ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 722.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\Sigma</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-3A3\" d=\"M666 247Q664 244 652 126T638 4V0H351Q131 0 95 0T57 5V6Q54 12 57 17L73 36Q89 54 121 90T182 159L305 299L56 644L55 658Q55 677 60 681Q63 683 351 683H638V679Q640 674 652 564T666 447V443H626V447Q618 505 604 543T559 605Q529 626 478 631T333 637H294H189L293 494Q314 465 345 422Q400 346 400 340Q400 338 399 337L154 57Q407 57 428 58Q476 60 508 68T551 83T575 103Q595 125 608 162T624 225L626 251H666V247Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-3A3\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-shaped bifurcation curves influenced by nonlinear boundary conditions for classes of reaction diffusion systems ", "webprogram_exclude": "0", "session_ids": ["Session/19369"], "source_sha256": "d832bfad4edcb6ccdc6a2c04882e6c8be9e12209a24b00f72148fb600c9fad33", "withdrawn": "", "abstract": "We analyse positive solutions to steady state reaction diffusion systems of the form:\n\n$$- \\Delta u  = \\lambda f_1(v) ;~ \\Omega$$ \n$$- \\Delta v  = \\lambda f_2(u) ;~ \\Omega$$ \n$$\\frac{\\partial u}{\\partial \\eta}+ \\sqrt{\\lambda}g_1(v)u  = 0;~ \\partial \\Omega$$ \n$$\\frac{\\partial v}{\\partial \\eta}+ \\sqrt{\\lambda}g_2(u)v  = 0;~\\partial \\Omega$$,\n\n\n \\noindent where $\\lambda>0$ is a parameter, $\\Omega$ is a bounded domain in $\\mathbb{R}^N$; $N > 1$ with smooth boundary $\\partial \\Omega$ or $\\Omega=(0,1)$, $\\frac{\\partial z}{\\partial \\eta}$ is the outward normal derivative of $z$, $f_1, f_2 \\in C([0, \\infty) ,  [0, \\infty))$  are increasing functions, differentiable on $[0, r)$ for some $r>0$, $f_1(0) = f_2(0) = 0$, $f_1'(0) = f_2'(0) = 1$, $ \\lim\\limits_{s \\to \\infty} \\frac{f_1(Mf_2(s))}{s} = 0 $ for each $M>0$ ($f_1, f_2$ satisfy a combined sublinear condition at infinity),   $g_1, g_2 \\in C\\big([0, \\infty) , (0, 1]\\big)$ are nonincreasing functions such that $g_1(0)= g_2(0)=1$, and $\\underline{g} := \\min\\left \\{\\lim\\limits_{s \\rightarrow \\infty} g_1(s),\\right.$ $\\left. \\lim\\limits_{s \\rightarrow \\infty} g_2(s)\\right\\} >0$. We discuss the existence of multiple positive solutions for certain ranges of $\\lambda$ leading to the occurrence of $\\Sigma$-shaped bifurcation diagrams. Our results are established via the method of sub-supersolutions.", "id": "Paper/68276", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68276"}, {"title": " Exploring the Impact of Instantaneous Feedback Through Assignments in Excel on Student Perceptions of Learning ", "webprogram_exclude": "0", "session_ids": ["Session/17812"], "source_sha256": "80d04f9167b1afc100313b18aa09dc7590370c863c2f79cb89dbc8beec994983", "withdrawn": "", "abstract": "This session will describe an ongoing study investigating the effects of providing instant feedback through self-grading Excel assignments. The impact on student learning outcomes, engagement, and satisfaction in early mathematics courses is analyzed. We gather student feedback to explore perceptions of how these tools influence their learning and confidence through a mixed-methods analysis. Additionally, we address the challenges of designing and implementing these assessments, offering insights into best practices for integrating technology-driven feedback tools. Preliminary findings suggest that self-grading spreadsheets promote active learning, improving student engagement, self-agency, and confidence. By providing instant feedback on students’ progress, these assessments promote mastery of mathematical concepts by facilitating real-time refinement and revision.", "id": "Paper/68280", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68280"}, {"title": " Convergence of symmetries and Ricci curvature ", "webprogram_exclude": "0", "session_ids": ["Session/18290"], "source_sha256": "8230cda64ea5e0dbe22e17df8e3db515c699bd857ce726f6c2cf52395edf80a7", "withdrawn": "", "abstract": "Equivariant Gromov-Hausdorff (eGH) convergence provides a framework that formalizes the idea of a sequence of groups of isometries acting on a sequence of spaces $(X_n)_n$ converging to a group of isometries acting on a limit space $X$. eGH has found several applications in the study of spaces with lower sectional and Ricci curvature bounds. In this presentation, we will discuss the  behavior of some algebraic and topological properties of Lie groups under eGH convergence.", "id": "Paper/68283", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68283"}, {"title": " Solutions to the forward and backward equations for some special queueing systems with q-step size transitions ", "webprogram_exclude": "0", "session_ids": ["Session/18343"], "source_sha256": "cad4e8a263e9338d96951abbbe7cadf776362937e5b6d6a7e29e68e15a91fde4", "withdrawn": "", "abstract": "We consider systems with banded matrices $A$ that have three diagonals with no zero entries: one along the main diagonal and the other two in the $\\it{qth}$ super and subdiagonal.  We show that these systems are diagonalizable and we use the diagonalization to obtain formulas for the matrix exponential $e^{At}$. These formulas provide a closed-form solution to queueing systems with $q$-step size transitions that have a transition matrix $A$.", "id": "Paper/68286", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68286"}, {"title": " Superconvergent projection methods for fourth order nonlinear Volterra-Hammerstein integro-differential equations ", "webprogram_exclude": "0", "session_ids": ["Session/19336"], "source_sha256": "d5fa68505f460c5f60048f483f0b18c449a0b63bf6ef206ab19b451ab2084734", "withdrawn": "", "abstract": "In this article, we find the approximate solution of the fourth order nonlinear Volterra–Hammerstein integro-differential equations employing Kumar-Sloan technique based Galerkin and collocation methods with piecewise polynomial as basis functions. The nonlinear kernel term present in the given equation involves derivatives of the unknown function up to the third order. Superconvergence rates are obtained in the proposed methods without resorting to the iterated versions of the traditional Galerkin and collocation methods. Additionally, the identical superconvergence results are derived for the derivatives of the approximate solution up to third order. Compared to traditional projection methods, the technique discussed is shown to be computationally more efficient as well. Finally, numerical experiments are presented to support the theoretical results.", "id": "Paper/68288", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68288"}, {"title": " The Bi-UFS Positive Conjecture for Algebraic Semidomains ", "webprogram_exclude": "0", "session_ids": ["Session/18240"], "source_sha256": "0cb500820d7847c2f1f549aa3b479974e341f9be3d3310257fef58a2344718b7", "withdrawn": "", "abstract": "A semidomain is called \\emph{bi-UFS} if both its additive monoid and its nonzero multiplicative monoid are unique factorization monoids. The \\emph{Bi-UFS Positive Conjecture} predicts that the only positive semidomain with this property is $\\mathbb{N}_0$. We prove this conjecture for finitely generated algebraic positive semidomains. In the cyclic case, we show that for every positive algebraic number $\\alpha$, the semidomain $\\mathbb{N}_0[\\alpha]$ is bi-UFS if and only if $\\alpha \\in \\mathbb{N}$, equivalently $\\mathbb{N}_0[\\alpha]=\\mathbb{N}_0$. The proof separates the quadratic case, where an analysis of the least additive atom larger than $1$ leaves only the examples $\\mathbb{N}_0[\\sqrt 2]$ and $\\mathbb{N}_0[(1+\\sqrt 5)/2]$ to exclude, from the higher-degree case, where explicit multiplicative identities force the minimal polynomial into impossible forms. We then give a Perron--Frobenius argument showing that if $\\alpha_1,\\ldots,\\alpha_n$ are positive algebraic numbers and $\\mathbb{N}_0[\\alpha_1,\\ldots,\\alpha_n]$ is bi-UFS then this semidomain is $\\mathbb{N}_0$. Finally we prove a reduction theorem for complex semidomains: every bi-UFS subsemidomain of $\\mathbb{C}$ that is not a UFD and has finitely many additive atoms is isomorphic to a positive semidomain. Consequently, every finitely generated algebraic bi-UFS semidomain over $\\mathbb{C}$ is either an integral domain or isomorphic to $\\mathbb{N}_0$.", "id": "Paper/68289", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68289"}, {"title": " Creating content for social media on advanced math topics ", "webprogram_exclude": "0", "session_ids": ["Session/18074"], "source_sha256": "5e17c088185b4dee9978fd52380c1c2796b2d58d8a04259a44a1443638398ac3", "withdrawn": "", "abstract": "In this talk I will talk about my process to create content for social media on (sometimes advanced) math topics. I will try to describe in detail the entire process, from ideation, planning, recording and editing. Then, I will also discuss what works and what does not work, and if time permits, we can discuss why share math in this format.", "id": "Paper/68293", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68293"}, {"title": " Solutions to the NLS with higher order dispersion ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "4ea4f9bba22eb8442d8650f9d1157577f26a38105e2221cdbd4ab673068fde6d", "withdrawn": "", "abstract": "We study a {\\it higher order} dispersion nonlinear Schr\\\"{o}dinger (NLS) equation with the $k$-Laplacian $(-\\Delta)^{k}$, and the potential term  expressed as a power nonlinearity (for any positive power). When $k=1$ we recover the NLS with a standard Laplacian and when $k=2$ we get the bi-harmonic NLS. We investigate local well-posedness of solutions to this higher order NLS equation on a subset of a Sobolev space by constructing a weighted space with polynomial weights. \nFurthermore, we numerically study the behavior of solution for different parameters of dispersion.", "id": "Paper/68299", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68299"}, {"title": " Skew-symmetric factorization varieties ", "webprogram_exclude": "0", "session_ids": ["Session/18356"], "source_sha256": "e621ffa7948f282bbfb245d400a4761590b40cb371133fb969512f3578425119", "withdrawn": "", "abstract": "We study skew-symmetric factorization varieties, obtained as closures of sets of square matrices expressible as products of skew-symmetric matrices, from the perspective of a computer-assisted proof. We use numerical and symbolic computations to detect symmetries on the varieties and interpolate low-degree defining equations. These computations do more than provide evidence: the structure visible in the output suggests general descriptions of the varieties and provides proof strategies that are difficult to see a priori. In particular, we give a set-theoretic description of all skew-symmetric factorization varieties by explicit equations. Also, we derive an intersection-theoretic formula for their degrees. This talk is based on a joint work with Jeong-Hoon Ju.", "id": "Paper/68301", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68301"}, {"title": " Lieb–Robinson Bounds in the Continuum and the Infinite-Volume Limit ", "webprogram_exclude": "0", "session_ids": ["Session/17925"], "source_sha256": "ef0c809a19f0498082986fd969fc82a2b26e40c1d5bb41c5238e83c1be2ad685", "withdrawn": "", "abstract": "Lieb–Robinson bounds constrain the propagation of particles or information in non-relativistic quantum many-body systems. They have primarily been established for lattice systems with finite-dimensional local Hilbert spaces and bounded interactions. Systems in the continuum fall outside this framework and are considerably more difficult to treat. In this talk, I will first discuss Lieb–Robinson bounds and their applications to continuum fermions with regularized pair interactions, based on joint work with B. Hinrichs and M. Lemm. I will then focus on the infinite-volume limit and present a general no-go result concerning strong continuity of the dynamics and invariance of the CAR algebra when the regularization is removed. Finally, I will discuss the implications for future work.", "id": "Paper/68303", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68303"}, {"title": " Inverse Problems for Costs and Controls in LQG MFGs via Mean Field Trajectories ", "webprogram_exclude": "0", "session_ids": ["Session/17781"], "source_sha256": "8cc241d93b3da68dcc607a7561ac26ed00c3653413de2d4ca8d8709981b0af46", "withdrawn": "", "abstract": "This work investigates inverse problems for Linear-Quadratic-Gaussian (LQG) Mean Field Games (MFGs) based entirely on the observation of mean-covariance trajectories. We address three sequential challenges: identifying the optimal control for observed initializations, determining the control for arbitrary initializations, and recovering consistent cost parameters. After establishing the existence and uniqueness of the forward Nash equilibrium under mild hypotheses, we analyze the injectivity of the parameter-to-trajectory mapping, demonstrating that it is inherently non-injective and providing sufficient conditions for parameter equivalence. We prove that while the optimal control is locally identifiable for observed initializations under minimal assumptions, global identifiability requires a deeper structural recovery of the game's costs. To bridge this gap, we propose a constructive semidefinite programming method to infer cost parameters that are strictly consistent with the observed population dynamics. Numerical experiments illustrate this method. This talk is based on: arxiv:2606.09302 (CDC'26).", "id": "Paper/68305", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68305"}, {"title": " A Unified Approximation Analysis for Controlled Interacting Particles and McKean-Vlasov Limit in Discrete-Time and Continuous-Time ", "webprogram_exclude": "0", "session_ids": ["Session/18274"], "source_sha256": "8f1bca1d8605a0a247efce4468b50912be8c3dd845a891ff47fca6ca97199262", "withdrawn": "", "abstract": "We study stochastic exchangeable teams with a finite number of agents and their mean-field limit with infinitely many agents in both discrete-time and continuous-time. (i) In discrete-time, we show that a sequence of exchangeable optimal policies for finite population settings (which satisfies a measure valued MDP formulation due to [Bauerle'23]) converges to a decentralized symmetric and conditionally independent (given the mean-field) policy for the infinite population problem, which is then globally optimal under both the centralized as well as the mean-field sharing decentralized information structure. This result  proves the optimality of the limiting measure-valued MDP (or equivalently McKean-Vlasov) control for a representative agent without an apriori restriction of symmetry in policies of individual agents. (ii) In continuous-time, for the McKean-Vlasov limit, by establishing continuity of the cost in control policy, we prove near-optimality of piecewise-constant policies, show that the discrete-time value functions (finite-horizon and discounted infinite-horizon) converge to their continuous-time counterparts as the time-step converges to zero, and that optimal discrete-time policies are near-optimal for the McKean-Vlasov problem. (iii) We then extend these approximation results to $N$-particle interacting systems under centralized or decentralized mean-field sharing information structure, proving that the obtained discrete-time McKean-Vlasov policy is asymptotically optimal as $N\\to \\infty$ and the time step goes to zero. Using discrete-time approximation as an intermediate step leads to complementary conditions to those in the literature (notably, due to [Lacker'17]). (iv) We thus develop a unified approximation framework for McKean-Vlasov optimal control problems via discrete-time McKean-Vlasov control (and associated numerical methods such as finite model approximations), and also show near optimality of such approximate policy solutions for the $N$-agent interacting model under centralized and decentralized control and in both discrete-time and continuous-time. Recent work studies extensions to multi-population models. [Joint work with Somnath Pradhan, Sina Sanjari, Naci Saldi, Connor Braun].", "id": "Paper/68306", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68306"}, {"title": " Mathematical foundations exposed the challenges of AI in materials discovery ", "webprogram_exclude": "0", "session_ids": ["Session/18272"], "source_sha256": "3efb31d5ac3bb50a46b42e65ab32f14e6f22765a5cec42f96807e287a4e62f74", "withdrawn": "", "abstract": "In November 2023, Google DeepMind reported in Nature the AI-generated database GNoME of simulated materials and claimed \"2.2 million new crystals – equivalent to nearly 800 years’ worth of knowledge\", quoted from https://deepmind.google/blog/millions-of-new-materials-discovered-with-deep-learning.\n\nIn June 2024, we reported thousands of exact duplicates in GNoME [1, Table 1], and many more near-duplicates. The underlying confusion arises from the fact that materials chemistry had no mathematical foundations. Indeed, any periodic crystal can be represented in infinitely many different ways, and conventional representations with reduced cells discontinuously change under almost any perturbation. \n\nThis ambiguity was resolved by a new mathematical definition of a crystal structure as a class of all cell-based representations that are equivalent under rigid motion [1, Definition 6].\n\nWe developed generically complete and continuous invariants that distinguish all non-duplicate periodic crystals in major databases within a few minutes on a modest desktop [2]. \n\nNow any dataset of experimental or simulated crystals can be visualized on maps with continuous and analytically defined invariant coordinates [3]. These invariants can be inverted to any generic periodic structure in 3 dimensions, recently extended to complete invariants under rigid motion with a Lipschitz continuous metric [4].\n\n[1] O.Anosova, V.Kurlin, M.Senechal. The importance of definitions in crystallography. IUCrJ v.11(4), p.453-463 (2024).\n\n[2] D.Widdowson, V.Kurlin.  Pointwise Distance Distributions for detecting near-duplicates in large materials databases. SIAM Journal on Applied Mathematics, v.86(3), p.898-918 (2026).\n\n[3] D.Widdowson, V.Kurlin. Geographic-style maps with a local novelty distance help navigate in the materials space. Scientific Reports v.15, 27588 (2025).\n\n[4] O.Anosova, D.Widdowson, V.Kurlin. Recognition of near-duplicate periodic patterns by continuous metrics with approximation guarantees. Pattern Recognition v.171, 112108 (2026).", "id": "Paper/68308", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68308"}, {"title": " Exceptional Virasoro extensions and the level-three Urod algebra of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.776ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex; margin-left: -0.041ex;\" viewBox=\"-17.5 -791.3 1195.4 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathfrak {sl}_2</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJFRAK-73\" d=\"M272 33Q284 33 290 70T296 138Q296 181 290 198T262 230Q257 232 246 232Q231 232 218 227T156 194L108 167L101 176Q90 192 75 219L69 230V284Q69 346 70 357V377L146 427Q181 450 202 464T223 477L225 476Q227 475 229 474Q231 472 242 466T270 450T296 431Q309 418 326 418Q342 418 361 429T392 450T403 459Q406 445 406 442Q406 440 384 421T338 382L316 363Q315 362 310 362Q292 362 251 371T173 396Q156 403 155 403Q143 386 143 342Q143 305 150 278T168 244Q171 242 181 242L190 243L315 300Q330 295 357 274Q358 273 362 270T366 266T369 261T372 253T373 239T374 217T374 185Q374 157 372 133T368 98T363 71T358 50L336 40Q288 20 255 2T211 -22T198 -29L190 -22Q181 -14 168 -3T138 19T104 38T70 46Q50 46 32 37T3 20T-9 11L-18 23L-1 41Q46 89 62 99T112 110Q141 110 157 103T225 62Q268 33 272 33Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJFRAK-6C\" d=\"M221 76L267 99Q268 98 269 96T271 88T270 82L262 76Q255 69 241 57T214 34L148 -20L98 56L99 89Q107 247 107 373Q107 494 101 621Q101 653 99 659V665L106 668L113 672L118 655Q122 642 131 617L138 597Q140 597 157 611L240 670L264 685Q265 685 270 680T276 674T269 667T247 647T219 617Q197 587 186 551T173 493T171 438Q171 376 175 282T179 147V117Q184 109 201 93T221 76Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJFRAK-73\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJFRAK-6C\" x=\"443\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-32\" x=\"1023\" y=\"-213\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18270"], "source_sha256": "87d7c0809156962e5fee27b7327d88c599903a64c0dd44dc258328b67580c80b", "withdrawn": "", "abstract": "Urod algebras, introduced by Bershtein–Feigin–Litvinov and developed by Arakawa–Creutzig–Feigin, equip the affine vertex algebra $\\mathbb{L}\\ell(\\mathfrak{sl}2)$ with a modified conformal vector. We show $\\ell=3$ is the last level whose Urod algebra splits into two Virasoro minimal models: it contains a conformal copy of $\\mathrm{Vir}_{3,11}\\otimes M^{(0)}$, with $M^{(0)}$ the exceptional $E_8$-type extension of the $(11,30)$ minimal model. Identifying $M^{(0)}$ with the simple principal $W$-algebra of type $G_2$ proves a conjecture of Milas–Penn–Sadowski, and Urod translation yields an infinite family of such extensions. This is joint work with Antun Milas.", "id": "Paper/68310", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68310"}, {"title": " Learning Spectra in Chaos. Transfer Operators on Banach Spaces ", "webprogram_exclude": "0", "session_ids": ["Session/18447"], "source_sha256": "da2a1ece1a328adfda6b9d115ada94bce8a3dd70be1c78793ae3488710c5f34a", "withdrawn": "", "abstract": "In a chaotic dynamical system, asymptotic prediction of individual trajectories is impossible. However, the statistical properties of `generic' trajectories are learnable using a operator-theoretic framework. The spectrum of the transfer operator (or Ruelle-Frobenius-Perron operator) encodes invariant probability densities, mixing rates, and coherent structures in complex systems. Rigorously recovering this information from finite data is challenging. In 1960, Ulam proposed a method for numerically learning the transfer operator, and conjectured that the learned operator converges in spectra. We show that for a wide class of dynamical systems, a modification to Ulam's original scheme converges in an entire range of function spaces, extending beyond the classical $L^1$ setting. In the process, we see what knowledge of which errors is required for general learned operators to converge in spectra.", "id": "Paper/68311", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68311"}, {"title": " Mock Theta Functions: From Appell–Lerch Sums to Hecke-Type Representations ", "webprogram_exclude": "0", "session_ids": ["Session/18333"], "source_sha256": "f44ff250ff469eb62462b0c61b2041d2f67ea8c0a16f4f98ccbeedad3328fbce", "withdrawn": "", "abstract": "Mock theta functions admit useful representations in terms of Appell--Lerch sums. In this talk, I will show how these representations can be transformed into Hecke-type representations for classical mock theta functions of several orders. The main tools are a few quadratic, minus-one, and cubic Appell--Lerch identities, which lead to explicit formulas involving finite inner sums and theta terms. I will also discuss Lambert-series identities for the second-order mock theta functions $A_2(q)$, $B_2(q)$, and $\\mu_2(q)$.", "id": "Paper/68312", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68312"}, {"title": " Regularity and acyclic complexes over arbitrary rings ", "webprogram_exclude": "0", "session_ids": ["Session/18371"], "source_sha256": "d80135277cbeb056290e44f7d371076edc5e7e99ec02e9cec6b8dfb7f325d981", "withdrawn": "", "abstract": "Motivated by classical regularity for noetherian rings and Bertin’s extension to coherent rings, we study $\\mathrm{FP}_{\\infty}$-regularity for arbitrary rings: every left module admitting a resolution by finitely generated projectives has finite projective dimension. Building on earlier work by the presenting author with Lars Winther Christensen and Peder Thompson, and by James Gillespie with Alina Iacob, we characterize this notion using acyclic complexes of level and absolutely clean modules, recovering the coherent case. We also characterize it by the vanishing of an associated singularity category. Finally, we extend Stenström’s characterization of weak global dimension as global right FP-injective dimension for right coherent rings, proving that global right absolutely clean dimension equals global left level dimension over any ring. This is joint work with James Gillespie and Marco A. Pérez.", "id": "Paper/68314", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68314"}, {"title": " DG Algebra Structures on Mapping Cones with an Application to Edge Ideals ", "webprogram_exclude": "0", "session_ids": ["Session/18025"], "source_sha256": "f779e92e890d738742e18e7df1f1f1535fa072e293f493273f0957b79fe93cbb", "withdrawn": "", "abstract": "We generalize a construction of Herzog and Takayama to obtain a  differential graded (dg) algebra structure on the cone of a map between a dg module and a dg algebra.  Under the right conditions, the construction may be applied to compute the minimal free resolutions of ideals \"built from\" complete intersections and of edge ideals of graphs obtained via suspension over a vertex cover.  This is joint work with Hugh Geller, Des Martin, and Matt Mastroeni.", "id": "Paper/68316", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68316"}, {"title": " A Sandwich Slice: Upper and Lower Bounds for the 1-Wasserstein Distance via Optimal Transport Potentials as Generalized Slicers ", "webprogram_exclude": "0", "session_ids": ["Session/17718"], "source_sha256": "7fb13256ab72c11eeb05fcffaa9cf3a1a6e5a1709f42ac4e91368b8f0cfe4a46", "withdrawn": "", "abstract": "We place max-sliced lower bounds and lifted min-sliced upper bounds for the 1-Wasserstein distance within a common framework. For 1-Lipschitz slicers, we show that the resulting \"sandwich\" inequalities collapses to equality precisely when an optimal ambient Kantorovich-Rubinstein potential factors through the slicer via a 1-Lipschitz function. In particular, every optimal Kantorovich-Rubinstein potential, used as a slicer, attains both bounds.", "id": "Paper/68321", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68321"}, {"title": " Bayesian Inversion of a Two-Compartment Transport Model for Dynamic Contrast-Enhanced Ultrasound ", "webprogram_exclude": "0", "session_ids": ["Session/18445"], "source_sha256": "dbb8708fbe71ca2dc69a5d3a2ca064395d65edf642a1e1e784d43153cedb9208", "withdrawn": "", "abstract": "Dynamic contrast-enhanced ultrasound tracks a microbubble contrast agent through tissue and yields spatially and temporally resolved concentration data, from which one would like to recover perfusion parameters. We model the agent by a coupled pair of first-order transport equations for the arterial and venous concentrations, with spatially varying velocity fields and a transfer coefficient linking the two compartments. Only the sum of the two concentrations is measured, so both compartments, both velocity fields, and the transfer field must be inferred from a single observed field, and the inflow boundary data are not directly available.\n\nWe formulate the recovery problem in a Bayesian framework, representing the unknown fields by Gaussian random fields and sampling by sequential tempered MCMC, and report on its behavior on three-dimensional in vivo data. Because only total concentration is observed at the inflow boundary, we describe a diagnostic that partitions it into arterial and venous contributions using time to peak, and state the assumptions this requires. Our main point is that close agreement between simulated and measured total concentration does not certify recovery of the underlying parameters. We discuss synthetic benchmarks with known ground truth and physiologically informed priors including velocity ranges by vessel type, and joint priors coupling transfer and velocity as routes to constraining the problem.", "id": "Paper/68323", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68323"}, {"title": " Efficient Randomized Approximation of Structured Linear Operators without Adjoint Access ", "webprogram_exclude": "0", "session_ids": ["Session/18447"], "source_sha256": "de1c0d3221422982b5b3fbe8ee6aa0f6e778282dc4af46e958794aa1523e94ec", "withdrawn": "", "abstract": "Approximating linear operators, whether finite or infinite dimensional, using only forward queries can be a challenging but common task when access to the adjoint is experimentally unavailable or difficult to construct computationally.   \nWe show that a priori local row space information can be sufficient for provably accurate, query-efficient and adjoint-free operator approximation. \nExisting methods for approximating linear elliptic solution operators with fast convergence rates often either rely on self-adjointness or require access to the adjoint operator, while recent adjoint-free operator learning methods can have prohibitively larger theoretical query complexity requirements.  \nOur approach extends the fixed-sparsity matrix approximation algorithm of [Amsel et al., arXiv, 2024] to the task of approximating a matrix with a structured matrix whose rows lie in prescribed subspaces, providing a general template for exploiting local row-space structure from forward queries alone.\nAs a concrete realization of this framework, we consider a class of Hilbert-Schmidt integral operators whose kernels are asymptotically smooth.\nIn this setting, the row subspaces are constructed using a hierarchical partition together with exponentially convergent separable polynomial approximations on sufficiently separated domains. \nThe resulting algorithm queries the action of the underlying operator on functions with standard Gaussian random coefficients in a finely discretized finite element space, thereby recovering an approximation of the unknown finite element discretization of the operator. \nWhile the number of degrees of freedom in this discretization grows polynomially with the inverse error tolerance, asymptotic smoothness and the hierarchical decomposition of each row ensure that only a polylogarithmic number of queries $\\mathcal{O}(\\text{polylog}(\\varepsilon^{-1}))$ is required to achieve the desired accuracy $\\varepsilon$ with high probability.", "id": "Paper/68324", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68324"}, {"title": " A nonlinear Li-Yau inequality and its consequences ", "webprogram_exclude": "0", "session_ids": ["Session/18050"], "source_sha256": "a5d5e69be6480649514218cf93703421ac1caffd7f26711855fe29ab0772889c", "withdrawn": "", "abstract": "We prove a sharp nonlinear version of the celebrated Li-Yau inequality for positive solutions of the normalized parabolic $p$-Laplacian equation \n\\[\nu_t = \\Delta u + (p-2)|\\nabla u|^{-2}\\nabla^2u(\\nabla u,\\nabla u),\\ \\ \\  1<p<\\infty,\r\n\\]\r\non a closed Riemannian manifold with nonnegative Ricci curvature, the equation being interpreted in the viscosity sense on the critical set of the solution. The constant is best possible, even within the class of closed manifolds: it is attained identically by an explicit self-similar solution in flat $\\Rn$, and its sharpness transfers to the compact setting through a large-torus limit along the flat tori $\\mathbb R^n/(L\\mathbb Z)^n$, $L \\to \\infty$. The proof rests on an exact Bochner-type identity for a family of uniformly parabolic approximating flows in which the second-order regularization and the first-order eikonal term are decoupled: for this family the maximum principle applies with the sharp constant, uniformly in the regularization parameter, and with no assumption on the critical set of the solution. The identity is moreover form-invariant under the classical $\\alpha$-relaxation of the Li-Yau functional; as a consequence we also obtain the corresponding inequality on closed manifolds with $\\operatorname{Ric} \\ge -\\kappa$ (again with no assumption beyond the Ricci lower bound), and, on complete noncompact manifolds with $\\operatorname{Ric} \\ge 0$, the sharp inequality for the approximating flows -- again with no assumption on the critical set -- under a cutoff hypothesis on the distance function (automatic in $\\Rn$, and, for $p \\ge 2$, under nonnegative sectional curvature) and a qualitative polynomial growth condition on the Li-Yau quantity, satisfied, with exponent zero, by the extremal profile. A sharp global Harnack inequality follows. Joint work with Agnid Banerjee and Hamidreza Mahmoudian.", "id": "Paper/68325", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68325"}, {"title": " Infinite-Horizon Optimal Control of Jump-Diffusion Models for Pollution-Dependent Disasters ", "webprogram_exclude": "0", "session_ids": ["Session/17471"], "source_sha256": "1cc074377fe10b619183782da3b2cbaa82eeb00ca9bb66a4a88151aa2699a7ba", "withdrawn": "", "abstract": "This paper develops a unified framework for stochastic growth models with environmental risk, in which rare but catastrophic shocks interact with capital accumulation and pollution. The analysis is based on a Poisson point process, yielding non-local Hamilton–Jacobi–Bellman equations with closed-form solutions and a composite state variable measuring exposure to rare shocks. Disaster risk is endogenized through pollution-dependent intensity and extended to state-dependent events of varying magnitude. The framework shows how environmental degradation amplifies macroeconomic vulnerability and strengthens abatement incentives. Technically, it delivers tractable jump-diffusion control problems whose HJB equation decomposes into capital and pollution components under a power-type value function. This is a joint work with Daria Sakhanda (ETH Zürich).", "id": "Paper/68327", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68327"}, {"title": " Nonlinear stability of continuously self-similar naked singularities for the Einstein-scalar field equations ", "webprogram_exclude": "0", "session_ids": ["Session/18148"], "source_sha256": "09b2ef1ba8f4c63f9aecab8771601985e7ff72832fcc3d1125645504168cadc7", "withdrawn": "", "abstract": "As part of the Weak Cosmic Censorship (WCC) conjecture, it has long been speculated by physicists that naked singularity solutions to the Einstein equations should not exist. However, the construction of a family of continuously self-similar naked singularity spacetimes by Christodoulou for the Einstein-scalar field equations drastically changes the paradigm. Nonetheless, it has been shown that these naked singularity solutions are unstable to some rough perturbations, thus non-generic within this class of rough solutions. In complete contrast, in a recent work with Singh, we prove that there exists an open set of the initial data leading to naked singularities in a localized Hölder class, therefore falsifying the WCC conjecture for the Einstein-scalar field equation in this function class. Our work showcases that the precise formulation of the WCC conjecture is open to debate.", "id": "Paper/68328", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68328"}, {"title": " Light cone bounds for a class of bosonic Hamiltonians ", "webprogram_exclude": "0", "session_ids": ["Session/18296"], "source_sha256": "fac774bcabb5677c58913f9b3ada319dfc90aebe4713f645867d68f7beb76080", "withdrawn": "", "abstract": "A fundamental result in quantum spin systems is the finite speed of information propagation: the Heisenberg time evolution of a local observable stays mostly confined within a linearly expanding ball defined by the Lieb-Robinson velocity. Standard derivations fail for lattice bosonic models like Bose-Hubbard Hamiltonians due to unbounded local energies, making rigorous propagation bounds challenging. In this talk, we present the recent progress on this problem.", "id": "Paper/68331", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68331"}, {"title": " Data-driven methods for protein folding prediction ", "webprogram_exclude": "0", "session_ids": ["Session/18358"], "source_sha256": "a0d365ba8d5e6a3534e2edb238f6643017a19496dc7fb438d0842d160f069431", "withdrawn": "", "abstract": "Two authors of Google's computer program AlphaFold2 received  the Nobel Prize in  Chemistry  2024. This program uses a data-driven approach to protein folding prediction by training on the Protein Data Bank (PDB).\n\nThe PDB contains 260K+ proteins whose structures were computationally predicted by fitting geometric embeddings of atoms to noisy electron densities, which are scalar functions on a 3-dimensional space.  \n\nThe CASP (Critical Assessment of Structure Prediction) compares structures that are computationally generated only from a sequence of amino acids with structures that are partially based on limited experimental data, such as X-ray diffraction patterns, like in the PDB. These comparisons use distances that fail the triangle inequality (and often symmetry), which makes clustering outputs unreliable [1].\n\nA mathematical classification of protein chains under rigid motion by complete, bi-Lipschitz , and linear-time invariants [2] detected thousands of unexpected duplicate chains, many of which raised concerns of data integrity and were confirmed by some authors [3].  This invariant-based approach has been extended to all real data in the emerging area of Geometric Data Science [4, Problem 1.4.5].\n\nMore recently, a rigorous analysis of the PDB and AlphaFold2 (latest version 6) datasets detected numerous violations of the expected geometry in chemical bond lengths and angles, as well as clashes of atoms whose positions  were predicted to be too close. Structural biologists define a serious clash between non-bonded atoms if their distance is less than the sum of van der Waals radius minus 0.4 Angstroms, which is about 40% of the smallest interatomic distance.  \n\n[1] S.Rass et al. Metricizing the Euclidean space toward desired distance relations in point clouds. Trans. Information Forensics and Security v.19, p.7304-7319 (2024).\n\n[2] O.Anosova et al. A complete and bi-continuous invariant of protein backbones under rigid motion.  MATCH Comm. Math. Comp. Chemistry, v.94(1), p.97-134 (2025).\n\n[3] A.Wlodawer et al. Duplicate entries in the Protein Data Bank: how to detect and handle them. Acta Crystallographica D, v.81(4), p.170-180 (2025).\n\n[4] O.Anosova, V.Kurlin. Geometric Data Science (290+ pages), arxiv:2512:05040, latest version at https://kurlin.org/Geometric-Data-Science-book.pdf.", "id": "Paper/68333", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68333"}, {"title": " Seifert algorithm for null-homologous links in 3-manifolds ", "webprogram_exclude": "0", "session_ids": ["Session/18087"], "source_sha256": "06544be7815c8b2bbf7ca61187d5a7d106bbaf5a744f092ca0da8a436f2e30fa", "withdrawn": "", "abstract": "The classical Seifert algorithm provides an explicit construction of a Seifert surface for any link in $S^3$. Alegria and Menasco extended this construction to integral homology $3$-spheres using Heegaard diagrams. However, the $2$-dimensional Heegaard diagrams make it impossible to visualize entire links together with their Seifert surfaces simultaneously, so explicit computations of knot invariants are challenging. We extend the Seifert algorithm to null-homologous knots in arbitrary $3$-manifolds via surgery on framed links in $S^3$. Our construction allows us to encode entire links and their Seifert surfaces in the complement of the corresponding framed link, overcoming the limitations of Heegaard diagrams. As applications, we obtain a linking number formula between null-homologous links in arbitrary $3$-manifolds and compute several knot invariants, including the Alexander polynomial, knot signature, and knot genus, and describe how to construct surgery diagrams for integral surgery on null-homologous knots in arbitrary $3$-manifolds.", "id": "Paper/68334", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68334"}, {"title": " Structure and Metabolism in P. aeruginosa Biofilms ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "179f5a41f3c1a53cad072146848d4e3e6276347f6cdeb1b7e9c482f90da5973f", "withdrawn": "", "abstract": "Pseudomonas aeruginosa is a ubiquitous bacterium, capable of forming antibiotic-resistant biofilms that colonize medical equipment and implants, causing a significant fraction of hospital acquired infections. Recently, P. aeruginosa biofilms have been shown to develop regions of vertical nematic order, concurrent with changes in metabolic activity. This observed nematic order is sensitive to nutrient availability, and changes dramatically for P. aeruginosa with mutations to intracellular signaling pathways or outer membrane morphology. How this biofilm microstructure impacts resource availability and, consequentially, metabolic activity is not well understood.  To address this question, we  model resource concentrations as a coupled system of nonlinear reaction-diffusion equations at steady state with unknown spatially varying diffusivity and Hill-type uptake kinetics. Using an inverse problem approach, we infer underlying nutrient concentrations from experimentally measured metabolic activity, hence determining how diffusivity must vary in space to reproduce the observations. Comparing inferred diffusivity with biofilm structure, we find that higher effective diffusivity in ordered regions improves oxygen availability in the biofilm, supporting increased metabolic activity. This work has broad implications regarding how bacteria can control their global collective nutrient uptake–or, conversely, their antibiotic intake–by local modulation of the biofilm microarchitecture.", "id": "Paper/68336", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68336"}, {"title": " Coamenability and Strong Ergodicity: II<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.875ex\" height=\"1.343ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -289 807.5 578.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">_\\infty</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-221E\" x=\"0\" y=\"-213\"></use>\n</g>\n</svg> and Beyond ", "webprogram_exclude": "0", "session_ids": ["Session/18383"], "source_sha256": "3ac1aaa677e16337db407f603c5e67e529664292c041190f3fe02ff260bc9684", "withdrawn": "", "abstract": "Recently, Ben Hayes showed that if $\\mathcal{S} \\subset \\mathcal{R}$ is a coamenable inclusion of ergodic, probability measure preserving (p.m.p.) equivalence relations, then $\\mathcal{S}$ is strongly ergodic if and only if $\\mathcal{R}$ is. We generalize this result to the non-p.m.p. case. We highlight the nuances of passing to the \"non-tracial\" setting.", "id": "Paper/68338", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68338"}, {"title": " On Hausdorff dimension of pinned configuration sets via Fourier Integral Operators ", "webprogram_exclude": "0", "session_ids": ["Session/17815"], "source_sha256": "892c9b0860fbc2bf25a678a5a79728c7f95ec732cc5492b2b976cd970bd159db", "withdrawn": "", "abstract": "Let $\\Phi\\times Y\\to\\mathbb{R}^p$ be a smooth two-point configuration map, where $X\\subset\\mathbb{R}^{d_X}$ and $Y\\subset\\mathbb{R}^{d_Y}$ are open sets. Assuming that the family of generalized Radon transforms associated with $\\Phi$ satisfies an $L^2$-based Sobolev estimate with smoothing order $\\alpha_\\Phi>0$, we study pinned configuration sets\n$$\n\\Delta_\\Phi^y(A):=\\{\\Phi(x,y)\\in A\\}\n$$\nfor compact sets $A\\subset X$ and $B\\subset Y$. We show that if\n$\\dim_H A+\\dim_H B>d_X+d_Y-2\\alpha_\\Phi,$\nthen there exists $y\\in B$ such that $\\Delta_\\Phi^y(A)$ has positive $p$-dimensional Lebesgue measure. This generalizes the pinned Falconer distance set problem to a broad class of mappings.\n\nIf, more strongly,\n$\\dim_H A+\\dim_H B>d_X+d_Y-2\\alpha_\\Phi+p$, \nthen $\\Delta_\\Phi^y(A)$ contains a nonempty open ball for some $y\\in B$.\n\nWe also obtain Hausdorff-dimension estimates for the corresponding fibers\n\\[\n\\{x\\in A:\\Phi(x,y)=t\\}\n\\]\nand bounds for the Hausdorff dimension of exceptional sets of pins. The method is based on the Fourier integral operators approach introduced by Greenleaf, Iosevich, and Taylor. Our results apply to several nontransverse families of projections for which the standard Peres-Schlag transversality condition fails.\n\nThis is joint work with A. Greenleaf, E. Palsson, and G. Psaromiligkos", "id": "Paper/68341", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68341"}, {"title": " Support for modules and bimodules ", "webprogram_exclude": "0", "session_ids": ["Session/17949"], "source_sha256": "e2ad6a97870a5061c36d0ea90df2818e6df609c6820a8ad0a912c1ddb7883aa6", "withdrawn": "", "abstract": "We will discuss two types of topological spaces associated to modules and to bimodules for some types of rings, namely the Balmer support and the cohomological support. These spaces are important tools for understanding the structure of categories of modules and bimodules, and are understood best in classical settings such as finite group representations. We will present some results for the bimodule setting in particular.", "id": "Paper/68342", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68342"}, {"title": " Machine Computation of the Slice Spectral Sequence of a <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.716ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 1169.4 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">C_8</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-43\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-43\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-38\" x=\"1011\" y=\"-213\"></use>\n</g>\n</svg>-equivariant height-4 Lubin-Tate theory ", "webprogram_exclude": "0", "session_ids": ["Session/17701"], "source_sha256": "9b3f970ed915d8f1ad72e8bedc9fa189711a2642362c962e40bb0522212f490c", "withdrawn": "", "abstract": "In 2009, Hill, Hopkins, and Ravenel resolved the celebrated Kervaire invariant one problem in all dimensions except 126. Their proof uses equivariant homotopy theory and the slice spectral sequence to establish Detection, Periodicity, and Gap Theorems for a spectrum constructed from \\(MU^{((C_8))}\\), ruling out Kervaire invariant one elements in dimensions greater than 126. A complete computation of the \\(C_8\\)-equivariant homotopy groups of \\(MU^{((C_8))}\\) remains open. Moreover, the precise Adams differentials supported by the higher Kervaire classes \\(h_j^2\\), for \\(j\\geq 7\\), remain unknown. \n\nIn this talk, I will briefly review this history and present work in progress on a machine computation of the slice spectral sequence for truncated \\(BP^{((C_8))}\\), toward determining its \\(C_8\\)-equivariant homotopy groups. This project combines established mathematics with code developed collaboratively by humans and AI to manage the large amounts of data arising in the computation. This is joint with Zhipeng Duan, Guchuan Li, Xiaolin Danny Shi, Zhouli Xu, Yu Zhang, and Foling Zou.", "id": "Paper/68355", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68355"}, {"title": " Product and Quotient Set Dominance in Finite Groups ", "webprogram_exclude": "0", "session_ids": ["Session/19362"], "source_sha256": "86b6ea0d6280868c5f29d20383aa24f3cb95560c76ec37c0141a96586e2fbcb1", "withdrawn": "", "abstract": "A classic problem in additive number theory asks whether a given subset of integers has more sums or differences. This inquiry naturally extends to finite groups, where one compares the sizes of the product set $AA$ and the quotient set $AA^{-1}$ for a subset $A \\subseteq G$. A finite group is considered product-dominant if it contains a higher proportion of subsets where $|AA| > |AA^{-1}|$, and quotient-dominant if the reverse is true. In this paper, we establish statistical criteria to determine the dominance behavior of large finite groups by analyzing the moments of the random variable $d(A) := |AA| - |AA^{-1}|$. By translating product and quotient relationships into graph-theoretic constructions, we compute these moments through counting independent sets.  Our main result demonstrates that for a growing sequence of finite groups $G_k$ with center size $Z_k$ and involution count $T_k$, the condition $Z_k = o(T_k)$ implies the groups are eventually product-dominant. Conversely, if $T_k \\cdot \\sqrt{3}^{R_k/Z_k} = o(Z_k)$ (where $R_k$ denotes the number of elements whose square is central), the groups are eventually quotient-dominant. Using these asymptotic conditions, we resolve the Miller-Vissuet conjecture by proving that all dihedral groups $D_n$ for $n \\geq 3$ are product-dominant. Furthermore, we classify the dominance behavior of several major families of groups, proving that symmetric groups and non-abelian finite simple groups are product-dominant, while groups of odd order and certain abelian groups are quotient-dominant. Finally, for groups that fall outside our asymptotic conditions, we derive an explicit formula for the first moment utilizing the irreducible characters and conjugacy classes of the group.", "id": "Paper/68358", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68358"}, {"title": " Biological functions and functional modules originated in structure of chemical reaction network ", "webprogram_exclude": "0", "session_ids": ["Session/18257"], "source_sha256": "7210708ff7fe4c0753e5a0c90d93e59c2e53bf9cd4cc288fa476abc2e9423b8e", "withdrawn": "", "abstract": "In living cells, numerous chemical reactions are interconnected by sharing substrates and products, forming a reaction network. Various functions of cells emerge from dynamics of such interconnected system. Cells regulate amount of key chemicals by controlling amount/activity of enzymes, thereby achieving control of cellular functions. However, in such an interconnected system, can different chemicals responsible for different biological functions be controlled independently? We mathematically demonstrate that “modularity”, where parts of a system are controlled independently of others, arises solely from network topology. We found that the qualitative response of chemical concentrations to changes in enzyme amount/activity are localized to finite ranges in a network, and each range is determined by a subnetwork called a “buffering structure”, that is defined by the equation $\\lambda≔-$(# of chemicals)$+$(# of reactions)$-$(# of cycles)$+$(# of conserved quantities)$=0$ from local topology of a network. Using the cell cycle system as an example, we show that buffering structures actually exist in living organisms, performing important roles. In the cell cycle, the G1-S and G2-M transitions are strictly controlled by distinct protein complexes, requiring the activation of different complexes at different phases. Analysis of the cell cycle network revealed that the two complexes belong to different buffering structures. Moreover, by comparing theoretical predictions with experimental verification, we theoretically predict the necessity of an unknown reaction and experimentally confirm it.", "id": "Paper/68359", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68359"}, {"title": " Duality of Convex Bifunctions ", "webprogram_exclude": "0", "session_ids": ["Session/18069"], "source_sha256": "961f5dd579e995aaa1731fbd5976c8d882227b3522bdab9c838a974d8861b79c", "withdrawn": "", "abstract": "Optimization problems with different cost structures in different regions arise in optimal control, path planning, transportation, and models of motion through heterogeneous media. A representative example is the Elvis problem, in which an optimal path passes through regions separated by an interface. The location at which the path meets the interface must be determined together with the motion occurring within each region.\nThis work introduces a convex-analytic formulation of such problems using convex bifunctions obtained from perspective transformations. These bifunctions provide a unified way to represent the relationship between the displacement of a path and the parameter governing its scale or duration. The regional costs and the interface constraint can then be incorporated into a single convex optimization framework.\n\nParticular attention is given to the duality theory associated with this formulation. Fenchel conjugacy and perturbation methods are used to obtain a dual representation of the problem and to investigate conditions under which the primal and dual values agree. The resulting framework also provides a systematic description of optimality, existence, and sensitivity with respect to perturbations of the original data.\nThe geometric structure of the problem is reflected in the interaction between the regional costs and the interface constraint. This interaction leads to a generalized balance condition at an optimal interface point. In smooth cases, the condition is related to familiar refraction principles, while the convex formulation continues to apply when the regional costs or the interface are nonsmooth.\n\nThe approach provides a general framework for studying optimization problems with piecewise convex costs and intermediate constraints. Although motivated by the Elvis problem, the results are applicable to a broader class of interface and piecewise optimal-control problems.", "id": "Paper/68361", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68361"}, {"title": " Dynamics for complex quadratic networks, templates and mutations ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "604248bd0a1d8ac1d04e247a73cf762c9a3cdf55dc43e75afbc21843d0842477", "withdrawn": "", "abstract": "Over nearly a century, the discrete dynamics of single iterated maps in the complex plane have developed into a rich and mature research field. Among the best studied examples is the family of quadratic polynomials, whose complex iterations provide classical constructions of fractal asymptotic sets. These systems therefore form a mathematically simple yet extraordinarily rich class of examples, one that has nonetheless seen surprisingly limited use in the modeling of natural phenomena.\n\nWe explore three novel directions that extend the classical theory of complex quadratic iterations: (1) to interactive networks, (2) to random iterations, and (3) to perturbations and mutations. Each direction is aimed at addressing, within a unified and canonical framework, a fundamental open problem in neuroscience and medicine. In all three settings, the systems exhibit nontrivial long-term dynamics that can be described by asymptotic sets -- Mandelbrot and Julia sets -- with distinctive topological signatures and properties that go well beyond those arising in single-map iteration. Understanding the complexity of these sets requires a combined analytical and computational approach. We will investigate several of these problems and highlight their relevance through applications to neural networks and broader open questions in neuroscience.", "id": "Paper/68365", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68365"}, {"title": " The Ungar Games ", "webprogram_exclude": "0", "session_ids": ["Session/18286"], "source_sha256": "021674b7d145c754382a90938604e53aeaf3d896c52c16632b7300e0fc809d35", "withdrawn": "", "abstract": "Let $L$ be a finite lattice. Inspired by Ungar's solution to the famous \\emph{slopes problem}, we define an \\emph{Ungar move} to be an operation that sends an element $x\\in L$ to the meet of $\\{x\\}\\cup T$, where $T$ is a subset of the set of elements covered by $x$. We introduce the following \\emph{Ungar game}. Starting at the top element of $L$, two players---Atniss and Eeta---take turns making nontrivial Ungar moves; the first player who cannot do so loses the game.  Atniss plays first.  We say $L$ is an \\emph{Atniss win} (respectively, \\emph{Eeta win}) if Atniss (respectively, Eeta) has a winning strategy in the Ungar game on $L$. This talk will discuss the enumeration of Eeta wins in various lattices of interest.", "id": "Paper/68366", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68366"}, {"title": " Algebraic foundations of plane hyperbolic geometry ", "webprogram_exclude": "0", "session_ids": ["Session/19352"], "source_sha256": "3c7214202f80452f55201d049628f5312c4bc2fc36de41bb160b6167bbc1f336", "withdrawn": "", "abstract": "In this talk we establish a connection between the algebraic foundation of hyperbolic coordinate geometry and the axioms of Hilbert for Hyperbolic plane geometry. This connection comes about by extending the Appendix to Chapter 1 in Luther Eisenhart textbook Coordinate Geometry to hyperbolic geometry. The Appendix is extended by replacing the Euclidean formulas with their corresponding ones from hyperbolic geometry. These formulas carry over easy to hyperbolic geometry, but not all. One such formula is the one that is equivalent to the hyperbolic parallel axiom.", "id": "Paper/68367", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68367"}, {"title": " Some recent progress on long-term average impulse and singular control problems ", "webprogram_exclude": "0", "session_ids": ["Session/18293"], "source_sha256": "a28abce9bd58b1a6aefaa54f68ef326130df6458c49abf74782c65636be182d9", "withdrawn": "", "abstract": "This work analyzes and explicitly solves a class of long-term average impulse control problems and a related class of singular control problems. The underlying process is a general one-dimensional diffusion with appropriate boundary behavior. The model is motivated by applications such as the optimal long-term management of renewable resources and financial portfolio management. The goal is  to maximize the long-term average reward, consisting of a running reward and income from either discrete impulses or singular actions. In addition to the long-term average objective, we will briefly consider the long-term expected total reward functional and its relation to overtaking optimality. Key connections between the impulse and singular control problems are displayed. \n\nThe related ergodic impulse control problem with mean-field interaction is also discussed. In particular, we establish the existence of and explicitly characterize an equilibrium strategy within a large class of policies under mild conditions.  The mean field control problem, in which agents cooperate with each other, aiming to realize a common maximal long-term average profit, is formulated and solved.", "id": "Paper/68368", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68368"}, {"title": " Optimization-based Limiting for Invariant-domain-preserving High-order Schemes in Compressible Flow Simulations ", "webprogram_exclude": "0", "session_ids": ["Session/18444"], "source_sha256": "0bdb3c41ea1bd2a1dcbd929476d4cabff3825508b726c10106eb9bd055bc9d0c", "withdrawn": "", "abstract": "Numerical methods for compressible flow simulations must simultaneously achieve high-order accuracy and global conservation while preserving physically admissible states, particularly in the presence of strong shocks and low density/pressure regions. In this talk, we present an optimization-based limiting framework for constructing high-order schemes that preserve invariant domains and global conservation. The limiting procedure is formulated as a constrained optimization problem, with an explicit and efficient projection onto the admissible set as a key ingredient. Douglas-Rachford and Davis-Yin splitting methods are then employed to efficiently solve the resulting global minimization problem. The framework is broadly applicable to high-order discretizations of compressible flow equations and naturally incorporated into discontinuous Galerkin methods while maintaining high-order accuracy. We demonstrate the effectiveness and robustness of the $\\ell^2$- and $\\ell^1$-based optimization limiters through numerical experiments for challenging benchmarks. We also briefly discuss a recent extension of the framework to ideal magnetohydrodynamics, where the projection onto the MHD admissible set can be reduced to an efficient one-dimensional minimization problem.", "id": "Paper/68369", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68369"}, {"title": " Interpreting small models ", "webprogram_exclude": "0", "session_ids": ["Session/17705"], "source_sha256": "91054daedadb74584cf826ad9e07bcfe6c89aad1ff9c23c45001e6c396ad2e04", "withdrawn": "", "abstract": "Several years of effort by mechanistic interpretability researchers have made neural networks and language models somewhat interpretable. Still, the field is far behind: we are nowhere close to fully interpreting language models with millions of parameters, let alone frontier-scale foundation models. We follow the Alignment Research Center's recently proposed matching-sampling principle and present work on reverse engineering RNNs and transformers that solve algorithmic tasks.", "id": "Paper/68370", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68370"}, {"title": " Randomized Sketching for Practical Large-Scale Tucker Tensor Arithmetic ", "webprogram_exclude": "0", "session_ids": ["Session/17849"], "source_sha256": "62887db8d6057d7f29918342fd4a351239e2fb2b124c44c92693613927721f63", "withdrawn": "", "abstract": "Adding tensors stored in Tucker format is a fundamental operation in scientific computing, arising naturally in PDE solvers, uncertainty quantification, and data-driven modeling. However, naive approaches suffer from rapid rank growth and exploding memory costs. In this talk, I will present a sketching-based framework that performs compressed arithmetic directly on the factor matrices and core tensors, avoiding the formation of large intermediates while controlling rank and preserving accuracy. By exploiting the algebraic structure of Khatri-Rao and Kronecker products, the method achieves substantial computational savings over direct summation and recompression. I will discuss the computational complexity of the approach and illustrate its effectiveness on problems including a parameter-dependent elliptic PDE solved via GMRES and a linear transport equation discretized with high-order discontinuous Galerkin methods. This talk will be mainly focused on this manuscript: https://arxiv.org/pdf/2603.13532", "id": "Paper/68371", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68371"}, {"title": " Conjecture-Driven AI for Mathematical Discovery ", "webprogram_exclude": "0", "session_ids": ["Session/18130"], "source_sha256": "1c23e3cdd03936646bc0b266edb86c6f7b53329a67ecce6f47bb7438c1095ddf", "withdrawn": "", "abstract": "Recent AI systems have become increasingly capable of solving difficult mathematical problems, but mathematical discovery requires more than proving statements supplied in advance. We present an iterative framework in which automated conjecturing, structured mathematical data, symbolic search, counterexample generation, computational experiments, formal verification, and language-model reasoning work together. Rather than treating false conjectures as failures, the system records their counterexamples and uses them to refine definitions, identify missing hypotheses, and generate stronger questions. Multiple search agents explore different targets and statement forms, while an advisor coordinates the resulting evidence and identifies deeper conjectures suggested collectively by the search. We illustrate how this process can produce new invariants, extremal constructions, proof ideas, and conjectures that resist sustained attempts at both proof and refutation. The broader aim is an AI mathematician that does not merely answer existing questions, but builds the data, concepts, and problems needed for continued mathematical discovery.", "id": "Paper/68372", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68372"}, {"title": " Factor Rings and Groups of Units of Cubic Extensions ", "webprogram_exclude": "0", "session_ids": ["Session/19361"], "source_sha256": "4591c19b62e49aa0e2ef45a2b3aa6aa19681ed710d3b7bc945c201879713270c", "withdrawn": "", "abstract": "Quadratic extensions, and their factor rings and groups of units have enjoyed a recent focus from Allan, Sittinger, Morales and others. Utilizing similar and elementary techniques, we explore factor ring compositions and quotients of groups of units in cubic extensions of the integers. In addition to showing our classification, in this talk we will dive into some specific examples that show the breadth of the cubic landscape.", "id": "Paper/68373", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68373"}, {"title": " From Collective Cellular Behavior to Plant Shapes ", "webprogram_exclude": "0", "session_ids": ["Session/17383"], "source_sha256": "70bb2c4ae962e9a7c6886f28ab44d7079dff51040df57be58f1be07626338d68", "withdrawn": "", "abstract": "Plant growth and development is an example of an emergent-behavior process, where local cell interactions, signaling, and feedback give rise to global patterns and forms. During one stage in the lifecycle of the fern Ceratopteris, cell behavior transforms the plant tissue from round to heart-shaped, with meristem cells at the heart notch having notable regenerative properties. The mechanisms driving spatiotemporal differences in cell behavior and cell fate choices remain unclear, and our work combines predictive modeling and experiment to shed light on signaling dynamics. In this talk, I explore plant growth using mechanistic modeling and data-driven approaches, and we investigate how growth and division at the cellular scale can generate complex, robust patterns at larger scales.", "id": "Paper/68375", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68375"}, {"title": " Matching Correlated Random Geometric Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18312"], "source_sha256": "19cd7cecdabf2ae4cdb0f6f6bcc4209015b29a0c4c7b0dd09b5fa724d22c10b9", "withdrawn": "", "abstract": "We study graph matching for two correlated random geometric graphs whose vertex labels have been permuted. The graphs are generated from correlated latent points on the high-dimensional sphere, with edges determined by thresholded inner products. We give a polynomial-time algorithm that achieves exact recovery of the hidden matching for any fixed positive correlation. We also characterize, up to constant factors, the information-theoretic threshold for exact recovery over a broad range of dimensions.\n\nThis talk is based on joint work with Dong Huang, Ankang Jiao, and Zhangsong Li.", "id": "Paper/68377", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68377"}, {"title": " Mapping the Mind: Assessing Spatial Reasoning in Graph Theory Tasks ", "webprogram_exclude": "0", "session_ids": ["Session/19341"], "source_sha256": "9e0ed3492da0371a6509813c8b9c4024b69de67f5b96e71ecb063cd7aa36958a", "withdrawn": "", "abstract": "Spatial reasoning refers to a person's ability to visualize and manipulate spatial figures, understand relationships, and form shapes. It is well established that strong spatial skills demonstrate advantages for future STEM performance, and notably, there is extensive correlation linking spatial skill to mathematics performance. Despite this, spatial reasoning is often overlooked in mathematics curricula at all levels. Most university-level STEM materials are presented abstractly, and these 2-D representations often pose significant difficulty for students who cannot \"decode\" a 2-D drawing into a 3-D mental image. Despite this, manipulatives are still not readily available for use in advanced math coursework.  \n\nOur study takes a step toward filling this gap by examining the types of spatial reasoning students exhibit when solving graph theory tasks. Participant data was gathered through a 30-minute task-based clinical interview focused on undergraduate mathematics or math education majors. To examine the spatial reasoning students exhibited, Uttal et al.'s (2013) 2x2 classification of spatial skills framework was utilized. Tasks required students to determine planarity, utilize an online manipulative tool to investigate properties of planar graphs, and attempt to create a non-planar graph.  \n\nInterviews provided clear evidence for all four quadrants of the Uttal et al. (2013) framework. One of the strongest themes present in data analysis was the prevalence of real-world analogies in students' thinking, as students drew on physical, 3-D experiences to solve 2-D tasks. Participants strongly relied on physical metaphors created from their lived, physical experiences, such as folded origami paper cranes, fanning decks of cards, rubber bands, or routing cables and outlets, to \"decode\" abstract graphs.  \n\nWhile graph theory tasks are often presented in a static, two-dimensional format, students' cognitive processing is deeply rooted in their three-dimensional, lived experiences. Instructors should consider explicitly leveraging physical manipulatives or 3-D analogies to support decoding skills and equip students to tackle complex, abstract mathematical problems.", "id": "Paper/68380", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68380"}, {"title": " Quantifying Features and Irregularities in Zebrafish Patterns Using the Sweeping-plane Filtration ", "webprogram_exclude": "0", "session_ids": ["Session/18039"], "source_sha256": "fb92b4c726add9cbdc269144bada30ee6beffb497cfe1c2e87729af20b1aa907", "withdrawn": "", "abstract": "Zebrafish are known for their dark blue and gold striped skin patterns which arise from the interactions between different types of pigment cells. We show interest in understanding variability that emerges from cell behavior. We develop an interpretable framework based in topological data analysis to classify and quantify those patterns. Using a sweeping-plane filtration approach, we classify patterns based on their topological signature, identifying robust features such as the counts and widths of stripes, breaks, and spots. This allows us to comprehensively quantify the pattern features and imperfections, offering potential applications in developmental biology.", "id": "Paper/68382", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68382"}, {"title": " Interlace Polynomials of Decorated Path Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18206"], "source_sha256": "e689458bac23e239ca57bc9cd4d99b32b9df738eff0c31187b2f10b18cafe220", "withdrawn": "", "abstract": "In this talk, we present the interlace polynomials of a family of decorated path graphs obtained by attaching a cycle of length ($m$) to each vertex of a path with length ($n$). We investigate how the cycle length and path length affect the resulting interlace polynomial. We show linear recurrences, generating functions and patterns of the coefficients of the polynomials, providing additional details for the triangle decorated ($m=3$) and square decorated ($m=4$) path graphs. We present tools for further investigation of the interlace polynomials of decorated path graphs.", "id": "Paper/68384", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68384"}, {"title": " Topological Data Analysis Framework to Characterize the Spatiotemporal Dynamics in Biological Pattern Formation ", "webprogram_exclude": "0", "session_ids": ["Session/18357"], "source_sha256": "aae45d55fe138abaeb2d0ce9b3260ee98641f48b20f2a1e072c5075631ded424", "withdrawn": "", "abstract": "Complex biological patterns emerge from local interactions in many systems, generating coherent structures across space and time. In this talk, I investigate spatiotemporal pattern formation on growing domains through topological data analysis, with zebrafish striped skin patterns as a case study. We propose a method that employs a sublevel set filtration to characterize the dynamics of pattern formation and degradation over time. By reinterpreting time as a filtration parameter in persistent homology, we estimate the times of normal developmental events and abnormalities in pattern development. This allows us to identify the formation of a new stripe, or the degradation of a stripe into spots. Examining the interplay between temporal dynamics and spatial organization, we explore mechanisms through which patterns emerge, evolve, and stabilize.", "id": "Paper/68385", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68385"}, {"title": " Authenticated Partial Correction: A Case Study ", "webprogram_exclude": "0", "session_ids": ["Session/18020"], "source_sha256": "ca1a56b94d99a26532cd905859da37892a4ceb1c8701f133aa8085122ef1a437", "withdrawn": "", "abstract": "Authenticated partial correction over an adversarial multiple-access channel (MAC) requires that the receiver correct all legitimate users' messages when the adversary does not act, and at least some fixed portion of the messages when the adversary is present. This talk focuses on a family of adversarial MACs where all inputs (including that of the adversary) are binary, and the channel output is the real-addition sum of the inputs. We  present bounds on the codebook sizes of legitimate users and discuss designing good codes for authenticated partial correction over this channel.", "id": "Paper/68387", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68387"}, {"title": " On the existence and stability of positive steady-states for a noncooperative nonlocal-diffusive systems ", "webprogram_exclude": "0", "session_ids": ["Session/18441"], "source_sha256": "db4b622665d217dda278ea29962c334fe483858bf8bc9b5b16fde1cc9bb62df2", "withdrawn": "", "abstract": "In this talk, we present our recent study on the global dynamics of positive solutions for a class of population models featuring nonlocal dispersal operators in spatially heterogeneous environments. The inclusion of inter-stage competition renders the dynamical system nonmonotone, while the solution operator lacks compactness. Together, these features present major mathematical obstacles to establishing the existence, uniqueness, and stability of positive steady states under population persistence. We prove that the system admits at least one positive steady state whenever the population persists, provided that either one inter-stage competition term is proportionally bounded by the product of the inter-stage growth rates, or one subpopulation disperses sufficiently slowly. Finally, we discuss several partial results regarding the global stability of these positive steady states.", "id": "Paper/68389", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68389"}, {"title": " Ergodic McKean-Vlasov Games: Verification Theorems and Linear-Quadratic Applications ", "webprogram_exclude": "0", "session_ids": ["Session/18328"], "source_sha256": "9076894741f90f924bacf009972d613eb5e06082a30306aaa67f67ff3010289e", "withdrawn": "", "abstract": "This work develops a general framework for two-player ergodic nonzero-sum stochastic differential games with McKean-Vlasov dynamics. A verification theorem is established, linking solutions of a system of coupled Hamilton-Jacobi-Bellman (HJB) master equations to Nash equilibria, which are characterized via an auxiliary bias optimal control problem formulated on the space of probability measures. We demonstrate that the value functions of this auxiliary control problem are uniquely determined, up to an additive constant, by the uniqueness of the invariant measure associated with the optimally controlled state process. The framework is further illustrated in a Linear-Quadratic-Gaussian (LQG) setting, where explicit solutions to the master equations are obtained by exploiting their polynomial structure in the measure variables.", "id": "Paper/68390", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68390"}, {"title": " Non-uniqueness of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"3.807ex\" height=\"2.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -1006.6 1639.1 1152.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathcal {C}^{1,\\alpha }</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJCAL-43\" d=\"M201 -25Q167 -25 136 -14T75 23T29 94T12 202Q12 290 50 394T161 574Q227 642 303 673T433 704Q435 705 457 705Q533 701 533 640Q533 606 507 548T464 474Q431 444 396 444Q381 444 381 453Q381 459 388 473T407 513T428 563Q433 580 433 594Q433 636 381 636Q314 636 260 594T175 489T128 363T112 247Q112 157 153 101T273 44Q347 44 398 121Q413 144 437 157T481 171Q496 171 496 160Q496 150 476 123Q426 56 350 16T201 -25Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJCAL-43\" x=\"0\" y=\"0\"></use>\n<g transform=\"translate(535,432)\">\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-31\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-2C\" x=\"500\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-3B1\" x=\"779\" y=\"0\"></use>\n</g>\n</g>\n</svg> isometric embeddings between contact manifolds ", "webprogram_exclude": "0", "session_ids": ["Session/17952"], "source_sha256": "ae85c6e7dfbaaeea9756a4a9ee316bfed7b45545a7f2d961fa2a3497a362251d", "withdrawn": "", "abstract": "Isometric embeddings between a domain manifold and a target manifold are differentiable maps $f$ such that the pullback of the target metric $h$ coincides with the metric $g$ in the domain manifold. This problem can also be formulated as a non-linear PDE via $\\nabla f^{\\top}h\\nabla f = g$. In the case of contact manifolds, it is additionally required that the embedding preserves a certain restriction on the tangent bundle.\n\nWe prove that the Nash iteration scheme can be quantified in order to construct infinitely many $\\mathcal{C}^{1,\\alpha}$ isometric embeddings for contact manifolds. In this way, we extend existing results by D'Ambra regarding non-uniqueness for $\\mathcal{C}^{1}$ regularity. The strategy of the proof follows a paper by Conti, De Lellis and Székelyhidi Jr.\\ on the Riemannian case. The main difficulty in the context of contact manifolds is to keep the additional linear constraint coming from the contact setting along the iteration procedure.\n\nIn the larger program of a quantitative analysis of isometric embeddings between sub-Riemannian manifolds, our result can be seen as an important first step. Another aspect is the flexibility of this convex integration method: the geometric constraint coming from the contact condition is just one special case of a (potentially large) class of admissible constraints, under which this scheme can still be applied.\n\nThis is joint work with László Székelyhidi Jr.", "id": "Paper/68391", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68391"}, {"title": " Action of derived local-at-<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.259ex\" height=\"2.009ex\" style=\"vertical-align: -0.671ex; margin-left: -0.089ex;\" viewBox=\"-38.5 -576.1 542 865.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">p</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-70\" d=\"M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-70\" x=\"0\" y=\"0\"></use>\n</g>\n</svg> Hecke algebra on cohomomology of modular curve ", "webprogram_exclude": "0", "session_ids": ["Session/19367"], "source_sha256": "2d477286529aa2c8754769f387fab8c998b0fed84056fc6a2da7558f476c0173", "withdrawn": "", "abstract": "In recent years, there has been growing interests in using derived enhancements in understanding structures/phenomena in the Langlands programme.  Such leads to interest in studying derived Hecke algebra and its action (e.g. Venkatesh, Schneider, etc.) Contrary to Venkatesh, which is a more global approach, we are interested in local information. Specifically,  using Emerton’s completed cohomology, we will give a canonical action of Schneider’s differential-graded (DG) Hecke algebra on cohomology of modular curve. As this DG algebra is much larger than the classical Hecke algebra, meaning there is additional information in its action,  we will explain some general methods in analyzing this DG-action and how one can use such additional DG structure. Surprisingly, this purely local derived structure gives us global Galois-theoretic information.", "id": "Paper/68392", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68392"}, {"title": " A survey for resonant <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"5.082ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 2188.2 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">(p,q)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-70\" d=\"M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-71\" d=\"M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-70\" x=\"389\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2C\" x=\"893\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-71\" x=\"1338\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"1798\" y=\"0\"></use>\n</g>\n</svg>-equations with Robin boundary condition ", "webprogram_exclude": "0", "session_ids": ["Session/17446"], "source_sha256": "258d917bcf272553feeb1eb6bcf7958d8701d4b1667f75c8038fa130e06c7b86", "withdrawn": "", "abstract": "\\begin{document}\n\\footnote{The publication of this paper has been partly supported by the University of Piraeus Research Center}\nWe consider a nonlinear nonhomogeneous Robin problem driven by the sum of a $p$-Laplacian and of $q$-Laplacian(a $(p,q)$-equation). The reaction term is a Caratheodory function which is resonant at $\\pm\\infty$ with respect to any nonprincipal variational eigenvalue of the Robin $p$-Laplacian. Using variational methods together with Morse theory (critical groups), we show the existence of at least three nontrivial smooth solutions.\n$\\footnote{The publication of this paper has been partly supported by the University of Piraeus Research Center}$\n\\end{document}", "id": "Paper/68394", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68394"}, {"title": " Resource-Aware Algorithm Formalization in Lean ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "b8972490fa427205c347d8f4351a354ec3cfca447661813782f0f55b473f3588", "withdrawn": "", "abstract": "Autoformalization in mathematics has improved substantially, helped by large libraries such as Mathlib and AI proof assistants. Computer science algorithms pose a different challenge: a textbook proof usually makes informal assumptions about resources, such as which operations count as constant time, which data representation is being used, and how per-unit operation costs lead to asymptotic bounds. \nHowever, existing research does not yet provide a standard interface for expressing and varying these cost assumptions across algorithm formalizations. Motivated by case studies in mergesort, breadth-first search, and depth-first search, we develop ResourceAwareLean as a flexible framework for resource-aware algorithm formalization. ResourceAwareLean uses free monad structures to represent algorithms as abstract programs over cost-relevant operations, which are then interpreted by interchangeable handlers associated with different cost models. To extend the framework to randomized algorithms, we introduce RandCostM, which models computations as joint distributions over outputs and branch-specific costs. Finally, we develop a preliminary autoformalization pipeline to explore how this approach could scale to other algorithms, such as Dijkstra's algorithm.", "id": "Paper/68396", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68396"}, {"title": " Algorithmic Reconstruction of Denominator Bounds ", "webprogram_exclude": "0", "session_ids": ["Session/18261"], "source_sha256": "a342262fc5ad67b56c90313d1f2e1fa8c26d829349bb1fa626642d2678097eb8", "withdrawn": "", "abstract": "The strength of a rational approximation $a_n/b_n$ to $x$ depends both on its approximation error and on the reduced denominator $b_n/\\gcd(a_n,b_n)$. While the error can be estimated by standard analytic methods, such as the saddle-point method, the cancellations that reduce the denominator are much harder to detect. Rhin and Viola famously obtained unusually strong denominator bounds from symmetries of Mellin-transform integrals~\\cite{RhinViola1996,RhinViola2001}; numerical evidence suggests that these bounds are sharp up to subexponential factors.\n\nWe present an algorithm for discovering similarly sharp bounds from exact arithmetic data. Given a rational sequence $u_n$, we sample $v_p(u_n)$ for many indices $n$ and primes $p$ and plot the results against $n/p$. The samples often collapse onto a finite piecewise-constant rule, possibly depending also on the residue class of $p$ modulo a fixed integer. We call this rule a \\emph{valuation profile} and denote it by $f$. Ap\\'ery's $\\zeta(3)$ construction~\\cite{Apery1979} gives the basic example:\n\\[\nD_n=\\operatorname{lcm}(1,\\ldots,n)^3,\n\\qquad f(x)=3\\cdot\\mathbf{1}_{[1,\\infty)}(x).\n\\]\nOnce reconstructed, such a profile predicts exponential denominator growth and yields an explicit candidate denominator bound.\n\nWe describe how these bounds guide the search for linear forms capable of proving irrationality, and provide the arithmetic input needed in the holonomy-bound methods of Calegari, Dimitrov, and Tang~\\cite{CalegariDimitrovTang2025}.\nBelow, we illustrate the method using the coefficients of Krammer's $G$-function, whose pattern separates according to $p \\bmod 15$ (Figure~\\ref{fig:krammer-profile}), and a two-parameter family, for which the data reconstruct a polygonal valuation function (Figure~\\ref{fig:cmf-crystal}).", "id": "Paper/68397", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68397"}, {"title": " Semigroup Solutions for A Multilayered Interactive PDE System ", "webprogram_exclude": "0", "session_ids": ["Session/18351"], "source_sha256": "cb28b63c342e3bb96acaf0dfc6beb74b26b73ed2f863a333671ce1a1deaece20", "withdrawn": "", "abstract": "In this talk, we consider semigroup wellposedness for a coupled system of partial differential equations which describe the interaction of a viscous incompressible fluid with a thermoelastic plate possessing poroelastic characteristics. The configuration consists of two fluid subdomains separated by a deformable porous interface, thereby inducing nonstandard coupling conditions through which both mechanical and fluid variables are transmitted across the plate. The governing equations comprise the Navier-Stokes system in the bulk regions, coupled via continuity of velocity, stress balance, and thermal flux to a damped thermoelastic plate equation with an intrinsic heat equation on the interface.", "id": "Paper/68400", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68400"}, {"title": " Translations in q-colored carpets ", "webprogram_exclude": "0", "session_ids": ["Session/18233"], "source_sha256": "92d6dd297406bc62a136fec09e75df6542e17cc84f0eb01a22e88a5a79b14eaf", "withdrawn": "", "abstract": "This talk is an an introduction to $q$-colorings of carpets and the beautiful pictures of carpets that result. This will be followed by a proof that a $q$-colored carpet admits an oblique translation if and only if the carpet is periodic and admits a diagonal translation. Further, if a $q$-colored carpet admits a horizontal or vertical translation, then a finite number of rows or columns can be removed to obtain a carpet with a diagonal translation.", "id": "Paper/68404", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68404"}, {"title": " Lieb-Robinson Bound for a Class of Two-Dimensional Fermionic Systems with a Constant Magnetic Field ", "webprogram_exclude": "0", "session_ids": ["Session/17925"], "source_sha256": "b155fca0b22a1ef79c9003f0cf09e3c962932fa2a25eba8cb4fc3bc89f8496d6", "withdrawn": "", "abstract": "Based on joint work with Bruno Nachtergaele and Robert Sims, we prove a Lieb-Robinson estimate for electrons in $\\mathbb{R}^2$ subject to a short-range interaction, a uniform perpendicular magnetic field, and a periodic potential. To achieve this goal, the pointwise interaction is smeared out over a $L^1$-normalized Gaussian of width $\\sigma > 0$ to ensure the interaction is bounded when supported on a finite region. We first establish propagation bounds on the single particle dynamics of these Gaussian particles as these are necessary to prove a Lieb-Robinson bound for the dynamics $\\tau_t^{\\Lambda}$ of the canonical anticommutation algebra over $L^2(\\mathbb{R}^2)$, $\\mathcal{A}_{CAR}$, governed by interactions supported in $\\Lambda \\subset \\mathbb{R}^2$. Crucially, this estimate is independent of $\\Lambda$, which allows us to prove the main theorem of this work regarding the existence of $\\tau_t^{\\Lambda}$ in the thermodynamic limit, i.e. $\\Lambda \\uparrow \\mathbb{R}^2$. With suitable assumptions on the\nHamiltonian, there exists a strongly continuous 1-parameter group of automorphisms of $\\mathcal{A}_{CAR}$, denoted $\\{\\tau_t\\}_{t\\in\\mathbb{R}}$, such that for all $A \\in \\mathcal{A}_{CAR}$ and any exhaustive sequence of subsets $(\\Lambda_n)$ such that $\\cup_n \\Lambda_n = \\mathbb{R}^2$, $\\lim_{n\\rightarrow\\infty} \\tau_t^{\\Lambda_n}(A) = \\tau_t(A)$ in the operator norm topology. This convergence is uniform in $t$ over compact\nsubsets of $\\mathbb{R}$.", "id": "Paper/68405", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68405"}, {"title": " Rigorous Guarantees for Efficient Thermal and Ground State Preparation via System–Bath Interaction Models ", "webprogram_exclude": "0", "session_ids": ["Session/17702"], "source_sha256": "1a22b2cb8fa678c24b16e8e11b0363b2bc91bcf13c60202a4fab55c79808ba1e", "withdrawn": "", "abstract": "Dissipative state preparation uses engineered open quantum system dynamics to prepare quantum many-body states. A central challenge is to \\emph{ensure both rigorous guarantees on stationary-state accuracy and efficient, physically accessible implementations}. Recent interaction-based approaches provide a promising framework toward this goal. However, their analysis typically relies on two limiting assumptions: a weak-coupling approximation leading to Lindbladian dynamics, and a long-time limit in which the effective jump operators take the Davies form. In this talk, I will present a new theoretical framework that goes beyond these two limitations. We show that, even when the system–bath coupling strength is chosen independently of the desired preparation accuracy, the induced quantum channel can still admit the target thermal or ground state as an approximate fixed point with arbitrarily high precision. The analysis develops new techniques for controlling higher-order terms in the Dyson expansion and for estimating the associated multidimensional operator Fourier transforms. Using these tools, we further obtain improved end-to-end complexity bounds for thermal and ground state preparation using interaction-based algorithms.", "id": "Paper/68408", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68408"}, {"title": " Randomized Tucker-Sketched GMRES ", "webprogram_exclude": "0", "session_ids": ["Session/18032"], "source_sha256": "a3a5266888534274cede0da51030a236af10688805ccab3d60e4ce86566b7483", "withdrawn": "", "abstract": "We address the problem of solving large-scale tensor-structured linear systems in the Tucker format. In this setting, standard iterative solvers such as GMRES face a fundamental bottleneck: the multilinear ranks of the Krylov basis vectors grow with the iteration count, leading to rapidly increasing tensor operation costs and memory requirements.\nTo overcome these challenges, we propose two randomized algorithms within the sketched GMRES framework that replace full Arnoldi orthogonalization with short recurrences. The first, RHOSVD-Tucker sGMRES, uses randomized HOSVD with per-iteration rank selection, providing robustness across a wide range of problems. The second method, MLN-Tucker sGMRES, leverages the multilinear Nystr\\\"om approximation with a fixed rank, enabling streaming computations; the streamability of the approximation further allows, at no additional cost, a memory-efficient reconstruction of the solution from a compact sketched representation of the Krylov basis.\nBoth methods outperform standard low-rank Tucker solvers in symmetric and non-symmetric settings.", "id": "Paper/68409", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68409"}, {"title": " Research by Non-Experts \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18329"], "source_sha256": "10ea09a472be28e14bc6e3cbc8b7190b8295a1fbc8d39bb89d49cbda7d367e6e", "withdrawn": "", "abstract": "With the aid of machines, major conjectures have fallen.  But many smaller conjectures have purported solutions, some from mathematicians without experience on related problems and others from the general public.  How should mathematicians work with the public to uphold  community standards?  What are our responsibilities and how do we welcome newcomers?", "id": "Paper/68418", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68418"}, {"title": " One-Step Spectral Dynamics of the Neural Tangent Kernel under Feature Learning ", "webprogram_exclude": "0", "session_ids": ["Session/17703"], "source_sha256": "4ff2299a25cd07b99e88a375eda418e27935b64d34d0eff912e9e42c0ba967ed", "withdrawn": "", "abstract": "The empirical neural tangent kernel (NTK) evolves during feature learning, but its full spectrum is not fully understood beyond initialization. We study a two-layer mean-field network with Gaussian data in a proportional high-dimensional limit of width, samples, and dimension, deriving a one-step prediction for the limiting NTK spectrum. The theory agrees with finite-dimensional experiments across isotropic and anisotropic settings, while repeated application of the transition map remains accurate only over the early stages of training. These observations suggest that NTK spectra admit simple local dynamical descriptions, while long-time evolution requires additional temporal de-correlation.", "id": "Paper/68420", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68420"}, {"title": " Exponential Decay for a Klein-Gordon-Schrödinger System with locally Distributed Damping and applications ", "webprogram_exclude": "0", "session_ids": ["Session/18254"], "source_sha256": "874303dade2886e4b7b88f3ff22d57d70aaec66f83500efbae292a2c25298d02", "withdrawn": "", "abstract": "\\begin{abstract}\n$\\footnote{The publication of this paper has been partly supported by the University of Pireaus Research Center}$\n\\noindent The following coupled damped Klein-Gordon-Schr\\\"{o}dinger equations are considered\n\\begin{eqnarray*}\ni\\psi_{t} +\\kappa \\Delta \\psi+i\\alpha b(x)\\psi &=& \\phi \\psi \\chi(\\omega),\\\\\n\\phi_{tt}- \\Delta \\phi +\\phi +\\lambda(x) \\phi_t &=&- Re \\grad \\psi \\chi(\\omega),\n\\end{eqnarray*}\n\\noindent where $\\Omega$ is a bounded domain of $\\mathbb{R}^{2},$ with smooth boundary $\\Gamma$ and $\\omega$ is a neighbourhood of $\\partial \\Omega$ satisfying the geometric control condition.  The aim of the paper is to prove the existence, uniqueness and\nuniform decay for the solutions.\n$\\footnote{The publication of this paper has been partly supported by the University of Pireaus Research Center}$\n\\end{abstract}", "id": "Paper/68422", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68422"}, {"title": " The obstacle problem for a fourth order parabolic equation with a logarithmic nonlinearity ", "webprogram_exclude": "0", "session_ids": ["Session/17883"], "source_sha256": "70926afd10108e9855849c8955be4841402e28a0d2a4a9783661b5ce1f45ddcd", "withdrawn": "", "abstract": "In this talk, we consider an obstacle problem for a fourth-order parabolic equation with a logarithmic nonlinearity, whose associated energy functional is unbounded from below. Using the minimizing movements method, we establish local-in-time existence and uniqueness of weak solutions and identify the gradient structure of the evolution. We also characterize the maximal existence time in terms of the growth of an appropriate norm of the solution. Finally, we show that, for a natural class of initial data and nonnegative obstacles, solutions blow up in finite time.", "id": "Paper/68423", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68423"}, {"title": " Using Machine Learning Methods to Detect GPS Spoofing and Jamming ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "cf0f873354b72053c46397edf374898d45b92b3f98ba53754f05a2a0bf22df45", "withdrawn": "", "abstract": "The purpose of this experiment was to figure out which machine learning model would be the most accurate for detecting GPS jamming and spoofing. In this experiment, a multilayer perceptron model, a random forest model, and a histogram-based gradient boosting model were used. First, the spoofing data was downloaded from Mendeley Data and then preprocessed to extract the features from the data. Then the jamming data was downloaded from Zenodo, and a convolutional neural network was used to process the data. The jamming data was in the form of images, so the convolutional neural network was used to transform the images into arrays that the machine learning models could interpret. Then the number of features in the arrays was reduced using principal component analysis. After all the data preprocessing was finished, parameter grids were made for each model. For spoofing, multiple data sampling methods were tested to balance the class distribution. After identifying the optimal parameters and data sampling methods for spoofing, the models were trained and then tested a total of 10 times. SHAP was used to identify the most important features for each model in spoofing detection. The histogram-based gradient boosting model performed the best at detecting GPS spoofing with an accuracy of 93.6\\%. The multilayer perceptron performed the best at detecting GPS jamming with an accuracy of 96.9\\%. The accurate detection protects critical infrastructure that relies on GPS and prevents disruptions relating to the use of positioning and timing systems.", "id": "Paper/68424", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68424"}, {"title": " The Fort Number and Fractional Zero Forcing Number of Random Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18207"], "source_sha256": "e0005840a115e7e9a792b75e0909f3eb4807021030a37d5f6af94044f540341b", "withdrawn": "", "abstract": "For a graph $G$, the fort number of $G$, denoted $ft(G)$, is the maximum number of disjoint forts that may be packed on $G$.  The fractional zero forcing number of $G$, denoted $Z^*(G)$, is the optimal value of the integral relaxation of the fort cover model for computing $Z(G)$.  Duality of linear programs implies $ft(G) \\leq Z^*(G) \\leq Z(G)$.  It has been conjectured that $Z^*(G) \\leq M(G)$.  We present original results concerning the fort number and fractional zero forcing number of random graphs, and compare these results to previous bounds on the expected value of the maximum nullity of random graphs as evidence that this conjecture holds.", "id": "Paper/68425", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68425"}, {"title": " multiple nontrivial solutions for resonant Neumann problems ", "webprogram_exclude": "0", "session_ids": ["Session/18103"], "source_sha256": "49d6c0cbd28ea7384e8cdb895b231454595d236ef701b0d21e91c36f5e31a3ce", "withdrawn": "", "abstract": "$\\footnote{The publication of this paper has been partly supported by the University of Pireaus Research Center}$\nwe consider semilinear second order elliptic neumann problems which are resonant both at infinity (with respect to an eigenvalue) and at zero (with respect to the principal eigenvalue). Using techniques from Morse Theory compined with variational methods we are able to show that the problem has at least four nontrivial smooth solutions.", "id": "Paper/68428", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68428"}, {"title": " Using Machine Learning to Diagnose Alzheimer’s Disease ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "131711825658d714ad40911ea7c792dff9883694bb7d2d2c6e49f52e22ab99b5", "withdrawn": "", "abstract": "The purpose of this project was to investigate whether various machine learning models (multilayer perceptron, random forest, and support vector machine) could analyze different types of data (neuroimaging, genetic, and demographic) to diagnose Alzheimer's and mild cognitive impairment (MCI). The experiment showed machine learning could be used to accurately diagnose individuals with Alzheimer's and mild cognitive impairment earlier and get them faster treatment. The data consisted of neuroimaging data, single nucleotide polymorphisms (SNP), and demographic data (age and gender), downloaded from Alzheimer's Disease Neuroimaging Initiative (ADNI). The neuroimaging data was processed through the FreeSurfer software, and gives the volumes of the subsections of the brain. SHapley Additive exPlanations (SHAP) value analysis also revealed some sections of the brain that had a high predictive value, signaling that their volumes may have relations to Alzheimer's, which can be further looked into as potential diagnostic indicators. The procedure included preprocessing the downloaded data, designing the models, and testing each model with One-vs-One multi-class classification ten times. The results were then evaluated on metrics such as accuracy, precision, recall, and f1 score. In conclusion, this project demonstrated that multilayer perceptron (MLP) can effectively analyze the three types of data to accurately diagnose patients with Alzheimer's, with an overall accuracy of 89.1%. Furthermore, combining the neuroimaging and SNPs results in a greater model accuracy. This shows that machine learning approaches can enhance diagnosis of Alzheimer's and MCI. Future work will focus on evaluating additional models, gathering more data, and looking into important features.", "id": "Paper/68429", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68429"}, {"title": " A Survey of Pairs Trading under Geometric Brownian Motion Models ", "webprogram_exclude": "0", "session_ids": ["Session/18058"], "source_sha256": "50f9e4bc9e8c1e68a4f340fecaf180e2df536d115cd98f2e651ae81d4ae4b1da", "withdrawn": "", "abstract": "This talk will present a survey of recent work on the topic of pairs trading.  Pairs trading refers to the method of simultaneously buying and selling a pair of assets, typically stocks.  In practice since the 1980s, pairs trading can be beneficial, because it can be profitable both when markets are trending up and when they are trending down.  The strategy involves monitoring the price movements of two assets relative to one another.  When the prices of the assets move apart, and one becomes more valuable than the other, we assume their prices will converge again.  In this case, one should buy the asset which is at the lower price point and sell short the asset which is at the higher price point, later reversing these positions when the formerly weaker asset overtakes the formerly stronger one.  The key consideration is when to initiate the trading positions, and this survey presents some theoretical findings on that question.", "id": "Paper/68430", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68430"}, {"title": " Connections Between Ramsey Theory and Anti-Ramsey Theory: Gallai–van der Waerden Number ", "webprogram_exclude": "0", "session_ids": ["Session/18240"], "source_sha256": "6f3a5bd7ec849af6568c2e7f1fd65445eff4a1e71363561f8f0b4e638787078c", "withdrawn": "", "abstract": "Mathematicians have studied prime numbers and linear equations for thousands of years. Despite this long history, some connections between primes and linear equations remain unexplained. One of these relationships lies at the intersection of two areas of mathematics, called Ramsey Theory and anti-Ramsey Theory. For example, consider the set $\\{1,2,3,4,5\\}$ colored with the three colors red, blue, and green as follows:$ \\{\\textcolor{red}{1}, \\textcolor{blue}{2}, \\textcolor{red}{3}, \\textcolor{green}{4}, \\textcolor{red}{5}\\}$. Now, consider the linear equation $x+y=2z$. A rainbow solution to the equation is $\\{\\textcolor{blue}{2},\\textcolor{red}{3},\\textcolor{green}{4}\\}$ since each number is colored distinctly and $\\textcolor{blue}{2} +\\textcolor{green}{4}= 2*\\textcolor{red}{3}$. A monochromatic solution is $\\{\\textcolor{red}{1}, \\textcolor{red}{3}, \\textcolor{red}{5}\\}$ since each number is colored the same and $\\textcolor{red}{1} + \\textcolor{red}{5} = 2 * \\textcolor{red}{3}$. In this talk, we will discuss deep connections between prime factorizations of numbers and rainbow and monochromatic solutions to $x+y=2z.$ In particular, we use modular arithmetic, which adds an extra level of complexity but also extra structure. This introduces new solution sets to the equation $x+y=2z$, such as $\\{2,5,1\\}$. We apply results from Abstract Algebra and Combinatorics to gain new insights into Ramsey and anti-Ramsey Theory.", "id": "Paper/68435", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68435"}, {"title": " Dominating Hadwiger’s Conjecture on Graphs with Independence Number Two ", "webprogram_exclude": "0", "session_ids": ["Session/16805"], "source_sha256": "77b5acb694b37ff4309e059fedbd560d78de4f10737d70c742aee9dcd80b058e", "withdrawn": "", "abstract": "Hadwiger's Conjecture from 1943 states that every graph with chromatic number $t$  contains a  $K_t$ minor.   Illingworth and Wood [arXiv:2405.14299]  introduced the concept  of  a ``dominating $K_t$ minor'' and asked whether   every graph with chromatic number $t$   contains a dominating $K_t$ minor.  This question is   a  substantial strengthening of   Hadwiger’s Conjecture.    Norin  referred to it as the ``Dominating Hadwiger's Conjecture'' and believes it is likely false.  In this paper   we first observe that a $t$-chromatic $G$ on $n$ vertices with independence number $\\alpha(G)\\le2$   contains a dominating  $K_t$ minor if and only if $G$ contains a dominating   $K_{\\lceil{n/2}\\rceil}$ minor. \nBuilding on this and using a deep result of Chudnovsky and Seymour on  packing seagulls,  we prove that every graph $G$ on $n$ vertices with   $\\alpha(G)\\le 2$ and  $2\\omega(G)\\ge \\lceil{n/2}\\rceil+1$ satisfies   the Dominating Hadwiger's Conjecture, where $\\omega(G)$ denotes the clique number of $G$. We  further prove that  every $H$-free graph  $G$ with $\\alpha(G)\\le 2$ satisfies  the Dominating Hadwiger's Conjecture, where    $H\\in\\{2K_1+P_4,   K_2+2K_2,   K_2+(K_1\\cup K_3), K_1+(K_1\\cup K_5), W_5^<,  W_5^-, W_5,   K_7^<, K_7^-, K_7\\}$ or  $H\\ne K_2\\cup K_3$ is a  graph on at most five vertices  such that  $\\alpha(H)\\le2$.", "id": "Paper/68436", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68436"}, {"title": " Sign-Changing Solutions for Neumann Boundary Value Problems with Nonhomogeneous Differential Operators ", "webprogram_exclude": "0", "session_ids": ["Session/19369"], "source_sha256": "23db7e5a08bb3e7ecbd0a22b5852e7d59547c56e75e3575c372a363455866ad6", "withdrawn": "", "abstract": "$\\footnote{The publication of this paper has been partly supported by the University of Pireaus Research Center}$\nThis work investigates a class of nonlinear elliptic equations subject to Neumann boundary conditions and involving a strictly monotone, nonhomogeneous differential operator. The framework is sufficiently general to cover several important operators, including the (p)-Laplacian, the ((p,q))-operator, and the generalized (p)-mean curvature operator. Our analysis combines variational arguments with carefully chosen truncation procedures, comparison principles, and tools from Morse theory, particularly critical group computations. Under the prescribed assumptions, we obtain a multiplicity result yielding three distinct nonzero smooth solutions: two of fixed sign, one strictly positive and the other strictly negative, and a third solution that changes sign. Moreover, we establish the presence of extremal solutions within the classes of positive and negative nontrivial solutions.\n$\\footnote{The publication of this paper has been partly supported by the University of Pireaus Research Center}$", "id": "Paper/68437", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68437"}, {"title": " Verifying Distinguishability of ODE Models through Matriods ", "webprogram_exclude": "0", "session_ids": ["Session/18319"], "source_sha256": "21d3a653455650277c8ac17b010c095e73203068cca6c43c941913eac66021a6", "withdrawn": "", "abstract": "Linear compartment models are widely used in pharmacokinetics, epidemiology, and ecology, and a central question is the indistinguishability problem: when do two distinct models produce the same observable inputoutput behavior? Two models are distinguishable precisely when their input-output equations differ, but computing these equations symbolically typically requires costly Grobner basis computations. We present a complementary approach using numerical algebraic geometry. By computing witness sets of projected varieties and identifying circuits of the associated algebraic matroids, we reduce the problem to detecting circuit relations that can certify indistinguishability.", "id": "Paper/68438", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68438"}, {"title": " Deleveraging When Investors Trade Again ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "b4cf6a5c96bf79b986b81aa2895b447ddd5774369445de681cf5fe75a2a888e4", "withdrawn": "", "abstract": "Motivated by auto-deleveraging (ADL) in derivatives markets, I study how a clearing institution should allocate a fixed quantity of contract terminations among investors who can subsequently trade again. In a three-participant model with exponential utility, the objective is to minimize the expected cash needed to cover negative account balances at final settlement. I construct two economies that differ only in one participant's cash buffer. For every permitted allocation, prices, trades, and final positions are identical on a common equilibrium branch where trading constraints remain slack. Yet both funding-shortfall objectives are strictly convex and have different unique minimizers. Thus, even the full trading-response map does not identify the optimal allocation within the stated information set. Cash changes which final states require additional funding without changing trading demand. I also give a benchmark in which the objective separates across accounts and optimal allocations balance marginal benefits, subject to allocation bounds. The poster will explain the construction using convexity, a comparison of the two objective curves, and the economic role of cash.", "id": "Paper/68439", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68439"}, {"title": " Kaczmarz Methods for Sparse, Distributed, and Infinite-Dimensional Recovery ", "webprogram_exclude": "0", "session_ids": ["Session/17908"], "source_sha256": "54ddf6a70548d38a5da72d4e6f810187f22d980f24a58eb6d6edf2e670f8a0bf", "withdrawn": "", "abstract": "The classical Kaczmarz method is among the simplest iterative schemes for solving linear systems: it processes one equation at a time by projecting onto the corresponding hyperplane. I will first discuss reshuffling Kaczmarz methods with sparse constraints, which combine the traditional Kaczmarz method with hard thresholding and admit linear convergence guarantees under suitable assumptions on the measurement matrix and algorithmic parameters. I will then turn to an operator/block Kaczmarz framework in Hilbert spaces, highlighting dimension-free average-regret bounds and the role of spectral measures in reconstruction. In particular, relaxed Kaczmarz iterations with relaxation parameter \\(0<\\lambda<2\\) converge for Fourier exponential systems associated with singular probability measures, yielding nonorthogonal Fourier expansions and illustrating a connection with harmonic analysis. If time permits, I will also describe a federated Kaczmarz method for linear systems whose rows are distributed across clients.", "id": "Paper/68440", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68440"}, {"title": " Curvature and Confinement: Resilience of Vegetation on Undulating Sloped Terrain ", "webprogram_exclude": "0", "session_ids": ["Session/18244"], "source_sha256": "14f1b37205be994d9a80d5546b811e194f6fbe2adddac0084e556333647981d3", "withdrawn": "", "abstract": "Vegetation in arid environments must overcome scarcity of resources, primarily of water, to survive. Yet we find vegetation in very arid environments all over the world. Early phenomenological models by Klausmeier (Klausmeier, Science (1999)) demonstrated that vegetation on sloped terrain is able to survive in arid conditions by breaking up into densely vegetated stripes along the elevation contours of the slope. Bare soil regions between the stripes collect water which flows downhill before being caught and captured by the vegetation stripe immediately following. The formation of vegetation patterns can then be seen as a mechanism for developing resilience against aridity. While there are multiple models of this type in use today, they are typically studied on idealized 1-dimensional slopes. In this talk, I will present new results on the formation of patterns on 2-dimensional undulating slopes in a phenomenological model similar to Klausmeier’s. Using a combination of numerical simulations and reduction to 1-dimensional equations, we investigate links between the topography and the selected patterns, and the  resilience of vegetation as water becomes more scarce. This is a joint work with Punit Gandhi and Mary Silber.", "id": "Paper/68441", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68441"}, {"title": " Smooth implosion for the Boltzmann Equation ", "webprogram_exclude": "0", "session_ids": ["Session/17991"], "source_sha256": "f6dc53babfa9fbca204dcc26f20a4b1bb5f6186da3320123a9ea23d62df82ecf", "withdrawn": "", "abstract": "The Boltzmann equation describes the evolution of a dilute gas through a particle distribution in position and velocity, accounting for transport and collisions. The global well-posedness of solutions remains a very challenging open problem in the analysis of kinetic equations. \nIn this talk we present the first proof of existence of smooth implosion profiles for the Boltzmann equation for very hard potentials. The starting point is a compressible Euler solution that is smooth for t<T, but whose density concentrates at T. Such profiles were  first constructed by Merle–Raphaël–Rodnianski–Szeftel, with subsequent extensions by Buckmaster–Cao-Labora–Gómez-Serrano and most importantly by Shao, Wang, Wei and Zhang in 2025. Their results include the monatomic adiabatic exponent 5/3 and an explicit blow-up rate, relevant to  the Boltzmann equation. We show that there exists smooth initial data whose solutions are smooth until a finite time $T>0$. At this blow-up time, while the function remains bounded, all the Hölder norms become unbounded.\nThis work is a joint collaboration with Jiajie Chen, Sehyun Ji, Weiran Sun, and Jincheng Yang.", "id": "Paper/68443", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68443"}, {"title": " Variance-Feedback Noise in Interacting Diffusions: Shape Dynamics, Mean-Field Limits, and Finite-Size Transitions ", "webprogram_exclude": "0", "session_ids": ["Session/18342"], "source_sha256": "1ec20765909a2921f1dd4dc863c1b2fb67b90ce19a4a6eaf80d95cb53da19813", "withdrawn": "", "abstract": "We study a system of $N$ attractive interacting diffusions whose common and idiosyncratic Brownian forcing has amplitude $\\kappa(S_t^N)^q$, with $S_t^N$ the empirical variance of the system, $\\kappa>0$ and $q\\geq 0$.  For the power-law attraction $K(z)=|z|^p z$, for $p\\geq 0$, the feedback through the empirical variance gives the system critical homogeneity at $q=(p+2)/4$.  For this exponent an intrinsic time change separates the variance from the normalized centered configuration: the latter evolves autonomously on a unit sphere and, when it is not purely driven by common noise and the sphere has positive dimension,\nis a reversible elliptic diffusion with an explicit invariant Gibbs measure. In this case, for $p>0$, the stationary averaged dissipation gives an exact finite-particle trichotomy between consensus, recurrent excursions through arbitrarily small and large variance scales, and finite-time explosion. At critical homogeneity we also derive an autonomous unit-variance mean-field equation and its constrained free-energy dissipation identity. Across the subcritical, critical, and supercritical regimes, we establish well-posedness and boundary classifications and prove conditional propagation of chaos on intervals where the limiting solution is unique and nonexplosive. We connect the sharp finite-particle coercivity constants to a mean-field variational problem.  Finite-size It\\^o corrections enlarge the universal coercive consensus region. We solve the linear model, where $p=0$, completely, including invariant laws, explosion probabilities, noncommuting limits, and an $N^{-1/2}$ transition window.", "id": "Paper/68444", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68444"}, {"title": " Information theory for dimensionality reduction in dynamical systems ", "webprogram_exclude": "0", "session_ids": ["Session/17703"], "source_sha256": "1cf8bc5cdebd6f5850cd648b790e52c6ea7d2e2d77a46be18c3532cb52519a04", "withdrawn": "", "abstract": "The dynamics of many-body systems can often be captured in terms of only a few relevant variables. Mathematical and numerical approaches exist to identify these variables by exploiting a separation of time scales between slow relevant and fast irrelevant variables, but such a separation of scales is not always obvious or even available. In this work, we introduce an information-theoretic framework for dimensionality reduction in dynamical systems that bypasses this limitation by instead identifying relevant variables based on how predictive they are of the system's future. To do so, we mathematically formalize the intuition that model reduction is about keeping \"relevant\" information while throwing away \"irrelevant\" information. We characterize the solution of the resulting optimization problem and prove that it reduces to standard approaches when a separation of time scales is indeed present in the dynamics. Importantly, we find that within this framework, the problems of identifying relevant variables and identifying their effective dynamics decouple and may be solved separately. This makes the method tractable in practice and enables us to derive dimensionally-reduced variables from data with neural networks. Combined with existing equation learning methods, the procedure introduced in this work reveals the dynamical rules governing the system's evolution in a data-driven manner. We illustrate these tools in diverse settings including simulated chaotic systems, uncurated satellite recordings of atmospheric fluid flows, and experimental videos of cyanobacteria colonies in which we discover an emergent synchronization order parameter.", "id": "Paper/68445", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68445"}, {"title": " Twelve Years of Course Coordination: Evolution and Student Experiences ", "webprogram_exclude": "0", "session_ids": ["Session/18250"], "source_sha256": "16790ab7f0aa36cbffdf0d96fa258c8a797f0664dfe10f3c4022aa113a7306f0", "withdrawn": "", "abstract": "Course coordination can take many forms, from common textbooks and assessments to shared instructional practices and support structures for instructors and students. Sustainable coordination, however, is rarely established all at once. This presentation describes the twelve-year evolution of course coordination at the University of Illinois Chicago, a large public urban research university, across a multi-section mathematics program spanning Introductory Algebra, through Precalculus and Calculus, and Linear Algebra.\n\nIn the beginning, coordination primarily consisted of common textbooks, common final examinations, and similar syllabi. Course coordinator positions already existed, but coordination was relatively light, with few shared guidelines or structures. A significant shift occurred with the creation of dedicated Director of Precalculus and Director of Calculus positions, providing leadership for a more intentional approach to coordination. Over time, coordination expanded to include common course sites, syllabi, assessments, and evening exams.\n\nCoordination also increasingly focused on the student learning experience. Guided lecture sheets and coordinated discussion worksheets were developed and combined into course booklets. A Peer Learning Assistant program that began with two assistants in Calculus I has grown to over 60 assistants supporting coordinated mathematics courses. Active learning practices expanded across large lecture sections and smaller discussion sections, while institutional support grew through the Math and Science Learning Center.\n\nThe presentation connects this history with preliminary evidence from a recent multi-site study of course coordination. Student responses suggest relatively consistent classroom experiences across Precalculus, Calculus I, and Calculus II, generally stable affective outcomes, and a general preference for consistency across sections while allowing variation in pedagogy.\n\nThe presentation concludes with a discussion about balancing consistency and instructor autonomy and building sustainable coordination through shared resources, institutional support, and ongoing feedback.", "id": "Paper/68446", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68446"}, {"title": " A Comparison of Anderson Acceleration and Krylov Subspace Methods ", "webprogram_exclude": "0", "session_ids": ["Session/18239"], "source_sha256": "1b7687db4964b48068a80f6cd22463c847c03dc50d9a5b62a62a060c7b0d6b08", "withdrawn": "", "abstract": "Fixed-point iteration is a technique for finding an approximate solution of a fixed point map $x = g(x)$ by repeatedly applying $g$ to generate a sequence of iterates $x_k$ that ideally converge to the fixed-point. However, fixed-point iteration may converge slowly or fail to converge at all. A widely used method, Anderson acceleration (AA), improves the convergence of the iterates by forming an affine combination of $m$ previous residuals in a window in each step, such that the 2-norm is minimized, before forming the next iterate. Another popular method to solve the fixed-point problem is the generalized minimum residual method (GMRES), but full orthogonalization in each step can be memory prohibitive, leading practitioners to restarted and memory-aware variants like restarted GMRES (GMRES($m$)) and Orthomin. Walker and Ni (2011) showed that when $g$ is a linear map, AA iterates are closely related to GMRES iterates provided the window size is infinite. While this relation holds for AA with infinite window size, AA with a finite window (AA($m$)) in comparison to GMRES($m$) generally produces different iterates. However, restarted AA($m$) can have comparable results to GMRES($m$), and a modified AA($m$) algorithm can produce similar iterates to Orthomin. In this presentation, we introduce the AA algorithm and its variants, and investigate how they relate to GMRES, GMRES($m$), and Orthomin on linear problems.", "id": "Paper/68447", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68447"}, {"title": " Mathematical Modeling of Viral Myocarditis to Investigate the Mechanisms of Inflammation in the Heart ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "9fcacc279ba41a0c3bbced8e6bef9638f64476615a3b7cd240cb821fd42ca8a2", "withdrawn": "", "abstract": "Viral myocarditis is an inflammatory disease of the heart upon viral infection, which can contribute to the development of heart failure, particularly in young adults. Experimental evidence suggests that interactions between cardiac and immune cells play a central role in the progression of inflammation. However, the integrated contributions of these interacting populations to overall disease dynamics remain unclear. This project seeks to develop a mathematical model of viral myocarditis to identify the significant cellular interactions that contribute to excessive inflammation. We are constructing a within-host model formulated as a system of ordinary differential equations and simulated in MATLAB to capture interactions among cardiac cells, immune cells, virus, and inflammatory signaling molecules, all to describe biological processes. Model parameters are being estimated from published experimental data using literature-derived measurements and numerical curve fitting. These parameterized interactions will allow preliminary simulation of cardiac behavior during infection and inflammation. Numerical simulation and sensitivity analysis are subsequently performed to determine which biological processes exert the greatest influence on inflammatory outcomes. By integrating processes that are difficult to isolate experimentally, our model provides a framework for efficiently evaluating how changes in cellular interactions alter the progression of viral myocarditis. Identifying the interactions most responsible for persistent inflammation via model prediction may help prioritize mechanisms for further experimental investigation and potential therapeutic targeting.", "id": "Paper/68448", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68448"}, {"title": " Incorporating Repeated Multiple-Choice Assessments into a Large Calculus I Course ", "webprogram_exclude": "0", "session_ids": ["Session/18476"], "source_sha256": "dc60ca4c89a9497c1a261708df6ff53fc40d9f3fcdeb1c85bd9b43475f83ca7f", "withdrawn": "", "abstract": "Building on a previous introduction of multiple choice segments to exams in Fall 2024, in Fall 2025 re-testable multiple choice \"skills tests\" were incorporated into the non-major Calculus I (for life and social sciences) at Boston College.  The goals were to provide an opportunity for students to re-test on core skills (in a 400+ student course), and to help students with wildly divergent calculus background distinguish between skills they might have, and material they may still be struggling with.  Outcomes were positive enough that the same assessment scheme is being used this Fall.  We will discuss those outcomes, how other assessments were changed to accommodate the skills tests, touch on logistics, and share the surprising parts of implementing these exams.", "id": "Paper/68449", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68449"}, {"title": " From Hitchin theory to Habiro Rings ", "webprogram_exclude": "0", "session_ids": ["Session/18268"], "source_sha256": "5b5048e66a854a8dd4d6198ca9811131a116e0a6b2b181956ed1add78a541fd1", "withdrawn": "", "abstract": "In this talk I will present two parallel constructions of asymptotic expansions in Hitchin theory and the ones in Habiro rings. The presentation is based on joint work on quantum curves with Motohico Mulase and the geometry of the asymptotic expansions of Nahm sums in Habiro rings of Garoufalidis, Scholze, Wheeler and Zagier. The talk is also inspired by the discussions and work with Angela East and Kexuan Yang.", "id": "Paper/68450", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68450"}, {"title": " Stability in Trigonometric Curve Fitting ", "webprogram_exclude": "0", "session_ids": ["Session/18241"], "source_sha256": "a896ff6b511f18ffffcef437b4ff2201f85e5406e832331b7506a69bd6154e46", "withdrawn": "", "abstract": "Trigonometric polynomials are used to model data with rhythmic patterns, from tidal heights to seasonal temperature cycles. The coefficients of these polynomials are typically determined by solving a least-squares problem, and numerical stability is dependent on the conditioning of the associated design matrix. Small measurement errors can lead to ill-fitted curves, rendering results untrustworthy. In this work, we explore the conditioning of trigonometric least-squares fitting for arbitrary sampling distributions. Optimal stability is achieved when the sampling points are uniformly distributed, while clustering of points degrades numerical stability. Taking advantage of the structure of the design matrix, we obtain an explicit upper bound which relates the condition number to the spacing of sampling points using Gershgorin circle theorem. We confirm our theoretical results by performing numerical experiments with Julia, which show close agreement with the expected behavior. Our results provide practical guidance for experimental design: uniformly spaced measurements ensure reliable fits, while clustered data reduces trustworthiness.", "id": "Paper/68451", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68451"}, {"title": " On the Schubert support of Grothendieck polynomials ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "21b04a471554a6a042ad38cd0e4e35abda50435c76ab791170a2140ae2454c68", "withdrawn": "", "abstract": "Grothendieck polynomials were introduced by Lascoux and Sch\\\"utzenberger to study the $K$-theory of the complete flag variety. Monical, Tokcan, and Yong conjectured that the Newton polytopes of Grothendieck polynomials are saturated. M\\'esz\\'aros, Setiabrata, and St.~Dizier proposed additional conjectures concerning the monomial support posets of Grothendieck polynomials (ordered by divisibility). We propose a new perspective and study the \\emph{Schubert support} of Grothendieck polynomials, i.e., the set of permutations indexing terms in the expansions of Grothendieck polynomials in the Schubert basis. We propose three Schubert support conjectures that are analogs of these monomial support conjectures. Our main results confirm all three Schubert support conjectures for Grassmannian permutations and permutations of the form $1 \\times u$, where $u$ is a dominant permutation.\nWe also show that the first two conjectures hold for inverse fireworks permutations.", "id": "Paper/68452", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68452"}, {"title": " Hardy inequalities and the Landau equation ", "webprogram_exclude": "0", "session_ids": ["Session/18265"], "source_sha256": "2cd1e4afe56df3dfb3c694e95b9cbf75db3c62b56183e969203d40326e93ac8d", "withdrawn": "", "abstract": "The competition between diffusion and concentration is central to understanding regularity in kinetic equations. In this talk, we present an isotropic analogue of the spatially homogeneous Landau equation and show how Hardy’s inequality prevents finite-time singularities for a range of very soft interaction potentials. The key observation is that the classical weighted Hardy inequality yields a Poincaré inequality adapted to the equation, allowing diffusion to control the nonlinear growth term. This leads to bounds on suitable (L^p) norms and, through an iteration argument, local (L^\\infty) estimates and continued smoothness. This is a joint work with Nestor Guillen.", "id": "Paper/68453", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68453"}, {"title": " THE CONTINUUM MULTINOMIAL COEFFICIENT: CONVERGENCE, FACE STRATIFICATION, AND A PATH-MEASURE FORM OF THE KLEIN-GORDON PROPAGATOR ", "webprogram_exclude": "0", "session_ids": ["Session/19359"], "source_sha256": "1da9b4a5ae4e67c49836150e05344ad92b0b9c705f23895ac19e6473a0d25e3e", "withdrawn": "", "abstract": "The continuum multinomial coefficient is a continuous analog of the discrete multinomial coefficient. Just as the discrete coefficient measures lattice paths between points, this coefficient measures the volume of directed paths in $\\mathbb{R}^{l}$.\nIn this paper, we bound the terms of its formal expansion (found in previous work) to demonstrate that the continuum multinomial coefficient has an infinite radius of convergence, and is therefore bounded and Lebesgue integrable on each simplex $\\sum_{i}x_{i}\\le t$. We then invert the construction: an alternating sum of nonnegative measures supported on the coordinate faces of the path polytopes, with weights built from Stirling numbers of the first kind, recovers the discrete multinomial coefficient exactly after one backward finite difference in each variable. This is an Ehrhart-type stratification of the continuum coefficient, and complements the Todd operator extraction of the discrete coefficient in previous work. From these properties, we demonstrate that special transformations of the continuum multinomial coefficient correspond to the probability density function (pdf) of a sampling of random walk endpoints; these random walks share the Feynman checkerboard model's path weighting scheme. We demonstrate that the continuum multinomial distribution carries that weighting scheme, introduced by Feynman for the Dirac propagator in one space and one time dimension, into arbitrary dimension for the scalar propagator, and that it serves as a basis for a more rigorous definition of the Polyakov measure.", "id": "Paper/68454", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68454"}, {"title": " Pseudoperfect Numbers and the Jaccard Distance of Pseudoperfect Sets ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "e9403739c891a90508653bcdc40031925fc170922e9216ef8a5e253414135175", "withdrawn": "", "abstract": "Pseudoperfect numbers, a generalization of perfect numbers, are only a recently studied topic. Prior results show that numbers of the form $2^kp$ for a prime $p$ and integer $k$ satisfying $2^k < p < 2^{k+1}$ are primitive pseudoperfect, and that $\\tfrac{\\sigma(n)}{n} \\leq \\tfrac{832}{385}$ for primitive abundant numbers. In this project, we establish new results related to primitive pseudoperfect numbers by formulating constructions of specific primitive pseudoperfect numbers. For a subset of primitive pseudoperfect numbers, we establish an upper bound on $\\tfrac{\\sigma(n)}{n}$ of $\\tfrac{864}{385}$. We prove that there exist infinitely many pseudoperfect numbers with a fixed number of disjoint pseudoperfect sets. Finally, in relation to pseudoperfect sets, we explore the Jaccard distance, a metric evaluating the overlap of sets.", "id": "Paper/68456", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68456"}, {"title": " The Illustrative Power of Solvable Lattice Models ", "webprogram_exclude": "0", "session_ids": ["Session/18365"], "source_sha256": "5ecd97fc7a10312e1c0ce03605a20f6d095e956bf11a7840f0d45a8597d3909c", "withdrawn": "", "abstract": "It is well understood that algebraic equalities may be apparent in one context, yet remain challenging to construct as explicit weight-preserving bijections in another. With the Yang-Baxter equation, solvable lattice models provide a visual framework to uncover these identities using two components: boundary conditions and Boltzmann weights, which are realized diagrammatically as allowable paths on rectangular grids.\n\nBy thoughtfully varying these two components and introducing colored paths, mathematicians have recovered a rich dictionary of special functions in number theory and geometry. These lattice models can realize Schur functions, spherical and Iwahori Whittaker functions, Schubert and Grothendieck polynomials, and more.\n\nIn this talk, we will survey these known results and discuss how color refinements of lattice models can further be used to combinatorially explain these algebraic equalities as bijections. This presentation will highlight the broad visual methods alongside recent joint works with Ben Brubaker, Andy Hardt, and Karlee Westrem.", "id": "Paper/68458", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68458"}, {"title": " Pseudo-Cartan inclusions and regular ideals ", "webprogram_exclude": "0", "session_ids": ["Session/18382"], "source_sha256": "38f0b5cb0f22f8f98ea1c2313ca168c28f7006ac85fa04fec196cf0991eeff6e", "withdrawn": "", "abstract": "Cartan subalgebras play a vital role in understanding non-commutative operator algebras. The presence of these abelian subalgebras indicates a dynamical representation of the ambient algebra. Recent results have established that these subalgebras may provide classification information as well.  We study the preservation of pseudo-Cartan inclusions, those minimally embedded in a Cartan pair, under quotients by regular ideals and provide an example arising from a higher-rank graph.", "id": "Paper/68464", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68464"}, {"title": " FunSearch and SAT-Based Search for Weak Schur Partitions ", "webprogram_exclude": "0", "session_ids": ["Session/18369"], "source_sha256": "7f37da6f6a8a190697774e65b403cadc023bd4f9bc7826a975c94b4421a88524", "withdrawn": "", "abstract": "The weak Schur problem asks how large an interval of consecutive integers can be partitioned into a fixed number of classes with no class containing a monochromatic solution to $a+b=c$ with $a\\neq b$. We investigate whether FunSearch, an evolutionary program-search method guided by a large language model, can discover effective construction strategies for this classical combinatorial problem. In our adaptation, FunSearch evolves a \\texttt{priority} function used by a fixed greedy solver, while a separate validity check enforces the weakly sum-free condition. This approach matches the known exact values for two, three, and four classes and reaches $WS(5)\\geq195$. We then explore a complementary SAT-based approach. Guided by structural information from a 207-element construction communicated by Fred Rowley, our SAT search produces and verifies a \\emph{distinct} valid five-class partition of $\\{1,\\ldots,207\\}$. Thus, the strongest construction obtained in this project reaches $WS(5)\\geq207$, eleven integers beyond the best published lower bound of 196. The contrast between the two approaches also exposes a limitation of our FunSearch formulation: its greedy solver makes local, irreversible decisions, whereas SAT can enforce global structure across the whole partition.", "id": "Paper/68465", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68465"}, {"title": " Learning Step-Size Policies for Parametric ODE Integrators via Reinforcement Learning ", "webprogram_exclude": "0", "session_ids": ["Session/19322"], "source_sha256": "a3d87bb9639a2d4e0b63d7a60090e57627c66ba4fc19c047b7511d71b97a288f", "withdrawn": "", "abstract": "Many scientific and engineering applications require repeatedly solving a family of ordinary differential equations (ODEs) under varying system parameters. As the parameters change, the regions where the dynamics evolve rapidly or become stiff can also change, making a single fixed step size inefficient across the entire parameter space. Using a sufficiently small step size can ensure accuracy but often leads to excessive computational cost. Adaptive step-size methods provide a more efficient alternative by adjusting the step size according to the local dynamics; however, this adaptation process is repeated for each new parameter setting, typically through local error estimation.\nWe propose a reinforcement-learning-based approach that learns a step-size control policy for a family of parametric ODEs. Through trial and error during training, an actor-critic agent learns to adjust the integration step size based on the current integration state and system parameters. Once trained, the policy directly determines the step size during integration without requiring local error estimation, allowing the learned adaptation strategy to be reused across different parameter settings.\nAs a proof of concept, we apply the proposed approach to the Van der Pol oscillator over a range of system parameters. A single learned policy adapts the step size across different parameter regimes, including parameter values outside the training range. Across ten parameter values and five independently trained policies, the learned controller achieves a 60.7% reduction in function evaluations compared with a conventional adaptive Runge--Kutta solver, while maintaining a comparable magnitude of global error. These results demonstrate the potential of reinforcement learning to learn and reuse step-size adaptation strategies for efficient integration of parametric ODEs.", "id": "Paper/68467", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68467"}, {"title": " Weak Separation on the Annulus ", "webprogram_exclude": "0", "session_ids": ["Session/18241"], "source_sha256": "43a5df2f312368e0b7022d395c197f78444e1a1140f2d687a2eff063ab1ff1bb", "withdrawn": "", "abstract": "Weak separation is a combinatorial criterion on subsets of an ordered set, first introduced by Leclerc and Zelevinsky as a characterization of when two quantum Pl\\\"ucker coordinates quasicommute. Collections of pairwise weakly separated $k$-subsets defined from $n$ boundary points on a disk form a simplicial complex. Oh, Postnikov, and Speyer showed that these complexes are pseudomanifolds with boundary. \n\nIn this talk, we define weak separation on an annulus with marked boundary points, then discuss the simplicial complexes built by weakly separated collections of a fixed cardinality. We show that each component of the complexes constructed with two boundary points are shellable pseudomanifolds with boundary. We also show that the complex constructed from $3$-subsets in the case where the annulus has $n$ marked points on one boundary and none on the other is pure, has $n$ strongly connected components, and is homotopy equivalent to $S^{n-2}.$", "id": "Paper/68469", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68469"}, {"title": " Topological Properties of Annular Weak Separation Complexes ", "webprogram_exclude": "0", "session_ids": ["Session/19346"], "source_sha256": "f61d644370d5f9ec1f71bd60db797760dc2cf5f4943504f743acb035ed0cf736", "withdrawn": "", "abstract": "We generalize results by Oh, Postnikov, and Speyer about weak separation on a disk to an annulus with marked boundary points. We construct simplicial complexes out of weakly separated collections of a fixed cardinality analogous to those studied on the disk. We show that the components of the complexes constructed with two boundary points are shellable pseudomanifolds with boundary. We also show that the complex constructed from $3$-subsets in the case where the annulus has $n$ marked points on one boundary and none on the other is pure, has $n$ strongly connected components, and is homotopy equivalent to $S^{n-2}$.", "id": "Paper/68470", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68470"}, {"title": " Chain Behavior of the Stable Tamari Poset ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "c2bb0b81525121af37202e2ef15a248c1efcf2cb9386feb6da53b46572fb48c7", "withdrawn": "", "abstract": "The stable Tamari lattice extends the classical Tamari lattice, a central Catalan structure connected to Dyck paths, binary trees, associahedra, and other areas of algebraic combinatorics, to nonnegative integer sequences. Chains and antichains are fundamental structures in a poset, yet their enumeration remains subtle even for the classical Tamari lattice. We study the principal lower ideals generated by sequences of the form $(a,b,a)$, with $b>a$, and investigate their chain and antichain structure. For this family, we give explicit formulas and structural descriptions for several classes of chains and antichains, including saturated chains, maximal chains, and maximal antichains. Our results reveal regular patterns across the family and provide a systematic description of chain and antichain behavior in these stable Tamari lower ideals.", "id": "Paper/68473", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68473"}, {"title": " From Deficiency to Abundancy: Computational Experiments and Restrictions on Odd Perfect Numbers ", "webprogram_exclude": "0", "session_ids": ["Session/19361"], "source_sha256": "8cd1d0543279d38254aebc53ffac8cd76c2d562695bc31f8a958ecfcd7f9e91c", "withdrawn": "", "abstract": "Like many, the deceptively simple conjecture that no odd perfect number (OPN) exists and the plethora of results that point in that direction, has led me down the trail of multiple dead ends of its proof. That said, the results that are found along the way add to our understanding of how integers behave.\n\nThis led to the development, with Matthew Thomas, of the OPN Computational Sandbox, an open-source computational tool that allows users to vary prime factors and exponents, examine conditions required of odd perfect numbers, and observe how the divisor-sum ratio $\\sigma(N)/N$ changes. Most products examined in our experiments were abundant, with $\\sigma(N)/N>2$, while fewer were deficient. These observations prompted the question: what conditions on the prime factors and exponents cause a product to cross from above two to below two?\n\nIn this talk, I will explain how this question led to a restriction on odd perfect numbers not divisible by three: at least three non-Euler exponents must lie outside the residue class two modulo six. The argument uses $p^2+p+1$ to identify forced prime divisors, then combines congruences, abundancy estimates, and an exact finite computation. The proof requires no prescribed number of prime factors and no upper bound on the exponents or the size of $N$.\n A convergent series accounts for all contributions beyond the finite calculation. Complementary estimates identify combinations of primes that force abundancy above two, regardless of additional prime factors. The emphasis is on the progression from computational observations to exclusions of entire families of products.", "id": "Paper/68475", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68475"}, {"title": " Data Assimilation for Chemical Reaction Networks and Population Models via a Tunable Observer ", "webprogram_exclude": "0", "session_ids": ["Session/19337"], "source_sha256": "2a461167569edb52c6c5dafb5bbc4b281449ee302fc0085a8592d0d217f2ab19", "withdrawn": "", "abstract": "We consider the problem of state reconstruction for a nonlinear dynamical \nsystem from observations of a linear function of the state. We present a design\n method for a tunable observer and provide a general theorem which under \ncertain conditions guarantees exponential convergence of the observer regardless of initial error. Additional results are provided that apply this theorem to \nchemical reaction network models. Moreover, these results are illustrated \nvia examples of mass action form of chemical reaction networks where a subset of the \nspecies concentrations are observed. Numerical results are provided to show \nthe efficacy of our proposed observer. Numerical results are also shown \nfor the case of noisy observations and our observer is compared favorably with the\nparticle filter when the observation noise is small.", "id": "Paper/68476", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68476"}, {"title": " Gradient Descent When Gradient Flow Is Nonunique: Implicit Regularization Beyond the Positive Orthant ", "webprogram_exclude": "0", "session_ids": ["Session/18273"], "source_sha256": "ab4cd347d2daaba1849237468cb2d42e0a785f484431397585a66807735b3c03", "withdrawn": "", "abstract": "Gradient flow is commonly used as a continuous approximation of gradient descent. This connection becomes ambiguous when a reparametrization makes the gradient-flow equation nonunique: multiple trajectories may remain at, wait at, or cross the same singular point. This phenomenon can occur even when the loss is smooth and convex in the represented variable, with the degeneracy introduced entirely by the parametrization.\n\nI will present a change of variables based on integrating the reciprocal derivative of the parametrization. Under local conditions related to the Osgood criterion, the transformed—or dual—dynamics are uniquely solvable even though the original gradient flow is not. The same transformation also produces the mirror variable and Bregman geometry associated with the parametrization.\n\nI will then discuss gradient descent itself. For signed-power parametrizations, the depth of the first discrete crossing determines whether the vanishing-step limit crosses the singularity immediately, waits for a positive time, or becomes trapped. This yields a quantitative selection principle and extends to coupled coordinatewise dynamics with transverse singular crossings. I will conclude with ongoing work on generic selection, multidimensional delayed dynamics, and consequences for implicit regularization.", "id": "Paper/68477", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68477"}, {"title": " Amalgamating Lazarson and Non-Lazarson Matroids ", "webprogram_exclude": "0", "session_ids": ["Session/19366"], "source_sha256": "452978695e55a54f7c8380cd08499f1db9379bef9c8d433a8ab6663ec5c18792", "withdrawn": "", "abstract": "Until recently, it was an open question whether the dual of an algebraic matroid is algebraic; it has now been answered in the negative by Matt Larson and Tuong Le. We construct a family of matroids $M_p^{\\pm}$, one for each prime $p$, obtained as an amalgam of the Lazarson matroid $M_p$ and the non-Lazarson matroid $M_p^{-}$. Each $M_p^{\\pm}$ has an algebraic representation over characteristic $p$ consisting of only linear forms and monomials, but is representable over no field. We show that the dual of $M_p^{\\pm}$ is algebraic over characteristic $p$ as well, and show that this particular type of linear-monomial amalgam cannot produce a matroid with a non-algebraic dual if the monomial component is a circuit-hyperplane relaxation of its linearization.", "id": "Paper/68481", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68481"}, {"title": " On the alternating number of independent sets in a graph ", "webprogram_exclude": "0", "session_ids": ["Session/17900"], "source_sha256": "b51d18bc6251d6ad50191b98306aba4b5f56e816811d4f58373009550a597294", "withdrawn": "", "abstract": "The independence polynomial of a graph $G$ is defined by\n\\[\n\tI(G;x)=\\sum_{I\\in \\mathcal{I}(G)} x^{|I|},\n\\]\nwhere $\\mathcal{I}(G)$ is the set of all independent sets in $G$.  There has been much interest in the alternating number of independent sets in a graph, which is simply $I(G;-1)$, the independence polynomial evaluated at $-1$.  One reason this is a popular area of research is that it corresponds, e.g., to the reduced Euler characteristic of the independence complex of a graph.  Engst\\\"om proved an upper bound on $|I(G;-1)|$ in terms of the decycling of a graph $G$, i.e., the minimum size of a set of vertices $S$ so that $G-S$ is acyclic.  In particular, he proved $|I(G;-1)|\\leq 2^{\\phi(G)}$ where $\\phi(G)$ is the decycling number of $G$.  In this talk, we'll present some improvements of Engstr\\\"om's bound.  We'll also outline some research in which one tries to characterize extremal graphs for these bounds.  While much of this work has been done by others, our work in this area is joint with various subsets of Nathan Kahl, Yihan Carmen Li, and Phoebe Zielonka.", "id": "Paper/68482", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68482"}, {"title": " Gröbner Bases and Generalized Hamming Weights of Linear Codes ", "webprogram_exclude": "0", "session_ids": ["Session/18388"], "source_sha256": "dd0610ca19d26b3d8686e53a5744056a2330cdcebc6deab543f858c32c74c191", "withdrawn": "", "abstract": "For binary linear codes, Gr\\\"obner basis techniques have been used to determine the first and second generalized Hamming weights from an associated binomial ideal. In this talk, we consider a binomial ideal that extends this construction to linear codes over arbitrary finite fields. We discuss how Gr\\\"obner bases of these ideals can be used to study generalized Hamming weights and examine the limitations of this approach in the nonbinary case.", "id": "Paper/68490", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68490"}, {"title": " Optimization-based structure-preserving methods for the generalized Korteweg-de Vries equation ", "webprogram_exclude": "0", "session_ids": ["Session/17872"], "source_sha256": "b0c2f0992f2bb7fbeb35b8fb3ea081e3569db5a540009c2c7292b7398d19f5e8", "withdrawn": "", "abstract": "Structure-preserving numerical methods play a fundamental role in the long-time simulation of nonlinear dispersive waves by maintaining the physical invariants of the underlying system. Standard local discontinuous Galerkin (LDG) methods provide high-order accuracy and geometric flexibility, yet they generally do not preserve multiple invariants simultaneously. We develop optimization-based correction strategies that enforce discrete conservation properties for the generalized Korteweg--de Vries (gKdV) equation. Specifically, we propose two optimization methods based on Davis--Yin splitting (DYS) that preserve mass and energy or mass and the Hamiltonian, respectively, together with an alternating direction method of multipliers (ADMM) formulation that simultaneously preserves the discrete mass, energy, and Hamiltonian. Numerical experiments include noidal-wave and solitary-wave benchmarks. Numerical tests show that the proposed corrections enforces the prescribed conservation laws and retain the convergence order of the underlying LDG discretization. Furthermore, the optimization-based methods significantly improve the long-time accuracy of the numerical solutions compared with the uncorrected LDG method. Numerical results indicate that applying the optimization only every few time steps is sufficient to maintain the prescribed conservation properties, resulting in negligible computational overhead. These results provide an efficient, accurate, and robust framework for constructing invariant-preserving discontinuous Galerkin methods for nonlinear dispersive equations with multiple conserved quantities.", "id": "Paper/68491", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68491"}, {"title": " Cospectral Graphs for the Non-backtracking Matrix ", "webprogram_exclude": "0", "session_ids": ["Session/18227"], "source_sha256": "704d5a8ca251c994f1d0955b7f62677ba673f79b9f8b64bff84d9aaccc9559c4", "withdrawn": "", "abstract": "The non-backtracking matrix is the transition matrix for a walk in a graph which cannot traverse an edge twice in immediate succession. The spectral information of this matrix has seen great interest, notably in applications regarding network analysis. Constructions of cospectral graphs can begin to explore what information cannot be contained in the spectrum. In this talk, we prove structural results for the characteristic polynomial of this matrix, which lead to the construction of several families of cospectral graphs. We will also highlight curiosities found in the data for all cospectral graphs on eleven or fewer vertices.", "id": "Paper/68492", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68492"}, {"title": " The strong asymptotic local-to-global principle for orthoplicial sphere packings ", "webprogram_exclude": "0", "session_ids": ["Session/18366"], "source_sha256": "6d57ec50194cee3605545d10367a8fce4c4d9200b868429aa5ad2d892f77cdb7", "withdrawn": "", "abstract": "Using the circle method, we prove the strong asymptotic local-to-global principle for orthoplicial sphere packings. Sometimes each sphere in an orthoplicial sphere packing has a bend (1/radius) that is an integer. When all the bends are integers, which integers appear as bends? For a fixed orthoplicial sphere packing, there are certain congruence restrictions for bends modulo 4. The strong asymptotic local-to-global principle for orthoplicial sphere packings states that if a sufficiently large integer meets the congruence restrictions for the orthoplicial sphere packing, then the integer is the bend of a sphere in that packing.", "id": "Paper/68493", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68493"}, {"title": " Syzygies in toric geometry ", "webprogram_exclude": "0", "session_ids": ["Session/18318"], "source_sha256": "c36d1bd0d227736eb4b74d58f0f48f2851d6effd950bd6eeab145548462868a2", "withdrawn": "", "abstract": "A smooth normal toric variety $X$ is determined by a multigraded polynomial ring $S$ and a monomial ideal encoded by the fan of $X$. When a normal toric variety $Y$ is embedded into $X$, recent results show that the multigraded free $S$-resolution of the ideal for $Y$ has an abundance of rich combinatorial and geometric structure. We will discuss new developments for such resolutions.", "id": "Paper/68494", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68494"}, {"title": " Diffeomorphisms Arising from Monodromy in Linear Systems ", "webprogram_exclude": "0", "session_ids": ["Session/17904"], "source_sha256": "b214bcf5d3a806152e7083044bf31de2db11a0df3e879b741c4149c1ef505e3b", "withdrawn": "", "abstract": "For any family of smooth complex varieties, there is a monodromy representation valued in the mapping class group of the fiber, i.e. the group of isotopy classes of diffeomorphisms of the fiber.  This representation measures the topological complexity of the family, and is a natural tool to study the fundamental group of the base.  We study this representation for the universal family associated to a complete linear system, the simplest case being the universal family of hypersurfaces in projective space.  We focus in particular on the image of this representation; that is, which diffeomorphisms of the fiber arise from monodromy?  We survey our recent work on this question in the case of high-dimensional fibers, where we approach this problem using tools from Hodge theory, rational homotopy theory, geometric topology, and more.\nThis work is joint with Sidhanth Raman.", "id": "Paper/68495", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68495"}, {"title": " Cops, Robbers, and a Duck ", "webprogram_exclude": "0", "session_ids": ["Session/19360"], "source_sha256": "4a9edb42bd29d736937bc0c585543de7e48011fe6e32880bee0995b40de83743", "withdrawn": "", "abstract": "We combine the game of \\emph{Cops and Robbers} with the chess variant \\emph{Duck Chess} to create \\emph{Ducks and Robbers}. In this pursuit-evasion game, the cops and robbers may place an impenetrable ``duck'' after their moves to obstruct their opponents mobility. We also introduce \\emph{duck graphs} as an extension of regular graphs which record the movement routes taken by the players and how the duck blocks them. The duck cop number is the fewest cops needed to guarantee capture in this game.\n\nOur results include duck cop numbers for several familiar graph families, including trees, cycles, and hypercubes, as well as exact values or bounds for chess graphs. We also prove that the duck cop number is additive over connected components and characterize the graphs on which $k$ cops can guarantee capture. Finally, we prove that for any positive integers $p$ and $k$, there exists a graph with cop number $k$ and duck cop number $p$.", "id": "Paper/68496", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68496"}, {"title": " Nonsimplicial toric Nullstellensatz and stacky GKZ theory ", "webprogram_exclude": "0", "session_ids": ["Session/18285"], "source_sha256": "8cbf1df7515567f050b95f640610acf3f75f70cfef6d95461ebad75dbe08ac20", "withdrawn": "", "abstract": "Projective geometry and graded algebra are classically intertwined. Due to pioneering work of Cox and others, there is an enhancement of this algebro-geometric dictionary connecting the geometry of simplicial toric varieties to multigraded algebra, which fails in the nonsimplicial setting. We introduce a variant of the Cox ring using $\\mathbb{Q}$-Cartier divisors and use this\nto remedy various deficiencies of nonsimplicial toric varieties.", "id": "Paper/68497", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68497"}, {"title": " Compact Kahler fourfold without effective divisors and surfaces is torus or hyperkahler ", "webprogram_exclude": "0", "session_ids": ["Session/19358"], "source_sha256": "509bd8f89c5f31cd68f71bb8538445c4e4f810a12db57cf0ec0993612773bcc4", "withdrawn": "", "abstract": "We prove that compact kahler fourfold without effective divisors and surface is torus or hyperkahler resolving the a conjecture of Campana-Diemally-Verbitsky in dimension four.", "id": "Paper/68501", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68501"}, {"title": " The Bures metric and the quantum metric on the density space of a C*-algebra: the non-unital case ", "webprogram_exclude": "0", "session_ids": ["Session/17834"], "source_sha256": "926358f60dec67c0026bb6a22c89e5df9c015811fd9f42ba15b3f007fc225172", "withdrawn": "", "abstract": "Building off work of Farenick and Rahaman, we extend the definition of the density space and the Bures metric to the setting of non-unital C*-algebras equipped with a faithful trace and prove that the Bures metric is a metric in this case and that its topology is weaker than the topology induced by the C*-norm. Furthermore, we prove a Heine-Borel type theorem for C*-algebras and the density space. In particular, we prove that for any C*-algebra (unital or non-unital) equipped with a faithful trace, the density space equipped with the Bures metric topology is not compact if and only if the C*-algebra is infinite dimensional. We also exhibit several examples of sequences that have no converging sequence. Next, building off work from some of the authors, we extend the definition of the quantum metric on the density space to the non-unital C*-algebra case by introducing the notion of a quantum Lipschitz triple, which form a subclass of quantum locally compact metric spaces of Latrémolière that utilize Rieffel's notion of a quantum metric (we also introduce new classes of commutative and noncommutative quantum locally compact metric spaces). Furthermore, we prove that this quantum metric topology is weaker than the topology induced by the C*-norm and finish the article with an analysis of matrix-valued functions on the quantized interval, where the quantum metric topology on the density space is not compact and the quantum metric is not uniformly equivalent to both the Bures metric and the C*-norm induced metric. This is joint work with Karina Behera, Katrine von Bornemann Hjelmborg, Tron Omland, Gregory Wickham, Nicole Wu, and Adam M. Yassine. This work is partially supported by NSF grant DMS-2316892.", "id": "Paper/68503", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68503"}, {"title": " Affine and Lattice Structures in Regular <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.678ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 722.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbb {N}</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJAMS-4E\" d=\"M20 664Q20 666 31 683H142Q256 683 258 681Q259 680 279 653T342 572T422 468L582 259V425Q582 451 582 490T583 541Q583 611 573 628T522 648Q500 648 493 654Q484 665 493 679L500 683H691Q702 676 702 666Q702 657 698 652Q688 648 680 648Q633 648 627 612Q624 601 624 294V-8Q616 -20 607 -20Q601 -20 596 -15Q593 -13 371 270L156 548L153 319Q153 284 153 234T152 167Q152 103 156 78T172 44T213 34Q236 34 242 28Q253 17 242 3L236 -1H36Q24 6 24 16Q24 34 56 34Q58 35 69 36T86 40T100 50T109 72Q111 83 111 345V603L96 619Q72 643 44 648Q20 648 20 664ZM413 419L240 648H120L136 628Q137 626 361 341T587 54L589 68Q589 78 589 121V192L413 419Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJAMS-4E\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Graded Vertex Operator Algebras ", "webprogram_exclude": "0", "session_ids": ["Session/18270"], "source_sha256": "654b11696357af60a491490444cdbf4261dff6838aaefff26bab7cdf2ca9c782", "withdrawn": "", "abstract": "We study regular $\\mathbb{N}$-graded vertex operator algebras whose weight-zero subspace $V_0$ is a nontrivial finite-dimensional local Gorenstein algebra. We discuss how familiar structures from the CFT-type setting persist in this more general framework. Under suitable hypotheses, semisimple Lie subalgebras of $V_1$ generate affine vertex operator algebras at positive integral levels. When $V_1$ is solvable, the Gorenstein structure of $V_0$ leads to Heisenberg and lattice vertex operator subalgebras. We also discuss shifted lattice examples that illustrate new phenomena beyond CFT-type.", "id": "Paper/68504", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68504"}, {"title": " Bifurcation and Complex Dynamics in a Discrete Smith-Type Predator–Prey Model with Epidemiological Applications ", "webprogram_exclude": "0", "session_ids": ["Session/17446"], "source_sha256": "9752d26dd25f3ae2909aecc06bb5fab1a6fcd851a9bdecb678f44090abbe1b85", "withdrawn": "", "abstract": "This study investigates a discrete predator–prey model incorporating Smith-type prey growth, group-defense predation, and prey immigration. Conditions for positivity, boundedness, and local stability of the coexistence equilibrium are established. Using the discretization step as a bifurcation parameter, the analysis shows that the coexistence state can lose stability through Neimark–Sacker and period-doubling bifurcations, leading to quasiperiodic oscillations and chaotic dynamics. Normal-form and center-manifold analyses are employed to characterize these transitions, while numerical bifurcation diagrams, phase portraits, and maximum Lyapunov exponents illustrate the resulting complex behavior. A global sensitivity analysis identifies the parameters that most strongly influence the long-term dynamics. Finally, the model is calibrated using COVID-19 and tuberculosis surveillance data under a phenomenological interpretation, demonstrating its potential to reproduce observed epidemiological trends.", "id": "Paper/68505", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68505"}, {"title": " Tipping Points ", "webprogram_exclude": "0", "session_ids": ["Session/18082"], "source_sha256": "d844501996be9e6622d46561e7d209adc86725c64dc65ef0b21317118f9e9307", "withdrawn": "", "abstract": "I will talk about cone points in flat space and how they add interest to questions originally about uniformly hyperbolic space, especially in my corner of thermodynamic formalism. A geodesic hitting a cone point is not unlike my own journey making decisions, big and small, without being quite sure where they would land me. You'll hear about my journey as a person and as a mathematician as well, with the tipping points being clear in hindsight.", "id": "Paper/68507", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68507"}, {"title": " Understanding the role of human movement in infectious diseases ", "webprogram_exclude": "0", "session_ids": ["Session/17688"], "source_sha256": "9a660ef48cc757f3a9b5224b9fcf6eb4730b12eab4bf450ebf6671761e8c1e7e", "withdrawn": "", "abstract": "Mosquitos are known for being a source of infectious diseases and are a cause of great concern within the public health community. As traveling has become more accessible, diseases such as malaria have surfaced in areas in which it has not been previously detected. Additionally, factors such as mobility patterns, environmental changes, and local transmission characteristics play an important part in disease dynamics. Thus, a better understanding of mosquito-borne diseases is needed to determine the best course of action to undertake this serious threat. In this talk, we will explore how epidemiological and ecological features influence mosquito-borne diseases via a multi-patch compartmental model. The objective of this talk is to present analytical tools and methodology to help discern how human mobility and regional attributes combine to impact disease dynamics.", "id": "Paper/68508", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68508"}, {"title": " The algebra of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"6ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 2583.2 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">(G,\\sigma )</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-47\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q492 659 471 656T418 643T357 615T294 567T236 496T189 394T158 260Q156 242 156 221Q156 173 170 136T206 79T256 45T308 28T353 24Q407 24 452 47T514 106Q517 114 529 161T541 214Q541 222 528 224T468 227H431Q425 233 425 235T427 254Q431 267 437 273H454Q494 271 594 271Q634 271 659 271T695 272T707 272Q721 272 721 263Q721 261 719 249Q714 230 709 228Q706 227 694 227Q674 227 653 224Q646 221 643 215T629 164Q620 131 614 108Q589 6 586 3Q584 1 581 1Q571 1 553 21T530 52Q530 53 528 52T522 47Q448 -22 322 -22Q201 -22 126 55T50 252Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-3C3\" d=\"M184 -11Q116 -11 74 34T31 147Q31 247 104 333T274 430Q275 431 414 431H552Q553 430 555 429T559 427T562 425T565 422T567 420T569 416T570 412T571 407T572 401Q572 357 507 357Q500 357 490 357T476 358H416L421 348Q439 310 439 263Q439 153 359 71T184 -11ZM361 278Q361 358 276 358Q152 358 115 184Q114 180 114 178Q106 141 106 117Q106 67 131 47T188 26Q242 26 287 73Q316 103 334 153T356 233T361 278Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-47\" x=\"389\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2C\" x=\"1176\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-3C3\" x=\"1621\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"2193\" y=\"0\"></use>\n</g>\n</svg>-circulant matrices ", "webprogram_exclude": "0", "session_ids": ["Session/18255"], "source_sha256": "d56b6a7ff8a7b31824e3f154af9414bff66469b99164023d410a9d8d3b2e8121", "withdrawn": "", "abstract": "For a finite group $G$, $G$-circulant matrices are a generalization of circulant matrices.  The authors have studied the ring of ``joins'' of such matrices over a ring R.  We investigate a further generalization, the notion of $(G,\\sigma)$-circulant matrices (where $\\sigma$ presents an action of G on a finite set $S$); these also form a ring.  Just as circulant and G-circulant matrices allow definitions of circulant and G-circulant graphs, we can define $(G,\\sigma)$-circulant graphs.", "id": "Paper/68511", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68511"}, {"title": " Complex scaling for open waveguides ", "webprogram_exclude": "0", "session_ids": ["Session/17702"], "source_sha256": "19fd6547cec30f4c3e39c63721fdbcf6caf0af343e905bf2e325e681869f7fcc", "withdrawn": "", "abstract": "This talk concerns the Helmholtz scattering problem for open waveguide networks. We reduce the problem to a boundary integral equation (BIE) along an infinite interface orthogonal to the waveguides. The involved integral kernels decay slowly at infinity, but they admit analytic continuations into the complex plane. In the first and third quadrants, these continuations decay exponentially away from the real axis. Given suitable boundary data, we show that the solution to the BIE also has an analytic continuation which satisfies the same favorable decay properties. This allows us to deform the integration contour and efficiently truncate the computational domain. We present several numerical examples.", "id": "Paper/68512", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68512"}, {"title": " Iterated Function Systems and Dimensionality Reduction ", "webprogram_exclude": "0", "session_ids": ["Session/19336"], "source_sha256": "5c9df5c109ea343c2f3f9db6b0e328ae8a397ff759b209d9ff9a3c9e086e8bb2", "withdrawn": "", "abstract": "In this paper, we propose the idea of using iterated function systems (IFS's) for dimensionality reduction. IFS's are well-known tools for producing fractals whose Minkowski (and therefore Hausdorff) can be easily upper bounded. We show that one can find an IFS that generates a fractal of at most a given dimension that is ``close to'' a data set and suggest that moving all the points on that data set to the nearest point on the fractal can be uses for dimensionality reduction.", "id": "Paper/68513", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68513"}, {"title": " Long Directed Cycles in Vertex-Transitive Digraphs ", "webprogram_exclude": "0", "session_ids": ["Session/18360"], "source_sha256": "391f75d79240521d30bef688ada34dccdd14731d68e8f1352a03833fdc5e8de8", "withdrawn": "", "abstract": "How long a directed cycle must a connected vertex-transitive digraph contain? This question links graph theory with classical problems in group theory. Although such digraphs need not be Hamiltonian, Alspach asked in 1981 whether their longest directed cycles could miss arbitrarily many vertices.\n\nBuci\\'c, Hendrey, Mohar, Steiner and Yepremyan recently answered this question by constructing examples with $(1-o(1))\\log n$ omitted vertices, and conjectured that a linear number could be omitted. We prove this conjecture: for infinitely many $n$, we construct a connected vertex-transitive digraph with $n$ vertices in which every directed cycle misses at least $n/12$ vertices.\n\nIn the other direction, we show that every connected vertex-transitive digraph with $n\\geq 2$ vertices has a directed cycle of length $\\Omega(\\sqrt{n})$. This improves the previous guarantee of $\\Omega(n^{1/3})$ due to the same authors and gives a directed counterpart to Babai's classical 1979 bound for undirected vertex-transitive graphs.\n\nThis is joint work with Bowen Li.", "id": "Paper/68514", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68514"}, {"title": " The DP Color Function of Bipartite Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18360"], "source_sha256": "b589059fe973d34747758bb5d83b781ccc9b0f45f9c3fe05ab651789d4327b13", "withdrawn": "", "abstract": "DP-coloring (or correspondence coloring) is a generalization of list coloring that has been widely studied since its introduction by Dvo\\v{r}\\'{a}k and Postle in 2015. As the analogue of $P(G,q)$, the chromatic polynomial of a graph $G$, the DP color function of $G$, denoted by $P_{DP}(G,q)$, counts the minimum number of DP-colorings over all  $q$-fold covers of $G$. It follows that $P_{DP}(G,q) \\leq P(G,q)$.  It is known that there are graphs for which $P_{DP}(G,q) < P(G,q)$ for all sufficiently large $q$; in fact, all bipartite graphs containing a cycle have this property.  A fundamental open question about DP color functions asks whether, for every graph $G$, there exist $N \\in \\mathbb{N}$ and a polynomial $p$ such that $P_{DP}(G,q) = p(q)$ whenever $q \\geq N$.  We answer this question affirmatively for all bipartite graphs. Specifically, if $G$ is an $n$-vertex bipartite graph with $c$ components, then $P_{DP}(G,q) = (-1)^{n-c}q^c \\;T_G(1-q,1)$ for all sufficiently large $q$, where $T_G(x,y)$ is the Tutte polynomial of $G$. The ideas we develop also yield an asymptotic formula for $P(G,q)-P_{DP}(G,q)$ whenever the girth of $G$ is even.", "id": "Paper/68515", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68515"}, {"title": " Sensitivity Analysis of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.818ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 1213.4 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">R_0</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-52\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-30\" x=\"1074\" y=\"-213\"></use>\n</g>\n</svg> in a Mathematical Model of Dermo Disease in Oyster Population within a Bay Ecosystem ", "webprogram_exclude": "0", "session_ids": ["Session/18023"], "source_sha256": "ec9bad53ea7575d2b7b4e5edcbec2eb107cddc7d9e01de3e15fcc71ebb246b66", "withdrawn": "", "abstract": "Dermo disease caused by infection with Perkinsus marinus represents a significant source of mortality for the oyster population influencing its survival in affected areas. In this talk, a simple mathematical model of the spread of Dermo disease in oyster population is presented as a system of ordinary differential equations. The basic reproduction number $R_0$ is computed using the next generation method. Sensitivity analysis will be used to illustrate the impact of model parameters. This model will be applied to study the impact of Dermo disease in oysters population within a bay ecosystem.", "id": "Paper/68517", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68517"}, {"title": " Exotic Pattern Formation in Reaction-Diffusion Media ", "webprogram_exclude": "0", "session_ids": ["Session/19351"], "source_sha256": "915a4273c5292c743611cb457e390105f1effaec703983b64609b4bda4ae6d9b", "withdrawn": "", "abstract": "Reaction-diffusion dynamics in ideal homogeneous media typically produce regular patterns that are periodic in space or time, or fully synchronized oscillations, while localized structures such as oscillons usually rely on more specific nonlinear mechanisms, including bistability, subcriticality, or front pinning. Real media, however, are never perfectly homogeneous, and even weak, randomly distributed imperfections can fundamentally change this picture. Here, we show that such imperfections provide a simple and generic route to localized and mixed dynamics by inducing localization of Laplacian eigenmodes, which then interact nonlinearly with extended oscillatory modes. We study this mechanism in one, two, and three dimensions by discretizing the medium into lattices and exploiting the spectral structure of the graph Laplacian. Using the Brusselator and Zhabotinsky models, we uncover four characteristic states: stationary localized patterns, mixed states in which stationary localized regions are surrounded by synchronized oscillations, oscillons, and chimera patterns displaying the coexistence of coherent and incoherent dynamics. Our results show that localized and hybrid patterns need not rely on finely tuned nonlinear mechanisms: weak imperfections alone can provide a broadly accessible route to their emergence across spatial dimensions.", "id": "Paper/68519", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68519"}, {"title": " Permutation flows for the working mathematician ", "webprogram_exclude": "0", "session_ids": ["Session/18286"], "source_sha256": "e062d183f7173a648a4c1f2c921a562a9bf0358112a8ab7346eb8ea84a834bd9", "withdrawn": "", "abstract": "We introduce a new broadly unifying family of combinatorial objects, which we call permutation flows, associated with an acyclic directed graph $G$ together with a \\emph{framing}--a collection of total orders on the sets of incoming and outgoing edges at each vertex. This new family is combinatorially and geometrically rich: it contains as special cases multiple families of combinatorial objects that are frequently studied in the literature, and it characterizes completely a unimodular triangulation, defined by Danilov, Karzanov, and Koshevoy, of the unit-netflow flow polytope on $G$.  The model comes with an order structure on permutation flows which we call the weak order, and we use it to show that the $h^*$-polynomial of this flow polytope is the $G$-Eulerian polynomial.", "id": "Paper/68520", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68520"}, {"title": " On the Subtree Sequences and Log-Concavity ", "webprogram_exclude": "0", "session_ids": ["Session/18369"], "source_sha256": "377fbf81c9170c7e0e0e50aad7ba5fe84d09cd704a7f3c43aaef52681386472e", "withdrawn": "", "abstract": "\\begin{abstract}\nLet $s_k(T)$ denote the number of subtrees of a tree $T$ with exactly $k$ vertices. Ralaivaosaona and Wagner investigated the unimodality of this sequence through the lens of log-concavity, motivated by a question of Jamison. In this work, we set $s_k(T)$ as the sequence of the number of subtrees of $T$ with $k$ leaves and used computational processes to produce sequences that violate log-concavity, starting at the number of vertices of $T$, $N \\geq 14$\n\nFurthermore, we observed plausible evidence to establish a linear relationship which may be used to predict the approximate number of violations for the $N$ vertices, and there appears to be an approximately normal distribution in the lengths of the rows of violating trees, where a row is the longest walk starting at a central node until a leaf.   We conclude with an exploration of common structural features among the violating trees, including recurring tree shapes and index patterns at which log-concavity breaks.\n\nThis talk is jointly presented by Hamza Jivan and Vaishnav Venkat.\n\\end{abstract}", "id": "Paper/68522", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68522"}, {"title": " Weighted bond posets and a new chromatic symmetric function ", "webprogram_exclude": "0", "session_ids": ["Session/18375"], "source_sha256": "58687397baf14d9a8eea2db8f75cf41ae52c2c386d8416120dfe9f19a4ea6fe5", "withdrawn": "", "abstract": "The classical bond lattice of a graph was used in a formula of Whitney to compute the chromatic polynomial.  We use weighted versions of the bond lattice to introduce and study a new symmetric function analog of the chromatic polynomial.  The highest degree homogeneous component of this symmetric function is of particular interest. The parking function symmetric function introduced by Haiman arises as an example, as do symmetric functions studied by Gonz\\'alez D'Le\\'on in connection with multibracketed Lie algebras and with colored exterior algebras. Using the theory of lexicographic shellability, we prove that, for any chordal graph, our chromatic symmetric function is alternating e-positive. We conjecture that it is also Schur-log-concave, which specializes to  Huh's log-concavity theorem for the chromatic polynomial.", "id": "Paper/68525", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68525"}, {"title": " Lattices over the Weyl Algebra modulo <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.313ex\" height=\"2.843ex\" style=\"vertical-align: -0.671ex; margin-left: -0.089ex;\" viewBox=\"-38.5 -934.9 995.9 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">p^2</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-70\" d=\"M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-70\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-32\" x=\"712\" y=\"513\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/19342"], "source_sha256": "1ac4a727b2bcb649e14b1352cbd37eb4e23b45ee026e2df6a628734de9dae1f1", "withdrawn": "", "abstract": "Let $\\mathbf{k}$ be an algebraically closed field of characteristic $p>0$, and let $S=W_2(\\mathbf{k})$ be the ring of Witt vectors of length 2. We study representations of the first Weyl algebra which are finite rank free $S$-modules (lattices).\n\nGiven a lattice $M$ over $S[x]$, we show that $M$ admits a left module structure over the first Weyl algebra $S\\langle y, x\\rangle/(yx-xy-1)$ (equivalently, an $S$-linear connection) if and only if the trace of every $S[x]$-endomorphism of $M$ lies in the ideal $(p)$. This is further equivalent to the condition that every indecomposable summand of $M$ has rank divisible by $p$, and each such summand appears with multiplicity a multiple of $p$.\n\nMoreover, under the assumption that the action of $x$ is regular or subregular nilpotent modulo $p$ on each indecomposable summand, we fully classify all isomorphism classes of the Weyl module structures on $M$.", "id": "Paper/68528", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68528"}, {"title": " Apollonian Circle packings over a ring of integers ", "webprogram_exclude": "0", "session_ids": ["Session/18366"], "source_sha256": "8c6ba760dd2f6cda83854e42b11f7af66b80a5e5dc5c09e4196a3858aa9c6387", "withdrawn": "", "abstract": "Apollonian circle packings (ACPs) are a fractal created by continual inversion through 4 mutually tangent circles or a quadruple. \nAn integral ACP is when all the curvatures (1/radius) are integers. \nThe study of integral ACPs has many connections to geometry, number theory, group theory, etc. and leads to very nice illustrations. \nBut how much theory of integral ACPs still holds if we look at quadratic rings of integers as the curvatures? \nSome aspects still hold but we gain many more types of packings that are not covered by the integral case.\nIn this setting, the parameter space of Apollonian circle packings and Binary quadratic forms becomes very important to discover more about the arithmetic of these packings.\nWe will go over reduction theory for quadruples, how that is equivalent to reduction of binary quadratic fields, and how using the parameter space of Apollonian circle packings can be used to discover more about these packings.", "id": "Paper/68532", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68532"}, {"title": " Compact Quasi-Einstein Metrics of Constant Scalar Curvature in Low Dimension ", "webprogram_exclude": "0", "session_ids": ["Session/18290"], "source_sha256": "d84ac70840f72d5b3eb8937e82688f36308edc45697aba55567f10dd48a48bd1", "withdrawn": "", "abstract": "An m-quasi-Einstein metric on a Riemannian manifold (M,g) is a triple $(M,g,X)$ satisfying $Ric + \\frac{1}{2}\\mathcal{L}_X g - \\frac{1}{m} X^* \\otimes X^* = \\lambda g$, generalizing the Einstein metric. Classification results of quasi-Einstein metrics remain rare beyond dimension three. In this talk, I will present a full classification of compact $4$-dimensional, non-Einstein $m$-quasi-Einstein metrics with constant scalar curvature. Building on the fact that constant scalar curvature forces $X$ to be a Killing field of constant length, we reduce the problem to studying Riemannian manifolds whose Ricci tensor has two constant eigenvalues, one along a unit Killing field and the other on its orthogonal complement. This is joint work with Eric Cochran and William Wylie.", "id": "Paper/68533", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68533"}, {"title": " Identifiability Analysis on An Avian Influenza Model ", "webprogram_exclude": "0", "session_ids": ["Session/18127"], "source_sha256": "6e79ad4ae304f72b7fedd9aff97371956a8e3b5fc9a187f9dba4be6fa9d6ac76", "withdrawn": "", "abstract": "Avian influenza is an infectious disease that influences both wild and domestic birds across the world. Recently, we have witness an avian influenza outbreak in dairy cows in the United States that garners attention due to a possible strain mutation. Now, the transmission of avian influenza between humans is extremely rare, and it mostly affects people who are in close contact with infected birds. Although this scenario is uncommon, there have been multiple outbreaks that occur in small infection clusters with relatively low transmissibility and thus are too weak to cause a major outbreak. Studying subcritical transmission events is vital for determining whether avian influenza is close to reaching the threshold of the basic reproduction number being greater than one. In this talk, we will discuss the structural and practical identifiability of an avian influenza model. Furthermore, we will explore how identifiability influences key epidemiological measures.", "id": "Paper/68535", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68535"}, {"title": " Color 2-switches and color degree matrices ", "webprogram_exclude": "0", "session_ids": ["Session/18317"], "source_sha256": "e238b4bacc32370e9bfd1944838205d0cc8e8e9abde45d81daa80ef4f92a8173", "withdrawn": "", "abstract": "For two graphs with the same degree sequence, a classic result in graph theory provides a way to transform one to the other using a sequence of $2$-switches. Let $G$ be a graph with a $k$-coloring (which need not be a proper coloring). In this talk, we define the \\emph{color degree matrix} of $G$. We define color $2$-switches and use them to  prove that two $k$-colored graphs have the same color degree matrix if and only if there is a sequence of color $2$-switches that transforms one to the other. We call a graph property $\\cal P$ a \\emph{neighborhood balanced-color property} if whenever two $k$-colored graphs have the same color degree matrix, then both of them have $\\cal P$ or both do not have $\\cal P$. For any subset $S$ of neighborhood balanced-color properties, we discuss how to use color $2$-switches to construct connected graphs that have exactly the properties in $S$.", "id": "Paper/68536", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68536"}, {"title": " A Distributed Storage Technique Applied to Secure Distributed Matrix Multiplication ", "webprogram_exclude": "0", "session_ids": ["Session/18389"], "source_sha256": "cff85774a3652dd469655f059f0aa7e0b4377c660834eda74fa8d9a7d827ea2a", "withdrawn": "", "abstract": "The literature on the communication-efficient secure distributed matrix multiplication problem has focused on reducing the number of servers as a proxy for minimizing communication costs. However, R. A. Machado  et al. [1] adapted techniques from repair of Reed-Solomon codes to show that, in some situations, increasing the number of servers can reduce the total communication cost. In this talk, we present a new approach based on distributed storage techniques. We analyze its communication cost and characterize regimes for which they outperform the scheme of Machado et al. and other existing constructions in the literature.\n\n\n[1] R. A. Machado, R. G. L. D’Oliveira, S. E. Rouayheb and D. Heinlein, \"Field Trace Polynomial Codes for Secure Distributed Matrix Multiplication,\" 2021 XVII International Symposium \"Problems of Redundancy in Information and Control Systems\" (REDUNDANCY), Moscow, Russian Federation, 2021, pp. 188-193.", "id": "Paper/68537", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68537"}, {"title": " An Application of Topological Methods to EEG Data During DBS ", "webprogram_exclude": "0", "session_ids": ["Session/18007"], "source_sha256": "fcf7b594617d1e3f4203b62631c76223e46e8bca2646be1bca24449f46a40249", "withdrawn": "", "abstract": "Deep brain stimulation (DBS) is an FDA-approved neurosurgical intervention for intractable obsessive-compulsive disorder (OCD), but the exact therapeutic mechanism is unknown. We consider invasive stereo-EEG (sEEG) recordings with high spatiotemporal resolution from one patient with surgically implanted electrodes for comorbid treatment-resistant epilepsy. Previous work by a subset of the authors uses a directed measure of functional connectivity (phase slope index, or PSI) to identify a small subnetwork where connectivity changes directionality during DBS and is associated with clinical improvement.\n\nBeyond a few nodes, is there evidence of network-level reorganization correlated with DBS and clinical effect? To answer this, we consider an undirected measure of functional connectivity (weighted phase lag index, or wPLI) and investigate what network-level effects of DBS are revealed. While statistical properties of wPLI matrices with and without stimulation are nearly identical, topological analysis of the matrices reveals evidence of network-level changes in functional connectivity during stimulation consistent with a reorganization towards multiscale geometry. These results are a step towards understanding global connectivity changes associated with clinical improvement of intractable OCD induced by DBS. This is joint work with Mohamed A. Sherif, Michaela E. Alarie, Anna R. Kimata, Mei E. Tiemeyer, Nicole C. R. McLaughlin, Steven A. Rasmussen, and Wael F. Asaad.", "id": "Paper/68540", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68540"}, {"title": " On an Inverse Nodal Problem for a Class of Second-Order Differential Equations ", "webprogram_exclude": "0", "session_ids": ["Session/17965"], "source_sha256": "64db8344872612031c743dbcf9ad99e25f49ca3c05b69bc435e18dc1d7e0d9ac", "withdrawn": "", "abstract": "This work considers an inverse problem for a second-order differential equation on a finite interval with Dirichlet boundary conditions containing linear and quadratic powers of the spectral parameter. Using a Liouville transformation, the problem is converted to canonical form. Asymptotic expansions for the eigenvalues and the interior zeros (nodal points) of the eigenfunctions are analyzed via Prüfer techniques. We investigate the recovery of the coefficient functions from the distribution of nodal points and discuss conditions for uniqueness.", "id": "Paper/68541", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68541"}, {"title": " On an Extremal Inverse Problem for Dynamic Equations on Time Scales ", "webprogram_exclude": "0", "session_ids": ["Session/17965"], "source_sha256": "5d22aa9ec20bf54db40e777e2d7d6039ad969866cda85cde58972d7103266187", "withdrawn": "", "abstract": "This work examines an optimal inverse problem for a second-order linear dynamic equation on an arbitrary bounded time scale under Dirichlet boundary conditions. Given prescribed spectral data consisting of finite eigenvalues, we investigate the infimum of the norm of the potential functions associated with the problem. By establishing and employing generalized Lyapunov-type inequalities adapted to dynamic equations, together with variational principles on time scales, we analyze lower bounds for the potentials and explore conditions under which these extremal bounds can be attained. Applications to eigenvalue bounds and potential recovery in discrete, continuous, and hybrid settings are discussed.", "id": "Paper/68542", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68542"}, {"title": " Properties of algebraically defined edge-colored graphs ", "webprogram_exclude": "0", "session_ids": ["Session/19354"], "source_sha256": "d399acfff13d810ded744843444a5b3a94db0a026ec6a1f1f562c5fc73759f23", "withdrawn": "", "abstract": "Let $\\mathbb{F}$ denote a field.  In this talk, we consider edge-colorings of the complete bipartite graph where both partite sets are copies of $\\mathbb{F}^d$.  The color of each edge (red or blue) is determined according to whether the coordinates of its incident vertices satisfy predetermined polynomial equations.  We then discuss properties of these edge-colored graphs such as the existence and length of properly colored cycles and their proper diameters.", "id": "Paper/68544", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68544"}, {"title": " From Stock to SoC: Advising Students Across Modeling Domains ", "webprogram_exclude": "0", "session_ids": ["Session/18066"], "source_sha256": "27addbe9b0ea3f62268709101c7ae99962cd28e0c7c934fcf588cbdbdeb9229c", "withdrawn": "", "abstract": "What makes a good instructor may not be what makes a good modeling advisor. In structured quantitative courses, providing predetermined structure and worked examples is often among the basic responsibilities of an instructor: expectations should be explicit, and student work is evaluated against predefined criteria and established solution frameworks. Advising a student-initiated team for the Mathematical Contest in Modeling required a different instinct. The team grew out of my Mathematical Methods for Quantitative Finance course, where students had worked with stock prices, interest rates, and stochastic models. Yet they chose a smartphone battery-drain problem that initially seemed unrelated to their coursework. Before the contest, I emphasized a transferable modeling habit: begin with familiar structures and leverage the specialized knowledge you already have, then ask what carries over and what must change. Stock prices and battery state of charge (SoC), for example, can both be viewed as stochastic state variables, while battery discharge introduces distinct constraints and dynamics. Once the contest began, the students worked independently, ultimately developing a coupled stochastic model of SoC and degradation and using Monte Carlo simulation to study battery lifetime. My role was to prepare the environment rather than the solution through collaborative workflows, responsible AI practices, and a one-page “redline” summary that kept assumptions and the main argument visible. The team earned a “Successful Participant” designation. The experience reframed advising as structuring the conditions for students to transfer familiar reasoning across domains, make independent modeling choices, and justify their own path.", "id": "Paper/68546", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68546"}, {"title": " Small <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.07ex\" height=\"2.009ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -576.1 460.5 865.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">q</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-71\" d=\"M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-71\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-kernels in digraphs ", "webprogram_exclude": "0", "session_ids": ["Session/18339"], "source_sha256": "6687b6bfb68be8cf22319a64f423a73f5cc6b30da60a22122d7a493382c461ed", "withdrawn": "", "abstract": "An independent set $Q$ of a digraph $D$ is called a $q$-kernel if all vertices of $D$ are reachable from $Q$ via a directed path of length at most $q$. The small quasikernel conjecture of Erd\\H{o}s and Sz\\'ekely posits that every digraph $D$ with minimum in-degree $\\delta = 1$ has a $2$-kernel of size at most $\\frac{1}{2}|V(D)|$. In 2024, Spiro posed a more general question: What is the smallest constant $c_{\\delta,q}$ such that every digraph $D$ with minimum in-degree $\\delta$ has a $q$-kernel of size at most $c_{\\delta,q}|V(D)|$? We present new upper bounds for the constants $c_{\\delta,q}$ and conjecture that a simple lower bound construction is tight when $q\\geq 3$.", "id": "Paper/68547", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68547"}, {"title": " Kaplansky Decompositions of Polish Modules ", "webprogram_exclude": "0", "session_ids": ["Session/17949"], "source_sha256": "1a03f15bd4fc46c2206c41d78801d2b29308d29ef8b583fe8c107777065769f0", "withdrawn": "", "abstract": "Let $R$ be a countable ring. Given an $R$-module $A$, we call a decomposition\n$A = \\bigoplus_{i \\in I} N_i$ a \\emph{Kaplansky decomposition} if each $N_i$ is\ncountable. We characterize the uncountable Polish $R$-modules that admit a\nKaplansky decomposition: they are exactly the modules of the form\n$B \\oplus M^{\\omega}$, where $B$ and $M$ are countable and $M$ is\n$\\Sigma$-algebraically compact. The countable summand $B$ may moreover be taken\nto be an elementary submodule satisfying a mild closure condition, which makes\n$M^{\\omega}$ unique up to isomorphism, and hence an invariant of $A$.\nWe use this to characterize the countable rings admitting a free uncountable\nPolish $R$-module, generalizing results of Shelah and Solecki. This class of\nrings has a purely ring-theoretic description: it consists exactly of the\ncountable left perfect and right coherent rings, i.e.\\ the rings identified by\nChase's theorem on products of projective modules. We observe that these are\nalso exactly the countable $F$-rings, i.e.\\ those countable rings $R$ for which $R^{\\omega}$ is\nfree. Finally, we give a ring-theoretic characterization of the countable rings\n$R$ for which there exists an uncountable projective Polish $R$-module.", "id": "Paper/68550", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68550"}, {"title": " The splitting type of jet bundles on the projective line ", "webprogram_exclude": "0", "session_ids": ["Session/18030"], "source_sha256": "652ae8453e83dfc45f1a95c4fc3bf7212a937eb83b4bf7dba8c3f5fa997ff0cf", "withdrawn": "", "abstract": "Given a vector bundle E on a smooth variety X, one can associate to it its jet bundles, or bundles of principal parts. These bundles encode the Taylor expansions of local sections of E and arise naturally in the study of differential operators. When X is the projective line over a field K, jet bundles decompose as direct sums of line bundles, making it natural to study their splitting types. This question was studied by Maakestad in the early 2000s, and it is known that the splitting type depends in a nontrivial way on the characteristic of K. The goal of this talk is to give an explicit description of the splitting type in every characteristic. Joint work with Annet Kyomuhangi, Emanuela Marangone, and Ethan Reed.", "id": "Paper/68551", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68551"}, {"title": " O(n)-action on n-categories with adjoints ", "webprogram_exclude": "0", "session_ids": ["Session/19340"], "source_sha256": "960e105cdddc1a88dc4a14de0618fe51df5dd90323fe6458eb23a7d9967f54ca", "withdrawn": "", "abstract": "It is expected that the category of $n$-categories with adjoints admits an $\\mathrm{O}(n)$-action. Such an action follows from a sufficiently developed graphical calculus, for instance from the conjectural factorization-homology framework of Ayala--Francis. In this talk, we explain how to derive the $\\mathrm{O}(n)$-action from the more basic assumption of the cobordism hypothesis. If time permits, we discuss a generalization in which $n$ is allowed to vary, as well as a consequence for tensor products of categorical spectra with adjoints.", "id": "Paper/68552", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68552"}, {"title": " Cohomological Properties of Koszul Algebras: An Example ", "webprogram_exclude": "0", "session_ids": ["Session/18253"], "source_sha256": "215b2d4e389a819392432c9002f89dce46dcf8a25cc1d050a012cbf90c28d62c", "withdrawn": "", "abstract": "A finitely generated algebra over a field is (classically) Koszul if the residue field admits a linear resolution. We present an example of a Koszul algebra $R$ satisfying the following properties: (1) The cohomological support variety of $R$ is a hyperplane; and (2) The homotopy Lie algebra of $R$ has no nilpotent elements of degree 2. We will give an idea of the proofs and gadgets involved, in addition to providing a discussion as to why the existence of such a ring is interesting and somewhat surprising.", "id": "Paper/68553", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68553"}, {"title": " Curve-rigid codes from algebraic geometry ", "webprogram_exclude": "0", "session_ids": ["Session/18368"], "source_sha256": "3a2f57ab1d443645a7f1a40d5261b1e5bc0a2b042d514b37bcfb5662151e5739", "withdrawn": "", "abstract": "Algebraic coding theory studies how algebraic structures can be used to construct objects, referred to as codes, that enable reliable and efficient communication via their error-correcting capabilities. Because these codes are built from algebraic structures, they can inherit properties from the structure used to define them. For example, an algebraic geometry code inherits some automorphisms from the algebraic curve on which it is based. Code automorphisms play an important role in a number of applications in coding theory, including decoding, erasure recovery, local decodability, and local correctability. For applications to code-based cryptography, rigid codes, which are codes with a trivial monomial automorphism group, are of particular interest. While it is known that a random binary linear code of sufficiently large length and dimension satisfying some modest conditions is rigid with high probability, constructing explicit families of rigid codes remains challenging. In this talk, we present results relating to the permutation automorphism groups of certain two-point and three-point Hermitian codes. In particular, we define the notion of curve-rigid, and we present a family of curve-rigid three-point Hermitian codes.", "id": "Paper/68554", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68554"}, {"title": " Error Analysis for Operator Learning with Computed Models and Empirical Sampling ", "webprogram_exclude": "0", "session_ids": ["Session/17718"], "source_sha256": "bccb57fed9fe7790f17e8bcc241e64e3dd75107056dae59a7122a1ec21c2092b", "withdrawn": "", "abstract": "Operator-learning methods approximate mappings between function spaces from finitely many observations, but the approximation class, discretization, and sampling strategy used in practice are often themselves constructed from numerical data. This talk develops error analysis for such computed operator-learning pipelines. We study how perturbations in the model class and empirical information design affect stability, sample complexity, and the resulting approximation error, with particular attention to sampling strategies based on Christoffel or leverage information. The analysis identifies conditions under which guarantees derived for an ideal model persist for a computed one, as well as obstructions when important directions are not resolved by the available data. These results provide a framework for separating approximation, discretization, and information-design errors and for determining when data-dependent sampling can retain near-optimal recovery guarantees.", "id": "Paper/68556", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68556"}, {"title": " Nilpotent Elements in the Homotopy Lie Algebra ", "webprogram_exclude": "0", "session_ids": ["Session/18030"], "source_sha256": "28a50ea72d8c26c670e523d67bdca5b045282a82193f8fb69164d317b99d1db0", "withdrawn": "", "abstract": "The homotopy Lie algebra of a Noetherian local ring $R$ is a graded Lie algebra over its residue field that encodes information about the singularity of $R$. In this talk, we briefly introduce this object; then, will focus on the (non-) existence of certain types of elements of degree 2 in this Lie algebra, and we will subsequently relate this to properties of $R$.", "id": "Paper/68558", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68558"}, {"title": " Random Walks on Graphs: Hitting Probabilities and Last-Visit Distributions ", "webprogram_exclude": "0", "session_ids": ["Session/17106"], "source_sha256": "8acce75fad75fd39d0b0fc559c9fb251245e21bc27b23ba7004caa3ef021b96a", "withdrawn": "", "abstract": "\\begin{abstract}\nWe study a family of ``ant on a graph'' problems: an ant performs a simple (or weighted) random walk on a graph, coloring each vertex the first time it is visited, and we ask for the probability that a given vertex is the last to be colored, or that every ``sugar'' vertex is colored before the walk reaches a designated ``pesticide'' vertex. We begin with the classical gambler's ruin problem on the path and on the cycle (the $n$-clock), then generalize the underlying step distribution to obtain closed forms for hitting probabilities under endpoint-weighted, sigmoid-weighted, and general sequence-weighted walks. We extend the same questions to several standard graph families -- complete graphs, complete bipartite graphs, fan graphs, wheel graphs, spider trees, and book graphs -- deriving exact expressions for the relevant probabilities, several of which are governed by Fibonacci and Lucas numbers. We close with a recurrence-based approach to walks whose step size alternates, and a list of open problems. This is in joint with Mushtaq Kapasi, Steven Miller, Keon Moghaddam, Ananth Ramsankar, and Garrett Tresch.\n\\end{abstract}", "id": "Paper/68560", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68560"}, {"title": " Simplicial Neural Solvers for Time-Dependent PDEs on Unknown Manifolds ", "webprogram_exclude": "0", "session_ids": ["Session/18330"], "source_sha256": "f9f3e2adbf03bfee115be2b777797c89df0a8438a2fba3cc16eaa036f12f8acc", "withdrawn": "", "abstract": "Partial Differential Equations (PDEs) play a vital role in a wide range of scientific, engineering, and mathematical disciplines, as they describe complex phenomena involving functions of multiple variables and their rates of change. In many applications such as healthcare and Earth sciences,\nwe need to develop a PDE solution, given only a finite number of irregularly located estimates of the system's states that live on an unknown manifold such as incipient caries on the teeth surface or irregularly spaced weather stations in areas with variable terrain. Despite that such scenarios are widely met in various domains, from wildfire analytics to biomedical imaging, numerical solutions of PDEs on non-Euclidean domains, including deep learning (DL)-assisted solvers, remain substantially under-investigated comparing to their Euclidean counterparts. We aim to address this gap and focus on time-dependent PDEs defined on unknown Riemannian manifolds, treating these manifolds as the underlying domain. To approximate and evaluate differential operators and the associated PDE solutions on the unknown manifold, we leverage the tools of simplicial convolution, rooted in discrete exterior calculus, as the backbone for the DL-assisted solver. We discuss theoretical guarantees behind the proposed simplicial solver and illustrate its utility for a wide range of systems of non-linear PDEs. We find that the new simplicial neural solver attains the highly competitive performance, reducing the root mean squared error by at most 67\\% relative to the strongest curvature respecting method and by nearly an order of magnitude relative to solvers that are agnostic to geometry. We conclude by discussing how geometry can further boost neural  approaches for numerical PDEs.", "id": "Paper/68565", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68565"}, {"title": " Spectral Analysis and Grossly Determined Solutions for the One-Dimensional BGK Model ", "webprogram_exclude": "0", "session_ids": ["Session/18109"], "source_sha256": "b851beb8738ceaab76ce910aa42068e9be337f385b6b95d0bf41b759d5ca3f3c", "withdrawn": "", "abstract": "Building on our previous analysis of a simplified 1D BGK model, we consider the one-dimensional BGK model with conservation of mass, momentum, and energy. Using perturbation determinants, we study the spectrum and generalized eigenfunctions of the associated non-selfadjoint operator and discuss the extension of the generalized Fourier transform and Parseval identity to this rank-three setting. Our goal is to characterize decay toward grossly determined solutions in the sense of Truesdell and Muncaster.", "id": "Paper/68576", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68576"}, {"title": " Optimal Control of Periodic Nutrient Supply in a Free Boundary Avascular Tumor Growth Model ", "webprogram_exclude": "0", "session_ids": ["Session/19337"], "source_sha256": "3ab463d9bd5939ccce5e95aef25a68dec1df0657012601bc69ebe29b76a7fc4b", "withdrawn": "", "abstract": "We study an optimal control problem for a free-boundary model of spherical tumor\ngrowth under periodic nutrient supply control. The control is implemented by modifying the boundary condition of the nutrient concentration, reducing the supply available to the tumor from the surrounding healthy tissue. The biological goal is to determine an optimal drug dosing schedule that minimizes tumor size while limiting side effects of treatment.", "id": "Paper/68578", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68578"}, {"title": " Building Workforce Readiness Through Mathematical Modeling and STEM Learning ", "webprogram_exclude": "0", "session_ids": ["Session/18341"], "source_sha256": "611cafc12e36cb55e89efb8d451451b34bc8b249948331ec28215d50ef7a613b", "withdrawn": "", "abstract": "As employers increasingly emphasize transferable skills and skills based hiring, mathematics and other STEM courses can play an important role in preparing students for the workforce. This presentation describes the redesign of an undergraduate mathematical modeling course that intentionally integrates NACE Career Readiness Competencies with authentic, real world modeling experiences. Students work collaboratively to make assumptions, develop and evaluate models, use technology, and communicate recommendations through written and video presentations. Assignments and rubrics connect these experiences to critical thinking, communication, teamwork, technology, and professionalism. The presentation will highlight how mathematical modeling can bridge disciplinary learning, interdisciplinary STEM problem solving, and workforce readiness while helping students recognize and articulate the skills they develop through mathematics.", "id": "Paper/68579", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68579"}, {"title": " Schur–Weyl Duality for Wreath Product Algebras ", "webprogram_exclude": "0", "session_ids": ["Session/17666"], "source_sha256": "3392f3dbb2387881d08884545eeb53db9b0b2a7637cdeaeaca8b68e68c4005bd", "withdrawn": "", "abstract": "For more than a century, Schur--Weyl duality has been a cornerstone of representation theory.  Its original formulation links the representation theories of the general linear Lie algebra and the symmetric group, but it has since been widely generalized.  We will show that there is a common generalization that encompasses a number of these generalizations and provides many more, to boot.  This is joint work with Lauren Grimley.", "id": "Paper/68580", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68580"}, {"title": " Polynomial Eigenfunctions of the Hessian Determinant ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "a938cd5d73b02a4e800cd42bf3c8f43eacfd857590504491bee1e8c36a7f6edf", "withdrawn": "", "abstract": "Let $K=\\mathbb R$ or $\\mathbb C$, and let $\\lambda\\in K$ be nonzero.\nWe study polynomial solutions of\n$\\det D^2u=\\lambda u$. If $u$ has degree $d$ in $n$ variables, then\n$\\det D^2u$ has degree at most $n(d-2)$. If the highest-degree terms do\nnot cancel, degree comparison requires $n(d-2)=d$, which occurs only\nfor $(n,d)=(2,4)$ and $(n,d)=(3,3)$. Surprisingly, cancellation of the\nhighest-degree terms allows many additional inhomogeneous solutions.\n\nIn two variables, we classify all nonzero polynomial solutions and prove\nthat only degrees $4$ and $6$ occur. The quartic branch agrees with\nearlier work, while the sextic branch seems to be previously unknown. In three, four, and five variables,\nwe construct solutions in infinitely many degrees. In four and five variables, we obtain infinite families through a reduction to a one-dimensional backward heat equation. No solutions were found for $n>5$", "id": "Paper/68582", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68582"}, {"title": " Using Interactive Textbook Questions to Understand Student Thinking and Support Instruction ", "webprogram_exclude": "0", "session_ids": ["Session/18200"], "source_sha256": "492b3254a35117d99b5ec5e382203cd6c375bcdb43fe20f9ad52321bdc55b877", "withdrawn": "", "abstract": "PreTeXt-Runestone: Open Textbooks Engaging Undergraduates in STEM (PROTEUS) is a Development and Implementation project funded through NSF IUSE's Engaged Student Learning strand. Through STAR (composed of Students, Teachers, Authors, and Researchers) teams, we develop interactive textbook questions for open-source calculus and linear algebra textbooks hosted on the Runestone platform. The educational research component seeks to understand how groups of textbook users (STAR teams) work together to write interactive questions designed to elicit multiple ways of students’ thinking in classrooms, and how students and instructors use those interactive textbook questions. The Runestone platform collects comprehensive interaction data, including all student responses to embedded questions. The textbooks are freely available, and more than 120 courses currently use them. Analysis of Year 2 data revealed questions about what kind of feedback should be embedded within interactive questions to guide students toward the concepts each question targets, as current feedback often falls short of this goal. Instructors using the textbooks want to leverage student response data to tailor their teaching—identifying which concepts students find difficult or easy, and which questions most clearly reveal common misconceptions. This insight is essential for providing accurate, targeted feedback to students, understanding student difficulties and learning trajectories across their courses. In this talk we will share prototypes of representations of responses by type of questions that we are developing to be seen by teachers, with the goal of receiving comments by the audience about these prototypes.", "id": "Paper/68583", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68583"}, {"title": " INSPIREing the Next Generation of the STEM Workforce ", "webprogram_exclude": "0", "session_ids": ["Session/18200"], "source_sha256": "96c54fca549cc8853af10e8d6f51dc473108b0cae74b3d77c9eb9446b4c96e0c", "withdrawn": "", "abstract": "Preparing students for the STEM workforce requires more than disciplinary knowledge. Utah Tech University’s NSF funded S STEM INSPIRE Program combines scholarships, faculty mentoring, interdisciplinary research, and experiential learning to support academically talented students with financial need. Through a three semester experience, students from multiple STEM disciplines work together to address real world problems, develop and test prototypes, engage in design thinking and entrepreneurship, interact with industry, and present their work at conferences. The program intentionally develops critical thinking, problem solving, teamwork, communication, creativity, and professional awareness while helping students explore STEM career pathways. This presentation will highlight the INSPIRE model and discuss how integrating interdisciplinary research, mentoring, innovation, and workforce preparation can strengthen student engagement, persistence, and career readiness in STEM.", "id": "Paper/68586", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68586"}, {"title": " Antimagic Labelings of Cactus Graphs: Central Cactus Graphs with a Single Leaf Adjacent to a Noncentral Vertex ", "webprogram_exclude": "0", "session_ids": ["Session/17963"], "source_sha256": "7ba5d5100aa99e9406e21179991cea82846cfca962ef5beca661180cf91c4299", "withdrawn": "", "abstract": "Hartsfield and Ringel introduced the concept of antimagic graphs in 1990. A simple graph, $G$, with $n$ vertices and $m$ edges is said to admit an antimagic labeling if the edges can be assigned distinct labels from $\\{1, 2, \\dots, m\\}$ so that the vertex sums are pairwise distinct. A graph that admits such a labeling is considered antimagic. In 2010, Hefetz, M\\\"utze, and Schwartz introduced the notion of antimagic labelings on directed graphs, called digraphs. An antimagic orientation of $G$ is an assignment of directions to the edges of a graph such that the digraph admits an antimagic labeling. A cactus graph is a connected graph in which any two simple cycles have at most one vertex in common. A central cactus graph is a cactus graph where all simple cycles share a single vertex in common, the central vertex. A leaf of a cactus graph is a vertex of degree 1. Using methods that we have established for proving central cactus graphs with no leaves admit an antimagic orientation, we prove that central cactus graphs with a single leaf that is adjacent to a noncentral vertex admit an antimagic orientation.", "id": "Paper/68588", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68588"}, {"title": " A Stochastic Reaction - Advection Model for Axonal Prion Propagation ", "webprogram_exclude": "0", "session_ids": ["Session/19371"], "source_sha256": "62327560286bd0f9f85142ef5d58ff1825e378a4c47f59e69820547a4f096d5d", "withdrawn": "", "abstract": "Prion diseases are characterized by the misfolding of healthy proteins into toxic forms, which spread throughout the brain and cause other healthy proteins to misfold. Similar processes are also common to several neurodegenerative diseases, such as Alzheimer's Disease and Parkinson's Disease. The interaction between axonal transport, local biochemical dynamics, and network connectivity is not fully understood. As a proof-of-concept, we formulate a stochastic network reaction--advection toy model in which each neural region is represented by a one-dimensional axonal domain, \\(x\\in[0,L]\\). Over each region $i=1,\\ldots,N$, the toy model quantifies the concentration of toxic protein $u_i$ being advected anterogradely with velocity $v>0$ and extracellular toxic protein concentration $w_i$, where $u_i$ grows logistically and $w_i$ and $u_i$ continuously exchange across the cell membrane. To represent system noise, we include a multiplicative stochasticity component using a Wiener sheet. Inter-regional propagation is modeled through a directed weight matrix, where the toxic protein leaving region $i$ is partitioned and advected into other regions $j \\neq i$. The resulting system of stochastic partial differential equations is solved using a finite volume method with upwinding and Strang splitting. Simulations are performed on directed networks with $N=2$ and $N=3$ regions. The resulting graphs show a wave-like diffusion of the toxic protein concentration from one brain region/neuron through the axon to other brain regions/neurons. Our simulations suggest that as a prion disease takes effect in the brain, the buildup of toxic proteins may take place over several cycles of anterograde transport through the connectome.", "id": "Paper/68589", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68589"}, {"title": " Feynman Rules from Measures on Finite Directed Graph Embeddings ", "webprogram_exclude": "0", "session_ids": ["Session/17978"], "source_sha256": "fb5341af8bdb9505400a1c19f9bf25d038bbe9c0fffe5cb29ae2421024c48df0", "withdrawn": "", "abstract": "The continuum multinomial coefficient measures the volume of directed, monotonic paths in \\mathbbm{R}^d by summing over volumes of path polytopes. A companion manuscript under consideration demonstrates that this coefficient converges everywhere and is integrable; furthermore, a transformation of the variable is able to reproduce the d-dimensional relativistic scalar propagator. In this work, we generate random vectors from the endpoints of finite directed graph embeddings. We further analytically determine the joint pdf of these random vectors and connect it to the continuum multinomial coefficient. The resulting density recovers the position-space Feynman rules for a fixed finite graph.", "id": "Paper/68593", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68593"}, {"title": " Arithmetic Fourier Coefficients of Automorphic Forms in <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"8.638ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 3719.2 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">SL(3,\\mathbb {Z})</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-53\" d=\"M308 24Q367 24 416 76T466 197Q466 260 414 284Q308 311 278 321T236 341Q176 383 176 462Q176 523 208 573T273 648Q302 673 343 688T407 704H418H425Q521 704 564 640Q565 640 577 653T603 682T623 704Q624 704 627 704T632 705Q645 705 645 698T617 577T585 459T569 456Q549 456 549 465Q549 471 550 475Q550 478 551 494T553 520Q553 554 544 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y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"3329\" y=\"0\"></use>\n</g>\n</svg> with Application to the Eisenstein Series in <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"8.638ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 3719.2 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">SL(3,\\mathbb {Z})</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-53\" d=\"M308 24Q367 24 416 76T466 197Q466 260 414 284Q308 311 278 321T236 341Q176 383 176 462Q176 523 208 573T273 648Q302 673 343 688T407 704H418H425Q521 704 564 640Q565 640 577 653T603 682T623 704Q624 704 627 704T632 705Q645 705 645 698T617 577T585 459T569 456Q549 456 549 465Q549 471 550 475Q550 478 551 494T553 520Q553 554 544 579T526 616T501 641Q465 662 419 662Q362 662 313 616T263 510Q263 480 278 458T319 427Q323 425 389 408T456 390Q490 379 522 342T554 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-194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-53\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-4C\" x=\"645\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"1327\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-33\" x=\"1716\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2C\" x=\"2217\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJAMS-5A\" x=\"2662\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"3329\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/19361"], "source_sha256": "305c5051c811594a89f6576487911033616f0518ae89dbdcbb5dde48d80b0f20", "withdrawn": "", "abstract": "The Fourier Coefficients of automorphic forms are comprised of Whittaker functions and an arithmetic function. This arithmetic function, called the Arithmetic Fourier Coefficient, is the topic of interest for this talk. I will present on formulae to rewrite any Arithmetic Fourier Coefficient in terms of other, simpler Arithmetic Fourier Coefficients. I will do this twice: once in the case of automorphic forms in $SL(3,\\mathbb{Z})$ and once in the case of automorphic forms in $SL(4,\\mathbb{Z})$ using similar strategies and techniques. I will then demonstrate an application of this formula on the Eisenstein series in $SL(3,\\mathbb{Z})$, explicitly showing how the Arithmetic Fourier Coefficient of the Eisenstein Series in $SL(3,\\mathbb{Z})$ can be written in terms of divisor sums and how this aligns with previous representations.", "id": "Paper/68597", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68597"}, {"title": " Fractional Leibniz Rules for Product Function Spaces ", "webprogram_exclude": "0", "session_ids": ["Session/18256"], "source_sha256": "e15dcab6e9b2dc84e862bf0527ac9a947fea87548827ade74f6699979003f530", "withdrawn": "", "abstract": "Product ball quasi-Banach function spaces (pbQBFSs) offer a generalization of Lebesgue spaces and their extensions, providing a setting to unify results across many different function spaces. Due to preserving norm properties such as monotonicity, theory in corresponding Triebel-Lizorkin spaces can be developed with modest assumptions. Thus, in this talk we define and highlight properties associated to such product Triebel-Lizorkin spaces. This framework is then used to obtain bi-parameter fractional Leibniz rules for partial fractional differential operators in the setting of pbQBFSs.  These results will be applied in specific example spaces such as weighted mixed Lebesgue spaces.", "id": "Paper/68604", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68604"}, {"title": " Practical Aspects of Clustering with the Inner Product Laplacian ", "webprogram_exclude": "0", "session_ids": ["Session/18227"], "source_sha256": "6ef63167f1a796f4a8dc8509bfb66e847305761d7c6001b9362974df7b8ad4fe", "withdrawn": "", "abstract": "In 2025 Aksoy and Young introduced the inner product Laplacian, a common generalization of the combinatorial and normalized Laplacians formed by equipping the vertices and edges of the graph with inner product spaces.  In addition, they introduce a notion of “inner product conductance” where the size of sets of vertices and edges are measured in terms of their respective inner product spaces.  The inner product Laplacian and inner product conductance have been shown to be connected through a Cheeger-like inequality, leading to a generalized approach to spectral clustering.  In this talk, we highlight some practical issues related to spectral clustering with the inner product Laplacian, including complexity issues, practical spectral embeddings, and multi-way Cheeger inequalities.  This work is joint with Jonas Golm, Greg Roek, Geoff Sanders, and Nate Veldt.", "id": "Paper/68605", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68605"}, {"title": " Antimagic Labelings of Cactus Graphs: Modified Friendship Graphs with Multiple Leaves Adjacent to the Central Vertex ", "webprogram_exclude": "0", "session_ids": ["Session/18367"], "source_sha256": "dc5c06a3d5bb8765c3900bced60f64bab70c7363b4196a8bbbd0a7f8e15de757", "withdrawn": "", "abstract": "In 1990, Hartsfield and Ringel introduced the concept of antimagic graphs. An antimagic labeling of a simple graph, $G$, with $n$ vertices and $m$ edges is an assignment of distinct labels from $\\{1, 2, \\dots, m\\}$ to edges such that the vertex sums are pairwise distinct. A graph is considered antimagic if it admits an antimagic labeling. Hefetz, M\\\"utze, and Schwartz introduced the notion of antimagic labelings on directed graphs, called digraphs, in 2010. An antimagic orientation of a graph is an assignment of directions to the edges of a graph such that the digraph admits an antimagic labeling. A cactus graph is a connected graph in which any two simple cycles have at most one vertex in common. Friendship graphs are a type of cactus graph formed by joining cycles of length three to a single central vertex. A leaf of a cactus graph is a vertex of degree 1. We have proven that friendship graphs admit an antimagic orientation. We extend this to prove that modified friendship graphs with multiple leaves that are adjacent to the central vertex admit an antimagic orientation.", "id": "Paper/68613", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68613"}, {"title": " Student Driven Research Projects in the Calculus Sequence ", "webprogram_exclude": "0", "session_ids": ["Session/18081"], "source_sha256": "3a5caeaac0069fdb8bf178d9428252d11fbea0c3e30b28c87401a80288155104", "withdrawn": "", "abstract": "In this talk, I will discuss creating student driven research projects in Calculus classes. As an undergraduate student, I struggled with projects in math classes because it felt like high-stakes busy work; my grade relied solely on the final product of a project that didn't interest me. When tasked with creating research projects for my own Calculus 2 and Calculus 3 students for a Research Symposium, I prioritized creating research projects around students' interests and that rewarded students' effort on the project. Students picked the topic as long as it related to Calculus 2 or 3 and decided on actionable goals for the project. These actionable goals were the basis of the grade for their final product. The grade for the whole project was spread out over a series of check-in meetings, the final product, and a post-reflection. During these check-in meetings, students could re-evaluate and update these actionable goals. In this way, students were directly involved in not only designing a project that genuinely interested them, but in how that project would be graded. \n\nI will share the execution of these research projects, the student reception, and perceived successes and shortcomings.", "id": "Paper/68614", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68614"}, {"title": " Taking the Scenic Route: Making Mathematics for Social Media ", "webprogram_exclude": "0", "session_ids": ["Session/18074"], "source_sha256": "a09435a430ed583bc520ac4d24c1ead72d32594ee39c4b7f9cc8df8c33dbfd52", "withdrawn": "", "abstract": "Mathematics content on social media often begins with a difficult question: how do we make an idea accessible without removing what makes the mathematics interesting? In this talk, I will share the creative process behind Math Scribbles, from finding an idea worth exploring to turning it into short-form mathematical content. I will discuss how curiosity, math history, and the mathematics itself shape my videos, along with lessons learned from ideas that worked, does that did not, and the unexpected ways an audience can influence what gets made next. I will also discuss my evolving approach to mathematical communication and offer practical thoughts for students and mathematicians interested in creating mathematical content of their own.", "id": "Paper/68616", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68616"}, {"title": " Fourier transform of D-modules on prehomogeneous vector spaces ", "webprogram_exclude": "0", "session_ids": ["Session/18285"], "source_sha256": "aae59444b9b55bc2fd5ce4d5bb31c89ee7fbe748008b73fe4c02d65562b4f0c7", "withdrawn": "", "abstract": "In this talk we will discuss D-modules and their Fourier transform on prehomogeneous vector spaces (PVS). In general the information of Fourier transform of D-modules is difficult to determine, but special tools arising from PVS allow us to give an explicit description of the Fourier transform of a certain class of D-modules. This is joint work with Andras Lorincz.", "id": "Paper/68618", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68618"}, {"title": " Kolmogorov Problem and Wiener-type Criterion for the full Characterization of the Fundamental Singularity for the Burgers-type Equations ", "webprogram_exclude": "0", "session_ids": ["Session/18050"], "source_sha256": "5c3ac3acbc7bf4560e7e679b7947a8f1c1a850fdb152fad10b8fd3adac3b9365", "withdrawn": "", "abstract": "The major problem in the Analysis of PDEs is understanding the nature of singularities that reflect natural phenomena. This talk will present a full characterization of the fundamental boundary singularity and, equivalently, the unique solvability of the singular Dirichlet problem for the Burgers-type nonlinear parabolic equations. The results are threefold. We prove a new Wiener-type criterion for the \"geometric\" characterization of the removability of the fundamental singularity for arbitrary open sets in terms of the fine-topological thinness of the complementary set near the singularity point. In the special case when the surface of revolution, or its sheared image, forms the boundary of the open set near the singularity point, we establish a Kolmogorov-Petrovsky-type test to characterize the removability of the singularity and uniqueness. Finally, in the special case when a continuous graph locally represents the boundary of the open set, the minimal thinness criterion for the removability of the singularity is expressed in terms of the minimal regularity of the boundary manifold at the singularity point. In the more general framework, the talk outlines a program for the full characterization of the singularities formed by the elliptic and parabolic PDEs.", "id": "Paper/68619", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68619"}, {"title": " A Quantitative Framework for Observer Variability and Consensus Prediction in Renal Pathology ", "webprogram_exclude": "0", "session_ids": ["Session/17860"], "source_sha256": "3b0e98fe79822f1ce671b91fa23f9403d5cb2e388ed0f57a8c0460ebe76c1fe6", "withdrawn": "", "abstract": "Grading mesangial hypercellularity in renal biopsies is important for treatment decisions but relies on subjective microscopic assessment. We formulate this grading process as a latent-variable measurement problem, where an unobserved severity state is measured by two noisy observers.\n\nTwo pathologists independently graded 468 glomerular patches (0--3 scale) from 38 renal biopsies (33 IgA nephropathy and 5 minimal change disease) under a blinded, randomized design. A development set of 374 glomeruli with $|P_1-P_2|<2$ was used to estimate severity, with the mean observer score as a proxy for the latent state. The remaining 65 discordant cases with $|P_1-P_2|\\geq 2$ formed a separate test set without a consensus estimate. An EfficientNet-B2 regression model was trained with patient-level five-fold cross-validation as an image-based estimator of severity. Grad-CAM attention localized to mesangial regions, supporting biological plausibility of the learned representation.\n\nWe discuss the limitations of estimating a latent grade from two noisy observer measurements. Ongoing work extends this framework to stochastic birth--death and reaction--diffusion models of mesangial cell proliferation and matrix expansion. This connects the discrete pathology grade to an underlying continuous biological state and provides a path from statistical prediction toward dynamical modeling of disease progression.", "id": "Paper/68620", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68620"}, {"title": " Fluctuation impossibility results for stochastic burst networks ", "webprogram_exclude": "0", "session_ids": ["Session/17811"], "source_sha256": "c00e8e6d68e866bc9b1f0df8650cd49e867838ed3f8669699ad6ca041b6fd26c", "withdrawn": "", "abstract": "Feedback is a fundamental mechanism for controlling fluctuations in stochastic biochemical reaction networks. In a 2019 Physical Review Letters paper, Yan, Hilfinger, Vinnicombe, and Paulsson formulated a  conjecture asserting that feedback targeting production rates cannot simultaneously suppress fluctuations in every component of a broad class of networks. Recent work has begun to clarify this conjecture. The unit-birth case was essentially resolved recently by Hilfinger and collaborators using an information-theoretic approach. In  a separate work I isolated explicit checkable hypotheses on moments and birth rates under which the formal information-flow identities can be rigorously justified on the infinite state space. I will explain the main idea behind the argument and then turn to stochastic burst networks, where the story becomes more surprising: the natural extension of the conjecture is false for general burst distributions, but a corresponding impossibility result does hold for geometric bursts. I will present a simple counterexample, state the geometric-burst theorem, briefly indicate why the geometric law is special, and conclude with several questions suggested by these results.", "id": "Paper/68622", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68622"}, {"title": " SCMO: Stochastic Control for Optimization over Probability Measures on Infinite-Dimensional Spaces ", "webprogram_exclude": "0", "session_ids": ["Session/18274"], "source_sha256": "e5188e4dab7f605a8326efb83d51e532309b98e3ef0bcea4183f4bfbc2535e01", "withdrawn": "", "abstract": "We study objective-only optimization of possibly nonconvex and nonsmooth\nfunctionals over probability measures on a separable Hilbert space,\nallowing the optimizer to be intrinsically non-Dirac. We introduce SCMO\n(Stochastic Control Measure Optimizer), a gradient-free particle method\nderived from entropy-regularized mean-field stochastic control. After finite-particle\nand Galerkin approximations, a Cole--Hopf transform represents the optimal\nfeedback as a Gibbs-weighted terminal displacement. SCMO approximates this\nfeedback by sampling context clouds, replacing one particle at a time with\ncandidate draws, scoring the resulting empirical measures, and applying\nexponential reweighting.\n\nSCMO uses separate covariances for candidate proposals and particle updates,\ntermed matched when equal and nonmatched otherwise; our analysis covers both\nsettings. In the matched case, we establish\nPDE-free qualitative convergence and a projection-first quantitative bound\nseparating particle, Galerkin-projection, and entropy-regularization errors.\nFor the practical multi-context implementation with nonmatched covariance, we prove finite-candidate consistency and show that the signed, curvature-dependent effect of\nnonmatched covariance can reduce the resulting upper bound on the\napproximation error. Finally, experiments on function-space, trajectory-law, and contact-rich\nmanipulation problems show that SCMO handles nonsmooth and nonconvex\nobjectives, escapes suboptimal local basins, and recovers prescribed\nmultimodal, non-Dirac law structure.", "id": "Paper/68623", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68623"}, {"title": " An implementation for solving the S-unit equation ", "webprogram_exclude": "0", "session_ids": ["Session/18368"], "source_sha256": "bea227cf424b4b0a482e0ff8eb62725737d07e083add3155561f510b15213bf9", "withdrawn": "", "abstract": "We give an overview of an implementation for solving the S-unit\nequation x + y = 1.", "id": "Paper/68624", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68624"}, {"title": " Scattering results for radial solutions of focusing supercritical wave equations in even dimensions ", "webprogram_exclude": "0", "session_ids": ["Session/18342"], "source_sha256": "7215ec902a87ad2488b5442a7f062055b5777372399585b7624aea5b3910bf09", "withdrawn": "", "abstract": "Conditional well-posedness and scattering results for bounded solutions of nonlinear dispersive equations have been studied extensively. In particular, the program based on the concentration-compactness and rigidity methods, initiated by Kenig and Merle in 2008, has generated a vast body of literature. In this talk, we will review the applications of those methods for focusing energy-supercritical nonlinear wave equations and discuss the unique challenges posed by analogous problems in increasing even dimensions. One of the main goals is to review the changes to the essential steps of rigidity methods in dimension four versus higher even dimensions.", "id": "Paper/68626", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68626"}, {"title": " Algorithmic methods in geometric measure theory ", "webprogram_exclude": "0", "session_ids": ["Session/17815"], "source_sha256": "383e55af5a48592a206f8581afa7d5f064e316e2d44b695029c791e1f3007392", "withdrawn": "", "abstract": "I will introduce the computability-theoretic concept of Kolmogorov complexity and demonstrate how it can be used to obtain exciting results in geometric measure theory.", "id": "Paper/68627", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68627"}, {"title": " Routing functions for computing stability landscapes of ecological models ", "webprogram_exclude": "0", "session_ids": ["Session/18356"], "source_sha256": "35c0c466bb24f897959fc81ac5cf4e3626df8133becceccb34bff612713d8c3e", "withdrawn": "", "abstract": "Changes in environmental parameters can trigger major biological transitions, from ecosystem collapse to disease outbreaks. In this talk, we will present an algebraic framework for studying these transitions through the stability of steady states in ecological models. Using algorithms that combine the use of numerical algebraic geometry and routing functions, we identify connected regions of parameter space where the number and stability of feasible steady states remain constant. As case studies, we revisit the classical Levins-Culver competition-colonization model and a recent model of coral-bacteria symbioses. In the coral symbiosis model, our method uncovers complex stability regimes, including regions supporting limit cycles, that are inaccessible via traditional techniques.  These examples illustrate how algebraic methods can illuminate the dynamics of complex ecological systems.", "id": "Paper/68630", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68630"}, {"title": " A Curved BGG Correspondence for DG Algebras ", "webprogram_exclude": "0", "session_ids": ["Session/18025"], "source_sha256": "20562fdb6d316a52eac8347a38cb784777098a081a9a1b108186a30e57cf4954", "withdrawn": "", "abstract": "A famous correspondence of Bernstein-Gelfand-Gelfand gives an equivalence between the bounded derived categories of the symmetric and exterior algebras of a finite dimensional vector space over a field $k$. Working over a commutative Noetherian ring $R$, work of Amadeus Martin shows that this correspondence can be extended to replace the exterior algebra by a Koszul complex on any sequence of elements in $R$, provided the symmetric algebra is regarded appropriately with curvature. In this talk we will discuss a general version of this correspondence for DG-algebras. As an application, we give an extended version of a classical construction of resolutions due to Eisenbud-Shamash. This talk is based on joint work with Michael Brown, Mark Walker, and Ryan Watson.", "id": "Paper/68631", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68631"}, {"title": " Cancer Detection via Electrical Impedance Tomography and Optimal Control of Elliptic PDEs ", "webprogram_exclude": "0", "session_ids": ["Session/19337"], "source_sha256": "1dda33aff896788c1bc1d95367497730d93b1e2306bbd43045624f0792adfc39", "withdrawn": "", "abstract": "A new mathematical framework using the theory of Partial Differential Equations (PDE), inverse problems, and optimal control of systems with distributed parameters is developed to detect cancerous tumor growth in the human body. The Inverse Electrical Impedance Tomography (EIT) problem of recovering the electrical conductivity tensor and potential in the body based on the measurement of boundary voltages on the $m$ electrodes for a given electrode current is analyzed. The variational formulation is introduced as a PDE-constrained coefficient optimal control problem in Sobolev spaces. The novelty of the control-theoretic model is its adaptation to the clinical situation when additional \"voltage-to-current\" measurements can increase the size of the input data while keeping the size of the unknown parameters fixed. The existence of the optimal control and Fr\\'{e}chet differentiability in the Sobolev space, along with the optimality condition, and the convergence of the finite-difference method are proved. Numerical analysis of the simulated 3D model example demonstrates that by increasing the number of input boundary electrode currents from $m$ to $m^2$ through additional \"voltage-to-current\" measurements, the resolution of the electrical conductivity of the body identified via the gradient method in the Sobolev space framework is significantly improved.", "id": "Paper/68632", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68632"}, {"title": " <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"0.944ex\" height=\"1.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -576.1 406.5 721.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\epsilon</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-3F5\" d=\"M227 -11Q149 -11 95 41T40 174Q40 262 87 322Q121 367 173 396T287 430Q289 431 329 431H367Q382 426 382 411Q382 385 341 385H325H312Q191 385 154 277L150 265H327Q340 256 340 246Q340 228 320 219H138V217Q128 187 128 143Q128 77 160 52T231 26Q258 26 284 36T326 57T343 68Q350 68 354 58T358 39Q358 36 357 35Q354 31 337 21T289 0T227 -11Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-3F5\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Regularity and Compactness for the Cone Yang-Mills Functional ", "webprogram_exclude": "0", "session_ids": ["Session/19352"], "source_sha256": "72ac9cac31ef89f9ebe42ff0e3f65b2f369a7cedf1c786f5cf094afe16bdab88", "withdrawn": "", "abstract": "We introduce the cone Yang-Mills functional: a Yang-Mills-Higgs-type functional defined through the mapping cone complex. Here, the Higgs field interacts with the curvature through a closed 2-form representing a geometric structure of interest, e.g. a symplectic form or Ricci form. This framework allows us to incorporate the additional geometric data directly into a gauge-invariant functional, with the goal of constructing moduli spaces sensitive to the geometry. We prove a monotonicity formula, epsilon-regularity, and a compactness theorem in the sense of Nakajima as a first step towards studying these moduli spaces.", "id": "Paper/68633", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68633"}, {"title": " All the hyperplane slices (or sections) of a convex polytope ", "webprogram_exclude": "0", "session_ids": ["Session/18352"], "source_sha256": "12c250c33828bc6b1d69fc52dee476eccd68ade66911a0925bb564d0606da62e", "withdrawn": "", "abstract": "Abstract: For hundreds of years mathematicians have been fascinated with slicing high-dimensional mathematical objects as a way to get knowledge and intuition of higher dimensions. There are many classical results and conjectures about slices with hyperplanes (e.g., Bourgain’s conjecture, recently a theorem, on the relation of volume and area of slices). Sections or slicing is central to geometry, analysis,  and of course combinatorics too. \n\nIn my presentation I described a clean beautiful theory that shows an elegant structure we discovered on the space of all affine hyperplane sections of a convex polytope. It has many practical consequences:\n\n1) Given a d-dimensional convex polytope P, what is the ``best’’ slice of P by a hyperplane? For example, in analysis this can mean the slice that maximizes the volume. For a combinatorialists ``best slice’’ can mean one with the largest number of vertices! We have optimal algorithms to answer optimization questions.\n\n2) As we slice P with different hyperplanes, we create many different (d-1)-slices, which are also polytopes. E.g., for a 3-dimensional regular  cube there are 4 types of slices (triangles, quadrilaterals, pentagons, hexagons). We answer: How many combinatorially different slices are there for a polytope P? How can we count them all? Can we give lower/upper bounds on their number?  What are extremal cases? \n\n3) Given k polytopes P_1,P_2,...,P_k, in R^d is there a hyperplane slice that cuts all in half? When d=k, the famous Ham-Sandwich theorems says yes, but it does not say how to find the plane. An algorithm arises directly from the theory we developed.\n\nI will explain our powerful new algebraic combinatorial method that (a piece-wise semi-algebraic moduli space of slices) and an algorithmic framework that answers all these problems (and many others) in polynomial time when dim(P) is fixed. Moreover, we show  the problems have hard complexity otherwise.  \n\nThe results are joint work, presented in several papers, with Marie-Charlotte Brandenburg (U Bochum) and Chiara Meroni (ETH)  Antonio Torres and Gyivan López (UC Davis).   This talk will have lots of pretty pictures and will be understandable by everyone. I will present lots of open questions for enthusiastic researchers in the audience.", "id": "Paper/68636", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68636"}, {"title": " Symmetry Breaking, Pumping, and Pattern Formation in Stokes Flow Networks ", "webprogram_exclude": "0", "session_ids": ["Session/18222"], "source_sha256": "b1bc14dd283c3db688b4924307c44212694bc5ae4c5afac812de4028ab8dad1d", "withdrawn": "", "abstract": "Fluid flows can generate mechanical stresses that influence the growth and remodeling of biological transport networks, contributing to the emergence and remodeling of branched or loopy canals and other spatial patterns. Understanding this feedback first requires identifying how flow is generated, a particularly intriguing question in organisms without a centralized heart. At low Reynolds number, cyclic boundary deformations produce net transport only when the sequence of shapes breaks path-reversal symmetry. In a simple tube, this principle underlies peristaltic pumping; in a complex network, however, the relationship between deformation and transport also depends on network geometry.\nIn this talk we discuss a mechanism in which circulation emerges through the interaction of non-reciprocal deformation with geometric heterogeneity. Using reduced mathematical models and network simulations, we show that neither ingredient alone is sufficient: symmetry must be broken by both the deformation cycle and the network geometry. Vessel radii, lengths, and branching topology can then determine—and even reverse—the direction of flow. We illustrate this mechanism using the gastrovascular network of the moon jellyfish Aurelia aurita. The resulting interplay suggests a feedback loop in which canal geometry controls contraction-induced flow, while the associated mechanical stresses may, in turn, guide canal development and pattern formation.", "id": "Paper/68637", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68637"}, {"title": " Linear-Scaling Randomized Algorithms in High Dimensions ", "webprogram_exclude": "0", "session_ids": ["Session/18230"], "source_sha256": "e6689b85bfe2a68395ca4fe17a82cb52c5736098249a518f0ca41906eb92f633", "withdrawn": "", "abstract": "We introduce the TTStack sketch, a structured random projection tailored to the tensor train (TT) format that unifies existing TT-adapted sketching operators. By varying two integer parameters the block count $P$ and block rank $R$, TTStack interpolates between the Khatri-Rao sketch ($R=1$) and the Gaussian TT sketch ($P=1$). We prove that TTStack can preserve a subspace's geometry with high probability while acting as a linear dimensional reduction map through an Oblivious Subspace Embedding (OSE) property given parameters $R = \\mathcal{O}(d(r+\\log 1/\\delta))$ and $P = \\mathcal{O}(\\varepsilon^{-2})$, or alternatively achieve a more relaxed, yet useful guarantee through an Oblivious Subspace Injection (OSI) property under the more lenient condition $R = \\mathcal{O}(d)$ and $P = \\mathcal{O}(\\varepsilon^{-2}(r + \\log r/\\delta))$ which lends itself to natural parallelization. Both guarantees depend only linearly on the tensor order $d$ and on the subspace dimension $r$, in contrast to prior constructions that are known to suffer from the curse of dimensionality thus requiring an exponential scaling in $d$. This framework directly stablishes quasi-optimal error bounds for the low-rank factorization and randomized TT rounding in both the fixed-rank and fixed-precision regimes.", "id": "Paper/68641", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68641"}, {"title": " Complete Families of Curves in the Moduli Space of Genus g Curves ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "070db1ab82e08df30980e0798f0ba0399650e05c675e96278efc3788609856a4", "withdrawn": "", "abstract": "Let $\\mathcal{M}_g$ be the moduli space of smooth curves of genus $g$.  The image of a non-constant morphism from a curve $T$ to $\\mathcal{M}_g$ is a curve in $\\mathcal{M}_g$.  By work of Gonz\\'alez D\\'iez and Harvey, for every integer $g \\geq 3$, there exists a complete curve in $\\mathcal{M}_g$.  Here we generalize the construction to produce new complete curves in $\\mathcal{M}_g$.  We also find a formula for the genus of each curve $T$ using Galois theory for function fields.", "id": "Paper/68648", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68648"}, {"title": " On the Extension of Special Integral Transformations to quaternion-valued functions ", "webprogram_exclude": "0", "session_ids": ["Session/18336"], "source_sha256": "2b3f3d7133731e156a08b40b12fe203b674582105645b5316b6a4da948b531cf", "withdrawn": "", "abstract": "In the study of Phase-Space Representation in mathematical physics and quantum mechanics a class of integral transformations is generated as a representation of a unitary operator$,\\mu(A),$ called metaplectic representation of the symplectic group of matrices $Sp(n, \\R).$ Among these integral transformations are the fractional Fourier transformation, the special affine Fourier transformation, and the coupled fractional Fourier transformation.\n\nIn this talk we introduce some of these transformations and then discuss some recent developments in their extension to quaternion-valued functions and possibly to Octonion-valued functions.", "id": "Paper/68649", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68649"}, {"title": " Algebraic Secrets Behind Self-working Card Tricks ", "webprogram_exclude": "0", "session_ids": ["Session/18235"], "source_sha256": "8275b2123278890033e93c6627f11c2beabfc06208c1cebff1eb60227e9434dd", "withdrawn": "", "abstract": "Numerous self-working card tricks circulate widely on social media, yet they are almost always performed algorithmically without explaining the underlying mechanics. Behind many of these illusions lie straightforward algebraic principles that guarantee their outcomes. This talk demonstrates how selected card tricks can be deconstructed through basic algebraic modeling and reasoning. In addition to analyzing the mechanics of these tricks, we will discuss how to adapt them into engaging classroom activities for courses such as Intermediate Algebra or College Algebra to help students build intuition for symbolic expressions, pattern recognition, and problem solving.", "id": "Paper/68650", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68650"}, {"title": " Average covering radius of symmetric torus covers ", "webprogram_exclude": "0", "session_ids": ["Session/17902"], "source_sha256": "aab4b39478d7e169b025008acf06f2746185a900b5382d1e0053770eb55d0c1e", "withdrawn": "", "abstract": "One perspective from which we can approach the intriguing question, \"What is the shape of a random surface?\" is by considering typical properties of translation surfaces. In 2021, Masur-Rafi-Randecker found asymptotic bounds for the expected covering radius, a geometric property related to diameter for translation surfaces of any stratum. With Anthony Sanchez and Sunrose Shrestha, we develop theory to explicitly compute the expected covering radius for the family of doubled slit tori using methods that generalize to other surfaces of any genus. In this talk, we will discuss our motivations, methods, and future goals.", "id": "Paper/68652", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68652"}, {"title": " Balanced Edge-Colourings of Hypergraphs ", "webprogram_exclude": "0", "session_ids": ["Session/16805"], "source_sha256": "5ad5389d8b383e44eb51c60d7f8a0184c002e2e3c98330d298397ac1f89d348d", "withdrawn": "", "abstract": "Nash-Williams (1985) characterized connected detachments of graphs with prescribed splitting numbers. We extend this theory to edge-coloured hypergraphs, requiring simultaneously that each colour class retain its connectivity and that degrees and edge multiplicities be distributed as evenly as possible. In the $2$-uniform case our main theorem specializes to Nash-Williams's result, and in the coloured graph setting it resolves a 2003 conjecture of Hilton et al.\\ on connected amalgamations. We also obtain exact factorization results for complete multipartite hypergraphs, and a sharp $2$-edge-connected detachment theorem for small edge sizes. Finally, we introduce a relative-profile viewpoint for comparing different factors; in the $3$-uniform Baranyai setting this recovers the Fon-der-Flaass separation problem and leads to new stability questions and results.", "id": "Paper/68653", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68653"}, {"title": " Classification of horospherical invariant infinite measures ", "webprogram_exclude": "0", "session_ids": ["Session/18361"], "source_sha256": "307dc138907e6ff4a25e9b846c2cff1b12e5f2904c573ac5ca56a19410b7a26b", "withdrawn": "", "abstract": "In this talk, I will present the classification of horospherical invariant Radon measures for Anosov subgroups of arbitrary semisimple real algebraic groups. This generalizes the works of Burger and Roblin in rank one to higher ranks. At the same time, this extends the works of Furstenberg, Veech, and Dani, and a special case of Ratner's theorem for finite-volume homogeneous spaces to infinite-volume Anosov homogeneous spaces.\n\nEspecially, this resolves the open problems proposed by Landesberg--Lee--Lindenstrauss--Oh and by Oh. Our measure classification is in fact for a more general class of discrete subgroups, including relatively Anosov subgroups with respect to any parabolic subgroups, not necessarily minimal. Our method is rather geometric, not relying on continuous flows or ergodic theorems.\n\nIf time permits, I will also discuss the corresponding measure classification result for subgroups of mapping class groups. This is based on joint work with Inhyeok Choi.", "id": "Paper/68657", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68657"}, {"title": " A model of local and global reciprocity ", "webprogram_exclude": "0", "session_ids": ["Session/18039"], "source_sha256": "7de6954fe5d5ef9244da72b67d46aaa35924752c976b76683654dc1a66fc1c8c", "withdrawn": "", "abstract": "We often decide how to treat friends based on observations of their past behavior, whereas actions toward strangers are typically guided by their public reputations. These two kinds of information underlie two classical mechanisms for the evolution of cooperation---direct and indirect reciprocity---which have largely been studied in isolation. They are not interchangeable: we can recall the past actions of only a small circle of close contacts, whereas for the far larger pool of strangers we must rely on public reputations. Here we develop a mathematical framework built on this distinction. Each individual engages in direct reciprocity in local games within a finite neighborhood of friends, whose actions they observe directly, and in indirect reciprocity in global games with a large population of strangers, known only by reputation. Separating local and global interactions allows us to address two questions. First, can cooperation persist under a cognitively simple norm of judgment? We show that combining direct and indirect reciprocity resolves the scoring dilemma: conditional cooperators resist invasion by both unconditional cooperators and unconditional defectors, where indirect reciprocity alone would fail. Second, how should one treat a friend whose past behavior conflicts with their public reputation? We find that the strategies that maximize cooperation are forgiving---overlooking whichever piece of information is unfavorable---and that these forgiving strategies can often remain robust to invasion. By distinguishing between local and global scales of interaction and integrating information across them, our framework offers a more cognitively realistic account of how reciprocity sustains cooperation.", "id": "Paper/68660", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68660"}, {"title": " A metric boundary theory for Carnot groups ", "webprogram_exclude": "0", "session_ids": ["Session/17471"], "source_sha256": "b4b73c133c9beb39147208460f039de28897a3bff28081752082daa2f8830711", "withdrawn": "", "abstract": "In this talk, we will overview recent work which aims to develop a robust boundary theory for nilpotent groups. We will discuss properties of horofunction boundaries for Carnot groups, i.e., stratified nilpotent Lie groups equipped with left-invariant homogeneous metrics, focusing on the standard 3-dimensional Heisenberg group and two families which generalize this group, the higher Heisenberg groups and filiform Lie groups. In particular, we will see that filiform Lie groups provide the first-known examples of Carnot groups $G$ whose horofunction boundaries do not have dimension equal to $\\dim(G) – 1$.", "id": "Paper/68661", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68661"}, {"title": " Quiver varieties and root multiplicities in rank 3 ", "webprogram_exclude": "0", "session_ids": ["Session/18278"], "source_sha256": "7c1efbf747fac2bf49d0b749c9b3fa7f3e65f262f2c2511cf12cba119bba8c9f", "withdrawn": "", "abstract": "One can use the realization of crystals in terms of quiver varieties to give combinatorial upper bounds on dimensions of certain imaginary root spaces for symmetric Kac-Moody algebras. The general framework along with explicit combinatorics in rank 2 was published in 2021. This talk will focus on rank 3 cases.", "id": "Paper/68665", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68665"}, {"title": " Explorations of Projective SET Caps and Packings in <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"8.973ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 3863.2 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">PG(n, 2)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-50\" d=\"M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-47\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q492 659 471 656T418 643T357 615T294 567T236 496T189 394T158 260Q156 242 156 221Q156 173 170 136T206 79T256 45T308 28T353 24Q407 24 452 47T514 106Q517 114 529 161T541 214Q541 222 528 224T468 227H431Q425 233 425 235T427 254Q431 267 437 273H454Q494 271 594 271Q634 271 659 271T695 272T707 272Q721 272 721 263Q721 261 719 249Q714 230 709 228Q706 227 694 227Q674 227 653 224Q646 221 643 215T629 164Q620 131 614 108Q589 6 586 3Q584 1 581 1Q571 1 553 21T530 52Q530 53 528 52T522 47Q448 -22 322 -22Q201 -22 126 55T50 252Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-50\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-47\" x=\"751\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"1538\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-6E\" x=\"1927\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2C\" x=\"2528\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-32\" x=\"2973\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"3473\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18370"], "source_sha256": "3f99a70ac579b54aeb84699df559943e861984d260a9c3e3cf163a6782afdf12", "withdrawn": "", "abstract": "\\textit{Projective SET} is a variation of the popular card game, \\textit{SET}. It is a model for the finite projective geometry, $PG(n, 2)$. Like a set in \\textit{SET}, a projective set (P-SET) is a collection of three cards satisfying a certain condition, corresponding with a line in the respective geometry. A P-SET cap is a collection of cards containing no P-SETs. We are interested in all varieties of caps—maximum caps, non-maximum complete caps, the equivalence between certain caps, the extension of certain caps to higher dimensions—and their complementary concept, P-SET packings, which seek to maximize the number of P-SETs found within a set of cards.", "id": "Paper/68668", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68668"}, {"title": " Pseudo-magnetism in a strained discrete honeycomb lattice ", "webprogram_exclude": "0", "session_ids": ["Session/17804"], "source_sha256": "2d1ee03e24156c16ee22aa0eb35f936401e8c3c0ac6e0eecc566e37bc8583255", "withdrawn": "", "abstract": "Slowly-varying nonuniform strain in honeycomb media can generate an effective pseudo-magnetic field, even though the underlying medium is non-magnetic. This phenomenon was first discovered in graphene and later in photonic crystals, and other physical settings. In this talk, I will start from a discrete nearest-neighbor tight-binding model for a nonuniformly strained honeycomb medium. I will then show how this model leads to a continuum magnetic Dirac Hamiltonian that describes wave packets concentrated near a Dirac point of the undeformed structure. I will focus on unidirectional deformations with bounded gradients that preserve translation invariance along the armchair direction. In this setting, we prove the existence of eigenmodes that behave like plane waves along the armchair direction and are strongly localized in the transverse direction, together with quantitative correction estimates. These results apply to deformations that produce an approximately constant pseudo-magnetic field perpendicular to the plane. They also lead to nearly flat bands and, as a consequence, a very high density of states. These analytical results are also supported by numerical simulations of the corresponding deformations. This is joint work with Michael I. Weinstein.", "id": "Paper/68671", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68671"}, {"title": " Division-within-division and mitochondrial dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/18350"], "source_sha256": "c425fe958f2a11969b12e6fdd16b54b70adf9de4d44beb374a2b84b455ae43a1", "withdrawn": "", "abstract": "Many biological processes include branching phenomena, which may be called division-within-division. Typical examples include proliferation of extrachromosomal DNA in cells, or production of new virions in infected cells. Mathematically, the process was originally formalized by Kimmel (1997), as an infinite-type branching process, and later generalized by others, including Bansaye and his students, and Bobrowski. We present the original version and a two-type generalization by Bobrowski, originally designed as a model of oncogenes and tumor suppressor genes in cancer cells. Both versions lead to quasistationary distributions of certain kind. Recently, Lenderman and Kimmel developed an approach, based on division-within-division, to modeling homeostasis of human mitochondria, based on simplified biological assumptions. We conclude by presenting this latter model.", "id": "Paper/68672", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68672"}, {"title": " Groups with ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "0857ca4537fe6084b6e7f6e4abd0d2b495213f533003eab56f3bb235bc9ad97f", "withdrawn": "", "abstract": "\\begin{abstract}\nIsaacs studied a character-theoretic characterization of groups with \\(p\\)-length 1. In this paper, we generalize this result to the setting of an arbitrary set of primes \\(\\pi\\).\n\\end{abstract}", "id": "Paper/68673", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68673"}, {"title": " Dirichlet Priors to Born Rule: Evidential Uncertainty Across Classical and Quantum Learning Systems ", "webprogram_exclude": "0", "session_ids": ["Session/18272"], "source_sha256": "aba4650df3b01c1e90e9aa6ea01203f642361d91504bae8add6fce342cafe4ed", "withdrawn": "", "abstract": "The reliable deployment of deep learning in scientific discovery demands rigorous frameworks for reasoning under uncertainty. In this talk I will present recent work on uncertainty quantification via evidential deep learning (EDL), applied to the classification of jets in high-energy proton-proton collisions at the Large Hadron Collider. Unlike computationally prohibitive Bayesian ensemble methods, EDL treats inference as an evidence acquisition process, placing Dirichlet priors over class posteriors to produce calibrated epistemic uncertainty estimates in a single forward pass. Through hyperparameter optimization and analysis of uncertainty distributions across jet classes, latent space geometry, and out-of-distribution behavior, we uncover both the utility and pitfalls of EDL as an anomaly detection mechanism, and introduce a more effective uncertainty formulation beyond the foundational EDL setup — providing new insight into how evidential reasoning identifies novel data in high-dimensional classification tasks.\n\nI will then explore how this evidential framework connects naturally to classical and quantum reservoir computing. Echo state networks and quantum reservoirs offer lightweight temporal feature extraction amenable to evidential readout layers. This composition yields a principled anomaly detection architecture in which epistemic uncertainty flags out-of-distribution inputs, and in the quantum setting provides a mathematically natural decomposition of model uncertainty from irreducible quantum measurement uncertainty. The underlying structures define a largely unexplored research program at the intersection of probability theory, dynamical systems, and quantum information.", "id": "Paper/68674", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68674"}, {"title": " Classification of Left-Invariant Locally Conformally Symplectic Structures on Lie Groups with One-Dimensional Commutator Groups ", "webprogram_exclude": "0", "session_ids": ["Session/18380"], "source_sha256": "b5483d2a8a736f0c04f76af5486f1e6e5b0ba295ae710d3c98fa782457f6fe6f", "withdrawn": "", "abstract": "We study left-invariant locally conformally symplectic structures on even-dimensional Lie groups whose commutator group is one-dimensional. The combination of the locally conformally symplectic condition with the Lie algebra structure imposes constraints and provides a framework for classifying such structures. Within this setting, we investigate how these constraints relate to the underlying almost-Hermitian geometry.\n\nFurthermore, we discuss curvature conditions associated with canonical Hermitian connections and investigate special metrics arising from these conditions.", "id": "Paper/68675", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68675"}, {"title": " Impact of Data and Model Geometry on Learning Complexity in Deep Learning ", "webprogram_exclude": "0", "session_ids": ["Session/18036"], "source_sha256": "df219f870ac1eaf7e89ba4154f0e4edf9ff7e508b5ae94b2c35ea79f9c48e7af", "withdrawn": "", "abstract": "The utility of encoding geometric structure, such as known symmetries, into machine learning architectures has been demonstrated empirically in domains ranging from biology to computer vision. However, rigorous analysis of its impact on the learning complexity of neural networks remains largely unexplored. Recent advances in learning theory have shown that training shallow, fully connected neural networks, which are agnostic to data geometry, has exponential complexity in the statistical query model, a framework encompassing gradient descent. In this talk, we ask whether knowledge on data and model geometry is sufficient to alleviate the fundamental hardness of learning neural networks. We analyze two geometric settings: First, equivariant neural networks, a class of geometric architectures that explicitly encode symmetries; and second, learning neural networks under the manifold hypothesis, which assumes that high-dimensional input data lies on or near a low-dimensional manifold.", "id": "Paper/68680", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68680"}, {"title": " Quantum Optimal Control for Coherent Spin Dynamics of Radical Pairs via Pontryagin Maximum Principle ", "webprogram_exclude": "0", "session_ids": ["Session/18321"], "source_sha256": "9b777b3dfce890f6d3cda472f88fcb78be3aacae0c81bd852c36819a813094be", "withdrawn": "", "abstract": "This talk discusses the quantum optimal control problem for the identification of the optimal external electromagnetic field that drives the spin dynamics of radical pairs to a quantum coherent state through maximization of the triplet-to-singlet yield in biochemical reactions. The mathematical model is a Schr\\\"{o}dinger system with spin Hamiltonians given by the sum of Zeeman interaction and hyperfine coupling interaction terms. We introduce a one-parameter family of optimal control problems by coupling the Schr\\\"{o}dinger system to a control field through filtering equations for the electromagnetic field. Fr\\'echet differentiability and the Pontryagin Maximum Principle in Hilbert space are proved, and the bang-bang structure of the optimal control is established. A new iterative Pontryagin Maximum Principle (IPMP) method for the identification of the bang-bang optimal control is developed. Numerical simulations based on IPMP and the gradient projection method (GPM) in Hilbert spaces are pursued, and the convergence, stability, and the regularization effect are demonstrated. Comparative analysis of filtering with regular optimal electromagnetic field versus non-filtering with bang-bang optimal field ({\\it Abdulla et al., Quantum Sci. Technol., {\\bf9}, 4, 2024; Quantum, {\\bf 10}, 2096, 2026}) demonstrates that the change in the maxima of the singlet yield is less than 1\\%. The results open a venue for a potential experimental work on magnetoreception as a manifestation of quantum biological phenomena.", "id": "Paper/68681", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68681"}, {"title": " Numerical Approximation for Partially Observed Optimal Control of Stochastic Partial Differential Equations ", "webprogram_exclude": "0", "session_ids": ["Session/18293"], "source_sha256": "e2d552462027f851ef53d3732793ec9ec6e3bcaf3df3e0cfabf9e8667798feb5", "withdrawn": "", "abstract": "We consider numerical approximation of partially observed optimal control problems for stochastic partial differential equations in Hilbert spaces. The state dynamics are driven by an infinite-dimensional Wiener process, while only finite-dimensional noisy observations are available to the controller. We first derive a stochastic maximum principle that characterizes necessary conditions for optimality through an adjoint backward stochastic partial differential equation. Based on this characterization, we develop a numerical scheme that combines stochastic-gradient updates of the control with particle filtering to approximate the conditional distribution of the unobserved state. This provides a computational framework for implementing the stochastic maximum principle under partial observation without requiring direct solution of the associated infinite-dimensional filtering equation. Numerical experiments illustrate the performance of the proposed method.", "id": "Paper/68682", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68682"}, {"title": " Fully Discrete Error Analysis for a Cahn–Hilliard Cross-Diffusion System ", "webprogram_exclude": "0", "session_ids": ["Session/17702"], "source_sha256": "0831c5429f59326f8e88c739482210f5d5d1e0ee6ea84a75bf8b18a88cd5b335", "withdrawn": "", "abstract": "We consider a stabilized finite element approximation of a strongly coupled Cahn--Hilliard cross-diffusion system arising in lymphangiogenesis. Unlike the classical Cahn--Hilliard equation, the energy law controls a coupled flux rather than the gradient of the chemical potential itself. Consequently, the standard uniform estimate for the chemical potential in $L^2(0, T; H^1(\\Omega))$ is not directly available. By exploiting the structure of the cross-diffusion terms together with interpolation and discrete energy estimates, we establish a uniform bound for the chemical potential in $L^{4/3}(0, T; W^{1,6/5}(\\Omega))$. This weaker estimate is sufficient to control the nonlinear cross-diffusion terms and forms the key ingredient in the fully discrete error and convergence analysis. We also establish discrete energy stability and solvability of the finite element scheme, derive error estimates for the primary variables, and present numerical experiments supporting the theoretical results.", "id": "Paper/68684", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68684"}, {"title": " Effect of Delays in Transient Macrophage Dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/17972"], "source_sha256": "9a5b52dd3d68d1abc8d3a42c8f830011e0a7574e04a4ca42a225cf0cd922a4cb", "withdrawn": "", "abstract": "Macrophages exhibit remarkable phenotypic plasticity and play a central role in regulating immune responses and cancer progression. Previous mathematical models of macrophage polarization have demonstrated that nonlinear feedback mechanisms can generate multistability, which governs the transient dynamics of macrophage polarization. These models provide a foundation for understanding phenotype switching between pro-inflammatory (M1) and anti-inflammatory (M2) states. However, these models assume that intracellular signaling and differentiation occur instantaneously, neglecting biologically relevant delays associated with molecule production, cell proliferation, differentiation, and transport. In this talk, I will present our work that extends a previously developed bistable ODE model of macrophage polarization to a delay differential equation framework by incorporating biologically motivated intracellular time delays. We investigate how delays influence transient macrophage dynamics, stability, multistability, and basins of attraction. Numerical results indicate that, even when long-term equilibria are preserved, delays can substantially alter transient behavior by producing prolonged oscillatory transients, modifying switching dynamics, and reshaping basin boundaries. These delay-induced behaviors cannot be captured by the corresponding ODE model. This work provides new insight into the role of temporal processes in immune cell decision-making and establishes a foundation for developing delayed population-level models of macrophage dynamics in the tumor microenvironment.", "id": "Paper/68685", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68685"}, {"title": " Three algebras to understand the category <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"4.464ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 1922 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathcal S(6)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJCAL-53\" d=\"M554 512Q536 512 536 522Q536 525 539 539T542 564Q542 588 528 604Q515 616 482 625T410 635Q374 635 349 624T312 594T295 561T290 532Q290 505 303 482T342 442T378 419T409 404Q435 391 451 383T494 357T535 323T562 282T574 231Q574 133 464 56T220 -22Q138 -22 78 21T18 123Q18 184 61 227T156 274Q178 274 178 263Q178 260 177 258Q172 247 164 239T151 227T136 218L127 213L124 202Q118 186 118 163Q120 124 165 86T292 48Q374 48 423 86T473 186V193Q473 267 347 327Q268 364 239 389Q191 431 191 486Q191 547 242 600T356 679T470 705Q472 705 478 705T489 704Q551 704 596 682T642 610Q642 566 621 545Q592 516 554 512Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJCAL-53\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"642\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-36\" x=\"1032\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"1532\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18371"], "source_sha256": "57d95134804df7264427005243c0061cff1ca899a53940c81ecf740ff4480547", "withdrawn": "", "abstract": "The objects in the category $\\mathcal S(6)$ consist of a linear operator acting nilpotently on a finite-dimensional vector space with nilpotency index at most $6$, together with an invariant subspace.\n\nThree algebras help understand this category.  The first algebra is a finite-dimensional hereditary algebra which has $120$ indecomposable representations corresponding to the positive roots of the Dynkin diagram $\\mathbb E_8$.  Via tilting we obtain the second algebra; it turns out that most of its indecomposable modules are already linear operators with an invariant subspace.  Finally, to obtain all objects in $\\mathcal S(6)$, a tubular extension is needed.\n\nIt turns out that each indecomposable object in $\\mathcal S(6)$, not in the radical, carries a fine structure that is still determined by the underlying root of the Dynkin diagram $\\mathbb E_8$.  And conversely:  The Auslander-Reiten translation for $\\mathcal S(6)$ induces an action on the roots for $\\mathbb E_8$.  We will present and discuss the picture showing the orbit structure.", "id": "Paper/68686", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68686"}, {"title": " Explorations and Extensions of Happy Functions ", "webprogram_exclude": "0", "session_ids": ["Session/18205"], "source_sha256": "9c6976739430f32ed1defdb7143d4e0634fb1cd95d7250c1b4f25b22a2419c53", "withdrawn": "", "abstract": "The happy function splits a positive integer into its digits, squares each, and then sums the squares. If repeated applications of the happy function result in 1, then the original integer is called a happy number. An ongoing research collaboration, started as a Research Experience for Undergraduate Faculty project in summer 2014, studies extensions of happy functions. This talk will provide an overview of the research group work.  We will define the concept of an augmented generalized happy function, explore its characteristics, then create and define the concept of oases and mirages.  Continuing, we will consider happy functions extended to apply to Gaussian integers, what happy functions result if we replace the exponentiation function with a monic quadratic polynomial function with nonnegative coefficients, and happy functions using higher powers.  These extensions demonstrate the potential for rich research ground from a concept easily accessible to undergraduate students.  This work has been supported by AIM and ICERM through support for meetings in summers 2014, 2015, 2019, and 2024.", "id": "Paper/68690", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68690"}, {"title": " Moments of Products of Bessel Functions via the Method of Brackets \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18867"], "source_sha256": "e41a7683d4620d01322e02956566d8b9bc28d08fd43f5ab6ba1e9cc4377c7ecb", "withdrawn": "", "abstract": "The method of brackets is a new method used to evaluate improper integrals on \\([0,\\infty)\\) that is based upon Ramanujan’s Master Theorem. The method allows these integrals to be evaluated via solving systems of linear equations obtained from bracket series. This presentation focuses on using the method to evaluate integrals involving products of Bessel functions \\(J\\) and \\(K\\).", "id": "Paper/68696", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68696"}, {"title": " Koszul Orlik-Solomon Algebras from Non-Supersolvable Arrangements ", "webprogram_exclude": "0", "session_ids": ["Session/18253"], "source_sha256": "70712e19f77db37aa11dfa9f44ff584f999df562c7da1d559d88f8c5bd7eb560", "withdrawn": "", "abstract": "The cohomology ring of the complement of a  complex hyperplane arrangement is given by its Orlik--Solomon algebra.  It is known that the defining ideal of the Orlik--Solomon algebra has a quadratic Gr\\\"obner basis in the standard presentation if and only if the intersection lattice is supersolvable; such algebras are automatically Koszul.  In 1997, Shelton and Yuzvinsky posed the question as to whether all Koszul Orlik--Solomon algebras arise from supersolvable arrangements.  We answer this question negatively using three related constructions that produce non-supersolvable arrangements whose Orlik--Solomon algebras are Koszul.  Moreover, these arrangements may be chosen to be irreducible, realizable over $\\mathbb{Q}$, and of any rank $\\geq 3$. \nOur constructions rely on a result of Falk and Proudfoot which we strengthen and generalize.\nIn two of the three cases, we show non-supersolvability using a corrected form of a result of Ziegler regarding supersolvability of parallel connections. We also construct Koszul Orlik--Terao algebras coming from non-supersolvable arrangements.", "id": "Paper/68703", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68703"}, {"title": " A Complete and Bi-Continuous Invariant of Protein Backbones under Rigid Motion ", "webprogram_exclude": "0", "session_ids": ["Session/18078"], "source_sha256": "6c0e0e782a283d7ff444b96924e2e6903d219e8643f31fd4a1485209e8a773f5", "withdrawn": "", "abstract": "Since different geometric structures often have distinct functional properties, it is important to continuously quantify differences in rigid shapes of protein backbones. This enables accurate measurement of similarity between protein chains. However, many widely used measures of protein similarity fail axioms of a distance metric and discontinuously change under tiny perturbations of atoms.\n\nIn this talk, we present a complete invariant for protein backbones in 3-dimensional space that uniquely characterizes a backbone up to rigid motion. The invariant is Lipschitz bi-continuous in the sense that it changes up to a constant multiple of a maximum perturbation of atoms, and vice versa. This provides a mathematically robust and stable framework for comparing protein structures without relying on external reference structures or iterative alignments. The resulting invariant space admits low-dimensional, analytically defined coordinates that expose previously hidden patterns and variability across the protein universe[1].\n\nApplying this approach to an all-against-all structural analysis of over 700,000 protein chain structures in the Protein Data Bank (PDB) revealed thousands of duplicates in hours. Many of these cases correspond to duplicated or near duplicated entries[2]. Because the PDB currently lacks mechanisms for detecting such duplications, their presence can bias statistical analyses and machine learning models trained on structural data such as AlphaFold[3]. These results highlight both the utility of a mathematically rigorous invariant for protein geometry and the need for improved validation tools in structural databases. Incorporating invariant-based uniqueness checks into routine PDB deposition workflows could help identify duplicates, improve data quality for structural biology, and increase the reliability of downstream computational studies.\n\n[1] O.Anosova et al.,\"A Complete and Bi-Continuous Invariant of Protein Backbones under Rigid Motion,\" MATCH 94 (2025).\n\n[2] A. Wlodawer et al.， \"Duplicate entries in the Protein Data Bank: How to detect and\nhandle them,\" Acta Cryst. D81 (2025).\n\n[3] J. Jumper et al., \"Highly accurate protein structure prediction with alphafold,\" Nature 596 (2021)", "id": "Paper/68704", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68704"}, {"title": " Dirac operator based regularized maximum likelihood for Markov generators with dimension-free bridge error bounds ", "webprogram_exclude": "0", "session_ids": ["Session/19339"], "source_sha256": "5415e56ab54e0eb7b709c748948b5ecbc300a2ff5d7853fbd5ac6aa1d5daf8e7", "withdrawn": "", "abstract": "Bladt and Sorensen studied likelihood maximization for continuous time Markov chains, obtaining the maximum likelihood estimator either through an EM algorithm or through a Markov chain Monte Carlo procedure, and Albert established existence of the estimator from finitely many independent realizations. We take up the same problem under far harsher observation: for a finite state continuous time Markov jump process, only the two endpoints X(0) and X(T) of each realization are recorded.\n\nUnder this censoring the classical estimator does not exist. We then introduce a regularized likelihood functional and prove that it admits a maximizer. To enforce local movement we constrain the generator so that only neighboring zones carry nonzero transition rates. That sparsity is encoded through the graph Dirac operator, by asking the generator to lie in the subalgebra generated by the Dirac operator and the multiplication operators, so the constraint is algebraic. With a regularized estimator in hand we return to the missing trajectory. A Doob h transform gives the exact conditional law of the path at intermediate times, and embedding it in an expectation maximization framework yields approximations derived from first principles.\n\nIllustrated examples run throughout birth and death processes, the Lotka Volterra predator prey model, and a subset of pickup and dropoff locations of the Yellow Cab taxis in the streets of Manhattan. We show how the pipeline recovers the hidden location distribution and how it scales to larger graphs with sparse connectivity.", "id": "Paper/68705", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68705"}, {"title": " Integral points on surfaces over function fields ", "webprogram_exclude": "0", "session_ids": ["Session/17913"], "source_sha256": "f519b117ec972093c7248ed870dfbae8237636ae0a49b1407c019f37cbcc8f54", "withdrawn": "", "abstract": "Over function fields, we give new results for integral points on surfaces. The results are obtained by combining a method of Corvaja and Zannier with recent advances in Diophantine approximation. This is joint work with Zheng Xiao and Keping Huang.", "id": "Paper/68706", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68706"}, {"title": " A Geometric Derivation of Adaptive Step Sizes in the AdaGrad Family ", "webprogram_exclude": "0", "session_ids": ["Session/19352"], "source_sha256": "ec94b1c9eeb1aa7382613afb6313c94504b81564190931cfc88f7d821e0c5b13", "withdrawn": "", "abstract": "Adaptive gradient methods: AdaGrad, RMSProp, Adam and their descendants  scale each step by a running function of squared gradients. The form of that scaling has been arrived at largely by trial and error, and the stability constant in the denominator is treated as a tuning parameter with no particular meaning. We show that this family of step sizes admits a geometric derivation. Taking the cosine of the angle between the normal to the tangent hyperplane and the horizontal hyperplane as the annealing factor produces a denominator of the form $\\sqrt{g^2 + 1}$  in which the additive constant is the vertical component of the normal vector rather than a free parameter, and in which the resulting step saturates for large gradients and vanishes at a stationary point. We present this construction, the convergence analysis it supports in the deterministic convex and online stochastic settings, and what it suggests about why the AdaGrad family behaves as it does. We also discuss the choice of reference direction and reference plane, which determines whether the resulting scaling is global or coordinate-wise, and the consequences of that choice for both the analysis and the observed behavior.", "id": "Paper/68709", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68709"}, {"title": " Semistandard Young Tableaux and Dual SL<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.054ex\" height=\"1.676ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -432.6 453.9 721.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">_{3}</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-33\" x=\"0\" y=\"-213\"></use>\n</g>\n</svg> Webs in Gr(3,8) ", "webprogram_exclude": "0", "session_ids": ["Session/18370"], "source_sha256": "da2be3b1de55f5ef06a1614efcccafcc4f1400c779d7c499413568a3619f3257", "withdrawn": "", "abstract": "[Jointly presented by Deegan and Selvakumar]\n\nBipartite planar graphs, such as webs, are closely connected to the geometry of a Grassmannian, whose coordinate ring is a fundamental example of a cluster algebra. In small cases, Fraser-Lam-Le observe a phenomenon called web duality between basis webs. They conjecture that it is given by transposing certain combinatorial objects that correspond to each web, called standard Young tableaux. \n\n     Banaian-Catania-Gaetz-Moore-Musiker-Wright showed a direct link between this web duality and the expansion formulae of cluster variables. They extended web duality to Gr(3,12) and Gr(4,12) using standard tableaux, allowing the expansion formulae to be computed more explicitly, and providing strong evidence that web duality held more generally. \n\n     In this talk, we establish properties of semistandard Young tableaux of shape $(3,3,3)$ and their relationship to SL$_{3}$ webs. We test two natural constructions to investigate whether they extend web duality to Gr(3,8), and analyze the obstructions that arise with each approach. We also provide a method to construct dual webs from corresponding semi-standard tableaux. This is joint work with Yuv Saxena and Maya Zutshi.", "id": "Paper/68710", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68710"}, {"title": " From Valuing History to Teaching With It: Mathematics Instructors’ Perspectives on Indian and Global History of Mathematics ", "webprogram_exclude": "0", "session_ids": ["Session/17713"], "source_sha256": "9306dc2cdc417d38199acaa4448f085ff3779ff8250ba61c860b6f4c9235f3eb", "withdrawn": "", "abstract": "Scholarship on the history of mathematics provides how ideas developed over time and how those ideas have been created, debated, and revised. The history of mathematics can be a resource for teaching. But less is known about what mathematics instructors themselves consider and use history in undergraduate classrooms. This study examines instructors’ perspectives and practices on both global and Indian history. Indian history is a relevant case currently because India’s new national education policy asks for the integration of that history into education.  \n\nData were collected from 414 mathematics instructors in India using a questionnaire. For both global and Indian history, respondents placed relatively high value on using history in teaching, but their capability was lower, with practice being the lowest. This pattern suggests that limited practice of historical use is not likely due to only lack of valuing historical use in teaching. Capability responses changed by the type of historical use in questionnaire items: Instructors reported being more capable of using historical stories than of using historical paradoxes. The lower capability for using paradoxes suggests additional pedagogical work in engaging students with tensions that paradoxes can raise, which is different from mathematics instruction that is often expected to be clear.       \n\nAcross five historical uses in the questionnaire, instructors reported lower capability for using Indian history than for global history. In addition, instructors reported low syllabus and training support, and both of these were lower for Indian history than for global history. These patterns suggest the limited visibility of Indian historical perspectives in mathematics curricula. Beyond the visibility of Indian and global history in curricula, if we expect instructors to use Indian history beyond just stories of Indian mathematicians, they should receive training opportunities that could help them engage with historical problems, arguments, and paradoxes as resources, and how they address contextual constraints. In this study, a broader question for both historians and mathematics educators can be raised: how can we not only make historical scholarship, including non-Western mathematics history, visible in curricula but also make it usable to support teaching?", "id": "Paper/68711", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68711"}, {"title": " Null-Space Structure in Multiclass Logistic Regression Hessian Systems ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "07df205fff956be0558f5772a794e0b331d8a23ce78700aeef72c77bd2d5541e", "withdrawn": "", "abstract": "Multiclass logistic regression has an inherent parameter symmetry: adding the same vector to every class parameter vector shifts all logits equally and leaves the softmax probabilities unchanged. Thus the loss has zero curvature along these common-shift directions, producing a nontrivial null space in the unregularized Hessian. Regularization shifts the corresponding zero eigenvalues away from zero, but the resulting Newton systems become increasingly ill-conditioned as the regularization parameter decreases.\n\nWe characterize this symmetry-induced null space and investigate its effect on iterative solvers for the linear systems arising in Newton-type optimization. Using model systems \\(A_\\lambda = A_0 + \\lambda I\\), where \\(A_0\\) is singular and \\(\\lambda > 0\\) controls regularization, we compare Jacobi and Gauss-Seidel methods with null-space-corrected variants over a range of \\(\\lambda\\). As \\(\\lambda\\) approaches zero, the standard stationary methods require rapidly increasing iteration counts, whereas null-space correction substantially improves convergence in the nearly singular regime.\n\nWe also compare conjugate gradient with a null-space-corrected variant for multiclass logistic regression on MNIST and observe essentially identical convergence behavior. We show that the logistic-regression gradient is orthogonal to the symmetry-induced null space and that, with an initialization in the corresponding orthogonal complement, conjugate-gradient residuals and search directions remain in that subspace. These results clarify when explicit null-space correction is useful and explain why its effect differs substantially between stationary methods and conjugate gradient.", "id": "Paper/68712", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68712"}, {"title": " Greatest common divisors and an unlikely intersection type conjecture ", "webprogram_exclude": "0", "session_ids": ["Session/18263"], "source_sha256": "dde803e33f69c9f4189a7b6b168f1772d1b656e06e4512986e1936466ad03324", "withdrawn": "", "abstract": "We discuss recent results on greatest common divisors in Diophantine approximation and a new geometric conjecture inspired by a careful study of these results. This is joint work with Keping Huang.", "id": "Paper/68713", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68713"}, {"title": " Unidirectional Entropic Solutions of the Pressureless Euler Alignment System ", "webprogram_exclude": "0", "session_ids": ["Session/18283"], "source_sha256": "9a5608a8ce77687dd56ea7744822eb8df369f4d6e4bee5d077ef477f6ebe1b5d", "withdrawn": "", "abstract": "We develop a global wellposedness theory for weak solutions of the Euler Alignment system with measure-valued density $\\rho$, bounded and unidirectional velocity $\\mathbf{u} = (u,0, \\ldots, 0)$, and a communication protocol $\\phi$ that may be bounded or weakly singular. Our analysis reduces the system to a (possibly infinite) family of nonlocally coupled hyperbolic balance laws and establishes existence, uniqueness, and stability with respect to unidirectional perturbations for this reformulated system, before translating back to the level of density and velocity.  Our solutions can be approximated by sticky particle Cucker--Smale dynamics, with a quantitative rate of convergence if the initial data is sufficiently regular.", "id": "Paper/68715", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68715"}, {"title": " On an <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.637ex\" height=\"2.509ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -934.9 1135.4 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">L^2</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4C\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-4C\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-32\" x=\"963\" y=\"513\"></use>\n</g>\n</svg> identity for barred derivatives over a piecewise Levi-flat domain ", "webprogram_exclude": "0", "session_ids": ["Session/17887"], "source_sha256": "7f702158b31d8a35efaac85be5dae6f9ea22be53d0699dd289e7d06c060f01f1", "withdrawn": "", "abstract": "The basic $L^2$ inequality for barred derivatives over bounded pseudoconvex domains becomes an identity on the Hartogs triangle $\\mathbb{H}$ which is piecewise Levi-flat. It contrasts to the domains in $\\mathbb{C}^n$ ($n \\geq 2$) with the $C^2$-smooth boundary as each of them has $(0, 1)$-forms for which the $L^2$ inequality is strict. We find the condition for $(0, q)$-forms to be in $\\mathrm{dom}(\\overline{\\partial}^{*})$ and prove that the identity holds for all $(0, q)$-forms in $\\mathrm{dom}(\\overline{\\partial}^{*})$ with $C^{1}(\\overline{\\mathbb{H}})$ coefficients.", "id": "Paper/68716", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68716"}, {"title": " Transformer-based tools for log-concavity of combinatorial defined sequences ", "webprogram_exclude": "0", "session_ids": ["Session/18130"], "source_sha256": "ac25ec7559e26596b89d48c809d3b8188def4d99ddd2883733aec4c8a037eb55", "withdrawn": "", "abstract": "A sequence of integers $a_0,\\ldots,a_n$ is said to be log-concave if $a_i^2 \\geq a_{i-1}a_{I+1}$ for all $i$. This condition is generally strictly stronger than unimodality, and has become extremely popular recently due it its connection with the Hodge theory of matroids. In this talk I will share a handful of projects that I have run with undergraduate teams recently involving proving that certain combinatorially motivated sequences are \\emph{not} log concave using the transformer-based architecture Axplorer (previously PatternBoost). It will be argued that these machine learning tools appear to be especially well suited at finding counter-examples to log concavity.", "id": "Paper/68717", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68717"}, {"title": " Additional food enhances the bifurcation structure of predator competition models ", "webprogram_exclude": "0", "session_ids": ["Session/17860"], "source_sha256": "cc064caf369ab397d72ee831fd45cc6041cf46d77345d2d5702617da2b657004", "withdrawn": "", "abstract": "The concept of additional food suggests that providing predators with supplementary resources can improve their ability to regulate pest populations. In this study, we analyze a predator-prey model that incorporates both additional food supplementation and intraspecific competition among predators. We focus on the system’s bifurcation structure and identify parameter regimes in which the interior equilibrium undergoes a higher-codimension Bogdanov-Takens bifurcation. We derive analytical conditions for the critical parameter values and show that the equilibrium corresponds to a higher-codimension cusp singularity. These results offer insight into how additional food and predator competition together enhance complex population dynamics and have potential implications for sustainable pest management strategies.", "id": "Paper/68718", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68718"}, {"title": " TQFTs with defects and the stability of categorical spectra ", "webprogram_exclude": "0", "session_ids": ["Session/18287"], "source_sha256": "074eca529948efcde9efbf6b811ede1938b3ba3f25f31f632f0f0b05d34a1db0", "withdrawn": "", "abstract": "TQFTs with defects, or singularities, generalize ordinary TQFTs by allowing manifolds equipped with stratifications and singularities. Lurie sketched a classification theorem for fully extended TQFTs of this kind, generalizing the cobordism hypothesis. In this talk, we explain how this extra step can be understood as an instance of the stability of categorical spectra, a recently developed categorification of spectra.", "id": "Paper/68720", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68720"}, {"title": " Coherent Estimation of Risk Measures ", "webprogram_exclude": "0", "session_ids": ["Session/18332"], "source_sha256": "b9927460049969104339932bc02393c5c8eb9517bb170295e4858bcb524911c0", "withdrawn": "", "abstract": "One of the main tasks of any financial institution is managing its risk, which can arise from regulatory requirements or from the need for internal monitoring and control. At the same time, regulatory bodies are mandated to establish legislative frameworks and procedures to assess and manage the risks faced by financial institutions. In either case, the fundamental problem is to design adequate risk measurement tools that can capture the unobservable, usually highly complex, financial risk profiles based on limited data. While the general theory of risk measures is well established, the literature on measuring risk is comparatively sparse. We present a statistical framework for risk estimation inspired by the axiomatic theory of risk measures. This framework provides a canonical methodology for constructing estimators with both sound financial interpretation and desirable statistical properties, thereby unifying risk-measure theory, principles of capital adequacy, and practical statistical challenges in market risk.", "id": "Paper/68721", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68721"}, {"title": " Pro-Rata Market Design for Natural Resource Allocation ", "webprogram_exclude": "0", "session_ids": ["Session/18124"], "source_sha256": "cbee2d3edc54098782c50a26440481cb2c14be213ae264bc31335488a3af639f", "withdrawn": "", "abstract": "Motivated by groundwater markets, we develop and analyze a pro-rata mechanism within a competitive market in which agents trade allocated natural resources among themselves. We consider a general Markovian market framework in which prices are determined as a Nash equilibrium of a non-cooperative stochastic game. We show that the proposed pro-rata mechanism induces a unique allocation of the traded natural resource. Finally, by introducing an additional strategic agent acting as a regulator, endowed with her own action set, we propose several market design mechanisms aimed at ensuring the long-term sustainability of the underlying ecosystem.", "id": "Paper/68722", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68722"}, {"title": " Analogs of Frobenius thresholds in characteristic zero ", "webprogram_exclude": "0", "session_ids": ["Session/17929"], "source_sha256": "54ea2a864a9e35e026ead859401a6daf7e23e0cfa095bd4517516b5544a9470b", "withdrawn": "", "abstract": "Frobenius thresholds are a generalization of F-pure thresholds and they measure the growth of powers of one ideal against Frobenius powers of another.  In this talk I will discuss recent work exploring some characteristic zero analogs of Frobenius thresholds.", "id": "Paper/68724", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68724"}, {"title": " Multidesigns for the graph pair <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"11.028ex\" height=\"3.009ex\" style=\"vertical-align: -1.005ex;\" viewBox=\"0 -863.1 4748.3 1295.7\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">(2C_3,K_{3,3})</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 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transform=\"translate(849,-150)\">\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-33\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-2C\" x=\"500\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-33\" x=\"779\" y=\"0\"></use>\n</g>\n</g>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"4358\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/19354"], "source_sha256": "c6354ebf7969c5d7d67baab37a49c6d58f36ef18488a5fb162ed6a8e8f925189", "withdrawn": "", "abstract": "A $(G,H)$-multidecomposition of $K_n$ is a partition of its edge set into copies of $G$ and $H$, using at least one copy of each. We study the existence of $(G,H)$-multidecompositions of $K_n$, where $G=2C_3$, the disjoint union of two triangles, and $H=K_{3,3}$, the complete bipartite graph. Necessary conditions require $n\\equiv 0,1 \\pmod{3}$. We establish the existence of such multidecompositions for all admissible orders $n\\geq 6$, except $n=7,9,10$ and the possible exceptions $n=16$. In cases where a multidecomposition does not exist, we consider $(G,H)$-multipackings and $(G,H)$-multicoverings. We also analyze the cardinalities of the leaves and paddings associated with maximum $(G,H)$-multipackings and minimum $(G,H)$-multicoverings, respectively.", "id": "Paper/68725", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68725"}, {"title": " Schoenberg’s theorem and thresholding of correlation matrices ", "webprogram_exclude": "0", "session_ids": ["Session/17377"], "source_sha256": "841c0bc5dd900675583e3440cacc18dc480aa1840e0349eaea5cf1fe1147ffe4", "withdrawn": "", "abstract": "Joint work with James Eldred Pascoe\n\nStandard thresholding techniques for correlation matrices often destroy positive semidefiniteness. We investigate the construction of positive definite functions that vanish on specific sets $K\\subseteq [-1,1]$, ensuring that the thresholded matrix remains a valid correlation matrix. We establish existence results, define a criterion for faithfulness based on the linear coefficient of the normalized Gegenbauer expansion in analogy with Delsarte's method in coding theory, and provide bounds for thresholding at single points and pairs of points.\n\nWe prove that for correlation matrices of rank $n$, any soft-thresholding operator that preserves positive semidefiniteness necessarily induces a geometric collapse of the feature space, as quantified by an $\\mathcal{O}(1/n)$ bound on the faithfulness constant. Such phenomenon demonstrates that geometrically unbiased soft-thresholding limits the recoverable signal. Our main tools involve Schoenberg's theorem on positive definite kernels on the sphere and its consequences in coding theory (such as Delsarte's method). \n\nIf time permits, we shall see its consequences in sphere packing.", "id": "Paper/68726", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68726"}, {"title": " Fixed Point Theorems for Paired–Chatterjea Contraction in <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"0.998ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 429.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">b</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-62\" d=\"M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-62\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Metric Spaces ", "webprogram_exclude": "0", "session_ids": ["Session/18363"], "source_sha256": "5dba11176f028220cc094af41efcb23bef8dc5bf7f83f6a5fe256262f312418e", "withdrawn": "", "abstract": "We introduce the class of Paired–Chatterjea contractions in a complete $b$-metric space and establish a corresponding fixed point theorem. Under suitable contractive conditions, we show that fixed points exist if and only if the mapping has no periodic points of prime period 2, and that such a mapping has at most two fixed points. We further show that every Chatterjea-type contraction is a Paired–Chatterjea contraction and provide an example showing that the converse does not hold. Consequently, the paired formulation properly extends the Chatterjea-type framework and offers a broader setting for investigating fixed point and periodic point properties.", "id": "Paper/68728", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68728"}, {"title": " Combinatorics of Crystal Skeletons ", "webprogram_exclude": "0", "session_ids": ["Session/18067"], "source_sha256": "ca45b32c523476244d82dc4ffbc02872bd4a13696444ca3cc0710188ff900093", "withdrawn": "", "abstract": "The crystal skeleton, introduced by Maas-Gariépy, is obtained by contracting the quasicrystal components of a crystal graph, and models the expansion of a Schur function into Gessel's fundamental quasisymmetric functions. We give a self-contained combinatorial description of the crystal skeleton, and introduce an axiomatic characterization in analogy to Stembridge's local axioms for crystals.", "id": "Paper/68733", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68733"}, {"title": " Survival Analysis of Outplanted  Acropora  Corals in Guam Restoration Reefs ", "webprogram_exclude": "0", "session_ids": ["Session/17756"], "source_sha256": "318230e27a825fbe64e2eb09f41b5901b61a3216b6db281ecc7ee32f00b7c1fb", "withdrawn": "", "abstract": "Coral reefs are vital marine ecosystems that provide coastal protection, support biodiversity, and contribute substantially to local economies. However, coral populations are declining worldwide because of climate change, disease outbreaks, and other anthropogenic stressors. This study evaluates the survival of outplanted \\textit{Acropora} corals in Guam using data from a coral restoration program conducted between 2021 and 2025. More than 3,000 coral fragments representing seven \\textit{Acropora} species were outplanted at reef sites in Piti and Merizo using rope, pavement, and C-frame attachment methods. To analyze post-outplanting survival, we employed two complementary survival analysis techniques: the Turnbull estimator for interval-censored data and the Cox proportional hazards model to assess the effects of species, site, and outplanting method on mortality risk. Results indicate substantial mortality during the first year following outplanting, with survival patterns varying considerably among species and locations. Hazard ratio estimates from the Cox model identify both resilient and vulnerable taxa and quantify the relative influence of biological and environmental factors on survival outcomes. These findings provide data-driven guidance for species selection, site prioritization, and restoration design, contributing to more effective coral reef restoration strategies in Guam and other Indo-Pacific reef ecosystems.", "id": "Paper/68735", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68735"}, {"title": " Operators on Mittag-Leffler Functional Spaces ", "webprogram_exclude": "0", "session_ids": ["Session/19339"], "source_sha256": "65e1c3a4c1a1a14a2f7ff11cdcd711145b7e51f2ca6391209f678c3428ba48de", "withdrawn": "", "abstract": "Mittag-Leffler analysis extends white-noise analysis to a non-Gaussian setting by replacing the exponential in the Gaussian characteristic function with a Mittag-Leffler function. This framework gives rise to spaces of test and generalized functionals equipped with an analogue of the classical S-transform.\nIn this talk, we introduce several operator constructions on Mittag-Leffler functional spaces and define the symbols of linear operators acting in this setting. Our main result provides an analytic characterization for symbols in terms of holomorphy on appropriate neighborhoods of the underlying space. We conclude with a brief example illustrating how the symbol of an operator can be explicitly determined.", "id": "Paper/68739", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68739"}, {"title": " Recent advances in alias sampling ", "webprogram_exclude": "0", "session_ids": ["Session/18113"], "source_sha256": "9e28e4a17b699c9f4bf69ccc5380573258517fa52faf202d55b419d435a58457", "withdrawn": "", "abstract": "Alias sampling is widely used for state preparation in the construction of\nblock encodings and other quantum input models. Preparing an $n$-qubit state\nwith $N=2^n$ amplitudes by the standard method requires $\\mathcal{O}(N)$\nclassical preprocessing to build the alias table and $\\tilde{\\mathcal{O}}(N)$\ngates; moreover, the garbage state it leaves behind confines its use to block\nencoding. Compared to general method, for polynomial states we reduce the gate complexity exponentially, and compress the classical\npreprocessing exponentially as well. We further introduce a technique that\neliminates the garbage state entirely in the polynomial case, opening the door\nto using alias sampling for initial state preparation.", "id": "Paper/68740", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68740"}, {"title": " Contractions of Crystal Skeletons ", "webprogram_exclude": "0", "session_ids": ["Session/18376"], "source_sha256": "ca2ae9c28081e63234bfb31fd26d70d7a32830bb7c932c33373c7eda7423bf33", "withdrawn": "", "abstract": "A crystal skeleton is a graph obtained by contracting the quasicrystal components of an $\\mathfrak{sl}_n$-crystal $B(\\lambda)$, generalizing Assaf's dual equivalence graphs. We show that the crystal skeleton tiles further into quasicrystal skeletons, whose characters are the Young quasisymmetric Schur functions $\\mathcal{YQS}_\\alpha$, refining $s_\\lambda = \\sum_\\alpha \\mathcal{YQS}_\\alpha$. We characterize the edges moving between quasicrystal skeleton components, and show contracting them recovers Bruhat order.", "id": "Paper/68741", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68741"}, {"title": " DG-Resolutions via Discrete Morse Theory ", "webprogram_exclude": "0", "session_ids": ["Session/17373"], "source_sha256": "72602449c26ae2b72c88688d30c39a09b14be49aaf4138451240fc6474d289a7", "withdrawn": "", "abstract": "Let $I$ be a monomial ideal of the polynomial ring.  The Taylor resolution of $I$ has DG-algebra structure but is generally far from minimal.  One technique for approaching minimality is discrete Morse theory:  given a Morse matching, the quotient of Taylor by an associated trivial complex is again a resolution of $I$.  Because this quotient takes place in the category of DG-modules, it seems reasonable to hope that it will in many cases preserve the DG structure of the Taylor resolution.  We introduce a combinatorial condition on a Morse matching, \"Morse-closed\", which is sufficient for the resulting Morse resolution to have DG-algebra structure, and show that this condition is quite rare.  We classify the graphs whose edge ideals are Morse-closed.", "id": "Paper/68746", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68746"}, {"title": " Stochastic Regime Dynamics in Litecoin Mining: Environmental Damage, CEDI, and Decision Modeling ", "webprogram_exclude": "0", "session_ids": ["Session/17998"], "source_sha256": "50329b29fdbc7c38bb277aafb63565c4f0b869ea2729977896afdb8050340a8a", "withdrawn": "", "abstract": "We model the environmental-economic dynamics of Litecoin proof-of-work mining using a Cryptocurrency Environmental Damage Index (CEDI), which relates the social cost of carbon from mining-related emissions to mining revenue. Using weekly data from 2013–2025, we evaluate three hardware-efficiency scenarios and classify CEDI into four states: Low, Moderate, High, and Very High. We estimate transition probabilities among these states and examine persistence, regime durations, and changes associated with Litecoin halving events. Across the hardware scenarios, approximately 91\\% of weekly observations remain in the same CEDI state, while persistence within the combined High and Very High states exceeds 99\\%. The results also reveal substantial changes in CEDI around halving events and a prolonged Very High state in the most recent period. These transition probabilities provide a stochastic foundation for decision models in which mining revenue represents an economic reward and CEDI represents an environmental-cost state. The framework provides a basis for evaluating mining decisions under uncertainty.", "id": "Paper/68749", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68749"}, {"title": " WSVI: A Dimensionless Shape Family for Implied Volatility and Its Static No-Arbitrage Structure ", "webprogram_exclude": "0", "session_ids": ["Session/18332"], "source_sha256": "b6d0da8831d1bf1e69165a23adbb244e847d9460d905e523360d28afd6d9ba69", "withdrawn": "", "abstract": "W-shaped smiles appear in near-expiry options around binary events such as earnings, and have been associated with bimodal risk-neutral densities. The three-parameter eSSVI slice cannot produce them. This paper defines WSVI, a parametric family for implied volatility that admits negative at-the-forward curvature and bimodal implied densities, and develops its static no-arbitrage structure. The construction factorizes total variance into a level and a dimensionless shape of normalized log-moneyness. The shape extends the per-slice eSSVI form with bounded one-sided basis terms, which add flexibility in the interior while leaving the leading-order wing behavior controlled by the affine and quadratic components. We characterize the family's exact domain and write the butterfly, vertical spread, and calendar conditions directly in shape coordinates.", "id": "Paper/68753", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68753"}, {"title": " On Higher Dagger Categories ", "webprogram_exclude": "0", "session_ids": ["Session/18210"], "source_sha256": "be6ae55445743a761e0ce70f15b699a0509e779a2391dc95c489458e1d085b94", "withdrawn": "", "abstract": "Dagger categories play an important role as target categories of unitary quantum field theories. While dagger structures in ordinary category theory have a long history, their extension to higher categories requires a homotopy-coherent treatment of involutions and their compatibility with objects. Recently, Ferrer and collaborators introduced a model-independent definition of higher dagger categories and formulated a number of structural statements whose proofs were left open.\n\nIn this talk, I will construct concrete models for higher dagger categories, beginning with the $(\\infty,1)$-categorical case and extending to higher dimensions via reversal versions of Joyal’s cell categories $\\Theta_n$. I will explain their equivalence with the model-independent approach and use these models to prove several of the proposed statements.", "id": "Paper/68755", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68755"}, {"title": " Optimizing Metachronal Paddling with Reinforcement Learning at Low Reynolds Number ", "webprogram_exclude": "0", "session_ids": ["Session/18220"], "source_sha256": "112e612bbadb67d1c89573087ec02d9549a72c0b9ffc87953554ecbdbc308e97", "withdrawn": "", "abstract": "Metachronal paddling is a swimming strategy in which an organism oscillates sets of adjacent limbs with a constant phase lag, propagating a metachronal wave through its limbs and propelling it forward. This limb coordination strategy is utilized by swimmers across a wide range of Reynolds numbers, which suggests that this metachronal rhythm was selected for its optimality of swimming performance. In this study, we apply reinforcement learning to a swimmer at zero Reynolds number and investigate whether the learning algorithm selects this metachronal rhythm, or if other coordination patterns emerge. We design the swimmer agent with an elongated body and sets of paddles placed along the body for various fixed paddle spacings. We begin with rigid paddles to isolate the time coordination of the limbs, then add a hinge to allow the paddles to change their shape throughout the stroke. Based on paddle spacing and type, the swimmer agent learns qualitatively different coordination patterns.", "id": "Paper/68756", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68756"}, {"title": " Toeplitz Matrices from Fractional Differential Equations on Adaptive Meshes ", "webprogram_exclude": "0", "session_ids": ["Session/18032"], "source_sha256": "34f4a5c78359cb7c3870503209e2a0fdd7f7286c29f24bb56e7f055697aa98e5", "withdrawn": "", "abstract": "Toeplitz stiffness matrices commonly arise in the discretization of fractional differential equations (FDEs) on uniform meshes. Singularities inherent to FDEs, however, result in poor scaling for solvers on the uniform mesh. Adaptive refinement is a natural approach to deal with error from singularities, but means losing uniform Toeplitz structure of the stiffness matrix. We examine what Toeplitz-like or other structure remains in the stiffness matrix on the adaptive mesh, how different approaches to mesh refinement affect the resulting structure, and how this changes as the problem size grows. We discuss the implications for numerical solvers and matrix compressibility in pursuit of efficient FDE solvers.", "id": "Paper/68768", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68768"}, {"title": " Computational Analysis of Quantum Optimal Control of Radical-Pair Spin Dynamics Subjected to Filtering. ", "webprogram_exclude": "0", "session_ids": ["Session/18321"], "source_sha256": "0fd8eb7177d8795bf4e3720874c072e5d6e49765cf2949db200565e277a7cd5d", "withdrawn": "", "abstract": "This talk presents numerical methods for quantum optimal control of radical-pair spin dynamics, aiming to maximize the triplet-to-singlet yield through optimized electromagnetic fields. An Iterative Pontryagin Maximum Principle (IPMP) algorithm is developed for the computation of bang-bang optimal controls and compared with a Gradient Projection Method (GPM). Numerical simulations are performed in order to demonstrate convergence, stability, and regularization effects of the proposed approach. Comparisons between filtered regular controls and unfiltered bang-bang controls show that the loss in the maximal singlet yield is below 1\\%, indicating that experimentally realizable filtered fields retain near-optimal performance. These results provide computational support for future studies of quantum-coherent magnetoreception.", "id": "Paper/68772", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68772"}, {"title": " Birkhoff subpolytopes, order polytopes, and linear extensions ", "webprogram_exclude": "0", "session_ids": ["Session/18286"], "source_sha256": "363e6655c8d1e5666e695e1d1d96faa22c57b1995733ac680bc2f2323d6d510a", "withdrawn": "", "abstract": "In 2018, Davis and Sagan observed that a particular pattern-avoiding Birkhoff polytope has the same normalized volume as an order polytope, leading them to ask whether the two are unimodularly equivalent. Motivated by this question, we introduced the \\(c\\)-Birkhoff polytopes, indexed by Coxeter elements of the symmetric group, and proved that each is unimodularly equivalent to the order polytope of the heap of the \\(c\\)-sorting word of the longest permutation. The case \\(c=s_1s_2\\cdots s_n\\) answers Davis and Sagan’s question. This equivalence gives a structural explanation for a combinatorial volume formula: the normalized volume of a \\(c\\)-Birkhoff polytope equals the number of linear extensions of its associated heap poset.\nIt turned out that the c-Birkhoff polytope is just a special case of Birkhoff subpolytopes that is unimodularly equivalent to an order polytope. I will discuss ongoing work that discover a much larger family of Birkhoff subpolytopes with such a property, and therefore admit analogous linear-extension formulas for their normalized volumes.", "id": "Paper/68774", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68774"}, {"title": " The E-convex order on noncommutative laws ", "webprogram_exclude": "0", "session_ids": ["Session/18381"], "source_sha256": "0a82512de9e8e9867ecf8f2ee49259a5af36d5fa4265d19ce8d0d08e817f1576", "withdrawn": "", "abstract": "The notion of tracial E-convex functions was introduced by Gangbo, Jekel, Nam, and Shlyakhtenko. They play the role of convex functions in the study of Monge-Kantorovich duality for optimal transport in the setting of free probability.\n\nIn joint work with John Hopper, we study the E-convex order on noncommutative laws. In analogy with the case of probability measures, we prove a version of Strassen’s theorem characterizing when one law dominates another in this order. We also derive some applications to the theory of optimal couplings in free probability.", "id": "Paper/68775", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68775"}, {"title": " The Gromov–Ros conjecture for rank-one symmetric spaces of noncompact type ", "webprogram_exclude": "0", "session_ids": ["Session/18295"], "source_sha256": "b5a920f7a7487f9e25c19eadb79eea0526214942a47e76bd73b9311f3ab84dc2", "withdrawn": "", "abstract": "We prove the Gromov--Ros conjecture for every rank-one symmetric space of\nnoncompact type: finite-perimeter isoperimetric regions are precisely the\ngeodesic balls, up to ambient isometry and null sets.  The proof is organized\nuniformly in the root multiplicities $(p,q)$.  We introduce the volume radius\n\\[\n R(r)^n=n\\int_0^r\\sinh^{n-1}s\\,\\cosh^q s\\,ds,\n\\]\nwhich converts the polar volume form into\n$R^{n-1}dR\\,d\\sigma$.  Hence radial--angular stretches\n$R\\mapsto e^{t\\varphi(\\theta)}R$ have the exact Jacobian\n$e^{nt\\varphi}$.  Starting from a volume geometric median, a log-partition\ncorrection produces an exactly volume-preserving family of global\nbi-Lipschitz stretches.  The reduced-boundary area formula and the ambient\ncofactor yield a universal pointwise trace identity depending only on\n$(p,q)$ and the horizontal and vertical components of the\nmeasure-theoretic normal.  Its specializations for $q=1,3,7$ admit explicit\nstrict sign certificates, forcing the normal of an isoperimetric region to\nbe radial almost everywhere.  Isotropy invariance in BV and a\none-dimensional weighted endpoint comparison then force a single ball.\nFor complex hyperbolic space we additionally prove that every smooth bounded\nfixed-volume stable critical domain is a geodesic ball.  The resulting\ncomplex-hyperbolic isoperimetric theorem removes the geometric hypothesis in\nseveral sharp weighted-Bergman contraction, Faber--Krahn, and Lieb--Wehrl\ninequalities, and their high-weight scaling limit recovers holomorphic\nGaussian hypercontractivity.", "id": "Paper/68776", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68776"}, {"title": " Coordinate-wise Elephant Random Walk ", "webprogram_exclude": "0", "session_ids": ["Session/19370"], "source_sha256": "a98beb7f295163bc09d3ba86192199a67be72f385e759fb0ffd88db26260f005", "withdrawn": "", "abstract": "We introduce a non-Markovian random walk on the discrete hypercube $Q_k=\\{-1,1\\}^k$ in which each coordinate carries its own elephant-type memory. At each step, a coordinate $i$ is chosen uniformly and updated by sampling from its own past, repeating the sampled value with probability $p_i$ and reversing it otherwise. This produces a walk whose coordinates have separate memory histories but evolve through a common random clock. \n\nWe study memory decay, time averages along the walk and fluctuations of additive functionals of the process. For $p_i<1$, the empirical memory bias of each coordinate vanishes, with a change in decay rate at the classical elephant-walk threshold $p_i=3/4$. Comparing the process with a memoryless refresh chain yields a law of large numbers for bounded observables, with limiting average given by the uniform measure on the hypercube. Using a Poisson equation and the Walsh basis, we decompose additive functionals into a martingale term and explicit memory corrections. In the diffusive regime $\\max_i p_i <3/4$, this leads to a central limit theorem with an explicit asymptotic variance.", "id": "Paper/68780", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68780"}, {"title": " Fuzzy Geometry-Based Support Vector Machine ", "webprogram_exclude": "0", "session_ids": ["Session/18554"], "source_sha256": "6517ea105841d00fd1c07c40bde5b9b8c841d73db5e18cb66d8cb10fa81a743f", "withdrawn": "", "abstract": "In this paper a fuzzy geometry-based support vector machine (GFSVM) is proposed, which differs fundamentally from the existing Fuzzy Support Vector Machine (FSVM). In existing fuzzy support vector machine (FSVM) algorithms work by fuzzifying training data into fuzzy numbers by assigning membership functions. Each training sample is assigned a membership value that determines its relative importance during the optimisation process. Samples with higher memberships exert greater influence on the resulting separating hyperplane. In contrast, the proposed method treats all training data equally, as in the conventional SVM. Instead of representing data as discrete points, each data point is considered a fuzzy point with an associated membership function. This allows the classifier to incorporate the geometric characteristic of fuzziness directly into the learning process of the hyperplane. The proposed GFSVM method provides a mathematically compact algorithm supported by fuzzy geometry. Experiments on several publicly available datasets demonstrate its superior performance to existing SVM, Logistic Regression, and Linear Discriminant Analysis (LDA) in terms of accuracy, precision, recall, and F1-score.", "id": "Paper/68781", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68781"}, {"title": " Metrics on Reeb Spaces and Mapper Complexes ", "webprogram_exclude": "0", "session_ids": ["Session/18324"], "source_sha256": "1f092ca5c2388e78db1c65eeb59bb21799e361a707457405fd3bd34a81b33f2e", "withdrawn": "", "abstract": "Mapper is a construction from topological data analysis that turns a dataset $\\hat{X}$ into a graph, or more generally, a (simplicial) complex intended to summarize the large-scale structure of the dataset. Its construction is done with three additional ingredients: a lens function from $\\hat{X}$ to a lens space $Y$, a cover of $Y$, and a clustering algorithm on $X$. Mapper was originally introduced as a data-driven approximation to the Reeb graph (more generally, space) of , the space that our data $\\hat{X}$ was sampled from. Previous work has used notions from category theory to study the convergence of the mapper graph to the Reeb graph when the lens function takes values in Euclidean space and the diameters of the cover elements uniformly tend to zero.\n\nIn this talk, we present recent results from an ongoing project with Bala Krishnamoorthy, where we use tools from metric geometry to study the convergence and stability of mapper complexes to Reeb spaces. Our framework applies when the the underlying space $X$ comes equipped with a pseudometric and the lens function maps takes values in an arbitrary metric space.\n\nAlthough metrics on mapper graphs have been studied, the distinguishing feature of our metric is that it is derived from a natural metric on the Reeb space. Under mild assumptions on the underlying metric spaces and lens function, the topology induced by this natural metric agrees with the quotient topology on the Reeb space. We will discuss additional advantages of this Reeb space metric, and show how it can be approximated from a finite sample $\\hat{X}$ of $X$. We describe how it can be used to equip the Mapper complex with a metric and then show how they Gromov-Hausdorff convergence of the metric mapper complex to the metric Reeb space as the diameters of the covers uniformly go to zero. Time permitting, we will conclude by discussing how we will be using this framework to create computationally efficient algorithms for selecting optimal parameters for mapper.", "id": "Paper/68782", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68782"}, {"title": " Complexity, curvature and homological dimension of modules under linkage ", "webprogram_exclude": "0", "session_ids": ["Session/19342"], "source_sha256": "54e5734bcc1d7ebb84b2bcebe6abfca0fda28c4080e4a9e632fae4443eca2661", "withdrawn": "", "abstract": "In this article, we analyze how (projective and injective) complexity, curvature, and complete intersection dimension behave under linkage of modules and ideals. Let $R$ be a Gorenstein local ring. Consider a Gorenstein perfect ideal $\\mathfrak{a}$ (e.g., $\\mathfrak{a}$ is generated by an $R$-regular sequence). Let $M$ and $N$ be two Cohen-Macaulay $R$-modules linked by $\\mathfrak{a}$. We prove that $\\mathrm{cx}_R(M)= \\mathrm{inj\\,cx}_R(N)$ and $\\mathrm{curv}_R(M)= \\mathrm{inj\\,curv}_R(N)$. In particular, when $R$ is complete intersection, $\\mathrm{cx}_R(M)= \\mathrm{cx}_R(N)$ and $\\mathrm{curv}_R(M)= \\mathrm{curv}_R(N)$. Furthermore, we show that $\\mathrm{pd}_R(M)= \\mathrm{pd}_R(N)$ and $\\operatorname{CI-dim}_R(M)= \\operatorname{CI-dim}_R(N)$. If any of these dimensions is finite, it is equal to $\\mathrm{ht}(\\mathfrak{a})$. Similar results are obtained for linkage of ideals. All these results highly extend a classical result of Peskine and Szpiro in many directions. We construct several examples that complement our results. These also show how properties like `integrally closed', `$\\mathfrak{m}$-full' and `Burch' behave under linkage of ideals.", "id": "Paper/68783", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68783"}, {"title": " When does a Markov chain converge to its Steady State Distribution in a finite number of time steps? ", "webprogram_exclude": "0", "session_ids": ["Session/18343"], "source_sha256": "f56533fe2d7908837e70d34f1c25b8b59e0892fc89c4f03397a1b55d04e00215", "withdrawn": "", "abstract": "Consider a 3-state Markov chain having a $3 \\times 3$ 1-step transition matrix $P$ and its steady state distribution $\\vec{\\pi} = \\begin{bmatrix} \\pi_0 & \\pi_1 & \\pi_2 \\end{bmatrix}$. We study when $P = \\begin{bmatrix}\n    p(0,0) & p(0,1) & p(0,2) \\\\\n    p(1,0) & p(1,1) & p(1,2) \\\\\n    p(2,0) & p(2,1) & p(2,2)\n\\end{bmatrix}$ and $P^n = \\begin{bmatrix}\n    \\pi_0 & \\pi_1 & \\pi_2 \\\\\n    \\pi_0 & \\pi_1 & \\pi_2 \\\\\n    \\pi_0 & \\pi_1 & \\pi_2\n\\end{bmatrix}$ holds for the first time when $n = 1, 2, 3, \\dots$. It turns out that this can only happen when $n = 1$ or $n = 2$. When $n = 2$, $P$ is shown to have eigenvalues of $\\lambda_1 = 1$ and $\\lambda_2 = \\lambda_3 = 0$. For $P$ having dimension $d > 3$, then there exist examples such that $P^n = \\begin{bmatrix}\n    \\vec{\\pi} \\\\ \\vdots \\\\ \\vec{\\pi}\n\\end{bmatrix}$ for $P$'s steady state distribution $\\vec{\\pi} \\in \\mathbb{R}^d$ when $n = d - 1$.", "id": "Paper/68784", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68784"}, {"title": " Optimizing Green Supply Chain Inventory Policies with Order Volume Discounting Scheme under Trade Credit and Two-warehouse Environment ", "webprogram_exclude": "0", "session_ids": ["Session/19322"], "source_sha256": "75ea4ae1fd331e98f02cc96bded76a0b58d10075b898eb62b05d472c09a9d894", "withdrawn": "", "abstract": "Environmentally sustainable supply chain management has become increasingly important, particularly in developing countries. To remain competitive, supply chain participants adopt pricing and credit strategies that encourage larger orders and improve profitability. This study develops an integrated inventory model incorporating flexible quantity-dependent trade credit and all-unit quantity discounts. Under the proposed framework, the supplier offers longer credit periods and lower unit prices when the retailer purchases larger quantities. Since the retailer’s own warehouse has limited capacity, excess inventory is stored in a rented warehouse, resulting in additional holding costs. The model also considers carbon emissions generated during production, transportation, and storage activities. Thus, the framework simultaneously addresses economic and environmental concerns within a supplier–retailer supply chain. The objective is to determine the optimal ordering and inventory decisions that maximize the joint profit while accounting for capacity limitations, quantity-based discounts, trade credit, and carbon emissions. The existence of an optimal solution is established analytically, and an algorithm is developed to identify the global optimum. Numerical examples are presented to validate the model and examine the effects of key parameters. The resulting managerial insights provide useful guidance for designing profitable and environmentally responsible inventory policies in a supply chain system.", "id": "Paper/68787", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68787"}, {"title": " An NSGA-II Driven Bi-objective Inventory Optimization Model for Sustainable Closed-loop Supply Chains ", "webprogram_exclude": "0", "session_ids": ["Session/19322"], "source_sha256": "b5439dd4095b1b93978d416db89efb47b59408d6e062cf1663784d6c00036dba", "withdrawn": "", "abstract": "Nowadays, remanufacturing has emerged as a sustainable and cost-effective approach for restoring used products or components to their original functionality and performance standards. This study focuses on the remanufacturing of used products, considering key processes such as collection, inspection, repair, and reassembly, while accounting for their associated economic and environmental impacts. A comprehensive analysis of the costs and carbon emissions incurred at different stages of the system, including the primary manufacturer, primary retailer, collection center, and other relevant facilities, is presented. The main objective is to minimize the total system cost and carbon emissions associated with the remanufacturing process. To obtain optimal solutions, a bi-objective optimization model is formulated and solved using the Non-dominated Sorting Genetic Algorithm II (NSGA-II), which provides an effective trade-off between the two conflicting objectives. The major novelties of the proposed model include imperfect screening, quadratic demand, and unequal shipment policies. The effectiveness of the proposed model is demonstrated through a numerical example based on a case study, yielding a set of Pareto-optimal solutions. Furthermore, sensitivity analysis is conducted to examine the effects of key parameters on the model outcomes. The results indicate that the proposed approach can achieve up to a $65.21\\%$ reduction in total cost while simultaneously supporting sustainable remanufacturing practices and reducing environmental impacts.", "id": "Paper/68788", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68788"}, {"title": " Non-systematic recovery: a route to improve the Service Rate Region. ", "webprogram_exclude": "0", "session_ids": ["Session/18389"], "source_sha256": "6226f1700906a34dfd17fd220530b610632d85faaab532659f0af0771c523b72", "withdrawn": "", "abstract": "In the context of distributed data storage, the use of coding has recently emerged as an alternative to pure replication in the design of redundancy policies. Coding gives the system more flexibility to handle variations in the request volumes for the different data objects stored in the system. The Service Rate Region (SRR) is a polytope describing the types of requests that a certain coded system can support. The coded system is described by a $k\\times n$ full rank matrix $G$ over the finite field $\\mathbb{F}_q$, and the SRR of $G$ is often studied through the the linear code generated by $G$. Anyway, the polytope depends on the chosen $G$, and it is not a code invariant: in the literature, specific matrices are chosen for a given code, and especially systematic matrices are studied.\nIn this talk, we explore ways to pick a generator matrix of a code such that certain properties of the SRR are improved or maximized. We find that actually non-systematic matrices hold a potentially better SRR, and develop tools to find the best matrices for some codes. The examples we develop show that the non-systematic matrices we find have a larger SRR than systematic matrices generating the same code. In passing, we consider the connection of the SRR problem to other topics in coding theory, such as Private Information Retrieval codes and Majority Logic Decoding.", "id": "Paper/68789", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68789"}, {"title": " Reinforcement Learning-Based Adaptive Queue Management for Healthcare Systems with Time-Varying Rewards and Costs ", "webprogram_exclude": "0", "session_ids": ["Session/19337"], "source_sha256": "58cb0f70cfecf81df6c75f78148c34e36f731af7cf5904e6daa75fe086ca2cb8", "withdrawn": "", "abstract": "Efficient management of patient flow is a major challenge for hospitals, where time-varying patient arrivals, heterogeneous service requirements, and limited healthcare resources can lead to congestion and excessive waiting times. This study develops an application-oriented dynamic patient management framework for making adaptive service-capacity decisions in hospital queueing systems. The proposed framework considers heterogeneous patient flows and service providers, allowing different patient categories to be handled by service providers with potentially different service rates. Patient arrivals are modeled through a non-homogeneous Poisson process to represent the time-dependent variation commonly observed in hospital demand. A reinforcement learning approach based on Q-learning is then incorporated to dynamically determine operational actions, such as maintaining, adding, or reallocating service capacity, according to the observed queue state and system events. The learning framework enables the hospital system to respond to changing demand conditions rather than relying on fixed resource-allocation policies. The performance of the proposed approach is evaluated through simulation under varying patient-demand and service scenarios, with total patient waiting time and operational cost considered as key performance measures. The results indicate that adaptive resource allocation can improve patient-flow efficiency and reduce the adverse effects of congestion compared with conventional static queue management strategies. The proposed framework provides a data-driven decision-support approach for dynamic hospital resource management and offers a flexible foundation for extending reinforcement learning-based optimization to other healthcare service systems.", "id": "Paper/68790", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68790"}, {"title": " From Gaussian Mixtures to Ridgeline Varieties ", "webprogram_exclude": "0", "session_ids": ["Session/18356"], "source_sha256": "612a760cce23004950aabef51651bb67d285fc856aa1f291610f61351825a0fc", "withdrawn": "", "abstract": "Algebraic geometry has revealed hidden structure in a wide range of statistical models. This perspective has led, for instance, to Markov bases, phylogenetic invariants for evolutionary models, and new results in likelihood geometry. In this talk, we bring this perspective to Gaussian mixtures. Although their critical point equations involve both polynomial and exponential expressions, we associate algebraic varieties to Gaussian mixtures that encode their critical points. We introduce the ridgeline correspondence, together with its projection, the ridgeline variety. Our main result is a criterion on these varieties that allows us to determine when a Gaussian mixture density has only finitely many critical points.\n \n\\bibitem{JIR-CA}\n{\\sc C.~Am\\'endola, and J.I.~Rodriguez}, {\\em {A ridgeline correspondence criterion: the number of modes of a {G}aussian mixture is finite}},  (2026).\n\\newblock \\href{https://arxiv.org/abs/2608.28558}{\\texttt{arXiv:} \\texttt{2608.28558}}.", "id": "Paper/68792", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68792"}, {"title": " Exotic Surfaces in 4-Manifolds and Surface Corks ", "webprogram_exclude": "0", "session_ids": ["Session/18344"], "source_sha256": "06e46a98caa12715dc9fdbd3775515a3aca16ddb4c6eb76c861e5499bff6afd1", "withdrawn": "", "abstract": "A cork is a compact, contractible 4-manifold equipped with a boundary diffeomorphism. A fundamental result in 4-manifold topology states that any two exotic smooth structures on a closed, simply connected 4-manifold are related by a cork twist. In this talk, we introduce the notion of a surface cork, an analogous object for smoothly embedded closed surfaces in closed 4-manifolds, and discuss how surface cork twists relate certain known examples of exotic surfaces.", "id": "Paper/68793", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68793"}, {"title": " A Visual Catalog of Color Symmetries of the Wallpaper Groups ", "webprogram_exclude": "0", "session_ids": ["Session/17986"], "source_sha256": "6e4f3d01eedf6e923b8d9b38f573474639f058ec06579eb6df4496cf614573e0", "withdrawn": "", "abstract": "Colored periodic patterns, from Escher's tessellations to counterchange textile designs, \nare governed by color symmetry: a symmetry of the pattern is allowed to permute the colors \ninstead of preserving them. The colorings of a pattern with symmetry group G in which every \nsymmetry permutes the colors correspond to the subgroups H of G of finite index, the index \nbeing the number of colors. The color groups of the 17 wallpaper groups were enumerated in \nthe 1970s and 80s (Senechal, Jarratt and Schwarzenberger, Wieting, Grunbaum and Shephard), \nbut the results are tables of subgroups, not pictures, and a designer has no easy way to \nsee what the colorings look like or how to construct them.\n\nWe present a catalog that draws them. For every wallpaper group and every subgroup H up to \na given number of colors, an entry shows the fundamental domains of G and H with their \npairing transformations, the tilings of the plane by both, and the colored patterns \nthemselves: the coloring by orbits of H, which is unique, and the colorings by cosets of H, \none for each placement of H inside G; all of them coincide exactly when H is normal. \nA partition table displays the pattern as the union of the pieces f_i H g_j and makes the \npermutation of the colors visible. The subgroups are enumerated directly from the \npresentation of the group given by its fundamental domain, and each subgroup receives a \ncanonical name that does not depend on the choice of that domain. The images are generated \nwith our open source WebGL library SymmHub, which also lets users apply any color symmetry \nfrom the catalog to their own images in the browser. As a worked example we take Escher's \nperiodic drawing 70 (butterflies, 1948): its wings and its eyespots are two different \nplacements of the same three-color group 632/632[3], and only one of the three placements \nnever puts one color on two touching butterflies.\n\nThe catalog is available at https://bulatov.org", "id": "Paper/68795", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68795"}, {"title": " Density of wild initial data for the isentropic compressible Euler equations considering global-in-time admissible weak solutions ", "webprogram_exclude": "0", "session_ids": ["Session/18306"], "source_sha256": "5c0529ddf8d6b527cd7d2e2d15a761ee6d1c2e2a17223c5f1b255696cef63b1e", "withdrawn": "", "abstract": "Rather surprisingly, the technique of convex integration has revealed that for some initial data, many models studied in the field of mathematical fluid mechanics allow for a multitude of solutions. This talk is concerned with the question how large the set of such wild initial data is in the context of the isentropic Euler equations. We show that wild initial data form a dense set. In contrast to existing results in the literature, in this talk \"wild initial data\" are data which give rise to infinitely many global-in-time weak solutions which are admissible in the sense that the local energy inequality holds.\n\nThis talk is based on joint work with Daniel W. Boutros (IAS Princeton).", "id": "Paper/68796", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68796"}, {"title": " Erdős Distance Results for <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.211ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 521.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">k</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-6B\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Degenerate Graphs with <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.04ex\" height=\"1.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -576.1 878.5 721.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">m</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-6D\" x=\"0\" y=\"0\"></use>\n</g>\n</svg> Edges ", "webprogram_exclude": "0", "session_ids": ["Session/18369"], "source_sha256": "c1ddd60a01c71d4f135c7233fd29a5e00075e86fda800dd0a4ad2b539dced158", "withdrawn": "", "abstract": "The Erd\\H{o}s distinct distances problem asks for the minimum number of distinct distances determined by $N$ points, resolved in the plane by Guth and Katz. A natural generalization fixes a finite graph $G$ with $m$ edges and records, over all injective embeddings of $G$ into a finite point set $P \\subset \\mathbb{R}^d$, the vectors of edge-lengths realized; we write $\\Delta_G^\\circ(P)$ for this set of edge-distance vectors. Taking $G$ to be a single edge recovers the classical problem. Prior results are sharp but confined to special classes, such as rigid graphs or graphs with a Hamiltonian path, and largely to the plane. A graph is $k$-degenerate if its vertices can be ordered so that each has at most $k$ neighbors among those preceding it. We show that if $G$ is $k$-degenerate, then for every $d \\ge 2k+1$ (or $d \\ge 2k$ if $k$ is even) and every $\\varepsilon > 0$, $|\\Delta_G^\\circ(P)| \\gtrsim_{G,d,\\varepsilon} N^{m/(d-1)-\\varepsilon}$ for $|P| = N$. This provides a first general result for $k$-degenerate graphs in the discrete setting, holding uniformly over all finite graphs since every finite graph is $k$-degenerate for some finite $k$. It is motivated by the recent Falconer-type threshold $\\frac{d+k}{2}$ obtained for $k$-degenerate graphs in the continuous setting by Borges, Foster, Ou, Palsson, and Romero Acosta. The proof combines a bisector-energy estimate for pinned $k$-stars with an entropy argument, chained along a construction order of $G$ and bootstrapped across dimensions via an explicit degeneracy-indexed recursion.", "id": "Paper/68797", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68797"}, {"title": " Homological Dynamics in the context of Data Driven Dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/18304"], "source_sha256": "21fcd171725e43708b1fdf42ada6c97f854d239ecabc3423b0caf7e6443681a7", "withdrawn": "", "abstract": "The global dynamics of nonlinear systems described using the language of invariant sets can be both extremely complicated and vary dramatically as a function of parameters. One consequence of this richness is that there is no algorithm that can learn the global dynamics from countable data in general.  Homological dynamics provides a coarse, interpretable, and, most importantly, robust characterization of dynamics.  \n\nIn this talk, time permitting, I will cover several topics: a brief introduction to homological dynamics, a theorem that guarantees that a homological dynamics characterization of dynamics can be learned, an example of how these ideas can provide a probabilistic guarantee of the characterization of dynamics, and how, in practice, these ideas can be extended to high dimensional systems.", "id": "Paper/68799", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68799"}, {"title": " Densely Settled Arboreal Galois Groups ", "webprogram_exclude": "0", "session_ids": ["Session/18259"], "source_sha256": "847acb32b44456a194b9ad44df785357dea86cd585f7884c74ddac980dddce08", "withdrawn": "", "abstract": "Let $f$ be a quadratic rational function over a field $K$ of characteristic\nnot $2$, and fix a basepoint $a$. The iterated preimages of $a$ under $f$\nform a rooted binary tree $T$, and the absolute Galois group of $K$ acts on\n$T$, giving the arboreal Galois representation. Following Boston and Jones, a\ncycle of a tree automorphism is \\emph{stable} if its length strictly\nincreases at each subsequent level, and the automorphism is \\emph{settled} if\nthe proportion of vertices lying in stable cycles tends to $1$. A subgroup is\n\\emph{densely settled} if its settled elements are dense. Settledness\noriginates in questions about how the iterates of $f$ factor modulo primes, and Boston and Jones\nconjectured that arboreal Galois groups of quadratic polynomials are densely\nsettled.\n\nI will talk about recent work, part of it joint with ~Ko\\c{c}ak, on this\nconjecture and on its analogue for rational functions. For a natural class of\npostcritically finite quadratic polynomials we obtain dense settledness,\nwhile in the rational function setting settled elements can fail to exist entirely.", "id": "Paper/68800", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68800"}, {"title": " The Neumann problem for stochastic partial differential equations ", "webprogram_exclude": "0", "session_ids": ["Session/17947"], "source_sha256": "77ef7c8bdac051a20a5530389b88f36d448033c3b66752be4a747e477cff2d8f", "withdrawn": "", "abstract": "In this talk, we study second-order stochastic partial differential equations with Neumann boundary conditions in the half space. The coefficients may be random and are only assumed to be measurable in time. We introduce weighted function spaces for the Neumann problem and establish existence, uniqueness, and regularity of solutions. We also show improved boundary regularity compared with the corresponding Dirichlet problem under suitable assumptions.", "id": "Paper/68802", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68802"}, {"title": " Flexibility of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"4.08ex\" height=\"2.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -1006.6 1756.9 1152.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">C^{1,\\theta }</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-43\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-43\" x=\"0\" y=\"0\"></use>\n<g transform=\"translate(774,362)\">\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-31\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-2C\" x=\"500\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-3B8\" x=\"779\" y=\"0\"></use>\n</g>\n</g>\n</svg> Isometric Immersions ", "webprogram_exclude": "0", "session_ids": ["Session/17952"], "source_sha256": "3a27264d0450fca5a062160088f1133f5075864300330f20f7162cc4f34066a8", "withdrawn": "", "abstract": "The problem of isometrically embedding Riemannian manifolds into Euclidean space (that is, preserving the intrinsic length of curves) is a fundamental problem in differential geometry. Classical results indicate that sufficiently smooth isometries are often unique, up to translation and rotation. However, the Nash–Kuiper theorem presents the seemingly paradoxical abundance (or flexibility) of isometries that are only $C^1$ regular.  A natural question then arises: Do these uniqueness and flexibility properties extend to isometries of class $C^{1,\\theta}$ for $0 < \\theta < 1$, particularly when $\\theta$ is close to $1$ (uniqueness) or close to $0$ (flexibility)? Moreover, is there a sharp H\\\"older exponent $\\theta_0$ that separates these contrasting behaviors?\nIn my talk I will discuss recent advances regarding these questions.", "id": "Paper/68811", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68811"}, {"title": " On the distribution of integral quadratic forms ", "webprogram_exclude": "0", "session_ids": ["Session/17913"], "source_sha256": "f4faac896a4575b8b30fd3e1e995d8ea251287d68b980ebfbbaa074fbddbb419", "withdrawn": "", "abstract": "We discuss solutions to longstanding problems of Margulis and of Serre concerning the distribution of indefinite integral ternary quadratic forms and their minima. Time permitting, we also present more recent results concerning quadratic forms in arithmetic statistics and homogeneous dynamics, obtained using the methods and ideas developed in our first work.", "id": "Paper/68814", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68814"}, {"title": " The curse of tolerances in numerical algebraic geometry ", "webprogram_exclude": "0", "session_ids": ["Session/18355"], "source_sha256": "760038cce7ab63bc48d2009f8e4ffbc91d00e1e2e6aabdc38a5ac94e7909f1c4", "withdrawn": "", "abstract": "Numerical tolerances are simultaneously a nectar for my mathematical mind and the bane of my algorithmic existence.  Let's discuss aspects of judging the sameness, smallness, and bigness of computed floating point approximations of exact values in numeric algebraic geometry, with the goal of driving forward the field's ability to declare equality, zero, infinity.  Particularly of interest to me are deflation methods for singularities, path truncation for infinite solutions, and repeated computation of the same point using different methods.", "id": "Paper/68815", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68815"}, {"title": " Exterior Cone Condition for the Removability of the Poisson Kernel-type Singularities for the Second Order Elliptic PDEs ", "webprogram_exclude": "0", "session_ids": ["Session/19363"], "source_sha256": "8575c6ea14a4bdd580c9e76046ef2257727e156e08cb116be142187125c0c2c9", "withdrawn": "", "abstract": "In this talk, we demonstrate the geometric exterior cone condition for the removability of the Poisson kernel-type singularities, and equivalently the unique solvability of the singular Dirichlet problem for the second order elliptic PDEs in arbitrary open subsets of half-space and a ball.", "id": "Paper/68816", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68816"}, {"title": " The universal property of the <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"7.491ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 3225.2 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">(\\infty ,\\infty )</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-221E\" x=\"389\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2C\" x=\"1390\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-221E\" x=\"1835\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"2835\" y=\"0\"></use>\n</g>\n</svg>-category of spans ", "webprogram_exclude": "0", "session_ids": ["Session/18210"], "source_sha256": "b86130fc8f957c17d13298e0deace74fe77f11addba8d2da840c0f66a238d08f", "withdrawn": "", "abstract": "Higher categories of spans play an important role in geometry, representation theory, and topological field theory. In recent years, numerous universal properties governing functors out of higher categories of spans have been proven and used to great effect, but properties allowing the construction of functors into higher categories of spans have remained relatively thin on the ground. In this talk, based on recent joint work with Jonte G\\\"odicke and Quoc P. Ho I will present a new construction of the \\((\\infty,\\infty)\\)-category \\(\\operatorname{Span}_{\\infty}(\\mathcal{C})\\) of spans in an \\((\\infty,1)\\)-category \\(\\mathcal{C}\\) with sufficient limits, and show how it gives rise to a universal property characterizing functors into \\(\\operatorname{Span}_{\\infty}(\\mathcal{C})\\). Time permitting, I will explain how this universal property may be truncated to obtain universal properties for \\((\\infty,n)\\)-categories of spans.", "id": "Paper/68817", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68817"}, {"title": " Numerical Radius Inequalities and Their Generalizations for Special Classes of Matrices ", "webprogram_exclude": "0", "session_ids": ["Session/18230"], "source_sha256": "5be946b1656284aef90a1cd5283ea86030557fc48186bd13bf83931b897803f7", "withdrawn": "", "abstract": "\\documentclass[12pt, reqno]{amsart}\n\n\n\\usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, color}\n\n\n\\newcommand{\\M}{\\mathbb{M}_{n}}\n\n\\newcommand{\\C}{\\mathbb C}\n\n\\begin{document}\n\n\n\\title[Numerical Radius Inequalities and Their Generalizations for Special Classes of Matrices]{Numerical Radius Inequalities and Their Generalizations for Special Classes of Matrices}\n\n\\author[M. Alakhrass]{Mohammad Alakhrass}\t\n\n\\address{ Department of Mathematics, University of Sharjah , Sharjah 27272, UAE.}\n\\email{\\textcolor[rgb]{0.00,0.00,0.84}{malakhrass@sharjah.ac.ae}}\n\n\\subjclass[2010]{47A12, 47A30, 15A45, 15A60.}\n\n\n\n\n\n\\keywords{Sectorial-matrices, accretive-matrices, dissipative-matrices, General numerical radius,  Hadamard product}  \t\n\n\\begin{abstract}\nLet $\\M$ denote the algebra of linear operators acting on a finite-dimensional Hilbert space $H$ of dimension $n$. For $X\\in\\M$, the numerical radius of $X$ is defined by\n\\[\n\\omega(X)=\\sup\\left\\{|\\langle Xx,x\\rangle|:x\\in H,\\ \\|x\\|=1\\right\\}.\n\\]\nIn this talk, we consider several generalizations of the classical numerical radius and investigate inequalities associated with these quantities. Since their exact computation is generally difficult, even for the classical numerical radius, effective upper and lower bounds are of particular interest. We establish numerical radius inequalities for products (XY) and Hadamard products \\(X\\circ Y\\), with particular emphasis on sectorial matrices, that is, matrices whose numerical ranges are contained in sectors of the complex plane. The obtained inequalities provide extensions and refinements of several known numerical radius bounds and illustrate how sectoriality can be used to obtain sharper estimates for matrix products. \n\\end{abstract}\n\n\n\n\\maketitle\n\n\n\n\n\n\n\\begin{thebibliography}{9}\n\\bibitem{Alakhrass-2023} M. Alakhrass, Numerical radius of products of special matrices, Journal of Mathematical Inequalities, 17, 997-1006, (2023).\n\\bibitem{Yu-Popov-2003} Yu.M. Arlinski, A.B. Popov, On sectorial matrices, Linear Algebra Appl. 370, 370:133-146, (2003).\n2003;370:133-146.\n\\end{thebibliography}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\\end{document}", "id": "Paper/68821", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68821"}, {"title": " Algebraic Space-Filling Curves on Smooth Complete Toric Surfaces ", "webprogram_exclude": "0", "session_ids": ["Session/17373"], "source_sha256": "8eba5329ea1f87d6b22e78cbdea77fb5f9e5c763e514928b1934002cdd499b9b", "withdrawn": "", "abstract": "We classify all minimal divisor classes containing an irreducible space-filling curve, as well as all minimal divisor classes containing a geometrically irreducible space-filling curve, on every smooth complete toric surface over $\\mathbb{F}_q$. For smooth complete toric surfaces whose fans have at least five rays, we classify all divisor classes containing an irreducible space-filling curve, as well as all divisor classes containing a geometrically irreducible space-filling curve. Together with Homma and Kim’s results for $\\mathscr{H}_0$, our results show that the lower bound divisor class on a Hirzebruch surface $\\mathscr{H}_r$ contains an irreducible space-filling curve if and only if $(r,q)\\neq(0,2)$. Thus, the lower bound divisor class is the unique minimal divisor class containing an irreducible space-filling curve except when $(r,q)=(0,2)$. We characterize all space-filling curves in the lower bound divisor class on $\\mathscr{H}_r$ and show that every irreducible space-filling curve in the lower bound divisor class is smooth at every $\\mathbb{F}_q$-rational point.", "id": "Paper/68822", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68822"}, {"title": " A Survey of Directed Graph Labelings ", "webprogram_exclude": "0", "session_ids": ["Session/17963"], "source_sha256": "efa336aa5fabbc2a42c21ab082ede552885ba152fe3aa9fa4f55ffe941e07a2d", "withdrawn": "", "abstract": "While graph labeling has traditionally focused on undirected graphs, directed graph labelings have developed into a rich area of study in their own right. The study of directed labelings began in the 1980s with the work of Bloom and Hsu, and the past two decades have seen a substantial expansion of the field. In this talk, we will survey a range of labelings for directed graphs, examining how the presence of orientation changes familiar labeling ideas and gives rise to new ones. We will also consider questions that remain open and directions for future research.", "id": "Paper/68823", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68823"}, {"title": " Local Spectral-Sequence Resolutions of Discrete BGG Diagrams in Arbitrary Dimension ", "webprogram_exclude": "0", "session_ids": ["Session/18281"], "source_sha256": "b984ffbd4afedb1d08b43ddb332cc12e2335b66abcb5b0ed30a35e696d1c98a1", "withdrawn": "", "abstract": "We construct local spectral-sequence resolutions for the adjacent row and column subdiagrams of the discrete Bernstein–Gelfand–Gelfand (BGG) diagram of alternating form-valued differential forms in arbitrary dimension. The construction is based on filtered cone complexes associated with the algebraic linking maps appearing in the BGG diagram. In the case of adjacent rows, the cone construction yields the spaces forming the relevant  BGG complex, and the induced differential yields the higher-order zig-zag operator. A similar construction based on columns follows from the symmetry of double forms. This framework is motivated by the use of BGG complexes in deriving structure-preserving finite element discretizations for PDEs. We further discuss the additional compatibility conditions required for a global resolution of the discrete BGG diagram.", "id": "Paper/68826", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68826"}, {"title": " Machine Learning in Number Theory and Combinatorics: Sequence-to-Sequence Models and Generative Methods ", "webprogram_exclude": "0", "session_ids": ["Session/18130"], "source_sha256": "16a5ebeb783cb6a9792cd44a38b05cea9d4eb1a59eaa902c1965bc059e1f4fff", "withdrawn": "", "abstract": "Machine learning is rapidly emerging as a valuable tool in the pure mathematician’s toolkit. In this talk, we explore the intersection of modern AI, number theory, and combinatorics, highlighting recent developments involving transformer models. We focus on two complementary approaches: using sequence-to-sequence models to translate mathematical problems into solutions, and employing generative AI to discover novel and compelling examples that can inspire further mathematical progress.", "id": "Paper/68830", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68830"}, {"title": " Consensus-based algorithms for min–max problems: uniform-in-time propagation of chaos ", "webprogram_exclude": "0", "session_ids": ["Session/17781"], "source_sha256": "87cef8dc5d43b8aacd24a4dbee05d07d0351a3a1bb0040bec38456736c723b1f", "withdrawn": "", "abstract": "Consensus-based methods are derivative-free particle algorithms for non-convex optimization and min–max problems in machine learning. The focus of this talk is a consensus-based algorithm for saddle-point problems, in which two interacting particle populations play the competing roles. Via a coupling argument exploiting the decay and concentration of particle variances, we establish uniform-in-time propagation of chaos with L2 error of order $O(1/N_1 + 1/N_2)$: finitely many particles remain near a saddle point over arbitrarily long horizons, confirming the method's feasibility. I will also briefly mention a companion uniform-in-time weak propagation-of-chaos result, of order $O(1/N)$, for consensus-based optimization. Joint work with Erhan Bayraktar, Zhiyan Ding, and Hongyi Zhou.", "id": "Paper/68832", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68832"}, {"title": " Temporal central limit theorem for mixed-radix odometer discrepancy ", "webprogram_exclude": "0", "session_ids": ["Session/18100"], "source_sha256": "e334f4ce0de4286baa223710912138367489c8c35f8059fd0da1513240aadd07", "withdrawn": "", "abstract": "We study the local discrepancy of the mixed-radix van der Corput sequence associated with radices \\(b_1,b_2,\\ldots\\). Writing\n$B_m=b_1\\cdots b_m$ and \n$n=\\sum_{i\\geq0}c_i(n)B_i$,\nthe sequence consists of the rational numbers\n$\nx_n=\\sum_{i\\geq0}\\frac{c_i(n)}{B_{i+1}}$. This sequence is uniformly distributed and we wish to study its fluctuations about the uniform distribution.\n\nFor independent uniform random variables \\(Y,Z\\in[0,1)\\), we consider the discrepancy\n$\n\\mathcal D_H\n=\n\\sum_{n=0}^{\\lfloor HZ\\rfloor-1}\n\\bigl(\\mathbf 1_{[0,Y)}(x_n)-Y\\bigr).\n$\nUnder a natural non-concentration condition on the radices and a quantitative regularity condition on the time horizon \\(H\\), we prove a temporal central limit theorem for \\(\\mathcal D_H\\), with explicit centering, variance, and a rate in Kolmogorov distance. The proof uses an exact decomposition of the discrepancy into digit-level contributions and a total-variation coupling between the low digits of a uniformly sampled time and independent Haar-distributed digits. \nThe presentation will focus on the illustration of the main result and underlying mechanism for the CLT to hold. This is joint work with Maria Avdeeva.", "id": "Paper/68833", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68833"}, {"title": " Beyond Finite Multi-Indices: A Strict Extension of Mean Nonexpansiveness ", "webprogram_exclude": "0", "session_ids": ["Session/18363"], "source_sha256": "ef1242ba62af2af62bbc8e5487ad208b4dffb517e73938496603e36cb9bc39b8", "withdrawn": "", "abstract": "Mean nonexpansive mappings are traditionally defined by a finite\nmulti-index and therefore involve only finitely many iterates of a mapping.\nWe develop the corresponding theory for multi-indices with infinite support,\nso that the behavior of all iterates is incorporated into the definition.\n\nFor an infinite multi-index $\\beta=(\\beta_n)_{n\\geq 1}$, we obtain sharp upper\nbounds $b_m$ for the Lipschitz constants of the iterates of a\n$\\beta$-mean Lipschitzian mapping.\nBy transforming this recurrence into a discrete renewal-type equation, we\ndetermine its asymptotic behavior and prove, in the extended sense, that\n$ \\lim\\limits_{m\\to\\infty}b_m=\\sum_{n=1}^{\\infty}n\\beta_n.$\nWe then consider a sparse infinite multi-index such that $b_m\\to\\infty$. Using a\nsharp weighted-shift construction on $\\ell_1$, we obtain a $\\beta$-nonexpansive \nmapping $T$ such that $k(T^m)=b_m$ for every $m$. Since mean nonexpansive mappings \nassociated with finite multi-indices $\\alpha$ have uniformly Lipschitzian iterates, \n$T$ is not $\\alpha$-nonexpansive for any finite multi-index $\\alpha$. Consequently, \ninfinite multi-indices yield a strict extension of the finite theory. This also \ngives a strengthened answer to a question originating in the work of Goebel and \nJap\\'on Pineda.", "id": "Paper/68834", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68834"}, {"title": " Morphometric analysis of the retinal vasculature for glaucoma classification ", "webprogram_exclude": "0", "session_ids": ["Session/18358"], "source_sha256": "40501782e9ebe7866b1354bbc0113407709ba0900a28f8424a4eed8c1a9c97ff", "withdrawn": "", "abstract": "Impaired retinal blood flow and oxygenation have been shown to contribute to the progression of ocular diseases such as glaucoma.  Our theoretical modeling studies have demonstrated that heterogeneity in vascular network geometry can lead to localized defects in tissue oxygenation that would not be apparent from clinical measures of average tissue partial pressure of oxygen.  Vascular imaging modalities indicate that the vascular network geometry of the retina often differs among individuals regardless of their ocular health status.  We hypothesize that differences in vessel geometry can impact retinal tissue health and function.  In this work, we extract and identify morphological features in retinal vascular networks and correlate them to clinical diagnostic measurements.  Retinal vascular networks are extracted from 138 retinal oximetry images (84 controls and 54 OAG cases) and represented as shape graphs, structured sets of nodes connected by vessel segments. Morphological, anatomical, and demographic variables are used as predictors in regression models aimed to distinguish glaucoma from healthy individuals. We apply Minimum Redundancy Maximum Relevance (mRMR), a feature-selection method in machine learning, to identify a subset of features most informative for disease classification while minimizing redundant information.  The best performance was achieved using the combined morphological and anatomical feature set, for which mRMR selected 11 of 56 variables. The study concludes that extracting, quantifying, and analyzing morphological patterns of vascular networks will aid in identifying diagnostic factors that can be targeted with timely interventions in glaucoma patients.", "id": "Paper/68835", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68835"}, {"title": " Algebraic Identifiability in Independent Component Analysis Mixture Models ", "webprogram_exclude": "0", "session_ids": ["Session/18115"], "source_sha256": "12f1b29c6b018ec6be6a6f27ef9dc84d11bea3652fc4ca442e5688c5f2769fe2", "withdrawn": "", "abstract": "In this talk, we discuss independent component analysis (ICA) mixture models. These models consist of convex combinations of ICA densities. An ICA density is associated with a random vector whose coordinates become mutually independent after an invertible linear transformation. For instance, every Gaussian density is an ICA density, and therefore ICA mixture models are nonparametric extensions of the celebrated family of Gaussian mixtures.\n\nWe consider the method-of-moments approach to density estimation over an ICA mixture model: given samples arising from an unknown density in this model, how can we find the best estimate of that density using empirical averages computed from these samples? In particular, we establish when the defining parameters of a density in the ICA mixture model – including its mixing coefficients, linear transformations, and source moments – can be recovered, up to a finite class, from observed moments of order at most $d$. This property is called algebraic identifiability. For $n$-variate distributions and $d \\geq 3$, we prove algebraic identifiability for models with asymptotically up to $\\frac{1}{d!} n^{d-2}$ mixture components, and show that this is an asymptotically sharp bound on the number of mixture components. We finish by presenting a method-of-moments algorithm for density estimation over these models.", "id": "Paper/68836", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68836"}, {"title": " The most general theory of one-sided fractions ", "webprogram_exclude": "0", "session_ids": ["Session/17949"], "source_sha256": "0015455aa1eb28dbd4546a264af214b6fd7e65ad2d68097afdcf2af77f674e2a", "withdrawn": "", "abstract": "The Ore localization Theory of rings is a theory of one-sided fractions but it is not the most general one. The most general theory of one-side fractions will be presented in my talk.", "id": "Paper/68842", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68842"}, {"title": " A Structural View of Restarting Eigenvalue Algorithms ", "webprogram_exclude": "0", "session_ids": ["Session/18230"], "source_sha256": "a22ae76feeef975cfd7e5e603ba21d52475e1d2e324d78596c57a5b3c8177c02", "withdrawn": "", "abstract": "Given a tridiagonal or Hessenberg matrix, it has been well--established that, in exact arithmetic, applying some of its eigenvalues as shifts via the $QR$ strategy produces a particular structured matrix where the leading tridiagonal or Hessenberg block contains the non--shifted eigenvalues and the trailing block contains the shifted eigenvalues. We will show that the leading block can be created, up to sign differences, by an orthogonal similarity reduction of a certain arrowhead matrix constructed directly from the non--shifted eigenvalues and associated eigenvectors. This sets the foundation to show, in a novel way, that implicit restarts and thick restarts in both the Lanczos and Arnoldi algorithms are not just mathematically equivalent but are obtainable from one another by an orthogonal transformation.", "id": "Paper/68843", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68843"}, {"title": " Directed cell complexes ", "webprogram_exclude": "0", "session_ids": ["Session/18209"], "source_sha256": "ab8b98bf3944b991a7d6ca93e4fdf096b79453ba48a6baa15bef533b634ef686", "withdrawn": "", "abstract": "One perspective on the structure of a higher category is that it arises from iterated enrichment. From this, the Theta category, Segal-type models, etc. naturally emerge. Another perspective is that a higher category is a \"directed homotopy type\". Then, it makes sense to ask first: what is a directed cell complex? Even more basically, what is a directed ball? \nI will give an overview of my work on these questions, as well as the models of  higher categories based on it, jointly developed with Cl\\'emence Chanavat. In particular, I will talk about the surprising fact that Theta---or the \"equations of globular n-categories\"---are incomplete for the \"topologically sound\" relations satisfied by the pasting of directed cells; and argue that \"directed homotopy types\" are, properly, only a subclass of $(\\infty, \\infty)$-categories.", "id": "Paper/68847", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68847"}, {"title": " An Inverse Problem in Quantum Simulation ", "webprogram_exclude": "0", "session_ids": ["Session/18246"], "source_sha256": "6282c227e27acd7350447d79ebbd00aa096993ab16b796c11b5b3546057f4dcc", "withdrawn": "", "abstract": "Hamiltonian learning can be regarded as the inverse problem of quantum simulation: we consider a quantum system whose dynamics is governed by an unknown Hamiltonian operator, and design experimental protocols together with algorithms to recover the Hamiltonian. This is a natural task that is important in quantum metrology, sensing, device characterization, and validation of quantum simulation.\n\nIn this talk I will focus on several aspects of Hamiltonian learning that are unusual from a classical inverse problem perspective: the Heisenberg-limited scaling and the robustness against state preparation and measurement (SPAM) errors. I will discuss the central role played by quantum control in addressing these challenges, and recent progress in designing experimental-friendly protocols.", "id": "Paper/68850", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68850"}, {"title": " Advances in MFS for Severely Ill-Posed Elliptic Cauchy Problems ", "webprogram_exclude": "0", "session_ids": ["Session/17702"], "source_sha256": "d90264f51e3ebd469f1416ad104de2d8ac26b382ba08ed17bed301201c5cd013", "withdrawn": "", "abstract": "The method of fundamental solutions (MFS) is a mesh-free boundary collocation method for solving boundary value problems, but its application to elliptic Cauchy problems is challenging due to severe ill-posedness, noisy data, and source-point placement.\nWe present two MFS-based approaches. First, a multiscale hierarchical MFS (MH-MFS) progressively refines the Tikhonov regularization parameter, achieving accurate recovery with reduced computational cost compared with conventional MFS using the L-curve method. Second, for three-dimensional doubly connected domains, we develop a novel MFS framework that transforms the inverse Cauchy problem into a well-posed formulation. A new source-point strategy simplifies source-point placement and improves stability in complex three-dimensional geometries, while truncated singular value decomposition regularization further enhances robustness. Numerical experiments demonstrate the effectiveness of both approaches.", "id": "Paper/68853", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68853"}, {"title": " Non escape of mass for spherical means in horospherical actions ", "webprogram_exclude": "0", "session_ids": ["Session/18313"], "source_sha256": "9e334625f1ef03d4882c03257f3ced6739f34130f6ef794f95ee47efabd83868", "withdrawn": "", "abstract": "Classical ergodic theorems of R. Jones and M. Lacey established almost-everywhere convergence for spherical averages associated with $\\mathbb{R}^n$-actions, extending the well-known example of large spheres on tori. These results were built on the landmark maximal inequalities of E. Stein and J. Bourgain in harmonic analysis.\n\nIn the case of horospherical actions over homogeneous spaces - a long-standing question of Margulis and Lindenstrauss asks for an analogue of the spherical ergodic theorem with everywhere convergence. We present several non-escape-of-mass results for horospherical averages that provide progress toward this objective. The key ingredient is a new extension of the Kleinbock-Margulis non-divergence method based on a phenomenon we term subharmonicity at the cusp.", "id": "Paper/68854", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68854"}, {"title": " co-PEER: proof expert evaluation review lessons in ML for mathematics ", "webprogram_exclude": "0", "session_ids": ["Session/18190"], "source_sha256": "0a0c4d9abeeb7514ca7ace53045f83d13dede89e2b9bc5ed2996526dedde472c", "withdrawn": "", "abstract": "When trying to solve a problem, prove a conjecture, or check a proof, mathematicians use examples to test those conjectures, challenge proof steps, and revise statements. A counterexample can identify a missing premise, suggest a corrected lemma, or belong to an entire family of proof obstructions. A counterexample also raises mathematical questions: which additional assumptions, if any, make the claim true? Furthermore, proposed repairs require proofs of their own and may themselves admit counterexamples. We study how language models can construct, check, and reuse counterexamples during proof development by developing co-PEER, co-proof expert evaluation review (as in, peer review).\n\nCo-PEER audits informal proofs by producing checkable objections. It quotes a claim from an informal proof, constructs and independently checks a witness, and formalizes the refutation when a faithful Lean encoding is available. Each record links the counterexample and its checks to the location in the original proof and lists the assumptions that the checks leave unresolved. This division of labor resembles a prover--verifier protocol: an untrusted producer proposes evidence, and a separate checker evaluates explicit obligations.\n\nOur first three contributions study how ML can support mathematical reasoning, while the fourth develops mathematical results from ML-assisted\ncounterexample search: ML for mathematics, and mathematics from ML.", "id": "Paper/68856", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68856"}, {"title": " On the Bap Between Shellability and Vertex Decomposability ", "webprogram_exclude": "0", "session_ids": ["Session/17373"], "source_sha256": "72cf2881bee5190126e2e86499366e9a0df8d9e8d6be25b884b676f11c84eab0", "withdrawn": "", "abstract": "One of the most well-known combinatorial approaches to showing that a squarefree monomial ideal is Cohen--Macaulay is to study its associated Stanley--Reisner complex and prove that the complex is shellable. In fact, it is enough to show that the complex is constructible. Many well-studied classes of simplicial complexes satisfy an even stronger property: they are vertex decomposable. In this talk, we explore the gap between shellable simplicial complexes and vertex decomposable simplicial complexes.", "id": "Paper/68857", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68857"}, {"title": " Coherence-Aware Sampling for Euclidean Distance Matrix Completion ", "webprogram_exclude": "0", "session_ids": ["Session/18330"], "source_sha256": "9e86099e8c313b406b74915e934587c4fd1e9fea3fdc500bee247572c79bff17", "withdrawn": "", "abstract": "The problem of recovering a configuration of points from partial pairwise distances, referred to as the Euclidean Distance Geometry (EDG) problem, arises in a broad range of applications, including sensor network localization, molecular conformation, and manifold learning. Much of the optimization literature studying the EDG problem assumes a uniform sampling model for the pairwise distances, without any representation of the underlying geometry. In this talk, we propose a geometry-aware, non-uniform sampling scheme related to matrix incoherence that, when combined with a Riemannian optimization framework, provides provable convergence for arbitrarily coherent geometries. Existing methods that solve the EDG problem as a low-rank matrix completion task fail for these geometric configurations of points under a uniform sampling model unless every pairwise distance is sampled. This incoherence-based sampling scheme provides important insight into which edges are most important to sample in order for the underlying reconstruction to be unique, and we explore the connection between this geometric notion of incoherence and the rigidity of the underlying graph. Furthermore, we derive quantitative bounds showing that any point cloud can be algorithmically recovered with high probability if the number of sampled pairwise distances exceeds $\\mathcal{O}(n^{3/2}d^{3/2}\\log^{1/2} n)$, provided that the distances are sampled according to this scheme. For better-conditioned point clouds, this can be improved to $\\mathcal{O}(nd\\log n)$, which was not previously possible for arbitrarily coherent geometries. We also provide a provable initialization guarantee and thorough empirical evaluations on synthetic data, highlighting the state-of-the-art performance of this sampling methodology.", "id": "Paper/68858", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68858"}, {"title": " Towards stratified sampling for redistricting plans ", "webprogram_exclude": "0", "session_ids": ["Session/18310"], "source_sha256": "a711bf4b5493f6d17e2b6764470b52a54ca2727ef66d9ecb7733782e57c2803d", "withdrawn": "", "abstract": "Rapid algorithmic developments have accelerated the sampling of redistricting ensembles (balanced graph partitions), yet evaluating rare events and sampling complex target measures remains a core challenge due to the high-dimensional and combinatorial nature of the phase space.\nWe address a prerequisite for stratified sampling on this space: constructing and diagnosing candidate strata with suitable coverage and overlap.\nWe build a grammar on observed plans by clustering districts into representative ``letters'' and using them to form plan-level ``words.''\nA partition of unity over these words gives a soft assignment of plans to strata and allows us to estimate stratum masses and an overlap-induced flux matrix.\nWe demonstrate this computational pipeline using real-world congressional redistricting data from Connecticut and examine how strata learned from one target distribution behave under related distributions.\nThe resulting construction provides a foundation for future stratified sampling on spaces of redistricting plans or balanced graph partitions.", "id": "Paper/68860", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68860"}, {"title": " Product maps between Ekedahl-Oort strata of unitary Shimura varieties involving a superspecial factor ", "webprogram_exclude": "0", "session_ids": ["Session/19367"], "source_sha256": "1ef86f155dc7e79c59ea7811fac0b9ac1d35e15b03eca800599af7fdd2f02906", "withdrawn": "", "abstract": "The focus of this talk is on unitary Shiumura varieties $\\mathcal{M}(m,n)$. For any $a,b,c,d \\in \\mathbb{Z}_{\\geq 0}$, there is a natural \\emph{product map} $\\mathcal{M}(a,b) \\times \\mathcal{M}(c,d) \\to \\mathcal{M}(a+c,b+d)$, which induces a map on Ekedahl-Oort strata. In this talk we give results for product maps where at least one of the factors is superspecial. We describe maps with this property completely on the level of Weyl group coset representatives. We also characterize, on the level of Weyl group coset representatives, which Ekedahl-Oort strata of $\\mathcal{M}(m,n)$ admit a superspecial factor.", "id": "Paper/68861", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68861"}, {"title": " Plane partitions and spin adapted quantum states ", "webprogram_exclude": "0", "session_ids": ["Session/18253"], "source_sha256": "07348702093738002fb0c4bccec4f70f437834a1490ed081a251422a088eba94", "withdrawn": "", "abstract": "In quantum chemistry, the space of spin adapted quantum states of an electronic system with $m$ spin orbitals and $k$ electron pairs is modeled by the ${\\sf SU}(2)$-invariant space of the exterior power $\\wedge_{2k} \\mathbb{C}^{2m}$. We identify this invariant space with an Artinian commutative ring called the \\emph{excitation ring}, cut out by the $3\\times 3$ \\emph{generalized permanents} of a generic matrix. By computing a Gr\\\"obner basis for the excitation ring and bijecting its standard monomials with certain Dyck paths, we compute an explicit basis for the desired invariant space. This is joint work with Abigail Price and Svala Sverrisd\\'ottir.", "id": "Paper/68863", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68863"}, {"title": " Algebraic Invariants of Edge Ideals Under Suspensions ", "webprogram_exclude": "0", "session_ids": ["Session/18025"], "source_sha256": "bda22d7487be2b0107f8bfaecac22d8a78c8d76d521e0499530cfec800e5022b", "withdrawn": "", "abstract": "In this talk, we explore how algebraic invariants of edge ideals of graphs respond to suspensions of the underlying graph. We begin by recalling the full suspension of a graph, an operation known to preserve the regularity of the edge ideal while increasing its projective dimension by one. Motivated by this phenomenon, we concentrate on studying how the regularity, projective dimension, and $\\mathfrak{a}$-invariant change under \\textit{selective suspensions}. In particular, we focus on how these algebraic invariants changes when suspending over two complementary collection of vertices: minimal vertex covers and maximal independent sets.", "id": "Paper/68865", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68865"}, {"title": " Global Convergence of Adjoint Optimized Neural PDEs ", "webprogram_exclude": "0", "session_ids": ["Session/18280"], "source_sha256": "7a22ad28a40b8ab23be782071ae8bb8502af9adda757c16ba5280725470eee32", "withdrawn": "", "abstract": "Many engineering and scientific fields have recently become interested in modeling terms in partial differential equations (PDEs) with neural networks, which requires solving the inverse problem of learning neural network terms from observed data in order to approximate missing or unresolved physics in the PDE model. The resulting neural-network PDE model, being a function of the neural network parameters, can be calibrated to the available ground truth data by optimizing over the PDE using gradient descent, where the gradient is evaluated in a computationally efficient manner by solving an adjoint PDE. These neural PDE models have emerged as an important research area in scientific machine learning. In this work, we study the convergence of the adjoint gradient descent optimization method for training neural PDE models in the limit where both the number of hidden units and the training time tend to infinity. Specifically, for a general class of nonlinear parabolic PDEs with a neural network embedded in the source term, we prove convergence of the trained neural-network PDE solution to the target data (i.e., a global minimizer).  The theoretical results are illustrated and empirically validated by numerical studies.", "id": "Paper/68866", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68866"}, {"title": " Visual Aspects of Gaussian Periods and Analogues ", "webprogram_exclude": "0", "session_ids": ["Session/18100"], "source_sha256": "18c5f30617ea2650c62a796760bec7c8c642527c60d26fa6d59d75edcdfc2d03", "withdrawn": "", "abstract": "Gaussian periods have been studied for centuries in the realms of number theory, field theory, cryptography, and elsewhere. However, it was only within the last decade or so that they began to be studied from a visual perspective. By plotting Gaussian periods in the complex plane, various interesting and insightful patterns emerge, leading to various conjectures and theorems about their properties. In this talk, we offer a description of Gaussian periods, along with examples of the structure that can occur when plotting them in the complex plane. \n\nIn addition to this, we offer two ways in which this study can be generalized to other situations---one relating to supercharacter theory, the other relating to class field theory---along with discussions and visual examples of each.", "id": "Paper/68869", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68869"}, {"title": " The recency, contingency, and precarity of the world mathematical system ", "webprogram_exclude": "0", "session_ids": ["Session/18374"], "source_sha256": "ec9cfef203f3c3f9fbdf642df7d0795e1ecbec302862ff398a3ad1225cdf8769", "withdrawn": "", "abstract": "The world system of modern and contemporary mathematics, where ideas and careers routinely travel very long distances (if not actually all over the world), should be understood to be recent, contingent, and precarious. These characterizations matter differently to historians of mathematics and to mathematicians considering their history, and I will indicate the significance of that difference specific to understanding what matters about modern and contemporary mathematics. Historians and mathematicians have much in common in how they need to think about geography, infrastructures, institutions, and theories, and these commonalities can be a major resource and hazard for historical research and explanation. My presentation will focus on historical and methodological insights from my Situating International and Global Mathematics (SIGMA) collaborative research project (UKRI EP/X033961/1), which will be about to enter its fifth and final year.", "id": "Paper/68870", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68870"}, {"title": " A General Method for Enumerating Self-Avoiding Walks on Periodic Lattices ", "webprogram_exclude": "0", "session_ids": ["Session/19346"], "source_sha256": "2511636232163ec712e73465de6b93dda234a6a54601f387a6883f1f6d40b84c", "withdrawn": "", "abstract": "A growing self-avoiding walk (GSAW) is a walk on a graph that begins at a fixed vertex and grows one edge at a time. When there is no open vertex to extend the end of the walk to, we say the walk is trapped. GSAWs are used to mathematically model the growth and statistical properties of polymer chains. In 1984, Hemmer and Hemmer used Monte Carlo simulation to estimate the expected trapping length of a GSAW on the infinite rectangular lattice as approximately 71. Subsequent work has sought to obtain trapping length and displacement using exact enumeration rather than simulation. \n\nRecently, Pantone et al. studied walks on rectangular grids that have finite height and are infinite in one direction. They decomposed GSAWs into sequences of small, overlapping frames to construct combinatorial finite state machines that describe all possible walks. They used transfer matrix methods and generating functions to enumerate GSAWs according to their length and width.  \n\nIn this talk, we share a significant generalization of this approach, in which we replace the frame-by-frame construction with an edge-by-edge construction. We build combinatorial finite state machines that enumerate GSAWs on rectangular, triangular, and hexagonal grids, for example, using one common procedure. Our framework can handle enumeration of walks on any grid with a structure that is periodic, including ladder-shaped grids, 3D grids, grids with directed edges, and grids that expand in both the positive and negative directions simultaneously while other dimensions are bounded.", "id": "Paper/68872", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68872"}, {"title": " An Improved Quantum Algorithm for Convex-Body Volume Estimation ", "webprogram_exclude": "0", "session_ids": ["Session/18113"], "source_sha256": "bed95b819355151eb8fd0e706a568118264d65d0918a71e4ccfb2822536a000e", "withdrawn": "", "abstract": "In this talk, I will introduce a new quantum algorithm that estimates the volume of a convex body in $\\mathbb{R}^d$ to relative error $\\varepsilon$ using $\\widetilde{O} (d^{5/2}+d^{3/2}/\\varepsilon}$ membership queries. This improves the previous $\\widetilde{O}(d^3+d^{9/4}/\\varepsilon)$ query complexity upper bound obtained by combining the volume estimation algorithm of [Chakrabarti et al. (ACM TQC 2023)] with the product estimator of [Cornelissen–Hamoudi (SODA 2023)]. Our algorithm relies on two new techniques. First, we develop a new spectral analysis of the quantum walk, showing that even when the spectral gap of the Markov kernel is small, the quantum walk can still achieve a quadratic speedup over the classical warm-start mixing time, provided the input state satisfies a fourth-moment condition. Second, we develop a more efficient coherent normalization-constant estimator based on bridge sampling.", "id": "Paper/68873", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68873"}, {"title": " Interpretable Multimodal Pathway-Constrained Deep Learning with Sparse Hierarchical Representations for PAM50 Breast Cancer Subtyping ", "webprogram_exclude": "0", "session_ids": ["Session/17970"], "source_sha256": "16113c57aede2fae95a02534d6f75484d8c928ff4cf898bc37a9dd34f5e39691", "withdrawn": "i", "abstract": "Integrating complementary molecular measurements while preserving biological structure is a central challenge in breast cancer subtype classification. We developed a multimodal, pathway-constrained deep neural network integrating RNA expression and copy-number variation (CNV) for five-class PAM50 classification. RNA and CNV features were separately mapped onto 224 curated pathways and integrated through a 100-node hidden layer trained using adaptive subnetwork pruning. This architecture provides a traceable hierarchy from molecular features to modality-specific pathways and learned pathway combinations. A Transformer extension encoded hidden activations as tokens with learned node-identity embeddings, followed by two self-attention encoder layers, mean pooling, and a multilayer classifier. Model development used 974 TCGA-BRCA tumors with 10 repetitions of stratified five-fold cross-validation, followed by independent evaluation on 122 CPTAC-BRCA tumors. The pathway-constrained network achieved macro-AUROC values of 0.950 internally and 0.891 externally, with external balanced accuracy of 0.487 and macro-F1 of 0.322. Adding self-attention increased internal accuracy from 0.736 to 0.789, macro-F1 from 0.693 to 0.722, and Matthews correlation coefficient from 0.656 to 0.698. External effects varied across subtypes. Weight-based hidden-node composition analysis and signed class-conditional contribution scores for the base network characterized subtype-associated pathway patterns. The framework combines biologically structured multimodal integration with interpretable representation learning and enables systematic assessment of the predictive trade-offs introduced by downstream self-attention.", "id": "Paper/68874", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68874"}, {"title": " The Curriculum Microscope: Seeing How Modeling-First Calculus Travels across Institutions ", "webprogram_exclude": "0", "session_ids": ["Session/18199"], "source_sha256": "c99b1806b946aa6ef0f3179e81070b62c8266750a73391db2a83548101193d5a", "withdrawn": "", "abstract": "TPSE Math’s call to modernize undergraduate mathematics includes a modeling-first approach to calculus for the life sciences. UCLA has been a trailblazer in this arena, publishing Modeling Life (Garfinkel, Shevtsov, and Guo). The text centers authentic mathematical modeling of biological systems in the first semester, without requiring calculus as a prerequisite. Institutions across the country have developed courses using this textbook.\n\nAs part of the NSF-funded TAILOR project, we are studying what makes these adoptions successful and how institutions adapt the curriculum to their own students, prerequisites, and departmental culture.\n\nOne slice of the study confronts a fundamental challenge: curricula are easy to describe but difficult to view in full detail. Syllabi provide only a high-level overview and reveal little about what students actually encounter. Classroom observation offers important insight but is difficult to scale across institutions. Manually coding large archives of course materials is prohibitively time-consuming.\n\nTo address this challenge, we developed a curriculum microscope, an AI tool that analyzes the documents that students encounter in a course, including syllabi, exams,  labs, in-class activities, and homework. The tool identifies what students are explicitly asked to do across these materials and generates a list of observed learning objectives.\n\nWe will show how the curriculum microscope enabled the modeling-first community to articulate the learning objectives at the heart of the approach, examine how frequently objectives appear across institutions, and distinguish core curricular features from local adaptations.\n\nThis work lays the foundation for developing a test bank to investigate the kinds of student thinking that modeling-first courses foster.", "id": "Paper/68875", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68875"}, {"title": " Lévy Processes as weak limits of Rough Heston models ", "webprogram_exclude": "0", "session_ids": ["Session/18058"], "source_sha256": "85bb8fdc165a55bd87443593405cbe73deec1d8626580049f609fb2a4ea03861", "withdrawn": "", "abstract": "We investigate distributional scaling limits for the rough Hawkes–Heston stochastic volatility model, an affine extension of the rough Heston model that incorporates jumps. More precisely, the variance process features a self-exciting jump component, which also induces negative jumps in log-prices through a leverage parameter. Under a suitable rescaling, we prove that the integrated variance converges to a Lévy subordinator in the space of càdlàg functions endowed with the \\(M_1\\) topology, with inverse Gaussian processes arising as a special case. The time-\\(t\\) marginals of log-prices converge instead to those of a time-changed Lévy process belonging to a class that extends normal inverse Gaussian processes. We illustrate this marginal convergence through the corresponding implied volatility smiles.", "id": "Paper/68876", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68876"}, {"title": " Computing graded rings of Hilbert modular forms ", "webprogram_exclude": "0", "session_ids": ["Session/17450"], "source_sha256": "b1da97ddadb8d96272306e7d78f6918ae9988796439b7e5e201552b0c9351504", "withdrawn": "", "abstract": "We describe a practical algorithm for computing generators and relations for graded rings of Hilbert modular forms, by certifying that a presentation obtained from truncated \\(q\\)-expansions is complete.\nn particular, we recover several previously known graded-ring presentations for Hilbert modular surfaces.", "id": "Paper/68877", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68877"}, {"title": " Quantitative partial imaging in planar vector tomography ", "webprogram_exclude": "0", "session_ids": ["Session/18298"], "source_sha256": "bd028903f0b9c8d32ccb48bac0b3621c5ef1ad8cfbb0c93e5d3b1ce4e14c0be6", "withdrawn": "", "abstract": "In this work, we consider the problem of reconstructing a planar vector field from partial knowledge of its zeroth and first moment ray transforms. Different from existing works the data is known on a subset of lines, namely the ones intersecting a given arc. The problem is non-local and, for partial data, severely ill-posed. We present a reconstruction method which recovers the vector field in the convex hull of the arc, and it is joint work with A. Tamasan (UCF) and H. Fujiwara (Kyoto U).", "id": "Paper/68879", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68879"}, {"title": " Subspace Code Construction over the Complex Numbers Using Extended Multiplicative Characters ", "webprogram_exclude": "0", "session_ids": ["Session/18389"], "source_sha256": "ab3625b110dfa8c0a6ed502afbbfc378707e350609ea6aca5f3ddd1f00762f68", "withdrawn": "", "abstract": "We study the construction of complex-valued subspace codes from finite-field subspace codes for the analog operator channel over the complex numbers introduced by Soleymani and Mahdavifar. We show that the classical subspace metric provides at least the same error-and-erasure guarantees as the quasimetric introduced by Soleymani and Mahdavifar. We propose a new construction based on extended multiplicative characters, which preserves code size and minimum distance. Applied to Koetter–Kschischang codes, this construction produces complex codes with the same minimum distance.", "id": "Paper/68880", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68880"}, {"title": " Diagnosing and Correcting Spatial Dependence in Neighborhood-Level Regression: LM Tests, Spatial Lag, and Spatial Error Models ", "webprogram_exclude": "0", "session_ids": ["Session/19338"], "source_sha256": "e9b05465838a2900ab1a7a8ec939c2c8fba56404599dd6888260f0068bdf603c", "withdrawn": "", "abstract": "Ordinary least squares regression assumes independent errors — an assumption routinely violated in neighborhood-level data, where outcomes in nearby areas tend to be more similar than chance would predict. This talk examines spatial dependence as both a diagnostic problem and a modeling opportunity, using the distribution of public electric vehicle charging infrastructure across Dallas County, Texas as a motivating application.\n\nWe begin with Moran's I as a formal test for spatial autocorrelation in OLS residuals under a queen contiguity weight matrix. When dependence is detected, two structural corrections arise with distinct interpretations: the Spatial Lag Model (SLM), which incorporates a spatially weighted average of the outcome as a regressor, and the Spatial Error Model (SEM), which absorbs spatial structure into a correlated error process. We present the Lagrange Multiplier test framework — including robust variants that remain valid when both forms of misspecification are present — as a principled approach to choosing between these models. Both are estimated by maximum likelihood. We discuss the geometric intuition behind each model, their differing implications for coefficient interpretation, and practical guidance for applied researchers navigating this choice. Results from the EV application illustrate how ignoring spatial dependence distorts inference and how model selection meaningfully changes the conclusions drawn", "id": "Paper/68890", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68890"}, {"title": " Finding Rainbow Lengths for Simple Knotted Surfaces ", "webprogram_exclude": "0", "session_ids": ["Session/18370"], "source_sha256": "1e4dbe83218659ddbd34950ee17e26dcf4063bd35e0ab3467a1d584ee93975f3", "withdrawn": "", "abstract": "Mathematical knots can be thought of as strings tangled in 3-dimensional space with connected endpoints. Our research involves an extension of these knots into 4-dimensional space where we knot surfaces instead of strings. To visualize these surfaces, we use tri-plane diagrams with tangles spread across three planes, connected along a central axis. Previous work allows us to construct braided tri-plane diagrams for orientable surfaces called rainbow diagrams. We make use of these rainbow diagrams to find bounds on the invariants for some simple knotted surfaces, namely the rainbow length (number of crossings) and braid index (number of strands). In this talk, we discuss the rainbow length for the connected sum of $n$ tori, as well as determine a general upper bound for the rainbow length of connected sums of arbitrary knotted surfaces.", "id": "Paper/68891", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68891"}, {"title": " Uniform boundedness of rational points for abelian varieties over function fields ", "webprogram_exclude": "0", "session_ids": ["Session/17755"], "source_sha256": "f383a0589ebdfea5e931ad8024e7ca772e731bbb892874ca64cdb0f1db100483", "withdrawn": "", "abstract": "The famous Torsion Conjecture in arithmetic geometry predicts the existence of a uniform bound $B$ on the number of $K$-rational points of an abelian variety $A$ over a number field $K$, where $B$ depends only on $[K:\\mathbb{Q}]$ and $\\mathrm{dim}(A)$. In this talk, I will briefly discuss a proof of the characteristic 0 function field analogue of this conjecture. This is joint work with Jit Wu Yap.", "id": "Paper/68892", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68892"}, {"title": " The <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.339ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 576.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">h</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-68\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-polynomial of Edge Ideals via Independence Polynomials of Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "6246a34e721402638fa1d0145870193338b4921dd70506076708d0c1ed967dec", "withdrawn": "", "abstract": "The Hilbert series $HS_I(t)$ of an ideal $I$ in the polynomial ring $S = k[x_1, \\dots , x_n]$ over a field $k$ encodes algebraic information about the graded components of $I$. This series in its most reduced form can be expressed as a rational function in which the numerator is called the $h$-polynomial. In this poster, I will discuss the degree of the $h$-polynomial, denoted as $\\deg h_{S/I(G)}(t)$, of edge ideals of finite simple graphs $G$ and how to express this algebraic invariant entirely using only\ngraph-theoretic data. In particular, I will present results that directly relate $\\deg h_{S/I(G)}(t)$ to the independence polynomial of its underlying graph and how this relation can be used as a powerful tool to study algebraic properties of $I(G)$ and combinatorial properties of graph $G$.", "id": "Paper/68896", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68896"}, {"title": " Coherent Structures and Defects in Stripe Patterns: From Modulation Theory to Geometry and Machine Learning ", "webprogram_exclude": "0", "session_ids": ["Session/18244"], "source_sha256": "5965dcb72423fc42fcfb54193d78af984dc09e7376cada8c27bc6b42413b33d2", "withdrawn": "", "abstract": "Periodic stripe patterns and liquid crystals host a rich variety of coherent structures and topological singularities, from dislocations and disclinations to grain boundaries. In this talk, we discuss recent progress in modeling and characterizing line and point defects in smectic and nematic systems. We explore macroscopic 2D modulation theories and their variational formulations in the space of Special Functions of Bounded Variation (SBV), which naturally accommodate discontinuous gradients and energetic defect penalizations. In parallel, we discuss data-driven coordinate discovery and phase reconstruction frameworks designed to identify macroscopic phases and effective dynamics directly from microscopic pattern data.", "id": "Paper/68897", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68897"}, {"title": " Dynamics of Torque-Driven Particles Confined Between Two Parallel Walls: Application to Quincke Rotors ", "webprogram_exclude": "0", "session_ids": ["Session/19343"], "source_sha256": "76913cfd21eb28aa7789305ca6e7a0fc3878b50fff8418708aa01463b2bb4a7b", "withdrawn": "", "abstract": "Suspensions of torque-driven particles exhibit a wide range of collective behaviors arising from hydrodynamic interactions and additional interparticle forces. Developing predictive models for these systems requires accurately capturing both the fluid-mediated interactions and the effects of external fields in confined geometries. We model the hydrodynamic interactions of multiple torque-driven spherical particles near a single wall using prescribed constant torques. We investigate several approaches for incorporating the effects of a second confining wall and for coupling the hydrodynamics with electrostatic or magnetic interactions. As a specific application, we study Quincke rotors, in which dielectric particles spontaneously rotate under a uniform DC electric field. Experiments have shown that systems of two, three, and four spherical particles confined between parallel electrodes self-organize in the mid-plane perpendicular to the applied electric field, forming counter-rotating states with no net translation. This work provides a framework for investigating the collective dynamics of torque-driven particles, such as Quincke rotors, under two-wall confinement.\nThis research was supported by NSF-DMS award 2406625.", "id": "Paper/68901", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68901"}, {"title": " Approximate Ball Conditions and Boundary Regularity of Convex Bodies ", "webprogram_exclude": "0", "session_ids": ["Session/19346"], "source_sha256": "68ae1e1a415c510ccabe4e6bde0f7dca45d0c5ca8d9f2faed46014a58441273b", "withdrawn": "", "abstract": "Classical rolling ball conditions provide a geometric characterization of $C^{1,1}$ regularity for convex bodies: uniform control of interior tangent balls corresponds to a uniform bound on curvature. We introduce a scale dependent approximate inner ball condition that extends this principle to a lower H\\\"{o}lder regularity.\n\nFor $0<\\alpha\\leq 1$, we give a geometric characterization of convex bodies with $C^{1,\\alpha}$ boundary in terms of approximate inner closed balls whose radii decrease at a sufficiently slow rate as the approximation scale tends to zero. In the endpoint case $\\alpha=1$, the condition recovers the classical uniform inner rolling ball condition. More generally, the same framework extends to $C^{1,\\omega}$ boundaries for suitable moduli of continuity $\\omega$.\n\nThe proof relates the geometry of the approximate inner closed balls to quantitative control of the variation of supporting hyperplanes and outward normals. Thus H\\\"{o}lder continuity of the Gauss map is encoded directly by the rate at which approximate rolling balls can be placed inside the body. This gives a geometric interpretation of boundary regularity between arbitrary $C^1$ convex bodies and the classical $C^{1,1}$ setting.\n\nWe will discuss the characterization, its relation to curvature and rolling-ball geometry, and several consequences, including scale-dependent notions of reach and regularity questions for convex sets.", "id": "Paper/68902", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68902"}, {"title": " Working the Hadwiger-Nelson Problem with Young Children ", "webprogram_exclude": "0", "session_ids": ["Session/18211"], "source_sha256": "a47342ec96aaa5c755249cde761f3dc981a28dcadd890724699beb33920fc764", "withdrawn": "", "abstract": "The Hadwiger-Nelson Problem is an open geometric graph-theory problem about the chromatic number of the plane. In this talk, I will share an interpretation of the problem that a group of 7-year-olds explored for six weeks: the math questions the students explored, student questions and reactions, and the evolution of their understanding of the problem.", "id": "Paper/68904", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68904"}, {"title": " Max Bill and Equal-Area Triangles ", "webprogram_exclude": "0", "session_ids": ["Session/17986"], "source_sha256": "8bb09e018601bfa4b90bc0ff047542d8778cfc752f55c8944b01aa31c19a10d1", "withdrawn": "", "abstract": "We'll look at some mathematical problems suggested by a painting by the Swiss artist Max Bill, in which he cut a triangle into four smaller triangles, each a different shape but all of equal area.", "id": "Paper/68905", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68905"}, {"title": " Mathematical Values and Computing ", "webprogram_exclude": "0", "session_ids": ["Session/18208"], "source_sha256": "def933dda1dec88e0ff4a017e90806b67ba40a37ffa58cd88e3d74673dcf3696", "withdrawn": "", "abstract": "Advances in computing often force practitioners of a field to reckon with the field’s values.  This happened over a decade ago, as the popularity of interactive theorem provers and crowdsourced mathematics grew: in 2013, Ursula Martin and Alison Pease explained that “the growth in the use of computers in mathematics... has provoked debate, reflecting the contrast between the ‘logical’ and ‘human’ aspects of creating mathematics” (1).  A decade later, mathematicians reach for methodological and intellectual values to explain their objections to how AI companies have engaged in and communicated the results of LLM-assisted proof. In response to an AI company’s publication of a disproof of the Erdős unit distance conjecture without revealing how the proof was discovered (e.g. Were humans involved?  How many?  With what expertise? With how much money at their disposal?), Michael Harris implied that these practices go against the “certain values that have characterized the profession [of mathematics]” among which is “openness” and \"transparency about methodologies\" (2).  Many mathematicians have subsequently protested that mathematics is “about more than just proving theorems.”  But how often do our mathematical practices (with and without computing tools) align with transparency about methodology, and how often do mathematical practices reward promoting deep understanding over proving theorems?  This talk will explore more of what the declared values of mathematicians are, how well our mathematical practices align with these values, and ways that our uses of computing can align or misalign with these values.\n\nReferences\n(1) Martin, Ursula, and Alison Pease. \"Mathematical practice, crowdsourcing, and social machines.\" In International Conference on Intelligent Computer Mathematics. 2013.\n(2) Roberts, Siobhan. “As A.I. Makes Strides in Mathematics, Mathematicians Urge Caution.” The New York Times, 2 June 2026.", "id": "Paper/68906", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68906"}, {"title": " Recruiting and Running a COMAP Session for Computer Science Students ", "webprogram_exclude": "0", "session_ids": ["Session/18066"], "source_sha256": "3ef403cdb194be26e627cdee7f184ce6bebc73a2bb315b30f4436cc5926f2f0b", "withdrawn": "", "abstract": "In a small department that focuses primarily on pure mathematics, it can be challenging to recruit students to participate in COMAP.  In fact, we have found more success recruiting from our population of computer science students who have taken data science courses than recruiting from our own mathematics majors.  In this talk, we discuss successes and failures of recruitment strategies, methods of preparing non-math majors for a modeling contest, and how our department contributes to make the COMAP experience enjoyable for students and faculty.", "id": "Paper/68907", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68907"}, {"title": " Robust Solvers for FEMs for the Phase Field Crystal and Modified Phase Field Crystal Equation ", "webprogram_exclude": "0", "session_ids": ["Session/17926"], "source_sha256": "ccbc99b915ec4bbdc6b7c166833e41b3154482233cda411f327a230f3a95f713", "withdrawn": "", "abstract": "We develop robust and efficient solvers for the linear systems arising from the convex-splitting finite element discretization of two classes of phase field models: one parabolic in nature (the phase field crystal equation) and the other hyperbolic (the modified phase field crystal equation), both of which are nonlinear and involve sixth-order spatial derivatives. We discretize these equations using finite elements in space and convex splitting in time. The solver is based on a preconditioned minimal residual algorithm with a multigrid preconditioner. This work builds upon a previous work focused on the Cahn-Hilliard equation. The performances of the solvers are independent of the spacial mesh size and the equation parameter and mildly dependent on the time step size.", "id": "Paper/68909", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68909"}, {"title": " RaCSS:A Rank-CVE Signature Scheme ", "webprogram_exclude": "0", "session_ids": ["Session/18073"], "source_sha256": "3eaedcb529efd22904c81e6ee019101704ea575b3cf230aba6ee800c3bb9a841", "withdrawn": "", "abstract": "The rank metric represents a promising foundation for post-quantum cryptography, presenting smaller public keys than the Hamming metric at comparable signature sizes. We present a signature scheme, RaCSS, built on the rank metric that supersedes the rank-metric protocol from Bellini et al, which we also show is insecure. We provide proofs of the necessary properties of a Zero-Knowledge-Proof, and we compare it with the leading code- and lattice-based candidates in Round 2 of the NIST Call For Additional Digital Signatures process. At a public key of roughly 40 bytes and a signature of under 10 kB for 128 bits of security, RaCSS proves to be on par with these schemes. From RaCSS, we derive the first known linkable ring signature in the rank metric, a construction which has numerous applications to cryptocurrency and cybersecurity.", "id": "Paper/68910", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68910"}, {"title": " Veech groups of covers of the Chamanara surface ", "webprogram_exclude": "0", "session_ids": ["Session/18269"], "source_sha256": "e73fcc26f5536bf69630fd879254aeb8398f7b634d05a6cd4ac373df7a1786b0", "withdrawn": "", "abstract": "What Veech groups are possible for flat surfaces of finite area? Not much is known about this question, in contrast to the analogous question for flat surfaces of infinite area. The Chamanara surface is notable as an example of a finite-area translation surface. It has infinite topological type, interesting dynamics and a large Veech group. We characterize when finite abelian covers of the Chamanara surface have large Veech groups themselves, namely when their Veech group has finite index in that of the Chamanara surface. As an application, we prove that every free group arises as the projective Veech group of a finite-area infinite translation surface.", "id": "Paper/68912", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68912"}, {"title": " What survives of the Etzion–Silberstein conjecture? ", "webprogram_exclude": "0", "session_ids": ["Session/18387"], "source_sha256": "ffbc3eec71869c62f5e35dd1990a203f45c710116bd8c472f5caf0503d624714", "withdrawn": "", "abstract": "The Etzion–Silberstein conjecture has been a central existence problem for optimal Ferrers diagram rank-metric codes for more than fifteen years. Recent work on reducibility and irreducible Ferrers  diagrams has significantly clarified the structure of the problem, reducing a large collection of cases to a much smaller and more structured family.\n\nVery recently, a counterexample found by Prajapati (arXiv:2608.08478) showed that the linear version of the conjecture in its original form is false. Rather than closing the problem, however, this development opens a new phase: how much of the conjecture survives? Where and why can counterexamples occur? And what is the actual boundary between existence and non-existence?\n\nIn this talk, I will survey the current state of the problem and describe recent progress obtained jointly with Hugo Beeloo-Sauerbier Couvée, in which AI-assisted experimentation and mathematical exploration played a role in developing and testing some of the ideas behind the results. I will then discuss subsequent developments and what the recent counterexample tells us about the remaining picture, with the goal of moving from a universal existence conjecture towards a structural classification of Ferrers diagrams admitting optimal rank-metric codes.", "id": "Paper/68913", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68913"}, {"title": " ZZFormer: A Sliding Window Zigzag Persistent Homology Transformer for Repetitive Biological Sequences ", "webprogram_exclude": "0", "session_ids": ["Session/18105"], "source_sha256": "a18ef74cf761a926c449ab97667ea735dbbb8068570de7755b4e299f2cd45b8a", "withdrawn": "", "abstract": "Repeated patterns occur all over in biological sequences. The same motifs recur within and across DNA, RNA, and proteins as tandem repeats, microsatellites, transposable elements, and reused regulatory and structural elements. Accurately modeling such repetition is central to sequence analysis, but remains challenging for modern learning methods. While transformer architectures can capture long-range dependencies, they do not explicitly account for recurrence or cyclic structure, which are key features in many sequences. Here we introduce a topological framework for learning on sequences with repetition using zigzag persistent homology. We view sequence traversal as a walk on a k-mer graph, where a sliding window moves through the sequence, drawing edges between the consecutive k-mers. This construction detects and tracks repeated patterns through the appearance and persistence of loops. Building on this idea, we develop ZZFormer, a transformer architecture that incorporates zigzag topological structure directly into token embeddings, enabling end-to-end learning on variable-length sequences via cross-attention. This mechanism allows ZZFormer to reason directly about recurrence and repetition, rather than inferring such structure implicitly. This framework applies broadly to problems involving repeated or cyclic patterns. We demonstrate its effectiveness on tasks involving repetitive DNA, including classification of transposable element superfamilies and orders.", "id": "Paper/68914", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68914"}, {"title": " Weakened Gallai-Ramsey Numbers for Books ", "webprogram_exclude": "0", "session_ids": ["Session/19321"], "source_sha256": "02d602eeb86eef06f21d4ff3df140974297c01f28262350ca1b04ffea500ee5a", "withdrawn": "", "abstract": "For $1\\le s<t$ and any graph $G$, the weakened Gallai-Ramsey number $gr^t_s(G)$ is defined to be the least  $p\\in \\mathbb{N}$ such that every Gallai $t$-coloring of the edges of $K_p$ (i.e., a $t$-coloring that lacks rainbow triangles) contains a subgraph isomorphic to $G$ whose edges use at most $s$ of the colors.  In the case of a book graph $B_n:=K_2+nK_1$, Jakhar and Moun determined the values $gr^3_2(B_3)=6$ and $gr^3_2(B_4)=7$.  In this paper, we extend their results to $t>3$ colors, and we determine the values of $gr^3_2(B_n)$ for $5\\le n\\le 13$.  General lower bounds for $gr^t_2(B_n)$ are also given.", "id": "Paper/68915", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68915"}, {"title": " Quadratic Forms under Skew-Normal and Skew-Elliptical Models: A Unified Survey ", "webprogram_exclude": "0", "session_ids": ["Session/19364"], "source_sha256": "85fb332e7e98a58773b263bef93e73f7967a683d1b1e1570e42ccbfe21426405", "withdrawn": "", "abstract": "This article surveys the distribution theory of quadratic forms under\nskew-normal and skew-elliptical models. The review\nis organized around three distributions that play under skewness the roles\nplayed by the chi-square, Wishart, and $F$ distributions under normality: the\nnoncentral skew chi-square, the noncentral skew Wishart, and the noncentral\nskew $F$. Within this framework, the paper reviews exact finite-sample results\nfor quadratic-form densities, moment generating functions, characterization\ntheorems, independence conditions, Cochran-type decompositions, and\nmatrix-variate extensions, and it places these results in relation to the\nclosed and unified skew-normal families, singular and extended variants, and\nskew-elliptical and skew-$t$ generalizations. A central theme is that much of\nthe Gaussian algebra survives intact, while skewness enters through a\ntractable normal-CDF correction; in the central skew-elliptical case, an\ninvariance principle implies that even functions, including quadratic forms,\nare distribution-free with respect to the skewing mechanism. Applications to\nmixed models, variance components, generalized Hotelling $T^{2}$, genetic\nassociation and gene-set testing in genomics, stochastic\nfrontier analysis, spatial statistics, and Bayesian conjugacy are reviewed,\nand open problems in unified-family theory, heavy-tailed noncentral forms,\nhigh-dimensional asymptotics, and computation are highlighted.", "id": "Paper/68916", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68916"}, {"title": " Automorphic Form Twisted Shintani Zeta Function over Number Fields ", "webprogram_exclude": "0", "session_ids": ["Session/18010"], "source_sha256": "97883170107ed7365254b389f8da1a78a9364d3481e03b3c3e05b22972fea100", "withdrawn": "", "abstract": "In this talk, we will see the latest development on the analytic continuation of automorphic form twisted Shintani zeta function over number fields, using adeles. We will see historical background, and then move on to recent analytic developments.", "id": "Paper/68917", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68917"}, {"title": " A Streamfunction Focused Continuous Data Assimilation of a Finite Element Method of a Regularized Barotropic Vorticity Model of Geophysical Flow ", "webprogram_exclude": "0", "session_ids": ["Session/18258"], "source_sha256": "2eb92c79411848112189249098673a508ca864ee784308edd71e3d1a0e4f741b", "withdrawn": "", "abstract": "We consider continuous data assimilation applied to a finite element spatial discretization and backward difference temporal discretization of the barotropic vorticity model of geophysical flow in which only streamfunction data is incorporated. We emphasize that our algorithm only requires nudging of the streamfunction while achieving optimal long-time accuracy for the vorticity and streamfunction given any initial condition provided sufficient measurement data and properly chosen nudging parameter are given, resolving an open question from our previous paper. An interesting advantage of our scheme is that the restrictions on many of the parameters related to the numerical method are less severe. We conclude our paper with numerical tests supporting the analysis.", "id": "Paper/68918", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68918"}, {"title": " Nonlocal Curvature with Radial Monotonically Increasing Kernels ", "webprogram_exclude": "0", "session_ids": ["Session/18377"], "source_sha256": "e9a9eefc2a1bfd2c9d76a75ba9f955e33dc95a88c78a3938b49a7493d04fea01", "withdrawn": "", "abstract": "This talk will discuss recent developments in nonlocal curvature, a kernel-based extension of classical mean curvature.  Nonlocal mean curvature measures the imbalance of kernel-weighted interactions on the two sides of an interface. Under suitable regularity and nondegeneracy assumptions, recent theorems show that a bounded connected set with constant nonlocal mean curvature must be a ball when the interaction kernel is radial, nonnegative, and radially nonincreasing. We discuss the geometric role played by radial monotonicity and then explore how relaxing standard monotonicity assumptions on the kernel can lead to qualitatively different constant-curvature configurations.", "id": "Paper/68922", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68922"}, {"title": " On Cost-Induced Santaló Inequalities ", "webprogram_exclude": "0", "session_ids": ["Session/17749"], "source_sha256": "cc5108b2d46a7b44231bdca27ef3b39b6ae20888e7d3e7da5332175417c29929", "withdrawn": "", "abstract": "In this talk, we will discuss a transference mechanism that allows the lifting of affine isoperimetric Blashke-Santaló inequalities to functional Santaló inequalities in the setting of Polish measure spaces.  As a byproduct of this principle. we investigate new isoperimetric inequalities of these types in RCD$(k,\\infty)$ spaces, Gauss Space, spherical space, and on the hamming cube. If time permits, we will explore applications of this principle to optimal transport theory.", "id": "Paper/68923", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68923"}, {"title": " Practical Identifiability for Biological Systems Using Weak-form Parameter Inference ", "webprogram_exclude": "0", "session_ids": ["Session/18127"], "source_sha256": "f9b7ea4f39745273d847f5a34874a81cdbcb3a514f91d712b77dde95778b5a44", "withdrawn": "", "abstract": "Compartmental modeling of epidemiological systems provides insights into biological and behavioral interactions that cannot be observed directly. Accurate and robust parameter estimation is critical to applying such models as decision-making tools for public health interventions. A common approach to parameter estimation is nonlinear least squares using a forward solver. However, as model size and noise in data increase, these methods become computationally expensive to maintain accuracy in parameter estimates. In this work, we establish a weak-form based method of parameter estimation for systems with unobserved variables by generating weak-form input-output equations using differential algebra techniques. We show that practical identifiability of the weak-form system can be assessed more quickly in comparison to output error based parameter estimation using criteria informed by the error in observed variables. Finally, we demonstrate that using a weak-form based method to estimate transmission rates is computationally efficient and robust to noise.", "id": "Paper/68924", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68924"}, {"title": " TTStack Sketching and Adaptive Randomized Tensor Train Compression, with Applications to Quantum Chemistry ", "webprogram_exclude": "0", "session_ids": ["Session/18247"], "source_sha256": "2aed534f7813317587c8cc4c511fcdbf7fd7e6f817f88d8fc0a9695171c3ec06", "withdrawn": "", "abstract": "Tensor trains (TT), also known as matrix product states (MPS), represent high-dimensional data and functions as a chain of small low-rank factors, and are widely used in quantum physics and chemistry, the numerical solution of high-dimensional PDEs, and data analysis.  Randomized sketching has emerged as a powerful alternative to deterministic SVD-based compression in this format. Its practical use hinges on two questions: how large should the sketch be, and what rank does the compressed tensor actually need? \n\nThe TTStack sketch, a family of structured random projections whose embedding guarantees scale only linearly with the tensor order, provides a natural foundation for practical answers to both questions. In this talk, we show how TTStack can be used for adaptive randomized TT rounding, where ranks are not prescribed in advance but selected on the fly to meet a desired accuracy.  The sketch itself provides inexpensive estimates of the approximation error, so ranks can be chosen and accuracy controlled in one pass. \nWe also discuss how these sketches can be applied implicitly to structured objects that are never formed, such as linear combinations, operator–vector products, residuals and Hadamard products, and reused inside iterative solvers. \nFinally, we illustrate these ideas in electronic structure computations, where randomized compression combined with symmetry-preserving block-sparse tensor trains speeds up the iterative solution of many-body eigenvalue problems for molecular systems.", "id": "Paper/68925", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68925"}, {"title": " Breaking the Spell: Security Analysis of VDOO ", "webprogram_exclude": "0", "session_ids": ["Session/18073"], "source_sha256": "ad9ddbdab33bd30cf6913f5bd3922793f69341c5cbb4d475612e1ac331840f38", "withdrawn": "", "abstract": "VDOO is a Rainbow-like multivariate signature scheme that introduces a sequence of diagonal layers before two oil layers. These additional layers are intended to strengthen the construction against structural attacks. In this talk, we revisit the concrete security of VDOO using the Simple Attack, Rectangular MinRank, and Padded MinRank frameworks.", "id": "Paper/68926", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68926"}, {"title": " The Use of Artificial Boundary Conditions to Improve Resolution of EIT Images for Lung Monitoring in Three Dimensions ", "webprogram_exclude": "0", "session_ids": ["Session/19369"], "source_sha256": "78889a4e579d13f3073689786f00a0fd0c8b43b743c41510f9af44750338d50d", "withdrawn": "", "abstract": "Electrical impedance tomography (EIT) is a medical imaging modality governed by the generalized Laplace equation. In EIT, low frequency, low amplitude currents are applied on electrodes attached to the surface of a conducting body. The resulting voltages are then measured and an approximation of the internal conductivity distribution of the body is produced. Due to the severe ill-posedness of the inverse problem, the estimation of the internal conductivity by deterministic methods results in reconstructed images with low resolution.  \nTo reduce computational costs, it is typical to reduce the entire conducting body to only the domain in which the estimates are being computed. For imaging of the lungs, this computational domain is a portion of the torso. It is therefore helpful to introduce the idea of artificial boundary conditions on the cross-sections at which the torso is truncated. In this poster, an algorithm is developed that imposes artificial boundary conditions on the truncation surfaces in the form of a Dirichlet-to-Neumann map. Once these boundary conditions are formulated, they may be used as additional “measurements” in the inverse problem, thus leading to enhanced image resolution. Results in three dimensions will be shown demonstrating the effectiveness of the method.", "id": "Paper/68927", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68927"}, {"title": " Efficient quantum algorithms for linear matrix equations and applications ", "webprogram_exclude": "0", "session_ids": ["Session/18246"], "source_sha256": "0cb4d9ace4cae068983b522bcb05106e6d0d6d48ee22e43c8148b4d7c96f4159", "withdrawn": "", "abstract": "This presentation considers nearly-optimal quantum algorithms for solving linear matrix differential equations as well as the Sylvester matrix equation. These equations are fundamental in various disciplines, including physics, chemistry, and control theory. The proposed approach constructs the solution matrix X as a block-encoding, which contrasts other traditional methods that express the solution as a quantum state. The latter methods frequently result in exponentially small amplitudes due to normalization constraints; consequently, the block-encoding approach can output properties of the entries of X exponentially faster. Moreover, an end-to-end application is provided via the simulation of dissipative dynamics in non-interacting fermion systems, with extensions applicable to other physical systems. A comparative analysis with classical algorithms suggests substantial polynomial quantum speedups for lattice systems, and more pronounced speedups for quantum systems characterized by long-range interactions. Finally, a lower bound is established, demonstrating the optimality of the quantum algorithm for a broad class of problem instances.", "id": "Paper/68928", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68928"}, {"title": " Using Neural Network Behavioral Stylometry to Investigate Disputed Chess Games Between Paul Morphy and Frederick Deacon ", "webprogram_exclude": "0", "session_ids": ["Session/19345"], "source_sha256": "d17677d1c6e33f5823c927f56563472342fb8996ef07c664ec7132e320f528c8", "withdrawn": "", "abstract": "Paul Morphy (1837-1884) was a chess prodigy hailing from New Orleans. From a young age, Morphy was recognized to have an almost supernatural talent in chess, notably beating Hungarian Chess Master Johann L\\\"{o}wenthal in multiple games at the age of 12. Over the subsequent years his chess renown grew and at age 20, after studying in college, Morphy traveled to Europe to play some of the great chess players of his day.\n\nFollowing this trip, a controversy arose over two games reportedly played in London between Morphy and British master Frederick Deacon. While Deacon insisted the matches occurred, Morphy disputed their authenticity, leaving the historical record contested to this day.\n\nAdvances in computing allow us to investigate this argument. In a paper recently published by McIlroy-Young et al, the authors leveraged neural networks trained on open-source chess data to identify chess players based on their behavioral stylometry.\n\nWe apply these methods to the Morphy-Deacon controversy to analyze the likelihood that Paul Morphy and Frederick Deacon played these games, based on their behavioral style of play from past games in the historical record. This research aims to provide some measure of statistical and machine learning closure to the chess world on this long-standing debate.", "id": "Paper/68930", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68930"}, {"title": " Artin-Mazur and Ruelle’s zeta function in non archimedean dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/19357"], "source_sha256": "137ac498f375b5a1eb13e7bfcba516456aaf535becde18c720ad549bf87944b3", "withdrawn": "", "abstract": "Rational maps over non archimedean fields arise naturally in number theory as well as in the study of degenerations of complex dynamical systems. I will discuss our prior result on the rationality and meromorphicity of the Artin-Mazur and Ruelle's zeta function for subhyperbolic rational maps of one variable over a non-archimedean local fields, as well as more recent development on zeta function calculation in the completion  their algebraic closures.", "id": "Paper/68932", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68932"}, {"title": " Mathematics of immune cell engager therapies ", "webprogram_exclude": "0", "session_ids": ["Session/18222"], "source_sha256": "e49b3ecfd526e95a70946b90ac24b9e764a7863e042a7622510608100bcdce34", "withdrawn": "", "abstract": "In this talk I will discuss some novel immune cell engager therapies, which are a promising but complex new class of cancer treatment.  I will discuss how mathematical modeling can shed light on the mechanisms underlying these therapies and help optimize their design and predict clinical responses.", "id": "Paper/68936", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68936"}, {"title": " Who Coordinates Coordination? The Evolving Roles of Course Directors in Precalculus and Calculus ", "webprogram_exclude": "0", "session_ids": ["Session/18250"], "source_sha256": "01c30d7e97d56ad7cb2a479607866ce926404dcb1958ce4fa6346279f83f0f87", "withdrawn": "", "abstract": "Course coordination across multiple sections requires more than shared syllabi, assessments, and instructional materials. It requires leadership that establishes a vision and supports the people who develop, maintain, and adapt structures that shape instructors’ and students’ experiences across sections. This presentation examines the evolving roles of the Directors of Precalculus and Calculus at the University of Illinois Chicago and how these positions have supported increasingly intentional coordination.\n\nOver time, these roles have expanded beyond course logistics to supporting coordinators and instructors as they respond to changes in instructional practices, technology, accessibility, and student support. Examples include maintaining shared course materials, implementing accessibility guidelines, supporting transitions to new learning management systems, and working with institutional partners to organize course sites and grading platforms. Such work requires communication, collaboration, problem solving, and support while maintaining continuity for students.\n\nParticular attention is given to the student experience. Coordination can provide common expectations, comparable learning opportunities, consistent access to resources, and opportunities to collaborate with peers beyond individual sections. Preliminary findings from a recent multi-site study suggest relatively consistent classroom experiences across Precalculus, Calculus I, and Calculus II, along with generally stable affective outcomes. Students expressed a strong preference for consistency in course materials, homework, assessments, and grading, while allowing greater variation in pedagogy. Limited interaction with peers across sections also suggests an opportunity to make the broader coordinated learning community more visible to students.\n\nThe presentation concludes by considering coordination as a balance between consistency and instructor autonomy. Sustainable coordination requires shared structures, institutional support, collaboration, and feedback from instructors and students. Ultimately, effective coordination is not only about maintaining consistency across sections, but also about helping instructors adapt to change while creating a connected learning environment.", "id": "Paper/68939", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68939"}, {"title": " Algebraic Multigrid Preconditioners for a Multiscale Relativistic Fokker-Planck-Boltzmann Model ", "webprogram_exclude": "0", "session_ids": ["Session/17926"], "source_sha256": "27463d570116a4189397357c4006e1351df2b313e5c02c99608846e6ee671d11", "withdrawn": "", "abstract": "Runaway electrons in magnetically confined fusion plasmas are modeled by a relativistic Fokker-Planck-Boltzmann equation whose numerical discretization produces strongly nonsymmetric, advection-dominated systems with highly varying coefficients and sharp localized solution features. In this talk, we present a solution technique that combines local approximate ideal restriction ($\\ell$AIR), a reduction-based algebraic multigrid (AMG) method designed for nonsymmetric problems, with Krylov subspace methods and adaptive mesh refinement within the PETSc and hypre frameworks. The adaptive approach concentrates resolution in regions containing steep gradients and the high-energy runaway tail, while the $\\ell$AIR preconditioner provides robust linear convergence for both time-dependent and steady-state formulations. Numerical experiments over a range of electric-field strengths show that $\\ell$AIR maintains low and relatively stable iteration counts as the problem becomes increasingly advection dominated, whereas classical AMG approaches may converge slowly or fail to reach the required tolerances. The results illustrate the effectiveness of combining advanced multigrid techniques and adaptive discretization for challenging multiscale kinetic problems in scientific computing.", "id": "Paper/68941", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68941"}, {"title": " Dot Detectives: A Case Study in Math Circle Plan Iteration when Things Don’t Go as Expected ", "webprogram_exclude": "0", "session_ids": ["Session/18212"], "source_sha256": "cc74cdb997e28b6d4c158023e5e6bfce00c58448a32e4449e424fad7cf4283d7", "withdrawn": "", "abstract": "Math Circles of Chicago (MC2) holds math circles at a large scale. We have seven weekend Hubs, 70 math circles in after school programs, along with an extensive summer program. Our activities are traditional math circles that are designed for equitable access while still promoting the agency and investigatory nature of high quality math math enrichment. \n\nThis presentation will focus on an anchor activity for our new summer Rising 5th grade program. Dot Detectives is an activity that tries to address a well known mathematical result in a creative way to preserve as much student agency as possible while helping students reach a desired conclusion. MC2 introduced this plan for the first time in the summer of 2026 and 'things did not go as expected'. Here we'll think through the activity, look at how students responded, and discuss what general principles might be derived from iterating activity design when we pay close attention to student thinking.", "id": "Paper/68943", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68943"}, {"title": " Stability and Robustness of a Coupled Cell–Lumen Pump–Leak Model ", "webprogram_exclude": "0", "session_ids": ["Session/18039"], "source_sha256": "06940cce2a348729476e0176f5e944f8e6dcc9eeab0cc06b2f77b4ae65f103e9", "withdrawn": "", "abstract": "Cells must counter osmotic water influx driven by impermeant intracellular molecules to maintain stable volume and proper function. In epithelial tissues, cell volume and ion homeostasis are regulated through the coordinated activity of ion pumps, channels, and transporters. Classical five-dimensional differential-algebraic pump–leak equations (PLEs) provide a mathematical framework for describing these processes in single cells. Many epithelial functions, however, involve coupled transport between a cell and an enclosed lumen, motivating an extension of the single-cell framework. We develop a ten-dimensional pump–leak model that couples cellular and luminal ion concentrations, volumes, and electrical potentials. We derive analytical stationary solutions for both passive transport and active transport driven by the Na/K-ATPase and characterize their dependence on model parameters. We then analyze the stability and robustness of these solutions across physiologically relevant parameter regimes. This framework provides a tractable dynamical-systems approach for studying how coupled cell–lumen transport regulates epithelial homeostasis and how disruptions in transport mechanisms may lead to dysfunction.", "id": "Paper/68946", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68946"}, {"title": " Focus-Focus Singularities in 6 Dimensions ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "9e858e41cf0f0469a094e7775b9003a6f8918c948eec0c09ac9e8953a97a925f", "withdrawn": "", "abstract": "Integrable systems, or dynamical systems that possess the maximum number of conserved quantities, consist of a $2n$-dimensional symplectic manifold and a moment map  $F =(f_1,...,f_n): M \\rightarrow \\mathbb{R}^n$ whose components Poisson commute ($\\{ f_i, f_j\\} = 0$). The behaviors of these integrable systems are best studied by finding and categorizing singular points, where the fiber of a point in the image drops in dimension. For example, instead of an $n$-torus, the fiber of an elliptic singularity collapses to a point, and the fiber of a focus-focus singularity is a pinched torus. \n\nWhile 4-dimensional integrable systems have been studied extensively, 6-dimensional dynamics remain less explored. This research constructs and analyzes multiple 6-dimensional transition families (integrable systems governed by a parameter-dependent Hamiltonian $H_t$) that undergo a nodal trade, in which a singular point alters its topological type by passing through a degenerate state as $t$ varies. We classify the evolution of these singularities, detailing rank-1 transitions from elliptic-elliptic-regular to focus-focus-regular states ($\\text{EER} \\to \\text{FFR}$) as well as asymmetric rank-0 transitions. Finally, for a system with two fixed toric functions, we derive the general Hamiltonian form encompassing all valid integrable choices and categorize its complete singular set.", "id": "Paper/68947", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68947"}, {"title": " Minimizing fractional harmonic maps ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "e8d227a3d69ad339a690e0fcc7ed82e4d00d11c2445e2a395ecffe12e0f5dfe0", "withdrawn": "", "abstract": "We discuss the regularity of minimizing fractional harmonic maps and analyze the dimension of their singular sets. These are mappings $u\\in \\dot{W}^{s,p}(\\mathbb{R}^n,\\mathcal{N})$ into manifolds $\\mathcal{N}$ with sufficiently simple topology that minimize the nonlocal energy\n$$\\int_{\\mathbb{R}^n}\\int_{\\mathbb{R}^n}\\frac{|u(x)-u(y)|^p}{|x-y|^{n+sp}} \\;dx\\;dy.$$\nWe prove that these minimizers are locally H\\\"older continuous in a bounded domain $\\Omega$ outside a singular set $\\Sigma $ with Hausdorff dimension strictly smaller than $n-sp.$ We avoid the use of a monotonicity formula, which is unknown when $p \\neq 2$, by using a blow-up argument instead.", "id": "Paper/68957", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68957"}, {"title": " Counting Labelings of Graphs with Given Pinnacle Sets ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "9ddcd85dd17d2f554caa4e87f9c6e629bd234422b6999f936d748a1b71408faa", "withdrawn": "", "abstract": "Given a simple connected graph G with n vertices and a bijective labeling of the vertices using the integers [n] = {1, 2, . . . , n}, we say j ∈ [n] is a pinnacle of G if the label j on vertex v is larger than the labels of all the vertices neighboring v. Given a subset S ⊆ [n], if there exists a labeling of G such that S is the set of all pinnacles, then we say that S is an admissible pinnacle set of G. We explore the properties of pinnacle sets as well as enumerate how many labelings of G result in particular pinnacle sets. We present results on certain graph families including complete multipartite graphs, path graphs, and cycle graphs.", "id": "Paper/68959", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68959"}, {"title": " Joint asymptotic expansions for Bessel functions ", "webprogram_exclude": "0", "session_ids": ["Session/17999"], "source_sha256": "f6af575bd658e0ebb8c65f414e64cb76cbb4725981c67b9f66c3297488b8e4c8", "withdrawn": "", "abstract": "We study the classical problem of finding asymptotics for the Bessel functions as both the argument and order approach infinity. We use geometric microlocal analysis, specifically blow-up analysis, to find asymptotics for the modulus and phase of the Bessel functions. This approach produces polyhomogeneous conormal joint asymptotic expansions, valid in any regime. It can also be used to give asymptotic expansions for zeroes of Bessel functions and their derivatives. This work has inspired several applications in spectral theory, including a proof of Polya's conjecture for the eigenvalue counting function in the disk.", "id": "Paper/68960", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68960"}, {"title": " The essential coexistence phenomenon in smooth dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/18065"], "source_sha256": "6c79da37914b52306a26c5c2c5a4edda2aefa1ebbbc1c68f4f40d1faa1bc2fa9", "withdrawn": "", "abstract": "A volume preserving dynamical system with discrete or continuous time on a compact smooth manifold M is said to exhibit the essential coexistence if M can be split into two invariant Borel subsets A and B of positive volume -- the chaotic and regular regions -- such that the action of the system on A is chaotic (has positive Kolmogorov-Sinai entropy) while its action on B is regular (has zero entropy). I will discuss some results on the essential coexistence in the setting of volume preserving and Hamiltonian systems and its connection with some major open problems in smooth dynamics.", "id": "Paper/68961", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68961"}, {"title": " Parallelising <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"3.189ex\" height=\"2.009ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -576.1 1373 865.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\star _\\mathbf {M}</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-22C6\" d=\"M210 282Q210 284 225 381T241 480Q241 484 245 484Q249 486 251 486Q258 486 260 477T272 406Q275 390 276 380Q290 286 290 282L388 299Q484 314 487 314H488Q497 314 497 302Q497 297 434 266Q416 257 404 251L315 206L361 118Q372 98 383 75T401 40L407 28Q407 16 395 16Q394 16 392 16L390 17L250 159L110 17L108 16Q106 16 105 16Q93 16 93 28L99 40Q105 52 116 75T139 118L185 206L96 251Q6 296 4 300Q3 301 3 302Q3 314 12 314H13Q16 314 112 299L210 282Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAINB-4D\" d=\"M314 0Q296 3 181 3T48 0H39V62H147V624H39V686H305Q316 679 323 667Q330 653 434 414L546 157L658 414Q766 662 773 674Q778 681 788 686H1052V624H944V62H1052V0H1040Q1016 3 874 3T708 0H696V62H804V341L803 618L786 580Q770 543 735 462T671 315Q540 13 536 9Q528 1 507 1Q485 1 477 9Q472 14 408 162T281 457T217 603Q215 603 215 334V62H323V0H314Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-22C6\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAINB-4D\" x=\"707\" y=\"-213\"></use>\n</g>\n</svg> Tensor Computations ", "webprogram_exclude": "0", "session_ids": ["Session/17849"], "source_sha256": "a82cf94270edcf97d8194def1b3da37a7b50e1169274631fd5f199af6da741b5", "withdrawn": "", "abstract": "This talk will focus on high-performance implementations of tensor SVD algorithms under the $\\star_\\mathbf{M}$ framework. Within the $\\star_\\mathbf{M}$ framework, tensors can be decomposed in a matrix-mimetic manner and inherit the approximation guarantees of matrix approximation methods. We shall describe the parallel computations needed to perform tSVDM-I, tSVDM-II, and M selection in this talk.", "id": "Paper/68963", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68963"}, {"title": " Comparing Signal-Based and Image-Based Representations for Scientific Classification ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "f1465d4822d457ba3a5d1dcd34c0d16f98c8a51aafbcfcfa6041ad23124dc4a6", "withdrawn": "", "abstract": "Scientific measurements may be represented in several mathematically meaningful ways, and each representation can emphasize different aspects of the data. This study considers how these choices affect classification across remote-sensing imagery and scientific time series. We work with the original measurements as well as forms derived from dimensionality reduction, signal compression, angular encoding, and Gramian fields. Their performance is studied using classical machine learning and deep neural networks over repeated experiments. In addition to overall accuracy, we consider class-level results, confusion matrices, and recurring patterns of error. Spatial prediction maps are used for image data to examine where misclassifications occur. The findings differ across the datasets. Gramian fields support strong classification in some cases, while direct signal methods or reduced features are more successful in others. Together, the results suggest that a good classification strategy begins with the data itself and with a careful decision about which mathematical form preserves the information needed for the problem.", "id": "Paper/68964", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68964"}, {"title": " Proofs in Progress: Student Engagement with AI Feedback ", "webprogram_exclude": "0", "session_ids": ["Session/17461"], "source_sha256": "711844bc00f269afc3140039b015d42af5bd43c98b3ce820507ac8b7cb91bf78", "withdrawn": "", "abstract": "Can AI feedback lower barriers to mathematical engagement while preserving the intellectual work necessary for learning? We explore this question through HaLLMos, a free, web-based tool that gives college students feedback on the proofs they write. HaLLMos follows a constitution, a set of principles developed by an advisory board of experts in mathematics and proof pedagogy. It also draws on curated feedback exemplars. Together, the constitution and exemplars guide feedback designed to help students develop their own mathematical arguments without supplying proofs for them. Since HaLLMos launched, students have submitted more than 35,000 proof attempts.\nDrawing on student and faculty interviews, surveys, and sequences of proof attempts, we examine how students use this feedback to develop and revise mathematical arguments. Student interviews suggest that HaLLMos provides a place to try out uncertain ideas and receive initial feedback before bringing questions to instructors. Submission histories offer a complementary view, showing how students revise arguments, respond to feedback, and approach related problems over time. We show how students use AI feedback to get started on proofs, experiment with ideas, and prepare for conversations with their instructors. We also examine tensions involved in supporting this engagement while preserving students’ ownership of their mathematical work and the intellectual effort necessary for learning.", "id": "Paper/68965", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68965"}, {"title": " Average Elliptic Curve Analouge of Artin’s Primitive Root Conjecture ", "webprogram_exclude": "0", "session_ids": ["Session/19367"], "source_sha256": "fde5b5011997b62299967ff7e320a01a73cba4defb541f8c4cec97962708d2e9", "withdrawn": "", "abstract": "Let $E$ be an elliptic curve over $\\mathbb{Q}$, and let $P \\in E(\\mathbb{Q})$ be a point of infinite order. For a prime $p$ of good reduction, we say $P$ is a primitive point modulo $p$ if $E(\\mathbb{F}_{p}) = \\langle P \\text{ mod } p\\rangle$. The Lang-Trotter primitive-point conjecture predicts the asymptotic density of primes such that $P$ is a primitive root, providing a natural elliptic curve analogue of Artin's primitive root conjecture. We prove an average version of this conjecture for the family of elliptic curves $y^2 + ay = x^3 + bx^2 + cx$ where $a,b,c \\in \\mathbb{Z}$ and $P = (0,0)$. More precisely, if $A,B,C \\geq x^{1+ \\epsilon}$, then the average, over $|a| \\leq A, |b| \\leq B, |c| \\leq C$ of the number of primes $p \\leq x$ for which $(0,0)$ generates $E(\\mathbb{F}_{p})$ is asymptotic to $C_{E,A} \\frac{x}{\\log x}$ where $C_{E,A} = \\prod \\left(1 - (\\ell^3 - \\ell - 1)/(\\ell^2(\\ell^2-1)(\\ell-1)) \\right) = 0.44014739 \\dots.$", "id": "Paper/68969", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68969"}, {"title": " Quantum Anticodes: a third course ", "webprogram_exclude": "0", "session_ids": ["Session/18387"], "source_sha256": "440ed5addec9812c7157bad1afef90ddb81fa3cad924a2148e9617a5091d2370", "withdrawn": "", "abstract": "We review the anticode formalism for quantum codes, then present the connections between quantum codes and isotropic subspaces in this light. We define higher invariants of isotropic subspaces, including Hamming weights and binomial moments, and relate them to relative invariants of the associated codes. Finally, we revisit the quantum-lego trace operation, showing how a higher invariant characterizes the “untracing” of a large code into smaller codes.", "id": "Paper/68970", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68970"}, {"title": " Singularity formation in kinetic equations ", "webprogram_exclude": "0", "session_ids": ["Session/18291"], "source_sha256": "f1caff9da6c26b7e440ad286e91566907ea7dac477626d186a5a04e99f11277d", "withdrawn": "", "abstract": "We discuss the construction of a smooth solution to very hard kinetic equations, that blows up in a self-similar fashion and exhibit implosion in macroscopic quantities. The solution is built around a local Maxwellian that corresponds to smooth imploding solution of compressible Euler. This is achieved by the stability analysis on macroscopic hydrodynamic quantities and the remaining microscopic kinetic quantities of the perturbation.", "id": "Paper/68971", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68971"}, {"title": " Transcendence of Taelman <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.583ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 681.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">L</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4C\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-4C\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Values for Virtually <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.066ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 889.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">K</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-4B\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Rational Anderson Modules ", "webprogram_exclude": "0", "session_ids": ["Session/17998"], "source_sha256": "1cec2b0c53fd713481e7cd270cfccb8d1bfaf03d801205bcd73b5b07109acb5f", "withdrawn": "", "abstract": "Taelman $L$-values are function field analogues of special values of classical $L$-functions and encode arithmetic information associated with Drinfeld modules and, more generally, Anderson modules. In this talk, I will discuss the transcendence of these values for a class of abelian Anderson modules defined over the ring of integers $\\mathcal{O}_F$ of a finite separable extension $F/K$.", "id": "Paper/68984", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68984"}, {"title": " Variants of the Zero Forcing Problem ", "webprogram_exclude": "0", "session_ids": ["Session/18369"], "source_sha256": "7f634acfb44caea8148c608d509a722b44bafa0e181b22183bb73e9948344a41", "withdrawn": "", "abstract": "Suppose $G = (V,E)$ is a simple, undirected graph. \\textit{Zero forcing} is a combinatorial process on $G$ that begins with a set of black vertices and repeatedly colors a white vertex black whenever it is the unique white neighbor of a black vertex. We define the zero forcing number $Z(G)$ to be the cardinality of the smallest black set that eventually forces the coloring of all of $V$. We define a symmetric matrix $\\textbf{A}$ to be \\textit{compatible} with $G$ if and only if $\\textbf{A}_{ij} \\neq 0$ for all $i$ and $j$ such that $\\{i,j\\}\\in E$. It is known that $Z(G)$ is an upper bound for the maximum nullity of all matrices compatible with $G$. The maximum nullity bounds the maximum multiplicity of a single eigenvalue, which yields useful information for the Inverse Eigenvalue Problem. In this talk, we present new findings for the zero forcing number of the Cartesian Product of path graphs and Generalized Petersen Graphs. Next, we examine the Inverse Eigenvalue Problem by studying the minimum number of distinct eigenvalues. \n\nIn addition, we look at variations of zero forcing: leaky zero forcing, $(\\alpha,\\beta)$-transmission zero forcing, and failed zero forcing. Leaky zero forcing is similar to zero forcing, except any $l$ number of vertices are \"leaky\", or unable to force. In $(\\alpha,\\beta)$-transmission zero forcing,  vertices are weighted and forcing occurs based on transmission thresholds. Failed zero forcing looks at the maximum number of vertices that fail to force the whole graph. We will discuss results on these three variations of zero forcing.", "id": "Paper/68985", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68985"}, {"title": " The <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"6.374ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 2744.2 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">(B, C)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-42\" d=\"M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-43\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-42\" x=\"389\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2C\" x=\"1149\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-43\" x=\"1594\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"2354\" y=\"0\"></use>\n</g>\n</svg>-core inverse of rectangular matrices ", "webprogram_exclude": "0", "session_ids": ["Session/18230"], "source_sha256": "2c40614fde9647bd853a8b09b17cd0c3f412317941dabff0ff4889338dfed5c7", "withdrawn": "", "abstract": "Let $A$ be an $m\\times n$ complex matrix and let $B,C$ be $n\\times m$ complex matrices. The main purpose of this article is to derive several new properties of the $(B, C)$-core inverse. Also, we introduce and investigate the dual $(B, C)$-core inverse in the context of rectangular matrices. The connection between (dual) $(B, C)$-core inverses and other generalized inverses is given. Finally, the minimum norm solution and least square solution to the equation are expressed by using the $(B, C)$-core inverse.", "id": "Paper/68986", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68986"}, {"title": " Probabilistic Edge Augmentation ", "webprogram_exclude": "0", "session_ids": ["Session/18105"], "source_sha256": "cd31591bc89c05e614c59d812a88967c5cd81a4cd06a327f463c3fbf19778853", "withdrawn": "", "abstract": "Probabilistic graphs are graphs in which each edge is only ``active'' with a certain probability. These objects are used to study the spread of information in social network analysis, the spread of disease in epidemiology, and lossy communication in the network robustness literature. They are also a key modeling abstraction in percolation theory. \n\nGiven two vertices u,v in a probabilistic graph G, a basic quantity of interest is their proximity, which is the probability that there exists a uv-path consisting entirely of active edges. We say that the reach of G is the minimum proximity across all vertex pairs. \n\nWe study edge augmentation (or link recommendation) in probabilistic graphs. Given G and a budget k, our goal is to add k new probabilistic edges to G while maximizing the reach of the resulting G'. We give the first algorithms for this problem with provable approximation guarantees. We also give complementary approximation lower bounds.\n\nOur techniques build on the related edge augmentation literature, but our probabilistic setting motivates some new analytical tools. We develop these by building on ideas from percolation theory.", "id": "Paper/68987", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68987"}, {"title": " Symmetry-Constrained Discovery of Governing Equations from Data ", "webprogram_exclude": "0", "session_ids": ["Session/17703"], "source_sha256": "35fe922704bc68f790d18125464ddc1a099b5c9930736c953dc4e2fd8985f830", "withdrawn": "", "abstract": "Discovering governing differential equations from data is fundamentally a model-selection problem over a large space of candidate equations. In many physical systems, however, this search space is strongly constrained by symmetry. In this talk, I will describe two complementary ways to incorporate Lie symmetries directly into data-driven equation discovery.\n\nFor dynamical systems governed by ODEs, a time-independent symmetry of the dynamics is equivalent to equivariance of the associated flow map, and infinitesimally imposes a commutation condition between the symmetry generator and the governing vector field. For linear group actions and finite function libraries, these conditions become explicit linear constraints on the coefficients of the candidate equation, reducing the admissible search space before fitting. I will then extend this perspective to differential equations with general Lie point symmetries. Using prolonged group actions on jet spaces, symmetric differential equations can be characterized in terms of differential invariants. Searching over functions of these invariants restricts the hypothesis space to equations satisfying the prescribed symmetry by construction.\n\nI will discuss how these ideas integrate with symbolic regression methods, and how symmetry-based reduction improves identifiability, robustness to noise, and recovery of parsimonious governing equations across several dynamical systems.", "id": "Paper/68988", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68988"}, {"title": " Singular Fibers of Bending Systems on Hexagon Spaces ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "2eb4d6241964ec75df0d1b5898ce169d9a6ac8eedb32d1837a202b85113bb5cd", "withdrawn": "", "abstract": "The moduli space $\\mathcal P(r_1,\\dots,r_n)$ of closed $n$-gons in $\\mathbb R^3$ with fixed side lengths $r_i>0$ modulo rigid rotations is a smooth $2(n-3)$-dimensional symplectic manifold for generic side lengths. Hamiltonian actions generated by diagonal bending flows yield completely integrable systems on these spaces, indexed by triangulations of the $n$-gon. For $n=6$, there are two combinatorially distinct integrable systems: the caterpillar (fan) system $F_{\\text{cat}} = (l_{12}, l_{56}, l_{123})$ and the symmetric (star) system $F_{\\text{sym}} = (l_{12}, l_{34}, l_{56})$. The image of the moment map $F: \\mathcal{P}(r) \\to \\mathbb{R}^3$ is a 3D convex moment polytope.\n\nA vertex of the moment polytope is Delzant if it is simple and smooth. At such points, the action is locally toric and the fiber is a single point. When a vertex is non-Delzant, the corresponding singular fiber can be a higher-dimensional manifold. We classify all conditions on generic side length vectors under which non-Delzant vertices appear for both bending systems and explicitly compute the topology of their singular fibers.\n\nIn the generic symmetric system, a non-Delzant vertex occurs if and only if two adjacent side lengths are equal (e.g., $r_1 = r_2$) and the others are at their extremes. Reconstruction reveals that every non-Delzant vertex in $F_{\\text{sym}}$ has a singular fiber diffeomorphic to $S^2$. In the generic caterpillar system, non-Delzant vertices arise either from an edge equality as above or when $z = l_{123} = 0$, causing the hexagon to decouple into two independent closed triangles $T_1 = (r_1,r_2,r_3)$ and $T_2 = (r_4,r_5,r_6)$. We prove that $F_{\\text{cat}}^{-1}(v) \\cong SO(3)$ if and only if both triangles strictly satisfy the triangle inequalities in this latter case. In all other generic non-Delzant cases, including degenerate triangles, the fiber is diffeomorphic to $S^2$. This completely classifies the topology of singular fibers over non-Delzant vertices in generic hexagon spaces.", "id": "Paper/68989", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68989"}, {"title": " Braid groups, elliptic fibrations, and resolving the quartic ", "webprogram_exclude": "0", "session_ids": ["Session/18297"], "source_sha256": "6bda1932c50245eb5522096f4349a2e13f3fd6dc5cfa882036a458956ec90686", "withdrawn": "", "abstract": "Ferrari’s classical solution of the quartic equation in 1540 gives rise to a map from configurations of four points in the complex plane to configurations of three points, inducing a surjective homomorphism $B_4 \\to B_3$ between braid groups. Building on work of Chen-Salter, I will explain how this map admits a geometric interpretation in terms of the universal elliptic curve. I will then describe how, for small levels $m$, the maps $B_4[m]\\to B_3[m]$ connect congruence subgroups of braid groups with a surprising array of classical geometric objects: K3 surfaces, the Hesse pencil, the platonic solids and more. This talk is based on joint work with Ethan Pesikoff.", "id": "Paper/68992", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68992"}, {"title": " GenAI for Teaching, Learning, and Assessment in Mathematics ", "webprogram_exclude": "0", "session_ids": ["Session/17461"], "source_sha256": "3b81f1ace8d293fc0df3998b7d4903e5020c7f6919de6a91a74906b99d1dbf3b", "withdrawn": "", "abstract": "The integration of generative AI tools into education is rapidly changing how we teach and learn, especially in mathematics, a subject considered rigorous. In this talk, we examine how generative tools are transforming mathematical teaching by enabling educators to create teaching materials, personalized assessments, and learning resources directly from their own content. These tools not only assist educators but also encourage pedagogical flexibility, enabling rapid adaptation to diverse learning needs and styles.\n\nWe’ll also explore how generative AI impacts student learning: from improved practice opportunities and instant feedback to concerns about overreliance, academic integrity, and digital access disparities. Using recent studies from Spring 2023 to 2026, we’ll highlight key trends in how students, faculty, and administrators vary in their adoption, awareness, and views of AI tools in math education.  This session will feature demonstrations on using AI for learning and teaching, AI-powered assessment creation, discussions of ethical and policy issues, and practical strategies for integrating these tools into your classroom while upholding rigor, creativity, and integrity.", "id": "Paper/68994", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68994"}, {"title": " Quantum Computing for Parameter Estimation in Epidemiological Models ", "webprogram_exclude": "0", "session_ids": ["Session/19365"], "source_sha256": "839c3794163d48fa89f8a5f45cdfd2f324f76e6739bcffd1725201ea6826d6d5", "withdrawn": "", "abstract": "Parameter estimation is a fundamental challenge in the calibration of ordinary differential equation (ODE) models, where repeated numerical integration can lead to high computational cost. In this work, we investigate whether quantum algorithms can be leveraged to assist parameter estimation in nonlinear dynamical systems. We develop a hybrid classical--quantum framework that reformulates a data-assimilation-augmented parameter estimation problem as a combinatorial optimization task. Model dynamics and data assimilation are enforced entirely on the classical side, while the resulting parameter estimation cost functional is discretized and approximated by a quadratic unconstrained binary optimization (QUBO) surrogate. This surrogate is mapped to an Ising Hamiltonian, and quantum optimizers are used to search for low-energy configurations corresponding to candidate parameter estimates. We apply the framework to SIS and SIR epidemic models. In this setting, the method is used to recover classical system parameters from partial state observations. Numerical experiments with synthetic data show that the proposed approach accurately recovers parameters while requiring ODE solves only on a prescribed coarse grid. The framework avoids quantum state tomography, illustrating a viable pathway for integrating quantum optimization into data-driven parameter estimation for nonlinear dynamical systems.", "id": "Paper/68996", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68996"}, {"title": " Structure Constant Formulas for the Universal Enveloping Algebras of the Nilpotent Lie Algebras of Dimension Five and Less ", "webprogram_exclude": "0", "session_ids": ["Session/17756"], "source_sha256": "a21d210dd92d75284c860e1c37f2c02c30fcc1241bf1734239fba688ff17b8b6", "withdrawn": "", "abstract": "Given a Lie algebra $L$, the  Poincar\\'{e}-Birkhoff-Witt (PBW) Theorem implies that every element of the universal enveloping algebra of $L$, $\\mathbf{U}(L)$, can be written as a unique linear combination of products of basis elements of $L$ in any fixed order. The coefficients of the resulting linear combination are referred to as the structure constants. The PBW Theorem tells us structure constants exist in $\\mathbf{U}(L)$, but it does not give us a way to find them. However, $\\mathbf{U}(L)$ is also equipped with the commutator bracket such that for all $x,y\\in L,$ $xy=yx+[x, y]$ in\n$\\mathbf{U}(L)$. Thus, we have a way to ``straighten'' or reorder products of basis elements into the preferred PBW order.\\\\\n\nEngel's Theorem states that a finite-dimensional Lie algebra $L$ is nilpotent if for all $x,y\\in L$, repeated bracketing of $x$ on $y$ eventually gives $0$. Libor \\v{S}nobl and Pavel Winternitz classified all of the Lie algebras of dimension six and smaller, including the nilpotent ones. Using this classification, we formulated and proved structure constant formulas for the universal enveloping algebras of all the nilpotent Lie algebras of dimension five and less.", "id": "Paper/68998", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/68998"}, {"title": " Three Positive Solutions for a Cross-Coupled p-Laplacian System with Indefinite Potential ", "webprogram_exclude": "0", "session_ids": ["Session/19369"], "source_sha256": "7f843129412a37e3e037999e336975baf092f9477d13310a00556c370f9d7a5d", "withdrawn": "", "abstract": "\\begin{abstract}\nWe establish the existence of at least three positive weak solutions to the\nDirichlet problem for the cross-coupled quasilinear system\n\\(-\\Delta_p u + V(x)\\varphi_p(u) = \\lambda f(v)\\),\n\\(-\\Delta_p v + V(x)\\varphi_p(v) = \\lambda g(u)\\)\non a smooth bounded domain $\\Omega \\subset \\mathbb{R}^N$,\nfor every $\\lambda$ in an explicit open interval. The nonlinearities\n$f, g$ are non-decreasing and obey the combined $p$-sublinearity of\nAli-Shivaji-Ramaswamy; the potential $V$ is allowed to change sign,\nsubject to a pointwise lower bound that keeps the principal eigenvalue of\n$-\\Delta_p + V\\varphi_p$ on $W_0^{1,p}(\\Omega)$ positive. The proof joins\nAmann's three-solution theorem to a radial subsolution whose construction\nabsorbs the positive part of the potential into a monotone auxiliary\nprofile, thereby preserving the comparison structure on which the method\ndepends. \n\\end{abstract}", "id": "Paper/69004", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69004"}, {"title": " CANCELLED-Enumeration of Additive Self-Dual Codes from Metacirculant Graphs \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/19345"], "source_sha256": "b981a9b3e0b32e818552e5f61a6b3ec2f0953c3bd6c2468ee7db16e86eaf6800", "withdrawn": "", "abstract": "We investigate the construction of additive self-dual codes over $\\mathbb{F}_4$ from metacirculant graphs, which yield quantum error-correcting codes over $\\mathbb{F}_2$ via the stabilizer framework. Using adjacency matrices of metacirculant graphs, we derive bounds on the minimum distance of the associated codes and demonstrate that these bounds are tight in several cases. Through computational enumeration in MAGMA, we classify Type I and Type II additive self-dual metacirculant codes of length up to 40, identifying families that achieve known extremal bounds and, in some cases, exceed previously established minimum distances. We conclude by outlining directions for future work, including isomorphism classes of metacirculant graphs and structural symmetries arising in their code constructions.", "id": "Paper/69007", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69007"}, {"title": " Landscapes of L-functions ", "webprogram_exclude": "0", "session_ids": ["Session/18366"], "source_sha256": "3db560252d6caf0d26349c148cd1ef145fa02a43f29fbb5bae1f572b048e5dc3", "withdrawn": "", "abstract": "We will discuss ways to visualize the collection of all L-functions.", "id": "Paper/69008", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69008"}, {"title": " Flow polytopes and a poset of linear recurrence systems ", "webprogram_exclude": "0", "session_ids": ["Session/18334"], "source_sha256": "fa1ebc6df50c595250a39f7da08232d1496f1f01277278fae5ebbb6431f4dec0", "withdrawn": "", "abstract": "We introduce the $G$-Fibonacci and $G$-Euler numbers associated to an acyclic directed graph $G$ with unique source and sink, respectively, as the number of vertices and normalized volume of the corresponding unit-netflow flow polytope $\\mathcal{F}_G$. These generalize the classical Fibonacci and Euler numbers, and motivate a broader study of flow polytopes arising from linear recurrence systems. For a fixed nonnegative integer sequence $x=(x_1,x_2,\\ldots, x_n)$, there are, in fact, many acyclic directed graphs with the same $G$-Fibonacci numbers. We show that this set of flow polytopes, $\\mathscr{L}(x)$, can be seen as the integer points of another polytope and that $\\mathscr{L}(x)$ comes with a natural poset structure. We discuss features of this poset for a few example sequences and give combinatorial interpretations for the different $G$-Euler numbers.", "id": "Paper/69009", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69009"}, {"title": " Scheduling and Admission with Static and Varying Continuous Resource Requirements ", "webprogram_exclude": "0", "session_ids": ["Session/18343"], "source_sha256": "5b9038b33bc27561fd974c23faadb4edc5ad569d449808e27b1ad431445de53d", "withdrawn": "", "abstract": "In modern computing systems, job resource requirements are massively heterogeneous by default, with thousands or millions of unique resource-requirement combinations. We introduce a new model with continuous resource-requirement distributions, both in the single-dimensional and multidimensional settings.\n\nIn the static requirement setting, we derive the first throughput-optimal family of scheduling policies, combining workload-driven resource discretization with existing class-based policies. \n\nIn the time-varying requirement setting, we introduce the first asymptotically throughput-optimal admission policy, based on a Poisson process with a carefully tuned rate.\n\nThis talk is based on two joint works with Chutong Gao, Izzy Grosof, and Willow Kowalik.", "id": "Paper/69015", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69015"}, {"title": " Randomized low-rank approximations for tensors under the <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"3.122ex\" height=\"2.009ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -576.1 1344 865.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\star _M</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-22C6\" d=\"M210 282Q210 284 225 381T241 480Q241 484 245 484Q249 486 251 486Q258 486 260 477T272 406Q275 390 276 380Q290 286 290 282L388 299Q484 314 487 314H488Q497 314 497 302Q497 297 434 266Q416 257 404 251L315 206L361 118Q372 98 383 75T401 40L407 28Q407 16 395 16Q394 16 392 16L390 17L250 159L110 17L108 16Q106 16 105 16Q93 16 93 28L99 40Q105 52 116 75T139 118L185 206L96 251Q6 296 4 300Q3 301 3 302Q3 314 12 314H13Q16 314 112 299L210 282Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4D\" d=\"M289 629Q289 635 232 637Q208 637 201 638T194 648Q194 649 196 659Q197 662 198 666T199 671T201 676T203 679T207 681T212 683T220 683T232 684Q238 684 262 684T307 683Q386 683 398 683T414 678Q415 674 451 396L487 117L510 154Q534 190 574 254T662 394Q837 673 839 675Q840 676 842 678T846 681L852 683H948Q965 683 988 683T1017 684Q1051 684 1051 673Q1051 668 1048 656T1045 643Q1041 637 1008 637Q968 636 957 634T939 623Q936 618 867 340T797 59Q797 55 798 54T805 50T822 48T855 46H886Q892 37 892 35Q892 19 885 5Q880 0 869 0Q864 0 828 1T736 2Q675 2 644 2T609 1Q592 1 592 11Q592 13 594 25Q598 41 602 43T625 46Q652 46 685 49Q699 52 704 61Q706 65 742 207T813 490T848 631L654 322Q458 10 453 5Q451 4 449 3Q444 0 433 0Q418 0 415 7Q413 11 374 317L335 624L267 354Q200 88 200 79Q206 46 272 46H282Q288 41 289 37T286 19Q282 3 278 1Q274 0 267 0Q265 0 255 0T221 1T157 2Q127 2 95 1T58 0Q43 0 39 2T35 11Q35 13 38 25T43 40Q45 46 65 46Q135 46 154 86Q158 92 223 354T289 629Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-22C6\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-4D\" x=\"707\" y=\"-213\"></use>\n</g>\n</svg> product ", "webprogram_exclude": "0", "session_ids": ["Session/17849"], "source_sha256": "414e44ecbf92da6fa113e7505c7268d80e7651b7a64394a1b24343a7fc852caf", "withdrawn": "", "abstract": "Multidimensional datasets are ubiquitous in applications throughout the sciences and engineering. At the heart of many computational algorithms are low-rank approximations. Many longstanding methods require the user to compress the data into a matrix which destroys any inherent multidimensional correlations. In addition, forming these approximations for very large datasets can be computationally challenging. In this talk, we address both of these issues by means of randomized tensor decompositions. In particular, we focus on the $\\star_M$ product and the associated $\\star_M$ singular value decomposition ($\\star_M$-SVD). We develop fixed-rank and energy-based sketching algorithms to produce low-rank approximations of the input tensors with properties similar to those of the $\\star_M$-SVD. We demonstrate the efficacy of our methods on both three- and four-", "id": "Paper/69017", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69017"}, {"title": " The Balanced Up-Down Walk ", "webprogram_exclude": "0", "session_ids": ["Session/18310"], "source_sha256": "dcd186c0e5546a017d876bf6fe90c27311298523ae335a443129dcc8c581e44d", "withdrawn": "", "abstract": "Markov chains based on spanning trees have been hugely influential in algorithms for assessing fairness in political redistricting. The input graph represents the geographic building blocks of a political jurisdiction. The goal is to output a large ensemble of random balanced graph partitions, often to understand a probability measure on partitions. ReCom and its variants -- the most widely-used class of Markov chains -- sample partitions by merging and splitting pairs of districts at a time. While these chains appear to run fast in practice, they can have trouble exploring the state space of all possible balanced partitions.\n\nWe propose a new Markov chain called the Balanced Up-Down (BUD) walk. The main idea is to run the Up-Down walk on the space of spanning trees, but require all steps to preserve the property that the tree is splittable into balanced subtrees. This chain generalizes the moves of two recently proposed Markov chains, the Cycle Walk and the Marked Edge Walk. We prove that the BUD walk is irreducible (meaning every possible tree is reachable) in several special cases. Notably, this includes a regime where ReCom suffers from locked configurations, from which there are no valid moves. We also explore algorithms and barriers to running the BUD walk efficiently, especially when parts are allowed to deviate from their ideal size within a certain tolerance. Finally, we empirically evaluate the usefulness of the BUD walk by comparing its performance to other existing methods for sampling partitions.", "id": "Paper/69018", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69018"}, {"title": " Temporal Structure of Cross-Model Agreement in Diffusion Models ", "webprogram_exclude": "0", "session_ids": ["Session/17705"], "source_sha256": "4f1db79cc8f1bd29f4b9ff35aa609f002633e1f1355d7c3c3d586108e3ae5121", "withdrawn": "", "abstract": "Independently trained diffusion models can exhibit substantial agreement: under deterministic DDIM sampling, they may produce nearly identical samples from the same initial noise, even when trained on disjoint data drawn from a common underlying distribution. We investigate when and how this agreement breaks down. By analyzing matched-noise trajectories through their joint geometry in data space, we find that trajectories often follow a common projected path during the early stages of denoising before separating and converging toward model-specific endpoints.\n\nTo characterize this temporal behavior, we introduce cross-model temporal injections, in which a partially denoised state from one model is transferred to the reverse process of another. These experiments measure when one learned reverse-time process can continue—or ``resume''—a trajectory produced by another. Later injections generally preserve more information about the source model’s eventual endpoint. When models are trained on disjoint subsets associated with different classes or modes of the data distribution, we observe a corresponding temporal crossover: early injections increasingly reflect the receiving model’s support, whereas later injections tend to retain the source model’s subset.\n\nThese results suggest that compatibility between independently learned diffusion processes is stage-dependent. Models may share substantial reverse-time geometry before their trajectories diverge, providing a temporal diagnostic of cross-model compatibility and raising the broader question of whether late-stage states already encode information about their eventual endpoints.", "id": "Paper/69019", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69019"}, {"title": " Parent Hamiltonians of Ergodic Matrix Product States ", "webprogram_exclude": "0", "session_ids": ["Session/18296"], "source_sha256": "d9665d2626ea458a01645f379000f1ba1ee1492be06dec77309c852453264eb3", "withdrawn": "", "abstract": "Matrix product states (MPS) capture many key physical attributes of quantum spin chains: translation-invariant MPS theory is in particular a very useful tool for understanding the gapped phases of one-dimensional quantum matter. In this talk, we discuss the theory of ergodic MPS (EMPS), which is an analogous theory of one-dimensional quantum matter for disordered (i.e., non-translation-invariant) systems. We describe a class of Hamiltonians---called parent Hamiltonians---which have EMPS as their ground states, and we give sufficient conditions for these parent Hamiltonians to have spectral gaps. We conclude with some open questions about EMPS.", "id": "Paper/69021", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69021"}, {"title": " Data-driven agent-based modeling of pattern formation in zebrafish ", "webprogram_exclude": "0", "session_ids": ["Session/18222"], "source_sha256": "bd1004065acdbcc04306258e886e4394c431a6d9de1fab5638bc3ef9f70d2891", "withdrawn": "", "abstract": "Pattern formation is present across the natural world, with examples including animal coats, plant tissue, and butterfly wings. Here I will focus on the example of pattern formation in zebrafish, which are named for their dark and light stripes. Mutant zebrafish, on the other hand, feature different skin patterns, including spots and labyrinth curves. All of these patterns form as the fish grow due to the interactions of tens of thousands of pigment cells. The longterm motivation for my work is to help identify the alterations to cell interactions that lead to mutant patterns. Toward this goal, I will overview how agent-based models can be used simulate pattern formation and make experimentally testable predictions. Because stochastic, microscopic models are not analytically tractable using traditional techniques, I will also describe how we are applying topological data analysis and Bayesian inference methods to quantify structure in messy, cell-based patterns and identify rules of behavior from data.", "id": "Paper/69022", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69022"}, {"title": " Gaps in the Most Frequent Sizes of Integer Sumsets ", "webprogram_exclude": "0", "session_ids": ["Session/17106"], "source_sha256": "a09bbe22cb1e9b882c63ece696c5f57e19f6b2c89baaa599a45a08895e08a151", "withdrawn": "", "abstract": "For a finite set of integers $A$, the $h$-fold sumset $hA$ is the set of all sums of $h$ elements of $A$, allowing repetition. Senger showed that, as $A$ ranges over four-element subsets of a sufficiently large interval, the $h$ most frequently occurring values of $|hA|$ are separated by consecutive triangular numbers, and conjectured similar patterns for larger sets. We prove this conjecture for every fixed $k \\ge 3$ and $h \\ge 2$. Specifically, we show that as $q \\rightarrow \\infty$, the most frequent values of $|hA|$ among $k$-element subsets $A \\subseteq \\{1,\\ldots,q\\}$, arranged in decreasing order, have consecutive gaps $\\binom{\\ell+k-2}{k-2}$ for $0 \\le \\ell < h$, and the largest possible sumset size is the most frequently occurring.", "id": "Paper/69024", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69024"}, {"title": " Splitting the Goldman-Turaev Lie bialgebra along a simple separating curve ", "webprogram_exclude": "0", "session_ids": ["Session/18287"], "source_sha256": "fe344df19882ab4be64c6bb1acdd60f55363dccec0cee760938f2b1ce9252426", "withdrawn": "", "abstract": "In this talk, I will introduce the notion of a double Lie bimodule, consisting of a Lie bialgebra $L$, a Lie $L$-bimodule $P$, and a double Lie bracket on $P$ satisfying suitable compatibility conditions. I will then describe an algebraic construction that combines two double Lie bimodules into a Lie bialgebra. As a geometric application, we prove a decomposition theorem for the Goldman–Turaev Lie bialgebra of an oriented surface in terms of the double Lie bimodules corresponding to the two surfaces with boundary obtained by cutting along a simple separating closed curve. This is joint work with Manuel Rivera.", "id": "Paper/69025", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69025"}, {"title": " Parameter-Free Regularization Preconditioners for Nearly Incompressible Poroelasticity with an Application to Spinal Cord Modeling ", "webprogram_exclude": "0", "session_ids": ["Session/17962"], "source_sha256": "a35bcb683a88bd73261263f5f975d306c0bcf0cb31e798b72629bb6187190375", "withdrawn": "", "abstract": "Poroelasticity provides a framework for coupling the deformation of biological tissues with fluid flow. For nearly incompressible tissues, however, a large Lamé parameter can cause locking and produce nearly singular saddle-point systems. In this talk, we present a parameter-free regularization and block-preconditioning approach for these systems. We first reformulate the original problem as an equivalent three-field system and then introduce a regularization based on identities inherent in the formulation, without altering the solution. Based on the resulting regularized system, we construct block Schur complement preconditioners that are straightforward to implement. We establish convergence estimates for preconditioned MINRES and GMRES that are robust with respect to the physical parameters and mesh size. Numerical experiments in two and three dimensions confirm the theoretical results, and a spinal cord simulation demonstrates the potential of the proposed approach for large-scale computational studies in biomechanics.", "id": "Paper/69026", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69026"}, {"title": " Dimension reduction for incompressible Stokes flow in thin channels ", "webprogram_exclude": "0", "session_ids": ["Session/17757"], "source_sha256": "be619029bcafc78bbf693d75adb6029fc27349cfdc2b0d8c9ac47d0be53dce25", "withdrawn": "", "abstract": "We study the thin-domain limit of the stationary incompressible Stokes system. After rescaling a channel of vanishing thickness to a fixed reference domain, the Stokes energy becomes anisotropic and the divergence-free constraint degenerates with the thickness parameter. This creates a dimension-reduction problem in which the limiting velocity retains a nontrivial transverse profile despite the collapse of the domain.\n\nI will present a variational analysis of this singular limit, focusing on compactness, the role of incompressibility, and the passage of boundary data to the limit. The reduced velocity can be expressed in terms of a pressure gradient, while conservation of mass determines the pressure through an effective lower-dimensional equation. The resulting equation is precisely the Reynolds equation from lubrication theory. This provides a variational derivation of the classical lubrication approximation.", "id": "Paper/69027", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69027"}, {"title": " Local topological order and boundary algebras for condensation in Levin-Wen systems ", "webprogram_exclude": "0", "session_ids": ["Session/18383"], "source_sha256": "edab1841882e830ca57bb956b17972204ba40987ab29ff2934d4f74f2dbdf52a", "withdrawn": "", "abstract": "Lattice models are discrete mathematical depictions of physical systems. In particular, the Levin-Wen model is constructed using a unitary fusion category $\\mathcal{C}$. Each vertex of the lattice is assigned a Hilbert space built from $\\mathcal{C}$, and observables supported in a finite region form a C*-algebra. There is a similar lattice model for anyon condensation in Levin-Wen systems given by Christian-Green-Huston-Penneys. In this talk, we will explain how this model satisfies the local topological order axioms. When a model satisfies these axioms, the resulting net of boundary C*-algebras give a powerful tool to rigorously analyze the entire system and have a natural interpretation in quantum error correction. I will then identify the resulting boundary C*-algebra of this model as an “$A$-augmented” fusion spin chain, where $A$ is a condensable algebra in the Drinfeld center of $\\mathcal{C}$. This work is joint with Julia Circele, Jiaqi Lu, David Penneys, and Greyson Wesley.", "id": "Paper/69028", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69028"}, {"title": " Stack Sorting and SAT Solving: Searching for Short Unsortables ", "webprogram_exclude": "0", "session_ids": ["Session/17943"], "source_sha256": "277f8a03e28b1c26ffd696aa81cfee7272b8a5d2f69a2e42541a3fc26204dae5", "withdrawn": "", "abstract": "A stack is a sorting machine that rearranges a permutation using last-in, first-out push/pop operations. A permutation of length $n$ is called stack-sortable if a stack can rearrange it to the identity permutation $123\\ldots{}n$. Knuth proved in \\emph{The Art of Computer Programming, Vol. 1} that a permutation is stack-sortable if and only if its entries avoid the pattern $231$.\n\nA permutation is called $k$-stack-sortable if it can be rearranged to the identity by $k$ stacks arranged in series, i.e., such that the output of each stack feeds into the input of the next. A few things are known about 2-stack-sortability: the shortest non-2-stack-sortable permutations have length 7, and 2-stack-sortability can be tested in polynomial time. However, the enumeration of 2-stack-sortable permutations is known only up to length 19.\n\nEven less is known about 3-stack-sortability! Previous work shows that the length of the shortest non-3-stack-sortable permutation is at least 14 and at most 38. In joint work with Vince Vatter, we show that every permutation of length at most 16 is 3-stack-sortable and exhibit a permutation of length 21 that is not, shrinking the set of possible lengths of the shortest non-3-stack-sortable permutation to $\\{17, 18, 19, 20, 21\\}$. We discuss how to formulate $k$-stack-sortability as a Boolean satisfiability problem---allowing us to test whether individual permutations are $k$-stack-sortable---and describe how to use this to search for an unsortable needle in a sortable haystack.", "id": "Paper/69031", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69031"}, {"title": " Student-included research at a PUI and the analysis of unfair tRNG distributions ", "webprogram_exclude": "0", "session_ids": ["Session/18256"], "source_sha256": "51cd0e71be73d7b09ed608df9aeb35639b6723a69c144faa2b0fd834ce3cab7c", "withdrawn": "", "abstract": "Research in analysis at a Primarily Undergraduate Institution (PUI) presents unique challenges. You may be the only faculty specialized in your sub-area and the problems you work on may be inaccessible to most students. In this talk, I discuss methods I've used to maintain an active research program, while also having opportunities to include students---all with varying degrees of success. In part, this talk will highlight a particular student researcher of mine that hadn't even taken Real Analysis at the time of the project. He worked on a carefully curated facet of a personal research project of mine that investigated the analytic properties of distributions associated with (unfair) true-Random Number Generators. I will share details on how this facet was identified, how the mentor/mentee relationship unfolded, and how my expectations changed over time, as well as the successes and challenges of the overall endeavor.", "id": "Paper/69034", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69034"}, {"title": " Persistence of certain conic singularities for minimal subvarieties of higher codimension ", "webprogram_exclude": "0", "session_ids": ["Session/17871"], "source_sha256": "8037ceee8018c3f8f7b53dbb24a4e10031f93da3cb41086b4793b05f6b2a5d3e", "withdrawn": "", "abstract": "Singularities naturally arise in geometric variational problems such as the theory of minimal submanifolds, and their local geometry is often modeled by minimal cones. In this talk, I will discuss persistence results for singularities of higher-codimension minimal subvarieties whose tangent cones have vanishing effective Morse index and effective nullity. I will also present a stronger persistence result for a class of minimal cones that includes all currently known examples with effective Morse index zero.\nPart of this talk is based on joint work with Alessandro Carlotto and Yangyang Li.", "id": "Paper/69035", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69035"}, {"title": " Improved Poly-Log Diameter Bounds for <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"8.218ex\" height=\"3.009ex\" style=\"vertical-align: -1.005ex;\" viewBox=\"0 -863.1 3538.4 1295.7\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathrm {SL}_{2}(\\mathbb {Z}_{p})</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-53\" d=\"M55 507Q55 590 112 647T243 704H257Q342 704 405 641L426 672Q431 679 436 687T446 700L449 704Q450 704 453 704T459 705H463Q466 705 472 699V462L466 456H448Q437 456 435 459T430 479Q413 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x=\"943\" y=\"-213\"></use>\n</g>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"3148\" y=\"0\"></use>\n</g>\n</svg> via Higher Commutators ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "7a58d28fec544b2e04c0754fda0e02f42daf62cc3584141fa71479641d0043d3", "withdrawn": "", "abstract": "The Solovay-Kitaev algorithm (see Dawson and Nielsen) gives a poly-log bound $\\mathcal{O}(\\log^{\\alpha}(1/\\epsilon))$ for approximating quantum gates in $\\mathrm{SU}(2)$ and $\\mathrm{SU}(d)$ with exponent $\\alpha<4$. Dinai extended this result to $\\text{SL}_{2}(\\mathbb{Z}_p)$ with identical exponent. Here, we introduce $p$-adic analogues of techniques on Elkasapy words from Kuperberg to $\\text{SL}_{2}(\\mathbb{Z}_{p})$, improving the poly-log diameter bound from Dinai to exponent $\\alpha > \\log_{\\phi}(2) \\approx 1.44042\\ldots$ arbitrarily close.", "id": "Paper/69036", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69036"}, {"title": " The Structure of Permutations Corresponding to the Hopf Link and Trefoil Knot. ", "webprogram_exclude": "0", "session_ids": ["Session/18385"], "source_sha256": "01168494edb9c36fc9bcffbb60d21a697cb3594dfaea7909f8b1ed3ef7f13b2c", "withdrawn": "", "abstract": "A standard way to represent knots or links is using a grid diagram. These grid diagrams resemble cycle diagrams of permutations. Previous work has classified permutations that correspond to unknots (or unlinks). Here, we study permutations whose cycle diagrams correspond to Hopf links and trefoil knots. We show how to reduce to the case of permutations that are derangement's (i.e., $\\sigma(i) \\neq i$ for all $i$) and have no entries on the off-diagonal (that is, $|\\sigma(i) - i| \\neq 1$ for all $i$, with $\\sigma(1) \\neq n$ and $\\sigma(n) \\neq 1$). Using ideas inspired by Seifert’s algorithm in topology---which constructs the boundary of a connected, oriented surface by smoothing crossings and joining the resulting loops with bands --- we develop a method to characterize all permutations associated with a Hopf link.", "id": "Paper/69037", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69037"}, {"title": " Agent-based, vertex-based, and continuum modeling of cell behavior in biological patterns ", "webprogram_exclude": "0", "session_ids": ["Session/18244"], "source_sha256": "18274e71c0d665a707b05bd00c16d2abb2c56df1f06c37dca46865deb210e2b9", "withdrawn": "", "abstract": "Many natural and social phenomena involve individual agents coming together to create group dynamics, whether the agents are drivers in a traffic jam, cells in a developing tissue, or locusts in a swarm. Different modeling approaches provide complementary insights into complex systems and face different challenges. For example, in the case of cellular patterns, vertex-based models describe cell shape, while more efficient agent-based models treat cells as particles. In both cases, it can be challenging to broadly characterize the behavior of these detailed models or address questions about model uniqueness—even quantitatively judging messy, agent-based patterns is not straightforward. Continuum models, which track the evolution of cell densities, are more amenable to analysis, but it is often difficult to relate their few parameters to specific cell interactions. In this talk, I will discuss our work combining inference, equation learning, and other approaches to more broadly characterize pattern systems and the relationship between different models of cell behavior.", "id": "Paper/69038", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69038"}, {"title": " Cases in Coordinated Calculus: Lessons Learned from Recitation Coordination and Generated Exams ", "webprogram_exclude": "0", "session_ids": ["Session/17971"], "source_sha256": "acffaa664704c3d91c296e5df83ba7ac742bdae269685e45025d3577ea9f5a51", "withdrawn": "", "abstract": "Course Coordination in first year calculus courses has a long history at the University of New Hampshire.  Faculty instructors develop a common syllabus, homework, quizzes, and exams. The team of faculty instructors, graduate teaching assistants (GTA) and learning assistants (LA) meet weekly to discuss course content and upcoming events. For the past five years, the implementation of learning assistants partially supported by an NSF-funded grant (NSF IUSE Award No. 2013427) has enhanced the coordination and learning experience for the students.  During this session, we describe the structure of our coordination and lessons learned in recent years.  We focus on two areas: recitation structure and common exam writing strategies. Our recitations are active learning-focused and run by a team of graduate teaching assistants (GTA) and undergraduate learning assistants (LA) and coordinated by the lecture instructor(s).  We will present results from student, GTA, and LA feedback surveys: what works well, what the challenges are, and recommendations for future teams. Exams are generated using instructor-written code that allows for practice and make-up exams to be generated on demand, reducing the load of exam writing for large, coordinated classes. We will discuss the lessons learned from several semesters of this exam structure.", "id": "Paper/69040", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69040"}, {"title": " Quantum (Hierarchical) Local Recovery ", "webprogram_exclude": "0", "session_ids": ["Session/18387"], "source_sha256": "eb39ab996e2083b4e12a7d1f0ff726e12b2c2faef498019275879c15e67cf54f", "withdrawn": "", "abstract": "Classical (hierarchical) locally recoverable codes (for erasure recovery) were developed for efficient data storage. Furthermore, erasure recovery has been demonstrated to be more efficient than error-correction. In recent years, their quantum counterparts are widely studied in the hope of developing quantum memories. This talk primarily focuses on locality in the quantum setting. The first half is devoted to CSS-type constructions: random as well as explicit, and a Singleton-like bound.\n\nThe second half turns to the entanglement-assisted setting, in which the two communicating parties share pre-established qudits, and addresses the notion of availability for quantum codes: several distinct sets of nodes capable of recovering the same failure. Defining availability is challenging for CSS-type codes, due to the dual-containment restriction; lifting this requirement in the entanglement-assisted setting permits far more flexible constructions. Here too the talk presents random and explicit constructions, along with a Singleton-like bound.", "id": "Paper/69043", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69043"}, {"title": " Cards on the Table: Connecting Linear Algebra Concepts Through Play ", "webprogram_exclude": "0", "session_ids": ["Session/17855"], "source_sha256": "25cc48247558d861bec5610a0462c7922675146ff027513265196f298fd14121", "withdrawn": "", "abstract": "Linear algebra is a dense web of interconnected ideas, yet students often learn these ideas as separate definitions, theorems, and procedures. For example, understanding why “if a matrix is non-invertible, then it has a zero eigenvalue” requires students to connect several concepts rather than apply a single procedure. We developed the Linear Algebra Card Game to make this web of connections emerge naturally through play. In small groups, students place cards representing linear algebra concepts, examples, and theorems in a shared grid and explain the mathematical relationships between them. Their peers then question, challenge, and ultimately judge these explanations. The game thereby shifts attention from performing procedures toward explaining and connecting mathematical ideas.\n\n\nIn this interactive talk, we will introduce the design and educational rationale of the game and invite participants to experience it themselves through a short round of play. We will share observations and student feedback from initial classroom pilots, illustrated with preliminary footage of students playing the game. Finally, we will discuss an ongoing mixed-methods Scholarship of Teaching and Learning study investigating whether the game supports students’ relational understanding, which learning processes emerge during gameplay, and how these relate to specific game mechanics.\n\n\nThe game is available as an open educational resource, alongside a professionally produced version, allowing educators to freely access, use, and adapt the materials. The session combines hands-on play with a research perspective on using game-based learning to foster conceptual discussion and relational understanding in linear algebra.", "id": "Paper/69045", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69045"}, {"title": " A microlocal sheaf-theoretic investigation of immersed Lagrangian fillings ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "d987681038b0360231e2c2c80efefd33e20028d2a31b2a8b1376ab35804b48e5", "withdrawn": "", "abstract": "We exhibit a family of immersed exact Lagrangian fillings of Legendrian $T(2, n)$ torus knots in $\\mathbb{R}^3$,\npairwise distinct up to Hamiltonian isotopy rel boundary, each of which has a single transverse action-0\ndouble point. These fillings are constructed as Lagrangian projections of certain Legendrian weaves,\nwhich are in turn parametrized by combinatorial objects we call pinched triangulations. We show that\nthese fillings are distinct with invariants derived from microlocal sheaf theory which are particularly\nstraightforward to compute for weave fillings.\nFinally, we interpret the above results in light of the cluster-algebraic correspondence between embedded exact Lagrangian fillings and toric charts, motivating a conjecture that the family of fillings we describe exhausts all exact Lagrangian fillings with a single action-0 double point.", "id": "Paper/69046", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69046"}, {"title": " Stability of Geometric Flows \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/17691"], "source_sha256": "172a36c50ceecd078f974b6b715ad9da1a92192512c933f91ba595c08d90e49d", "withdrawn": "", "abstract": "There are many notions of stability for geometric flows, and various techniques available to study them. We give a brief overview of these ideas and present new results for the Ricci flow on 4-dimensional spaces with bounded geometry.", "id": "Paper/69048", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69048"}, {"title": " How does nonnormality affect the convergence of Infinite GMRES? ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "7eb09bc00392d7646a59cdfe57a2843c3d4b87acdb0e4eff9e2691dd89036726", "withdrawn": "", "abstract": "Many applications require the solution of large-scale linear systems that have nonlinear parameter dependence. The Infinite GMRES algorithm, developed by Jarlebring and Correnty in 2022, converts these finite-dimensional systems into infinite-dimensional systems with linear parameter dependence. This transformation involves a linearization process that results in a system with a special companion-like structure. Due to the shift-invariance property of Krylov subspaces, all choices of parameter give the same Krylov subspaces. Thus performing the Arnoldi process for one parameter enables the efficient construction of the GMRES iterates for all parameter values. The special structure of the right-hand-side vector of the infinite-dimensional system allows this Arnoldi process to be executed with finite-dimensional vectors, where the dimension grows with every iteration. As such, Infinite GMRES uses finite-length Krylov basis vectors to solve an infinite-dimensional system. The special structure of the infinite-dimensional system invites further investigation into the convergence behavior of the Infinite GMRES residual norm. We aim to understand how various components of this system, including the size and nature of the block matrices, the number of blocks, and the choice of parameter value influence convergence behavior. In this presentation, we will discuss preliminary convergence results based on various tools of analysis, including the numerical range.", "id": "Paper/69049", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69049"}, {"title": " Dynamically-Informed Time-to-Collision: Regularity of the Hitting-Time Map and Provable Learning of the HJB Solution ", "webprogram_exclude": "0", "session_ids": ["Session/18280"], "source_sha256": "08384a4c2b22fb677617cca145409276b5462a607dcd2f5bbd9e4e0d8f04afa2", "withdrawn": "", "abstract": "Time-to-collision (TTC) is the standard surrogate safety measure in\nmicroscopic traffic modelling, and it is almost universally computed\nkinematically. When TTC is used as part of controller, this presumption contradicts the very dynamics the controller implements. We consider instead a \\emph{dynamically-informed} TTC, defined as the hitting time of the collision set under the model's own prediction flow, an optimal-velocity (OVM) system with measurable ($L^\\infty$) leader acceleration. This makes the collision estimate consistent with the dynamics, but introduces a circularity. Well-posedness of the closed loop then requires the map to be regular enough to serve as a coefficient, which is not automatic due to discontinuity and lack of Lipschitzness.\n\nThe first half of the talk establishes that regularity. On the domain of initial data whose trajectories meet the collision boundary \\emph{transversally}, we prove that TTC-map is locally Lipschitz, and in fact $C^1$. Two features drive the analysis. First, all estimates\nare built from a single uniform transversality margin on compact subsets. Second, generality of forces invokes that arguments are instead organized around \\emph{integrated} quantities, and differentiation along characteristics is replaced by a measure-theoretic argument showing that the set where the chain rule fails is Lebesgue-null.\n\nThe second half reinterprets TTC-map as the value function of a minimum-time problem and learns it. The dynamic programming principle\nyields a first-order HJB equation. We prove a two-sided convergence result for a\nphysics-informed formulation; the $L^2$ error of the learned value function is controlled by the square root of the total loss, via a co-area argument on the endpoint map (requiring a positive lower bound on its $2$-Jacobian) together with a change-of-variables estimate along the flow. At zero residual the conclusion sharpens to exact pointwise identification with the viscosity solution, and the $C^1$ regularity\nestablished earlier is precisely what makes this attainable in the smooth class. We close with a two-stage architecture for delay-free\ntrajectory prediction and platoon simulations showing disturbance attenuation under the learned controller.", "id": "Paper/69050", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69050"}, {"title": " Thin obstacle-type problems for the Bilaplacian ", "webprogram_exclude": "0", "session_ids": ["Session/18050"], "source_sha256": "14bd8fa4d3dc52fe2493c76e06a21ab9bb2a41404547e58260f8f8e445fbba26", "withdrawn": "", "abstract": "In this talk, we consider a class of obstacle-type problems involving a fourth-order elliptic operator. The possibly singular or degenerate operators we study arise naturally from extension procedures for higher-order fractional powers of the Laplacian and include two-phase boundary obstacle problems as a special case. After establishing well-posedness, we reformulate the problem as a coupled system of two second-order equations, featuring a possibly nonlinear and non-differentiable Neumann boundary coupling. We then discuss regularity properties of solutions and investigate the structure of the associated free boundary.", "id": "Paper/69052", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69052"}, {"title": " Regularity of Solutions of Lorentzian Optimal Transport. ", "webprogram_exclude": "0", "session_ids": ["Session/18331"], "source_sha256": "1b4f7bff96fdca96659213458a8a9aeff087b5cd79faf1ab7d07b6bd9cec0b7a", "withdrawn": "", "abstract": "Consider Lorentzian optimal transport, where the primal problem is to maximize the fractional time-separation cost $\\ell(x,y)^p$, with $p\\in (0,1)$. The Lorentz distance $\\ell(x,y)$ measures the maximum amount a particle can age while travelling from $x$ to $y$, so the optimal map maximizes expected fractional proper time between chronological source and target events. We study regularity of this map using the Ma-Trudinger-Wang framework.\n\n\nThe natural place to begin is flat Minkowski spacetime. Surprisingly, the Lorentzian MTW condition fails there, and smooth positive data can produce discontinuous optimal maps even when source and target events are uniformly timelike separated. This is in sharp contrast with the flat $\\mathbb{R}^n$ theory, where regularity of the quadratic cost is well established and the MTW tensor vanishes identically, showing that Lorentzian regularity is fundamentally different from its Riemannian counterpart.\n\n\n\nThis negative result leads naturally to the question of whether curvature can restore the favourable MTW sign.  We compute the MTW tensor on the Lorentzian model spacetimes. Minkowski and de Sitter remain unfavourable, while in anti-de Sitter space, at sufficiently long proper-time scales, timelike curvature focusing becomes strong enough to produce the favourable MTW sign. In this setting, we recover the MTW regularity theory.", "id": "Paper/69054", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69054"}, {"title": " Topology of Combinatorial Flag Varieties ", "webprogram_exclude": "0", "session_ids": ["Session/19321"], "source_sha256": "d6e1767dbaa8846f91738205ebf377ae9735ee31419c1b9a3466b7ebfdbd78e8", "withdrawn": "", "abstract": "We study the combinatorial flag varieties of type A defined by Borovik, Gelfand, and White, i.e., the order complex $\\Omega_n$ of the poset $\\mathbf{Q}(U_{n,n})$ of matroid quotients. We construct explicit embeddings from the lattice of flats of the Dilworth truncations $D_j(U_{n,n})$ into the critical faces of $\\Omega_n$. This categorifies and improves the lower bound of the Betti number $\\dim H_{n-2}(\\Omega_n)$ given by Borovik, Gelfand, and White. Furthermore, for finite projective geometries, we compute the character of the natural $\\mathrm{PGL}(3,q)$-action on $H_1(Q(\\mathrm{PG}(2,q)))$, yielding $\\dim H_1(Q(\\mathrm{PG}(2,q)))=(1+q+q^2)^2$. Using non-principal modular cuts in $\\mathrm{PG}(3,q)$, we derive a lower bound for $\\dim H_2(Q(\\mathrm{PG}(3,q)))$ and we prove a super-polynomial growth of $\\dim H_{r-2}(Q(PG(r-1,q)))$ with respect to $q$.", "id": "Paper/69056", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69056"}, {"title": " Nonlocal Biharmonic Operators with Clamped Boundary Conditions ", "webprogram_exclude": "0", "session_ids": ["Session/17883"], "source_sha256": "f560d4cc4f767d23370c77890f05c03ccd9ece11425e3802d767a2e3f512d016", "withdrawn": "", "abstract": "Nonlocal operators are utilized in modeling problems because of their capability of handling discontinuities and modeling a range of interactions through different choices for kernels. This includes several applications including  peridynamics, swarming behavior, and image processing. The biharmonic operator appears in many models, notably in the deformations of beams and plates. We consider two different ways of formulating a nonlocal biharmonic operator: using a fourth difference operator in the integrand or iterating the nonlocal Laplacian. In this talk, we compare and contrast various facets of these operators, including the two associated nonlocal clamped boundary value problems.", "id": "Paper/69059", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69059"}, {"title": " Classification of boundary and interface topological insulators ", "webprogram_exclude": "0", "session_ids": ["Session/18443"], "source_sha256": "50b49dd9dc2b8eb962ee9fe1dfe10c349f22b2208de8bd3a4a087a65fe1a45cd", "withdrawn": "", "abstract": "A surprising edge transport, displaying strong robustness to perturbations as an obstruction to Anderson localization, is guaranteed along interfaces separating two-dimensional insulators in different topological phases. We consider the related setting of insulators on a half space domain augmented with arbitrary boundary conditions generating self-adjoint realizations. We describe the moduli space of such terminations and describe a method to compute the asymmetry by means of a Maslov index, a form of bulk-edge correspondence allowing one to compute the invariant by linear algebra techniques.", "id": "Paper/69061", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69061"}, {"title": " Trace formula for billiard flow on 2D manifolds with concave boundary ", "webprogram_exclude": "0", "session_ids": ["Session/17999"], "source_sha256": "7ed9a37c924ede8d193ff25f41bf8623604666aa74618584a2e58c6f4fb65c64", "withdrawn": "", "abstract": "We study grazing closed trajectories of the billiard flow $\\varphi^t$ on a compact manifold $(\\Sigma,g)$ with concave boundary. Under a non-degeneracy condition, which is satisfied for example when $(\\Sigma,g)$ has dimension $n=2$ and negative sectional curvature, we compute the trace of a regularized pullback $E_{\\epsilon}(\\varphi^t)^* E_{\\epsilon}$ near a closed trajectory grazing once, thus proving an analogue of the Atiyah--Bott--Guillemin trace formula for closed billiard trajectories grazing once.", "id": "Paper/69062", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69062"}, {"title": " Long-term erosion of stability in a diverse marine planktonic community ", "webprogram_exclude": "0", "session_ids": ["Session/18023"], "source_sha256": "38765612d8d133035694c386a3bf5450c41abc86b4fc8ea9ddae8b69cddfb9b5", "withdrawn": "", "abstract": "The Northeast U.S. Shelf (NES) generates substantial economic value primarily through its fisheries and the broader coastal economy they support. Beyond fisheries, the ecosystem provides climate regulation, nutrient cycling, and habitat for culturally and ecologically important species. All of these ecosystem services depend on an extremely diverse and productive plankton community, whose energy and biomass are transferred through grazing to higher trophic levels (e.g., fish, birds, and mammals). That plankton community is seemingly stable and resilient, sustaining a seasonal rhythm of population cycles over centuries. Industries rely on that regularity.\n\nBut the times, they are a changin'. Coastal environments are increasingly subject to climate-related stressors including ocean acidification, marine heatwaves, rising seas, as well as stronger, more frequent storms. Could rising temperatures also be changing the way that the NES ecosystem responds to perturbations, that is, changing the ecosystem's stability?  \n\nTo address this question, we combined a 20-year plankton time series from the NES of unprecedented taxonomic and temporal resolution with recent extensions of stability theory and statistical methods to quantify time-varying community interactions and stability. To measure stability, we harnessed theoretical developments that enabled us to quantify stability metrics for nonequilibrium population dynamics, such as nonstationary seasonal cycles. To estimate interactions, we integrated different statistical tools to deal with the high taxonomic diversity (i.e., 30 or more planktonic taxa), high sampling frequency (i.e., sub-hourly observations), state dependent interactions, and nonstationary environmental conditions present in our data set. Notably, we uncovered a gradual increase in population variability and in interaction strengths associated with a decrease in stability over the 20-year period. Such loss of stability and increase in population variability have the potential to interact with climate stress and alter the function of the economically important food web at the NES.", "id": "Paper/69063", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69063"}, {"title": " Parameter identifiability of linear-compartmental mammillary models ", "webprogram_exclude": "0", "session_ids": ["Session/18127"], "source_sha256": "45bbd57f49455b97c7701de559b8fed36227e2304dd8f765008f56a7e7fc064a", "withdrawn": "", "abstract": "This talk addresses the problem of parameter identifiability – that is, the question of whether parameters can be recovered from data – for linear compartmental models.  For a class of linear compartmental models with one input and one output, namely, those for which the underlying graph is a bidirected tree, Bortner {\\em et al.}, in 2023, completely characterized which such models are structurally identifiability, which means that every parameter is generically locally identifiable.  In this talk, we delve deeper, by examining which individual parameters are locally versus globally identifiable. Specifically, we analyze mammillary models, which means that the underlying graph is a bidirected star (the model consists of a central compartment that is connected to all other compartments).  For these models, which fall into five infinite families, we determine which individual parameters are locally versus globally identifiable, and we give formulas for some of the globally identifiable parameters in terms of the coefficients of input-output equations.  Our proofs rely on a combinatorial formula due to Bortner {\\em et al.}\\ for these coefficients.", "id": "Paper/69067", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69067"}, {"title": " Graphs in the LATTICE ", "webprogram_exclude": "0", "session_ids": ["Session/18095"], "source_sha256": "be7eadd65186d111c2c8480b323d2f81899788daac03cd74c5afe3ffb438b139", "withdrawn": "", "abstract": "During the Summer 2026 LATTICE program, we made progress on three problems related to spatial graphs. We will summarize this progress.", "id": "Paper/69071", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69071"}, {"title": " Approximation Theory for Measure-to-Measure Operator Learning ", "webprogram_exclude": "0", "session_ids": ["Session/17919"], "source_sha256": "9b15f7c3f85c29ae8893efdce0fc2b060b03e1bcf1ff1b9c96223d7fe7a59523", "withdrawn": "", "abstract": "Many problems in data science and scientific machine learning are naturally formulated as operator learning problems between spaces of probability measures. Popular architectures for such problems, including transformers, approximate a given operator by a pushforward along a map which may itself depend on the input measure. This talk investigates whether such pushforward operators can universally approximate arbitrary continuous measure-to-measure operators. We first present a negative result which shows that pushforward operators cannot universally approximate operators between spaces of empirical measures. We then present a structural condition on a compact set $K$ of probability measures which is sufficient for pushforward to universally approximate continuous measure-to-measure operators defined on $K$. Notably, our structural condition includes non-absolutely continuous measures, making our theory compatible with the manifold hypothesis in machine learning. This is joint work with Takashi Furuya and Nicholas Nelsen.", "id": "Paper/69072", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69072"}, {"title": " Conjugacy classes and Hochschild cohomology of the <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"6.033ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 2597.5 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">Qd(p)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-51\" d=\"M399 -80Q399 -47 400 -30T402 -11V-7L387 -11Q341 -22 303 -22Q208 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435Q740 255 592 107Q529 47 461 16L444 8V3Q444 2 449 -24T470 -66T516 -82Q551 -82 583 -60T625 -3Q631 11 638 11Q647 11 649 2Q649 -6 639 -34T611 -100T557 -165T481 -194Q399 -194 399 -87V-80ZM636 468Q636 523 621 564T580 625T530 655T477 665Q429 665 379 640Q277 591 215 464T153 216Q153 110 207 59Q231 38 236 38V46Q236 86 269 120T347 155Q372 155 390 144T417 114T429 82T435 55L448 64Q512 108 557 185T619 334T636 468ZM314 18Q362 18 404 39L403 49Q399 104 366 115Q354 117 347 117Q344 117 341 117T337 118Q317 118 296 98T274 52Q274 18 314 18Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-64\" d=\"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-70\" d=\"M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-51\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-64\" x=\"791\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"1315\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-70\" x=\"1704\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"2208\" y=\"0\"></use>\n</g>\n</svg> groups ", "webprogram_exclude": "0", "session_ids": ["Session/19362"], "source_sha256": "a1310c30a6e0ede682e99cfc7851abee86043e7b5618dc45ddce9db61b1bca9e", "withdrawn": "", "abstract": "The group $Qd(p)=(\\mathbb{Z}_p \\times \\mathbb{Z}_p) \\rtimes SL(2,p)$ is a classic example in finite group theory and modular representation theory. In this talk, we describe a classification of the conjugacy classes of $\\mathrm{Qd}(p)$ and use this classification to determine their centralizer subgroups. These centralizers can be used for understanding the Hochschild cohomology of the group algebra $\\mathbb{F}_p[Qd(p)]$. We will describe our approach and discuss our progress in determining the dimensions of these cohomology groups. This joint work will be presented by Colin Lawson and Jane Long, both of Stephen F. Austin State University.", "id": "Paper/69073", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69073"}, {"title": " Regularizing the MHD variational principle ", "webprogram_exclude": "0", "session_ids": ["Session/18104"], "source_sha256": "b5100b8071f6ac0de68852f5665a6ac889df9699c436ed23efc0a7e5c12d038d", "withdrawn": "", "abstract": "Magnetic confinement concepts for fusion energy, including the tokamak and stellarator, depend on equilibrium solutions of the magnetohydrodynamic (MHD) equations with nested magnetic surfaces. However, in 1967, H. Grad conjectured that smooth solutions must have axial, helical, or plane-reflection symmetry. This poses a problem for the non-axisymmetric stellarator concept, as existence and regularity of the magnetic field is required for most stellarator theory and computations. In this talk, we will discuss how the equilibrium variational principle can be amended to include an averaged force from magnetic fluctuations, allowing for an existence theory of steady-state solutions. We demonstrate this through a novel numerical solver for the stellarator equilibrium problem with convergent force-balance both with and without nested surfaces.", "id": "Paper/69077", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69077"}, {"title": " Crosscap Bounds on Arborescent Links ", "webprogram_exclude": "0", "session_ids": ["Session/17998"], "source_sha256": "66c464294cb1140c36b827e54f4e6378fd9e35fbdeaadd0151db1ad9bfa7597b", "withdrawn": "", "abstract": "The crosscap number is the non-orientable analog of the knot genus, measuring the minimal complexity across all non-orientable spanning surfaces for a given knot or link. For several families of knots, the crosscap number is known exactly or bounded effectively. We extend this work by considering arborescent links, links built by plumbing twist bands according to a tree, and investigate how the structure of the tree constrains the crosscap number of an arborescent link.", "id": "Paper/69078", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69078"}, {"title": " Subconvexity of Short <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.211ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 521.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">k</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-6B\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Free Exponential Sums ", "webprogram_exclude": "0", "session_ids": ["Session/19367"], "source_sha256": "29dff6fae5a9dd9833249aadce08339e1186f95f69480aa59be98082eef39989", "withdrawn": "", "abstract": "Let $S_k(\\alpha;K)$ denote the exponential sum over $k$-free integers in the short interval $(N-K,N]$. For $s>0$, we prove essentially tight bounds on the $s$-th moments of $S_k(\\alpha;K)$ whenever $K \\gg N^{\\theta_{k,s}+\\epsilon}$ for some $\\theta_{k,s}<1/2$, generalizing and strengthening results of Sun and Keil. As an immediate consequence, we obtain a lower bound for the $L^1$-mean of the M\\\"obius-twisted exponential sum over short intervals of length at least $N^{0.49685}$.", "id": "Paper/69079", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69079"}, {"title": " Quantifying the Geographic Contribution of Cardiovascular Health to Cardiovascular Disease: A Bayesian Spatial Modeling Approach ", "webprogram_exclude": "0", "session_ids": ["Session/18095"], "source_sha256": "55702f889645c1a64333cdab2ae0b381eadbf68ae6f8313a6081ab66cb55d5d8", "withdrawn": "", "abstract": "Despite recent declines in US cardiovascular disease (CVD) mortality, considerable geographic disparities persist. Quantifying how much cardiovascular health (CVH) explains these disparities requires statistical methods that account for spatial dependence. We used the American Heart Association’s Life’s Essential 8 (LE8) framework to build a county-level CVH score and used a Bayesian spatial framework to model its contributions to geographic variation in CVD outcomes across three states representing different cardiovascular risk profiles: Georgia (159 counties, in the Stroke Belt); Texas (254 counties, Stroke Belt-adjacent); and California (58 counties, not in the Stroke Belt).\n\nUsing CDC PLACES data, the county-level LE8 (cLE8) score comprised eight CVD risk factors. Within each state, measures were decile-ranked and scored from 10 to 100, then averaged into an unweighted composite score, reflecting each county’s CVH relative to its state. Geographic patterning of cLE8 was evaluated using choropleth maps and global Moran’s I statistics.\n\nWe examined four outcomes: CVD and all-cause mortality, and stroke and coronary heart disease prevalence, via Poisson (mortality) and Gaussian (prevalence) models. For each outcome, age-adjusted models were compared to models including a cLE8 fixed effect, using non-spatial, intrinsic conditional autoregressive and Besag-York-Mollié correlation structures. The last partitions random-effect variance into spatial and non-spatial components, allowing estimation of the proportion of residual variation attributable to spatial dependence.\n\nModels were fit via Integrated Nested Laplace Approximation in R and compared using deviance information criterion and other fit statistics. We compared county-level random-effect variance components with and without cLE8, calculating percent change in residual variance, and mapping before and after adjustment to identify changes in residual spatial heterogeneity. cLE8 showed spatial patterning and was linked to more favorable outcomes, with variation by state and outcome. \n\nOur state-relative CVH score offers an efficient way to separate measured CVH effects from residual spatial variation, distinguishing explained disparities from persistent unexplained heterogeneity, thus informing targeted CVD prevention.", "id": "Paper/69080", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69080"}, {"title": " Twisting in braids, fibered knots, and the mapping class group ", "webprogram_exclude": "0", "session_ids": ["Session/17105"], "source_sha256": "d4c394c04466a3dba76a0c761c7eb18422bee73342af31fd345c4d68568f6ad3", "withdrawn": "", "abstract": "The fractional Dehn twist is, informally, a measurement of twisting that a map on a surface with boundary effects about the boundary component. In this talk I will describe collaborative work that emerged from the 2019 WiSCon conference related to the fractional Dehn twist coefficient. The talk will touch on results and questions in knot theory, braid groups, mapping class groups, and topology in three and four dimensions.", "id": "Paper/69082", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69082"}, {"title": " Representation asymptotics in the homology of pure graph braid groups ", "webprogram_exclude": "0", "session_ids": ["Session/18072"], "source_sha256": "69a85c6d2e10a3acf879c2134f07dcd58f8f41d354ab974789201a8b61a4afc1", "withdrawn": "", "abstract": "The homology groups of the unordered configuration spaces of a graph form a finitely generated module over the polynomial ring generated by its edges; in particular, each Betti number is eventually equal to a polynomial in the number of particles, an analogue of classical homological stability. Wishing to lift this result to an analogue of representation stability, one encounters the unavoidable fact that the corresponding algebraic structure at the level of ordered configuration spaces is non-Noetherian. Thus, finite generation results are likely to be neither useful nor within easy reach. Drawing on ideas from twisted algebra and factorization homology, we circumvent this obstacle to give a complete asymptotic calculation of the Betti numbers of pure graph braid groups over any field and, in characteristic zero, of the multiplicities of many irreducible representations of the symmetric groups. This talk represents joint work with Hainaut and Wawrykow, building on joint work with An and Drummond-Cole.", "id": "Paper/69083", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69083"}, {"title": " Odd Ramsey numbers of multipartite graphs and hypergraphs ", "webprogram_exclude": "0", "session_ids": ["Session/18339"], "source_sha256": "2451f977b443a406cbc57e3d1e37ded657c5b49087ae729a20415991636ba833", "withdrawn": "", "abstract": "Given a hypergraph $G$ and a subhypergraph $H$ of $G$, the \\emph{odd Ramsey number} $r_{odd}(G,H)$ is the minimum number of colors needed to edge-color $G$ so that every copy of $H$ in $G$ intersects some color class in an odd number of edges.\nGeneralizing a result of Bennet, Heath, and Zerbib in two different ways, in this talk we will walk through the ideas and intuition behind proving $r_{odd} \\left(K_{n,n}, K_{2,t} \\right)=\\frac{n}{t} + o(n)$ for all $t\\geq 2$,  and $r_{odd} \\left(\\mathcal{K}^{(k)}_{n,\\dots,n}, \\mathcal{K}^{(k)}_{1,\\dots,1,2,2} \\right) = \\frac{n}{2} + o(n)$ for all $k\\geq 2$.  The latter is the first result studying odd Ramsey numbers for hypergraphs.", "id": "Paper/69084", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69084"}, {"title": " Highest Weight Modules over the Quantum Periplectic Superalgebra of Type P ", "webprogram_exclude": "0", "session_ids": ["Session/17666"], "source_sha256": "0a77eae3247b72e9461f8c6f3b325e3d2bfb5d28b04f2e82ec3deb7a9d1ffda0", "withdrawn": "", "abstract": "Ahmed, Grantcharov, and Guay (2021, 2024) defined a new quantized enveloping superalgebra, $\\mathfrak{U}_q\\mathfrak{p}_n$, attached to the Lie superalgebra of type $P$. In this talk, we'll briefly discuss two representations of $\\mathfrak{U}_q\\mathfrak{p}_n$: a natural representation $\\mathbb{C}_q(n\\mid n)$ and a Drinfeld-Jimbo representation. We briefly describe how modules over $\\mathfrak{U}_q\\mathfrak{p}_n$ relate to modules over $\\mathfrak{p}_n$, and conclude with a main result that not every tensor representation of is completely reducible, if time permits. This work was done in collaboration with D. Grantcharov and N. Guay.", "id": "Paper/69086", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69086"}, {"title": " Negatively curved manifolds and Arithmeticity from coarse-geometric perspective ", "webprogram_exclude": "0", "session_ids": ["Session/18313"], "source_sha256": "bc8c2cb46e8cc989e189720341a7a3edd1d1027c277779d6768d7c4fd2c3946f", "withdrawn": "", "abstract": "Geometry of negatively curved Riemannian manifold $(M,g)$ can be \nencoded in a certain length function on the fundamental group\n$\\Gamma=\\pi_1(M)$ (the length function is the displacement \n$|\\gamma|_{g}={\\rm dist}_{(\\tilde{M},\\tilde{g})}(\\gamma.x,x)$\nin the universal cover. \nThis \"inside-out\" perspective allows to broaden the study of \nnegatively curved Riemannian structures on a manifold to the study\nof a wide class of length functions on Gromov hyperbolic groups, including word metrics, quasi-Fuchsian embeddings, metric coming from Anosov representation, Green metrics etc.\n\nIn this talk, I will describe this broader coarse-geometric framework, \nwill connect it to Marked Length Spectrum, \nand will discuss a characterization of \narithmetic locally symmetric manifolds in terms of abstract\ncommensurators with coarse-geometric constraints.\n\nBased on joint work with Yanlong Hao.", "id": "Paper/69089", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69089"}, {"title": " Three thousand obstructions to knotless embedding ", "webprogram_exclude": "0", "session_ids": ["Session/17808"], "source_sha256": "71b10c6a45a965767a87f4fa143ac30c79f7b89a562a7a1ab8c0364dfc6a82b2", "withdrawn": "", "abstract": "We present a list of 3028 obstructions to knotless embedding. This increases by an order of magnitude the 264 graphs mentioned in a 2017 survey of Flapan et al. It also builds on the study of knotted embeddings for graphs in $\\Nabla Y$ families initiated by Goldberg et al [GMN]. In [GMN] the authors mention a family of at least 0.6 million graphs. In contrast, our current work includes a set that includes at least 8 million cousins. We discuss our strategies to efficiently organize and sift through these large collections.", "id": "Paper/69090", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69090"}, {"title": " From Competition to Community: Student and Advisor Perspectives on Building a COMAP Modeling Program ", "webprogram_exclude": "0", "session_ids": ["Session/19005"], "source_sha256": "d3bb1f83a390ae0eef1de7de3615ec87e8094926c717cb971c8b18e6a465bd77", "withdrawn": "", "abstract": "Participating in COMAP’s Mathematical Contest in Modeling offers students an intensive opportunity to experience mathematical modeling as an open-ended, collaborative process. In this talk, a faculty advisor and student team leader reflect on their experiences preparing for, participating in, and extending the work of an MCM team at Indiana University South Bend.\n\nWe will discuss the contest from both student and advisor perspectives, including forming and preparing a team, approaching an unfamiliar problem under significant time constraints, making and defending assumptions, dividing responsibilities, and balancing mathematical sophistication with the need to produce a coherent model and written solution. Ryan Assis, a Computer Science major and team leader, will share insights from his team’s work on a lunar resource systems problem and how the experience developed into a presentation at the Indiana Section of the Mathematical Association of America, “Insights into COMAP Modeling: A Big-Picture Analysis of Approach, Assumptions, and Tradeoffs in Lunar Resource Systems.”\n\nWe will also reflect on what we learned from our first experiences with the contest and how those lessons are shaping our plans for future teams. In particular, we will discuss strategies for recruiting students across disciplines, preparing students for open-ended modeling, developing stronger team structures, and creating opportunities for students to continue sharing and developing their work after the contest. Our experience suggests that COMAP can serve not simply as a weekend competition, but as a catalyst for building a broader undergraduate mathematical modeling community.", "id": "Paper/69094", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69094"}, {"title": " A partition perimeter inequality and peakless Motzkin paths ", "webprogram_exclude": "0", "session_ids": ["Session/17968"], "source_sha256": "734e1d48d7cad454dfd760d184b17a7c1a6c2331a1134e7fa080a83b62e9b83e", "withdrawn": "", "abstract": "We present a proof of a bias in distinct partitions with fixed perimeter that have more odd parts than even parts compared to those with more even parts than odd parts. We additionally establish a bijection between distinct partitions with fixed perimeter that have the same number of odd parts as even parts and types of steps in peakless Motzkin paths.", "id": "Paper/69096", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69096"}, {"title": " Numerical Modeling of Blood Flow and Dissection in the Aorta ", "webprogram_exclude": "0", "session_ids": ["Session/18309"], "source_sha256": "6c66198b8b375401f214f9826fb7f3f75fd8af8b09231ad543a9dafbd969f76d", "withdrawn": "", "abstract": "Marfan syndrome (MFS) is a genetic connective tissue disorder that weakens the aorta and significantly elevates the risk of aortic dissection, resulting in death. This raises a critical need to accurately model and predict where an aortic dissection will occur and how it will propagate throughout the aorta to improve outcomes in patients with MFS. This work creates a two-part model for blood flow through the aorta and fracture propagation within the aortic wall. The flow of blood within the aorta is described using the time-dependent incompressible Navier-Stokes equations. Crack propagation is described using a phase-field model where a phase-field variable represents the crack within the aorta wall domain. Both models are discretized in space using the finite element method with $P_2-P_1$ elements. The blood flow model is discretized in time using the backward Euler method. Patient data is used in collaboration with Texas Children's Hospital and Baylor College of Medicine.", "id": "Paper/69097", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69097"}, {"title": " Computing Fréchet Means on Unknown Submanifolds of Riemannian Manifolds ", "webprogram_exclude": "0", "session_ids": ["Session/18273"], "source_sha256": "b6e0783980910a790d3990c2e99455a27245ae41ac052a99882b10e2c7c7c77b", "withdrawn": "", "abstract": "We study computation of the empirical Fr\\'{e}chet mean of data supported on an unknown compact Riemannian manifold $\\mathcal{M}_{1} \\subseteq \\mathcal{M}_{2}$. Given reference points $\\{z_{r}\\}_{r=1}^{N}$ from $\\mathcal{M}_{1}$, we minimize $f(x) = \\frac{1}{2N} \\sum_{r=1}^{N} d_{\\mathcal{M}_{1}}^{2}(x,z_{i})$ over $\\mathcal{M}_{1}$, without explicit access to $\\mathcal{M}_{1}$. Assuming access only to local sampler oracles on $\\mathcal{M}_{1}$, we propose a graph-based geodesic interpolation method that iteratively refines a local nearest-neighborhood graph and interpolates along graph geodesics. We interpret the algorithm as biased Riemannian SGD, with bias controlled by local metric equivalences between graph and manifold distances. As part of the analysis, we extend ISOMAP-type guarantees to embedded submanifolds of general Riemannian ambient spaces. Under geometric assumptions, we obtain an $\\mathcal{O}(1/T)$-type expected convergence guarantee where sampling $\\widetilde{\\mathcal{O}}(T^{4d+3})$ points over an algorithm run suffices with $d = \\dim(\\mathcal{M}_{1})$. These results provide a framework for provably computing constrained Fr\\'{e}chet means on unknown submanifolds using only graph-based approximations of intrinsic distances.", "id": "Paper/69098", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69098"}, {"title": " Infusing History into Mathematics and Engineering Classrooms ", "webprogram_exclude": "0", "session_ids": ["Session/17713"], "source_sha256": "2e1b5ce6cbddccf6a5e789fde60d4832cf466fa3630771aa493fb818ed9ea0b0", "withdrawn": "", "abstract": "This paper examines both the ways in which history has been incorporated into mathematics and engineering classrooms and the purposes that history can serve students in technical fields.  It considers broader professional, institutional, and federally funded efforts over the past several decades to embed historical perspectives into mathematics and engineering education, with particular attention to efforts by professional societies to support this work.  These initiatives are juxtaposed with the author’s own experience bringing the history of science, technology, engineering, and mathematics into technical education at her home institution. Drawing on examples from the author’s research and teaching, the paper explores how history can deepen students’ understanding of technical practice as a fundamentally human and social endeavor. Historical perspectives can also help students recognize the reciprocal relationship between society and science, technology, and mathematics. The paper aims to continue a broader dialogue about how and why we use history in mathematics and engineering classrooms, and how historical thinking can provide students with frameworks for understanding their own roles and responsibilities as professionals.", "id": "Paper/69099", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69099"}, {"title": " Falconer-Type Results for Cartesian Products of Ahlfors-Regular Salem Sets ", "webprogram_exclude": "0", "session_ids": ["Session/18369"], "source_sha256": "55efb74045e30c711f7ff86edf12d5673d903f85dc942fd7a058627cb2b97ff0", "withdrawn": "", "abstract": "Within Geometric Measure Theory, Falconer’s distance conjecture asks what threshold on the Hausdorff dimension of a compact set $E \\subseteq \\mathbb{R}^d$ is required for the set of distances between points in $E$ to be large (have positive Lebesgue measure or nonempty interior). A generalization of this problem takes a graph $G = (\\mathcal{V}, \\mathcal{E})$ and looks at the distance graph $\\Delta_G(E):= \\{(|\\phi(v_j)-\\phi(v_k)|)_{v_jv_k \\in \\mathcal{E}} : \\, \\phi : \\mathcal{V} \\hookrightarrow E\\}$, generated by injectively mapping vertices to points within $E$ and outputting a $\\left| \\mathcal{E} \\right|$ dimensional vector of edge lengths. Our work investigates the consequences of imposing further structure on $E$. Specifically, we look at the case where $E$ can be decomposed into a Cartesian product $\\prod_{j=1}^d E_j$, with $\\sum_{j=1}^d \\operatorname{dim}_F E_j > n$ for some $n \\in \\mathbb{R}$. Here $\\operatorname{dim}_F$ denotes Fourier dimension, a lower bound of a set's Hausdorff dimension. We show that for $k \\geq 2$, the $k$-star distance graph of $E$, $\\Delta^{k-star}(E)$, has positive $k$-dimensional Lebesgue measure whenever $d,n>k$, and nonempty interior when $d,n > 2k$, beating the current best-known bounds for general $k$-star distance graphs. If time permits, we will present further related results.", "id": "Paper/69100", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69100"}, {"title": " L-Differentiability of Functions on Adapted Wasserstein Space of Probability Laws of Stochastic Processes ", "webprogram_exclude": "0", "session_ids": ["Session/17945"], "source_sha256": "2b58c704beca561ec305451e573346459b40aca77caf6d3b044b2171e0c23518", "withdrawn": "", "abstract": "We develop the theory of the L-differentiation for functions on adapted Wasserstein space of probability laws of adapted stochastic processes. We work in the technical setting that underlies the probabilistic study of mean-field games/control problems and the characterizations of their value functions by partial differential equations on the Wasserstein space. By basing our work in this body of research literature, we intend that our work will produce the theoretical framework and technical tools of differentiation that will be useful to researchers who will later develop the analogous theory of PDE on adapted Wasserstein space for fully path-dependent mean-field games.  We discuss the immediate applications of our L-differentiation and differentiable optimization in our setting to market risk problems in mathematical finance.", "id": "Paper/69101", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69101"}, {"title": " Elastodynamics of Linearized State-Based Peridynamics with Fractional Singular Kernels: Well-Posedness and Asymptotics ", "webprogram_exclude": "0", "session_ids": ["Session/18378"], "source_sha256": "f3b244982d52f2c3017fb213111a5b2ab7d922fbda9d207292869c7983cadfda", "withdrawn": "", "abstract": "In this talk, we present a unified mathematical theory for the elastodynamics of linearized isotropic state-based peridynamic media equipped with fractional singular kernels on $\\mathbb{R}^d$. Parameterized by a peridynamic horizon $\\delta >0$ and fractional singularity order $s\\in(0,1)$, the governing vector-valued operator couples direct pairwise bond interactions with indirect, state-based volumetric dilatation.\nWe prove the global well-posedness of the Cauchy problem for rough initial data within vector-valued Bessel potential spaces [H^r(\\mathbb{R}^d)]^d for arbitrary regularity $r\\in \\mathbb{R}$. Furthermore, we study a one-dimensional equation with a singular forcing term and characterize the solution's large-time asymptotic behavior.", "id": "Paper/69102", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69102"}, {"title": " Remarks on Singularities in the Stefan Problem ", "webprogram_exclude": "0", "session_ids": ["Session/17947"], "source_sha256": "d23420582fc226e9f2843c8cb83a89bf217951c6fa1605cf6f1bf1d0008a87ec", "withdrawn": "", "abstract": "I will describe recent progress on understanding singularities in the two-phase Stefan problem, which is a classic free boundary problem modeling, for example, the shape of a melting piece of ice in water. This is based on joint work with Georg Weiss.", "id": "Paper/69103", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69103"}, {"title": " Front Propagation Dynamics in Fisher KPP Equations on Unbounded Metric Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18289"], "source_sha256": "6aac7810c15fa8dd82a01431027a798a9846927362dab77657e09556815dc328", "withdrawn": "", "abstract": "This talk focuses on the front propagation dynamics of Fisher-KPP equations\non unbounded metric graphs. There are several studies on front propagation\nphenomena in bistable equations on unbounded metric graphs. It is known that, in such equations, the network structure of the underlying environment may block the propagation of fronts. It will be shown in this talk that the network structure of the environment does not block the propagation of fronts in Fisher-KPP equations.\n\nSpecifically, we will show that on an unbounded metric graph with finitely\nmany edges, the Fisher-KPP equation exhibits the same minimal spreading speed $c^*$ as on the real line. Moreover, it admits a generalized traveling wave connecting the stable positive constant solution and the trivial solution, with an averaged speed $c$ for any $c > c^*$.", "id": "Paper/69109", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69109"}, {"title": " Discrete signature tensors in topological data analysis ", "webprogram_exclude": "0", "session_ids": ["Session/18303"], "source_sha256": "a90d817896a1e6424af999acb91db15abe1203156d1f86fbc20d8d4800d12bdc", "withdrawn": "", "abstract": "A limitation of persistence homology is that persistence modules lack structure that is necessary for statistical analysis and machine-learning integration. To this effect, an active pursuit in topological data analysis is to find convenient vectorizations, i.e. maps from persistent homology to mathematical objects that are suitable for machine-learning methods. \n\nIn this talk, I will introduce an approach for vectorization based on (a discrete version of) path signatures. I will argue that this approach is natural and describe its discriminative power. Time permitting, I will present an application to knotted proteins and show how the discrete signature captures fundamental structural information such as the protein's knot depth and structural homology class in a statistically significant way.", "id": "Paper/69116", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69116"}, {"title": " Spontaneous Kolmogorov-Arnold Geometry in Neural Networks ", "webprogram_exclude": "0", "session_ids": ["Session/17705"], "source_sha256": "b32eaf2b6563f8638ff53a5612b5744a5e63e3fefdcc0a56caa7c8a772ed0db7", "withdrawn": "", "abstract": "The Kolmogorov-Arnold (KA) theorem guarantees that any continuous function can be represented exactly by a one-hidden layer neural network of fixed width. \nThis representation uses universal but highly non-smooth \"inner functions,\" with a distinctive shape that we term KA geometry.\nWe ask whether KA geometry is special to the KA construction or might be present in neural networks of practical use.\nWe find avatars of KA geometry appear in ordinary neural networks, ranging from shallow MLPs trained on regression and (simple) image classification to (reasonably) LLMs.\nThis emergence occurs organically without prompting. \nWe discuss the extent to which KA geometry can be used to steer and interpret model behavior.", "id": "Paper/69118", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69118"}, {"title": " Dynamical behavior of diffusively coupled scalar differential equations as Wentzell boundary conditions ", "webprogram_exclude": "0", "session_ids": ["Session/18109"], "source_sha256": "684dcf391129f75f0c3c10cb1e26a93bb9a247f3fd56f4a3f75ce1fc75598721", "withdrawn": "", "abstract": "Two identical scalar dynamical systems coupled through a scalar diffusion equation are studied herein, with respect to bifurcations from a symmetric steady-state to symmetric and asymmetric steady-states and to in-phase and anti-phase oscillations. Numerical continuations based on the developed theory show the shape of the bifurcation branches and the attracting nonlinear states far from bifurcation onset and confirm their, for the most part, derived stability. This study extends the work on the dynamical properties of a single scalar dynamical system coupled to its own delay through an adjacent diffusion field and quantifies further the delay of diffusive information transmission between two such Wentzell boundaries. The mathematical system is motivated by modeling biological membranes with yet unknown effective local fluxes that are coupled to bulk diffusion.", "id": "Paper/69122", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69122"}, {"title": " One-dimensional fibers of tropical Hurwitz moduli maps ", "webprogram_exclude": "0", "session_ids": ["Session/18219"], "source_sha256": "6da4572510d8d282679f940d5742b028ad0701a7fe1b3b94d55b8d679b8df62f", "withdrawn": "", "abstract": "Many curve counting problems can be expressed as computing the degree of a map between moduli spaces. In tropical geometry, these problems can be studied using covers of metric graphs. In this talk, I will discuss a variation of the tropical Tevelev counting problem in which the relevant moduli map has one-dimensional fibers. Each fiber is itself a graph parametrizing tropical covers with prescribed stabilized source and target. I will explain how varying edge lengths and resolving contractions can be used to construct these fibers, and discuss how this description helps us study their connectedness and genus. This is joint work with Alessio Cela.", "id": "Paper/69125", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69125"}, {"title": " Impact of Non-Linear Demand and Production Constraints on Cost Pss-Through in the Airline Industry ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "b5370b9b18fe269e076e7b190c48088a4368a97552cb952e0eb084d7024876c9", "withdrawn": "", "abstract": "We study the pass-through of input cost shocks to output prices in a two-firm Cournot oligopoly, motivated by fare-setting behavior in the U.S. airline industry. Firms solve a constrained profit-maximization problem subject to capacity limits, and we characterize equilibrium behavior using Karush-Kuhn-Tucker conditions. We derive closed-form comparative statics for the pass-through rate under both isoelastic and quadratic demand specifications. A central result is that, in the interior (unconstrained) regime, the pass-through elasticity is independent of the degree of competition, a finding that contrasts with standard intuition from perfectly competitive and monopoly models. We establish a stability condition on the demand system's curvature parameters guaranteeing a well-behaved reaction-function equilibrium, while also showing how incorporating capacity constraints introduces additional Nash equilibria, and we characterize the conditions under which this multiplicity arises.", "id": "Paper/69130", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69130"}, {"title": " Scattering and inverse scattering theory in topological insulators ", "webprogram_exclude": "0", "session_ids": ["Session/17859"], "source_sha256": "b455d665ad107dd3dc1445fed938746afcca6aa3613510ef0f5bc5cf991d7f9b", "withdrawn": "", "abstract": "A surprising edge transport, displaying strong robustness to perturbations as an obstruction to Anderson localization, is guaranteed along interfaces separating two-dimensional insulators in different topological phases. After a brief review of their topological classification, we present a scattering theory for specific models allowing for a quantitative description of the asymmetric edge transport along the waveguide in the presence of perturbations. We will also present results on the corresponding inverse scattering theory and observe that the non-trivial topology shows up again as a topological obstruction.", "id": "Paper/69131", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69131"}, {"title": " Sustainable Standards-Based Grading Implementations for the Core Mathematics Sequence ", "webprogram_exclude": "0", "session_ids": ["Session/18440"], "source_sha256": "0ebda0c8a32ff2f815a737fb2e559fd4715362044dcd47662a0ec3ee708b35e8", "withdrawn": "", "abstract": "This talk will illustrate the implementation details and results from a standards-based grading (SBG) framework developed for use in a coordinated linear algebra course at Florida Polytechnic University. Developed over a year’s worth of SBG trials and experiments, this grading framework was developed with the long-term goal of being sustainable, scalable, and generalizable enough to implement in a variety of foundational Freshman-Sophomore level mathematics courses. Primary design goals include promoting student learning and success by providing ample opportunities to demonstrate mastery, while at the same time not overburdening instructors with excessive assessment creation, grading, and bookkeeping, in order to promote faculty support and systemic adoption. We will discuss the development of our SBG framework, the details of its implementation in linear algebra in Fall 2026, and the positive impact of the framework both in terms of student success and academic progression and in terms of student and faculty sentiment.", "id": "Paper/69139", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69139"}, {"title": " How Balanced Can a Graph Be? Exploring Balance Numbers of Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18317"], "source_sha256": "ed73ff538226b2815f1fd5d94c78b01260f5f08fde220bf32f08c6aaf33145cc", "withdrawn": "", "abstract": "A neighborhood balanced coloring of a graph is a coloring of the vertices using two colors, red and blue, such that the number of red and blue vertices in the neighborhood $N$($v$) are equal for all vertices $v.$  Such a coloring need not exist for a given graph, so we can instead ask how close a graph can come to being balanced.  We generalize neighborhood balanced colorings to $k$ colors, allowing the numbers of vertices of each color in a neighborhood to differ by at most $\\lambda$.  This leads us to define three related balance numbers, measuring the minimum possible imbalance with respect to open, closed, and vertex-dependent neighborhoods.  In this talk, I will introduce balance numbers, investigate relationships among them, and present selected results.  We will see how an existence question for balanced colorings can be viewed as an optimization problem: rather than asking whether perfect balance is possible, we can ask how balanced a graph can be.", "id": "Paper/69143", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69143"}, {"title": " Instance Aware Quantum Linear System Algorithms ", "webprogram_exclude": "0", "session_ids": ["Session/18246"], "source_sha256": "40e29b0a9365e719967d248e80393478638ffe3da0b9cf9da62f4f20c829a644", "withdrawn": "", "abstract": "Given a matrix \\(A\\) and a nonzero vector \\(\\vec b\\), the quantum linear system (QLS) problem asks for the preparation of a quantum state proportional to the solution \\(\\vec y=A^{-1}\\vec b\\). Existing QLS algorithms typically have runtimes that scale nearly linearly with the condition number \\(\\kappa(A)\\) and logarithmically with the inverse precision. However, the condition number is a worst-case property of the matrix and does not capture how the particular input vector \\(\\vec b\\) interacts with the singular subspaces of \\(A\\). As a result, condition-number-based complexity bounds can be overly pessimistic for structured problem instances.\n\nIn this talk, I will discuss recent progress on instance-aware quantum linear system algorithms that go beyond condition-number-based analysis. In particular, the relevant instance-dependent parameter takes the form $\n\\Gamma(A,\\vec b)\n=\n\\frac{\\left\\|(A^{-1})^\\dagger \\vec y\\right\\|}\n{\\|\\vec y\\|},\n\\qquad\n\\vec y=A^{-1}\\vec b,\n$ leading to a complexity dependence of approximately\n$\n\\frac{\\Gamma(A,\\vec b)}{\\epsilon}\n\\log\\!\\left(\\frac{1}{\\epsilon}\\right),\n$ under suitable normalization assumptions. Unlike \\(\\kappa(A)\\), this quantity depends on both the matrix and the particular solution direction and can be substantially smaller than the worst-case condition number.\n\nI will explain how this improvement arises from the connection between quantum walk and to electrical networks. I will also discuss how instance aware QLS algorithms can enable efficient end-to-end quantum algorithms for certain problem instances where conventional condition number based approaches fail.", "id": "Paper/69147", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69147"}, {"title": " Complete Non-Selfadjointness of Extensions of Symmetric Operators with Bounded Dissipative Perturbations ", "webprogram_exclude": "0", "session_ids": ["Session/18292"], "source_sha256": "1beba32555ee44f28071a9c541636473f7984897aa290752b00aafb36b1828c8", "withdrawn": "", "abstract": "Using boundary triples, we develop an abstract framework to investigate the complete non-selfadjointness of the maximally dissipative extensions of dissipative operators of the form $S+iV$, where $S$ is symmetric with equal finite defect indices and $V$ is a bounded non-negative operator. Our key example is the dissipative Schrödinger operator $−\\tfrac{d^2}{dx^2}+iV$ on the interval.\n\nThis is joint work with Andr\\'es Pati\\~{n}o and Monika Winklmeier.", "id": "Paper/69148", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69148"}, {"title": " Principal specializations of the t-chromatic symmetric function ", "webprogram_exclude": "0", "session_ids": ["Session/18375"], "source_sha256": "2f9d3211d6b6a7a6889fc10c71786aba93445e1ee211a51408b36849f21e2708", "withdrawn": "", "abstract": "We introduce the $t$-chromatic symmetric function $Z_G(\\mathbf{x};t)$, a variant of Stanley's chromatic symmetric function in which the variable $t$ records the number of distinct colors used in a proper coloring. Although $Z_G(\\mathbf{x};t)$ is equivalent to the chromatic symmetric function as a graph invariant, its principal specializations retain substantially more information than those of the chromatic symmetric function. \nThis construction is motivated by the work of Bajo--Beck--Vindas-Meléndez on the $q$-chromatic polynomial and the conjecture of Loehr--Warrington that the $n$th principal specialization of the chromatic symmetric function distinguishes trees on at most $n$ vertices, both of which stem from Stanley's longstanding question of whether the chromatic symmetric function distinguishes trees.\nWe show that the second principal specialization  of $Z_G(\\mathbf{x};t)$ does not distinguish caterpillars in general.\nWe then prove that the third principal specialization distinguishes and explicitly reconstructs caterpillars with three spine vertices as well as elongated bistars. Finally, we conjecture that the fourth principal specialization distinguishes all trees.", "id": "Paper/69151", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69151"}, {"title": " Correspondence Coloring Grids and Toroidal Grids ", "webprogram_exclude": "0", "session_ids": ["Session/16805"], "source_sha256": "1e9e6c562b1e227afabad9b88bb54c960b207d0c8f58252073cc9cdf2212eb94", "withdrawn": "", "abstract": "Correspondence coloring generalizes list coloring by replacing the requirement that adjacent vertices receive different colors with a system of matchings between their color sets. For each edge, a matching specifies which color choices at its endpoints conflict, and a correspondence coloring selects one color at each vertex while avoiding all such matched pairs. It is known that the list chromatic number of the grid \\(P_n \\square C_m\\) and the toroidal grid \\(C_n \\square C_{2m+2}\\) are both equal to 3, while the list chromatic number of the toroidal grid \\(C_{2n+1} \\square C_{2m+1}\\) is unknown but conjectured to be 3. We will present inductive techniques which bound the correspondence chromatic number of the grid \\(P_n \\square C_m\\) above, as well as discuss general 3-correspondence constructions for which the toroidal grid \\(C_n \\square C_m\\) cannot be colored.", "id": "Paper/69152", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69152"}, {"title": " Nonlinear stability of subextremal Kerr black holes ", "webprogram_exclude": "0", "session_ids": ["Session/18326"], "source_sha256": "64dc4ca91c7daba463e87f58d684704058f00531c34041c2447e322eb1274b9e", "withdrawn": "", "abstract": "I will describe some aspects of the recent proof of the nonlinear stability of subextremal Kerr black holes as solutions of Einstein's vacuum equations, with a focus on microlocal and spectral ingredients.", "id": "Paper/69155", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69155"}, {"title": " A New Graph Pebbling Parameter! ", "webprogram_exclude": "0", "session_ids": ["Session/19360"], "source_sha256": "3a02bfcd0b647a0095165e8a8ad2e465556a7b37877212f63689606c7b646a0a", "withdrawn": "", "abstract": "Graph pebbling is a model for solving the following discrete resource allocation question in a graph: can a given supply meet some predetermined demand? \nA pebbling step is defined as taking two pebbles from a vertex and placing one pebble on a neighboring vertex. \nGiven a graph $G$, the pebbling number $\\pi(G)$ is the minimum number of pebbles such that any supply of that many pebbles can satisfy any single demand through a sequence of pebbling steps. \\\\\n\nThis talk will briefly survey existing results and techniques used to determine the pebbling number, with a focus on grid graphs (Cartesian products of paths).\nAs a tool for producing bounds on pebbling numbers, we introduce a new pebbling parameter, the $t$-stack pebbling number $\\widehat{\\pi}_t(G)$, defined to be the minimum number $m$ such that from every supply of $m$ pebbles, one can move $t$ pebbles to some vertex via pebbling steps.\nWe will present introductory results on  $\\widehat{\\pi}_t(G)$ and illustrate its applications, especially to grid graphs.", "id": "Paper/69156", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69156"}, {"title": " Variational justification of the dimensional scaling technique in chemical physics ", "webprogram_exclude": "0", "session_ids": ["Session/18441"], "source_sha256": "1ef3d4c33acbb54eb17d9ef520af10e0ece4c1f511e9d7df763ae7de58062c5d", "withdrawn": "", "abstract": "The dimensional scaling (D-scaling) technique is a relatively “new” non-conventional approach to study multiparticle systems in molecular quantum mechanics. The D-scaling technique involves in general four steps: generalizing the Schrodinger equation to D-dimensions; transforming the problem to a suitably scaled space to remove the major D-dependence of the quantity to be determined; evaluating the scaled quantity at one or more special D-values, such as D=\\infty, where the computation is relatively “easy”; and obtaining an approximation for D = 3 by relating it to the special D-values through 1/D asymptotic expansion. The D-scaling technique enables the calculation of ground and excited state energies of quantum systems without solving numerically the Schrodinger equation with Coulomb potentials. Even though the D- scaling technique has been used in chemical physics as an effective tool to study multiparticle systems, it has not received much attentions from the mathematics community, possibly due to its nonstandard procedures to handle partial differential equations. The mathematical justification of the D-scaling technique remains to be established rigorously. By casting the problem in an appropriate variational setting and studying the corresponding minimization problem, we initiated the mathematical analysis of the D-scaling technique from the variational point of view. In this talk, I will present some recent progresses of variational justification of the dimensional scaling technique.", "id": "Paper/69160", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69160"}, {"title": " Global weak solutions for the interaction problem of an Ericksen–Leslie fluid with a rigid body ", "webprogram_exclude": "0", "session_ids": ["Session/18342"], "source_sha256": "50a428e5568321553f1ce2dd0a428492bf492f93975e099d901cee8b2ca2c976", "withdrawn": "", "abstract": "In this talk, we discuss the existence of global finite-energy weak solutions for a three-dimensional rigid body interacting with a nematic liquid crystal governed by the simplified Ericksen--Leslie system, including wall contact under a perfectly inelastic sticking law. \nThe director is sphere-valued and confined to a closed hemisphere.  \nBefore contact, a local compactness and a shrinking-collar density argument yield the constrained moving-domain formulation. \nAt contact, the director admits a strong $\\mathrm{L}^2$-trace.\nWe continue the constrained flow on the possibly non-Lipschitz residual domain by proving weak existence for the simplified Ericksen--Leslie model on arbitrary bounded open sets. \nThe global energy inequality contains the impact loss explicitly, and we obtain quantitative lower bounds for the first contact time. \n\nThis talk is based on joint work with Vinh Nguyen.", "id": "Paper/69162", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69162"}, {"title": " Pebbling in Generalized Johnson Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/19360"], "source_sha256": "cde3bbbcbcd1dc29243885bc0792fecc35cc9a1fea4b7dfa5b9c61cdcab74c5d", "withdrawn": "", "abstract": "Graph pebbling is a combinatorial game played on a graph, with pebbles placed on its vertices. \n    A pebbling step consists of removing two pebbles from one vertex and placing one pebble on an adjacent vertex.\n    The pebbling number $\\pi(G)$ of a graph $G$ is the smallest number $t$ such that, from any initial configuration of $t$ pebbles on the vertices of $G$, it is possible to place a pebble, through a sequence of pebbling steps, on any specified target vertex.\n\n    Let $m> k> i\\ge 0$ be integers. \n    The generalized Johnson graph $J(m,k,i)$ is defined to have as vertices all the $k$-element subsets of an $m$-element set, with edges joining two subsets that share exactly $i$ elements.\n    These graphs generalize several well-studied families of graphs: the original Johnson graph has $i=k-1$, the Kneser graphs have $i=0$, and the Petersen graph equals $J(5,2,0)$.\n    In this talk, we present results on the pebbling number of generalized Johnson graphs. \n    Using weight function methods, we develop new techniques, including the Orbit Lemma, to determine $\\pi(J(m,k,i))$ for various values of $m$, $k$, and $i$. \n    We conclude with conjectures on other special classes of vertex-transitive graphs.", "id": "Paper/69165", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69165"}, {"title": " Convex Hull Volumes in Hyperbolic 3-Space ", "webprogram_exclude": "0", "session_ids": ["Session/19346"], "source_sha256": "490f94d2a3cf8325049fe71ead9f9be05be360020a71408913425eb1e17e32c6", "withdrawn": "", "abstract": "We provide a geometric condition satisfied by certain closed subsets of the Riemann sphere which implies that their hyperbolic convex hulls in $\\Bbb{H}^3$ have infinite volume. As a corollary, we characterize continua in the Riemann sphere whose hyperbolic convex hulls have infinite volume, answering a question of Danny Calegari. Furthermore, we give a geometric characterization of planar self-similar sets whose hyperbolic convex hulls have infinite volume.", "id": "Paper/69166", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69166"}, {"title": " Invariants of ribbon tensor categories from 2- and 3-manifolds ", "webprogram_exclude": "0", "session_ids": ["Session/18379"], "source_sha256": "b4d773b90fc1b92655e796bbd04b325857b70204f2cf13e7f14e153804c3a589", "withdrawn": "", "abstract": "Many constructions in algebraic topology are built from some topological data and some algebraic data. For example, certain constructions of topological quantum field theories, skein modules, and the Kuperberg invariant all take as input certain manifolds and certain tensor categories. We may view such constructions as invariants of the manifold or as invariants of the tensor category. We take the latter perspective and investigate a handful of invariants of non-semisimple ribbon tensor categories built from 2- and 3-manifolds. \n\nWe investigate a non-semisimple generalization of modular data of modular finite tensor categories, admissible skein modules, and a Kuperberg-type invariant. The first of these is joint with L. Chang, Z. Wang, and Q. Zhang and is based on arXiv:2404.09314. The latter two are joint with R.P. Bakshi and M. Jubeir. In all of these cases, we consider examples arising from Hopf algebras.", "id": "Paper/69172", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69172"}, {"title": " Statistics under Scarcity - Jerzy Neyman and the Design of Hypothesis Testing, 1923-1933\" ", "webprogram_exclude": "0", "session_ids": ["Session/18374"], "source_sha256": "5441ce2964c81b4730bebc7106ebd2106350cdb84126e88c123e0713abb481b4", "withdrawn": "", "abstract": "Articulated by Polish statistician Jerzy Neyman in papers from 1927 to 1933, hypothesis testing—a method for deciding whether evidence supports or rejects a statistical claim—has become fundamental to statistical inference. In 1925, traveling to London—the epicenter of early 20th century statistics—under a newly independent Poland’s imperative to build its own statistical infrastructure, Neyman initially employed techniques that bore great resemblance to those of his mentors—eugenicists Karl Pearson and Ronald Fisher. Yet upon his return to Poland in 1929, the techniques he deployed moved decisively away from British influences. I argue that this divergence emerged as a strategic response to conditions of severe resource scarcity that plagued interwar Poland. Overwhelmed by the Great Depression, materials routine to British statistical life—made possible by royal or state backing—such as mathematical tables, calculating machines, and trained labor had become scarce in Poland. Amid these difficulties, the 1933 framework championed a logic of reduction, mobilizing novel techniques drawn from linear algebra and set theory, to recast complex problems into simpler ones. As Neyman himself cheerfully noted, instruments and tables designed for simpler problems could now be stretched to solve complex ones otherwise intractable or costly, making mathematical techniques literal resources deployed against material constraints. This project thus points to understanding mathematical knowledge as locally and materially dependent, that mathematical instruments set the very boundaries of valid and calculable statistical knowledge. It emphasizes studying conditions of statisticians during their routine work to understand their motivations for deploying mathematical techniques in specific ways. Finally, viewing the field from Neyman’s vantage point at the periphery—attempting to build statistical infrastructure while emulating established traditions—makes visible underexamined disciplinary assumptions when viewed from a disciplinary center such as Britain.", "id": "Paper/69173", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69173"}, {"title": " p-Bergman Spaces of Balanced Domains ", "webprogram_exclude": "0", "session_ids": ["Session/19362"], "source_sha256": "6c03587baaaf10339c80121b85cffa95c794c62308c8f1d9e3c3a28c6b1ec83f", "withdrawn": "", "abstract": "We investigate the possible dimensions of $p$-Bergman spaces of pseudoconvex balanced domains. For $1\\leq p<2$, we prove that the $p$-Bergman space of a pseudoconvex balanced domain in $\\mathbb{C}^2$ is either trivial or infinite-dimensional. This dichotomy of dimension fails for $p>2$: we construct pseudoconvex balanced domains $D_h \\subset \\mathbb{C}^n$ for which $\\dim A^p(D_h)=1$, for every $p\\geq 8$ whenever $n \\geq 2$. We also study the higher-dimensional setting, obtaining criteria for triviality and infinite-dimensionality of $p$-Bergman spaces of pseudoconvex balanced domains, with the relevant conditions expressed in terms of multiplier ideals.", "id": "Paper/69174", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69174"}, {"title": " Idempotent Channels and Metastability in Dissipative Quantum Dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/18113"], "source_sha256": "c2d818c97da7ac5c82ac34f243cb170bf7815059a6e26f29fbd321f76d9f653c", "withdrawn": "", "abstract": "Metastable dynamics in open quantum many-body systems often exhibits a separation of timescales, suggesting that the long-lived dynamics should admit a low-dimensional reduced description. This is the quantum analogue of coarse-graining classical continuous-time Markov chains into effective dynamics between metastable phases. We propose a theoretical framework for constructing such reduced quantum dynamics from idempotent unital completely positive (UCP) maps. From an operator-algebraic perspective, we show that a UCP map that is approximately idempotent is close to an exactly idempotent UCP map. This may be viewed as a generalization of Kitaev’s result on almost-idempotent quantum channels (Kitaev, 2024), under the additional assumption that the Riesz projection onto the slow subspace has constant rank. In many-body settings, this corresponds to a finite-dimensional family of metastable phases. We explain how the resulting idempotent channel identifies the effective slow algebra and gives rise to reduced dynamics for metastable many-body systems. Technically, the result builds on a factorization theorem for UCP maps together with the structure theory of finite-dimensional $C^\\ast$-algebras. We obtain quantitative error bounds both in completely bounded (cb) norm and in a weighted norm adapted to metastable states. We also discuss potential applications to slow nonequilibrium dissipative dynamics, dissipative quantum algorithms, and rate-theoretic descriptions of quantum Markov semigroups. This is joint work with L. Lin and M. Ragone.", "id": "Paper/69175", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69175"}, {"title": " Bounding the number of conjugacy classes from below ", "webprogram_exclude": "0", "session_ids": ["Session/18264"], "source_sha256": "3086dea6636c7407b42c3269d7ce03af913970427bb278991748e850c176ad37", "withdrawn": "", "abstract": "In 2000 L. H\\'{e}thelyi and B. K\\\"{u}lshammer proved that for finite solvable groups $G$ of order divisible by a prime $p$\nwe have $k(G)\\geq 2\\sqrt{p-1} $, where $k(G)$ is the number of conjugacy classes of $G$. This was the origin of a by now extensive and still growing body of literature on generalizations and strengthenings of this bound of all kinds.  We will review some of these and, in particular, discuss some of the latest results on this topic,\nwhich are refined statements involving both the number of conjugacy classes of $p$-elements and the number of conjugacy classes of $p'$-elements of $G$. These results were obtained in collaboration with \nB. \\c{C}{\\i}narc{\\i}, A. Mar\\'oti, and I. I. Simion.", "id": "Paper/69177", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69177"}, {"title": " The Order of the Non-universal Tree of a Hilbert Space with Respect to the Haar Basis ", "webprogram_exclude": "0", "session_ids": ["Session/19339"], "source_sha256": "bb57c905f590ee453a7d0d165d9db663f2253088730824d54190898db60bfe66", "withdrawn": "", "abstract": "In his 1994 doctoral thesis, Bossard introduced the notion of the non-universal tree $T_{NU}(X)$ associated with each separable Banach space $X$ which does not contain an isomorphic copy of $C(2^\\mathbb N)$. Together with the order operation defined on well-founded trees, we obtain a method of classifying the complexity of separable Banach spaces by the degree of isomorphism of finite-dimensional subspaces of $C(2^\\mathbb N)$. Despite further refinement of this concept in later years, we are unaware of any specific instances of direct exhibitions of the order of the non-universal tree for a concrete space and basis. We show that if $H$ is any separable Hilbert space, then $o(T_{NU}(H))=ω+1$ when taken with respect to the Haar basis for $C(2^\\mathbb N)$, demonstrating that the class of Hilbert spaces is the least complex class with respect to this measurement when considering this basis.", "id": "Paper/69180", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69180"}, {"title": " On Faster Algorithms for Tensor Isomorphism ", "webprogram_exclude": "0", "session_ids": ["Session/16950"], "source_sha256": "469798bf2447a30d6bfef6521b567af4c0218fcea7ca1a5c0259b603030fda74", "withdrawn": "", "abstract": "This talk will focus on the computational complexity of the tensor isomorphism problem. This problem has recently received increasing attention due to its connection to other isomorphism problems, and its applications in computational group theory and cryptography.\n\nI will discuss recent progress on faster algorithms for tensor isomorphism over different underlying fields and rings. I will also discuss how this progress has led to faster algorithms for other problems.\n\nBased on joint work with Josh Grochow, Gábor Ivanyos, Euan J. Mendoza, Youming Qiao, Kate Stange, and Chuanqi Zhang.", "id": "Paper/69182", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69182"}, {"title": " Homological mirror symmetry for theta divisors ", "webprogram_exclude": "0", "session_ids": ["Session/17105"], "source_sha256": "6835eae488b8b0dc04c5d3dab4d8720174b06309896decf5adf3ddb73b1dc114", "withdrawn": "", "abstract": "We will describe the correspondence under homological mirror symmetry (HMS) between the complex moduli of theta divisors in principally polarized abelian varieties and the Kaehler moduli of the mirror Landau-Ginzburg models. We will also mention some open questions. This is based on joint work with Haniya Azam, Catherine Cannizzo, and Chiu-Chu Melissa Liu.", "id": "Paper/69183", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69183"}, {"title": " Adaptive-Rank Tensor Methods for Thermal Radiative Transfer Applications ", "webprogram_exclude": "0", "session_ids": ["Session/17926"], "source_sha256": "3d7a5fac279b1045d36c16e4134654d5280800d138c0adedafe7bac69fadefd7", "withdrawn": "", "abstract": "Thermal radiative transfer models the transport of photons and their exchange of energy with a background material. High-fidelity kinetic descriptions of the radiation field generally depend on space, angle, energy, and time, which creates substantial storage and computational demands even on relatively coarse discretizations. Radiation–material interactions also introduce stiff nonlinear coupling, which motivates the adoption of implicit time discretizations. In this talk, I will describe our ongoing work on adaptive-rank tensor methods that use a compressed representation of the kinetic solution to reduce the computational cost of these simulations. In our approach, the kinetic solution is coupled to a lower-dimensional moment system, which is closed using the low-rank kinetic solution, to reduce the stiffness of the system. I will discuss some of the challenges of maintaining accuracy and solver robustness, along with strategies we are exploring to address them. Selected benchmark calculations will illustrate current progress as well as open questions.", "id": "Paper/69184", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69184"}, {"title": " Producing Math Content for the 2swap YouTube Channel ", "webprogram_exclude": "0", "session_ids": ["Session/18322"], "source_sha256": "2d261e7b5641a667653c3c002a14135992558d541f6bfa748c058ce95bb5474c", "withdrawn": "", "abstract": "The 2swap YouTube channel publishes videos explaining emergent systems in mathematics, including dynamical systems and board game strategy. These videos are made with a custom, open-source rendering engine called \"swaptube,\" specialized to easily produce the visuals of emergent systems. It abstracts away details related to timeline and transition, allowing the user to simply express the video as a sequence of keyframes, defined by the system's generating parameters at each keyframe. In this talk, I discuss the software and production workflow used to create 2swap videos, emphasizing lessons learned from abandoned videos and how they have influenced design decisions made in the production process. The audience will leave with a working sense of how to make a 2swap-style video of their own.", "id": "Paper/69187", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69187"}, {"title": " Known and expected <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"4.13ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 1778.3 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">M_{23}</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4D\" d=\"M289 629Q289 635 232 637Q208 637 201 638T194 648Q194 649 196 659Q197 662 198 666T199 671T201 676T203 679T207 681T212 683T220 683T232 684Q238 684 262 684T307 683Q386 683 398 683T414 678Q415 674 451 396L487 117L510 154Q534 190 574 254T662 394Q837 673 839 675Q840 676 842 678T846 681L852 683H948Q965 683 988 683T1017 684Q1051 684 1051 673Q1051 668 1048 656T1045 643Q1041 637 1008 637Q968 636 957 634T939 623Q936 618 867 340T797 59Q797 55 798 54T805 50T822 48T855 46H886Q892 37 892 35Q892 19 885 5Q880 0 869 0Q864 0 828 1T736 2Q675 2 644 2T609 1Q592 1 592 11Q592 13 594 25Q598 41 602 43T625 46Q652 46 685 49Q699 52 704 61Q706 65 742 207T813 490T848 631L654 322Q458 10 453 5Q451 4 449 3Q444 0 433 0Q418 0 415 7Q413 11 374 317L335 624L267 354Q200 88 200 79Q206 46 272 46H282Q288 41 289 37T286 19Q282 3 278 1Q274 0 267 0Q265 0 255 0T221 1T157 2Q127 2 95 1T58 0Q43 0 39 2T35 11Q35 13 38 25T43 40Q45 46 65 46Q135 46 154 86Q158 92 223 354T289 629Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-4D\" x=\"0\" y=\"0\"></use>\n<g transform=\"translate(970,-150)\">\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-32\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-33\" x=\"500\" y=\"0\"></use>\n</g>\n</g>\n</svg> fields ", "webprogram_exclude": "0", "session_ids": ["Session/18263"], "source_sha256": "2ab13f37fd04e1774ddd379d7af4fa1e4469acf6a49ffcc1d15367d9aae0080d", "withdrawn": "", "abstract": "For a permutation group $G$, one can ask where the absolute discriminants of known number fields with Galois group G fit within the unknown list of all such discriminants.  We present first thoughts in the case of the Mathieu group $M_{23}$ of order $2^7 3^2 5 \\cdot 7 \\cdot 11 \\cdot 23$.  This group is\nattractive for a case study since the list of known fields only became non-empty in August 2026 by an explicit one-parameter family found in a landmark paper of Huang, Jackson, Lee, Poonen, Pries, and Zhang.\n\nWe expect the number of discriminants $\\leq X$ from the family to grow as $c X^{1/26}$ while Malle's conjecture says that the number of all discriminants grows as $c X^{1/8}$.   Related to this thinness, we find the explicit small fraction of possible $p$-adic behaviors that occur in the family.  This comparison is complicated only at the six prime divisors of $|M_{23}|$. At 2, 3, and 23, many types of wildness are present in the family, and many more are allowed to be present in general $M_{23}$ fields.  At $5$, $7$, and $11$, a field in the family is necessarily tame, but many types of wildness can be present in general $M_{23}$ fields.   At the other primes $p$, the exponents on $p$ occurring from a discriminant in the family are $0$, $8$, and $22$ (if $(p/23)=1$).  For general $M_{23}$ fields, 12, 14, 16, 18 (if $(p/7)=1$), and 20 (if $(p/7)$, $(p/11)$, or $(p/15)$ is 1) are also possible.\n\nSmallest possible discriminants are a locus of interest complementary to asymptotic growth.   We think it likely that the discriminant $2^{44} 7^8 23^{24}$ found by the six authors is the smallest coming from the family, even though the family also gives fields in which $2$ and $3$ are unramified and $23$ is tamely ramified. However we expect the root discriminant $(2^{44} 7^8 23^{24})^{1/23} \\approx 195.328$ is not the smallest overall, because the Mathieu group $M_{24}$ has a field with root discriminant $(2^{64} 751^8)^{1/24} \\approx 57.716$.", "id": "Paper/69192", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69192"}, {"title": " Picard Rank Jumps and Special Cycles for K3 Surfaces over Global Fields ", "webprogram_exclude": "0", "session_ids": ["Session/18263"], "source_sha256": "ec0084d642e4b7d67cb24c99cdcd824ba602b1e53ab5b47ed8233d5b78aba2df", "withdrawn": "", "abstract": "For an algebraic K3 surface $X$ over a global field $K$, the geometric Neron-Severi group $NS(\\bar{X})$ is well-known to always be contained in that of its reduction $X_p$ modulo a good prime $p$ of $K$ via the specialization map. When $K$ is a number field, allowing for finite extensions of $K$, Charles describes the density of primes for which this map is an isomorphism. Works of Costa, Elsenhans and Jahnel extend this result, introducing the so-called jump character to detect additional jumps in Picard rank. In this talk, we answer this question over a global field $K$ without passing to a field extension by giving an exact formula for the density of primes yielding each Picard rank difference. Additionally, we present a generalization of this question that studies how often a reduction of $X$ gains a line bundle representing a fixed square class under the intersection pairing, corresponding to intersections with families of special divisors on GSpin Shimura varieties and prove a density 0 result for sufficiently generic families.", "id": "Paper/69193", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69193"}, {"title": " Single-Orbit Recovery of Group Law via an Optimization Principle ", "webprogram_exclude": "0", "session_ids": ["Session/19350"], "source_sha256": "0696be75bbd34bb34ede38d774c1b42d943e6452d6e9fa13578abc361411b7e0", "withdrawn": "", "abstract": "The objective of this paper is to identify a finite group based on the orbit of a vector under its action. When a finite group acts unitarily on a Hilbert space, the associated Gram matrix lies in the group \nalgebra and satisfies identities that encode the algebraic group structure. We ask about the converse: Given a Gram matrix obtained from the orbit of a vector under the group action, can one recover the underlying\n\\emph{abstract} group structure? Our main result identifies a short list of conditions on a family of orthogonal matrices that force the family\nto be the right regular representation of a finite group. Building on this characterization, we\ndevelop a staged optimization framework that enforces these conditions progressively.\nNumerical experiments on the dihedral group $D_4$ and the tetrahedral rotation group $A_4$\nrecover $D_4$ exactly and all twelve $A_4$ matrices up to modest precision.", "id": "Paper/69195", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69195"}, {"title": " A Ghost Lemma for Commutative Ring Homomorphisms and Applications to Singularities ", "webprogram_exclude": "0", "session_ids": ["Session/18347"], "source_sha256": "0d1be59d88fbd13973c1081010f58ff84ecb3680c8d7dd6710e0177a4838bada", "withdrawn": "", "abstract": "We adapt the theory of ghost maps from the setting of module homomorphisms to the setting of commutative ring homomorphisms using Andr\\'{e}-Quillen homology. The Frobenius endomorphism gives a primary example of a ghost map in this setting. We prove an analogue of the ghost lemma in this setting and use it to deduce a characteristic independent generalization of Kunz's theorem and an analog for complete intersection rings.", "id": "Paper/69199", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69199"}, {"title": " Romantic Space and the History of the Concept of Space ", "webprogram_exclude": "0", "session_ids": ["Session/18373"], "source_sha256": "2c26ad25643337e7344e41633466ff36af692ae07e25440c3b6b0fb09baa42b0", "withdrawn": "", "abstract": "Over the last five years or so my colleague James R. Hofmann and I have been arguing about space. Hofmann, the anglophone biographer of André-Marie Ampère, objected to my description of Ampère’s electrodynamic experimental investigations of electromagnetic effects around a current carrying wire as a construction of what I called “Romantic Space.” Hofmann insisted that Ampère was a committed believer in Newtonian absolute space and that therefore what I called Romantic Space, “is simply the incorporation of Newtonian space into a cognitive process” and was therefore not what I claimed it to be, an early nineteenth century understanding of the concept of space. Generously, Hofmann did concede that I might be driving at something like an “exploratory stage in in creative mathematicians’ thought prior to formalization,” but if I was, he was unable to grasp it. There the matter stood until this year when a Brazilian historian of science, João Paulo Martins de Castro Chaib, published a paper, entirely independent of my own work, in which he used a materialist Marxist analysis of Ampère’s work to reach a conclusion not far from mine. In this paper, I look more closely at Chaib’s work on Ampère to defend my claims about Romantic Space and attempt a clearer articulation of Ampère’s investigation of electromagnetism as an exploratory stage in a creative mathematician’s thought prior to formalization.", "id": "Paper/69202", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69202"}, {"title": " Reimagining Mathematics Story Problems with AI: Supporting Teacher Learning and Instructional Practice ", "webprogram_exclude": "0", "session_ids": ["Session/18262"], "source_sha256": "93ca6df3ceb4eeaa2fafcba1dca56323437890775f7679418ead659563c04571", "withdrawn": "", "abstract": "High-quality mathematics story problems play a critical role in supporting students’ conceptual understanding, problem-solving competencies, and ability to connect real-world contexts to mathematical representations (National Council of Teachers of Mathematics, 2014). However, designing effective story problems remains a challenge for teachers, who must balance contextual relevance, linguistic clarity, mathematical accuracy, and developmental appropriateness. As artificial intelligence (AI) tools become increasingly accessible in educational settings, it is essential to understand how teachers can utilize these tools to enhance their task design practices and deepen their mathematical reasoning. This study investigates how preservice and in-service teachers enrolled in elementary mathematics methods courses at a southeastern U.S. university used the Math Story Word Problem and Multiple Explanation tools in MagicSchool.ai to generate, analyze, and revise mathematical story problems. Participants examined the mathematical demands and potential student misconceptions embedded within AI-generated story problems, evaluated the relevance of the contextual scenarios, and compared their own solution strategies with those produced by AI. Analysis of teacher artifacts and reflections showed that while teachers’ strategies often aligned with AI-generated approaches, particularly when traditional algorithms were used, AI also introduced teachers to unfamiliar strategies that expanded their problem-solving repertoire. Teachers further noted that AI provided limited visual representations and rarely incorporated manipulatives or models essential for supporting conceptual understanding. Findings suggest that structured engagement with AI can deepen teachers’ mathematical thinking, enhance their capacity to design effective story problems, and promote more reflective, student-centered instructional practices. Implications for teacher education and K–12 mathematics classrooms are discussed.", "id": "Paper/69204", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69204"}, {"title": " Fishing for Cospectral Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "49baf1283af49fd6fb552c7539054673159873b504a63a674489a20c6e88e1e4", "withdrawn": "", "abstract": "A graph is defined by its vertices and edges, and its spectral properties are determined by the eigenvalues of matrices associated with the graph structure. Cospectral graphs are non-isomorphic graphs that share the same eigenvalue spectrum for a given matrix. Understanding these cospectral pairs is essential, as it reveals both what can and cannot be determined about graph structure from spectral information alone. This paper provides constructions for generating cospectral graph pairs with respect to the signless Laplacian and distance signless Laplacian matrices. We generalize previous constructions by Lorenzen and extend the Godsil-McKay switching method to these matrices, accounting for nearly all cospectral pairs with a small number of vertices. These constructions provide tools for generating families of cospectral graphs and provide insight into the structure of spectral graph theory.", "id": "Paper/69205", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69205"}, {"title": " An Anatomically-Informed Linearized Electrical Impedance Tomography Reconstruction Algorithm for Real-Time Cardiopulmonary Imaging ", "webprogram_exclude": "0", "session_ids": ["Session/18298"], "source_sha256": "e877e7cecf5792795c8478a22af41179666e8985ae0a1fe915ba29770dd58ee9", "withdrawn": "", "abstract": "Electrical Impedance Tomography (EIT) is a real-time, non-ionizing medical imaging modality for visualizing the electrical structure of a body based on measurements made on the boundary. Electrical currents are applied through electrodes placed on the body and the resulting voltage measurements made on those electrodes are used to solve the inverse problem for the conductivity distribution on the interior. While the speed, portability, and low cost of EIT imaging are desirable for clinical use, due to the ill-posed nature of this problem, poor spatial resolution of images remains an issue. The Mean 3-Dimensional Atlas Newton (M3AN) algorithm looks to improve spatial resolution using the trusted one-step Gauss-Newton reconstruction approach by implementing an anatomically-informed initial guess based on the mean conductivity distribution of an anatomical atlas constructed from CT scans. Results using this algorithm on archival clinical data are shown for both ventilation and pulsatile perfusion imaging.", "id": "Paper/69213", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69213"}, {"title": " Continuous Data Assimilation with Learned Surrogate Dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/17919"], "source_sha256": "6c92171863b5918e60f96cb09cef05b4b0a0acbe0af23e0a3bbf4fe8631876ac", "withdrawn": "", "abstract": "Continuous data assimilation seeks to estimate the state of a dynamical system from partial observations. In many applications, however, the state dynamics are unknown or prohibitively expensive to simulate at the required resolution, leading to model error. Motivated by this challenge and the increasing adoption of machine learning surrogates in data assimilation, this paper develops a unified finite-dimensional analysis of nudging algorithms that employ learned surrogate models of the dynamics. We first establish general conditions on the dynamics and observations that guarantee accurate tracking for nudging with the true dynamics model, both in the noise-free and noisy settings. We then show that nudging algorithms that employ surrogate models retain exponential convergence up to an explicit error floor that quantifies the effects of surrogate approximation error and observation noise. Finally, we analyze surrogate models obtained by learning either the vector field or the short-time solution map of the system, and quantify the amount of training data needed to ensure accurate nudging in the noise-free setting. Numerical experiments support the theory.", "id": "Paper/69216", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69216"}, {"title": " A counting formula for Coxeter-type arrangements: Geometry and beyond ", "webprogram_exclude": "0", "session_ids": ["Session/19340"], "source_sha256": "ec34b0cb80476edcf18e054ae6e3b29bc1cc04abbc8c031a66f06887454744c5", "withdrawn": "", "abstract": "In 2018, Bernardi established a formula for counting the number of regions of a deformation of the braid arrangement as a signed sum over certain decorated trees. In joint work with Aaron Lin, we show, via a bijection with certain faces, that this signed sum has a geometric interpretation in terms of an Euler characteristic. In joint work with Olivier Bernardi, we use this insight to generalize the signed sum to other Coxeter types. To do so, we establish a new labeling of the faces of the $m$-Catalan arrangement of type B, C, and D by \\textit{marked capped trees}.", "id": "Paper/69222", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69222"}, {"title": " Non-conformist (but maybe conformal) techniques for geometric temari ", "webprogram_exclude": "0", "session_ids": ["Session/18232"], "source_sha256": "a7504a40ff178f470bf2f6aa127a1f8e82b51cb6c0dfeead3f055b48f96b6511", "withdrawn": "", "abstract": "Temari embroidery is a traditional Japanese craft. One starts with a mari, a 3-dimensional ball with an outer .5\"-thick firm layer through which one can stick a sturdy needle, covered by an 'unwoven skin' of fine colored thread tightly wrapped around the whole ball so as to cover the underlying layer completely. By stitching through the .5\" mantle, with needle stick holes in the unwoven skin that close up automatically, this mari is then embroidered in contrasting colors, often in very geometric patterns; the end result is a temari. \n\nTo help in setting up the pattern, various traditional techniques have been developed that typically use basic spherical geometry to set up a lattice of threads on the mari that are then used as a guideline for further stitching. Many of these techniques use some measuring devices and/or look-up tables to compute lengths of different basic segments or angles in the guideline pattern. \n\nWe propose a method that uses links between platonic solids to place pins on a mari that approximate the locations of the 20 vertices of a dodecahedron, without using guidelines; this is then followed by an iterative algorithm that in each step moves just one pin slightly, gradually reducing errors in the pin locations. The entire process can be carried out by eye (although one of us likes to combine this with some measurements), nevertheless ending up with a remarkably precise result. The 20 pin locations can then be used to design various patterns with icosahedral symmetry. Even when applied to mari that are visibly not perfectly round balls, the method works sufficiently well to lead to temari that are surprisingly pleasing and convincingly evoke icosahedral symmetry despite their imperfection. \n\nWe discuss mathematical aspects of the different steps, and show numerical simulations illustrating convergence of the iterative procedure. So far, we have no proof of convergence, but maybe someone in the audience can help.", "id": "Paper/69223", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69223"}, {"title": " Weak<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.054ex\" height=\"2.009ex\" style=\"vertical-align: -0.171ex;\" viewBox=\"0 -791.3 453.9 865.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">^*</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2217\" d=\"M229 286Q216 420 216 436Q216 454 240 464Q241 464 245 464T251 465Q263 464 273 456T283 436Q283 419 277 356T270 286L328 328Q384 369 389 372T399 375Q412 375 423 365T435 338Q435 325 425 315Q420 312 357 282T289 250L355 219L425 184Q434 175 434 161Q434 146 425 136T401 125Q393 125 383 131T328 171L270 213Q283 79 283 63Q283 53 276 44T250 35Q231 35 224 44T216 63Q216 80 222 143T229 213L171 171Q115 130 110 127Q106 124 100 124Q87 124 76 134T64 161Q64 166 64 169T67 175T72 181T81 188T94 195T113 204T138 215T170 230T210 250L74 315Q65 324 65 338Q65 353 74 363T98 374Q106 374 116 368T171 328L229 286Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-2217\" x=\"0\" y=\"513\"></use>\n</g>\n</svg> Sequential Cyclicity and Logarithmic Criteria in Radially Weighted Besov Spaces ", "webprogram_exclude": "0", "session_ids": ["Session/17377"], "source_sha256": "a32fd82f9bdb9c6461aac13aaed8ec56d741a48ff31f10a9cb13342da5d6b5ab", "withdrawn": "", "abstract": "\\begin{abstract}\nLet $\\mathcal{H}=B_\\omega^N$ be a radially weighted Besov space of holomorphic functions on the unit ball $\\mathbb{B}_d\\subseteq\\mathbb{C}^d$, and let $\\operatorname{Mult}(\\mathcal{H})$ denote its multiplier algebra. A function is cyclic if its polynomial multiples are dense in $\\mathcal{H}$. We study cyclicity through the stronger multiplier-algebraic notion of \\emph{weak$^*$ sequential cyclicity}: a multiplier $\\varphi$ has this property if there are multipliers $\\psi_n$ such that\n\\[\n\\psi_n\\varphi\\longrightarrow 1\n\\]\nin the weak$^*$ topology of $\\operatorname{Mult}(\\mathcal{H})$. Weak$^*$ sequential cyclicity implies cyclicity, and the two notions coincide for multipliers in normalized complete Pick spaces. Outside the complete Pick setting, however, the converse can fail. We also establish a comparison principle: if $|\\varphi|\\leq |g|$ on $\\mathbb{B}_d$ and $\\varphi$ is weak$^*$ sequentially cyclic, then so is $g$.\n\nThese ideas yield logarithmic criteria for cyclicity. Suppose\n\\[\nf\\in\\mathcal{H}\\cap H^\\infty(\\mathbb{B}_d),\n\\qquad 0<|f|\\leq1,\n\\qquad F=\\log\\frac{1}{f}.\n\\]\nWe replace the classical bounded-argument assumption by the translated-sector condition\n\\[\n|\\operatorname{Im}F|\\leq A+B\\operatorname{Re}F,\n\\]\nwhich permits genuinely unbounded argument. If $F$ belongs to the weak$^*$ sequential Smirnov class associated with $\\mathcal{H}$, then $f$ is cyclic. A converse holds under weak$^*$ sequential cyclicity. Consequently, in normalized complete Pick spaces, the sector condition gives a characterization of cyclicity in terms of the Smirnov membership of $\\log(1/f)$. The method also applies beyond the complete Pick setting, including the Hardy space $H^2(\\partial\\mathbb{B}_d)$ for $d\\geq2$.\n\nFinally, we identify the sharp universal power-growth threshold. Under the same Smirnov hypothesis, an estimate\n\\[\n|\\operatorname{Im}F|\\leq A+B(\\operatorname{Re}F)^p\n\\]\nforces cyclicity for $0<p\\leq1$. For every $p>1$, the conclusion fails already in $H^2(\\mathbb{D})$ and, by lifting, in the Drury--Arveson space; the counterexamples contain a nonconstant singular inner divisor. These results provide new insight into cyclicity phenomena in radially weighted Besov spaces, including spaces without the complete Pick property.\n\n\\end{abstract}", "id": "Paper/69224", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69224"}, {"title": " Out of the Margins: Images and perspectives from the AWM records, 1971–1985 ", "webprogram_exclude": "0", "session_ids": ["Session/18373"], "source_sha256": "5454a1bb13d466350753fcc3fec44ef7faba85076ded31def5939e49e37a0864", "withdrawn": "", "abstract": "The Association for Women in Mathematics (AWM) was founded in 1971 during the second wave of feminism in the United States to improve the position of women in math and encourage women and girls to study and seek careers in the field. Its records at Smith College comprise a rich and varied collection of materials illuminating not only the  actions and inner workings of the Association but also the significance of its work to both its membership and the broader public and the junctions of professional and domestic life during a watershed period for women's rights. \n\nIn this talk, we consider the reach and scope of AWM activities between 1971 and 1985 through the lens of unpublished letters, memos, reports, and marginalia, and the light they shed on member and public interests, practical and ideological challenges, and the changing landscape for women in mathematics during this period.", "id": "Paper/69229", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69229"}, {"title": " A Cubical Approach to <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"6.562ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 2825.2 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">(\\infty ,n)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-221E\" x=\"389\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2C\" x=\"1390\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-6E\" x=\"1835\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"2435\" y=\"0\"></use>\n</g>\n</svg>-categories with Adjoints ", "webprogram_exclude": "0", "session_ids": ["Session/18000"], "source_sha256": "90ff80b7108754c314f3f358ad43591d04a21d403607c788e80dd9664fe131b5", "withdrawn": "", "abstract": "In this talk we will discuss a cubical model for $(\\infty,n)$-categories with adjoints. We will show how this perspective allows for a description of the symmetries and monoidal structure on the $(\\infty,1)$-category of $(\\infty,n)$-categories with adjoints. Finally, we will exhibit the $(\\infty,n)$-category of framed bordisms in this model and describe its higher adjoints.", "id": "Paper/69231", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69231"}, {"title": " Numerical Analysis of Quasistatic Nonlocal Damage Evolution with Memory ", "webprogram_exclude": "0", "session_ids": ["Session/18377"], "source_sha256": "0993a3a25bb6c14882dc31a617ed818fddac7d4eba3f143b0673b8581a74ddfc", "withdrawn": "", "abstract": "Nonlocal models provide a natural framework for describing damage initiation and crack propagation without requiring an a priori specification of crack paths. In particular, peridynamic models incorporate spatial nonlocality through interactions between material points and can account for the gradual accumulation of damage under cyclic loading. In previous work, we established existence and uniqueness results for a quasistatic bond-based peridynamic model with memory, in which a history-dependent damage factor couples the deformation field to the nonlocal force operator. We also developed an iterative procedure for discrete bond-breaking evolution based on the Newton–Kantorovich framework.\n\nBuilding on these analytical results, this work will investigate the numerical approximation of quasistatic damage evolution under cyclic and variable loading. We will develop and analyze a computational scheme for tracking the evolution of the damage field and the associated displacement solution as bonds progressively lose their load-bearing capacity. Particular attention will be given to the influence of the nonlocal horizon, spatial discretization, loading history, and damage evolution on the resulting fracture patterns. Numerical experiments will be used to examine crack nucleation and propagation under repeated loading and to explore the relationship between accumulated damage and macroscopic failure.\n\nThe ultimate goal is to establish a mathematically grounded and computationally efficient framework for predicting damage evolution in materials subjected to complex loading histories. This approach may provide a foundation for future multiscale studies of fatigue and fracture using nonlocal continuum models.", "id": "Paper/69235", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69235"}, {"title": " Extremal Counts for Graph Colorings ", "webprogram_exclude": "0", "session_ids": ["Session/18367"], "source_sha256": "524373e9b105d0d6c1acad8ed236b64bd016c2f5c3dc2764359fa67e22c37d43", "withdrawn": "", "abstract": "For graphs $G$ and $H$, an $H$-coloring of $G$ is an assignment of colors to the vertices of $G$, with the colors being vertices of $H$, subject to the constraint that the colors on adjacent vertices of $G$ must be adjacent in $H$. By appropriate choice of $H$, $H$-colorings can encode independent sets in $G$, proper colorings of $G$, Widom-Rowlinson configurations on $G$, and many other graph notions. Siderenko showed that amongst all trees on $m$ vertices, the star graph $S_m$ maximizes the number of $H$-colorings for any graph $H$. Bruy\\`ere and M\\'elot considered a refinement of a special case of this result. They show that amongst all connected graphs on $n$ vertices and with independence number $\\alpha$ a modification of the balanced union of cliques, called $ZC_{n,\\alpha}$, is the unique maximizer of the homomorphism count into the target graph which encodes the count of independent sets in $G$.\n\nWe conjecture that in this setting, $ZC_{n,\\alpha}$ is the maximizer of the homomorphism count for a much larger family of target graphs. In this talk we report on progress in this direction.", "id": "Paper/69236", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69236"}, {"title": " An introduction to the stationary Hall equation ", "webprogram_exclude": "0", "session_ids": ["Session/18291"], "source_sha256": "3bfdef41b49c3829acb1575b397d779674bd6438da46bea0c42433e8cf716c41", "withdrawn": "", "abstract": "In this talk, we will focus on the question of non-uniqueness of solutions to the stationary Hall system $$\\Delta B + J \\times B = 0\\\\ div(B) = 0$$ in some low regularity classes.\n\nOn the one hand, this system exhibits a div-curl structure, suggesting the use of compensated compactness to study this question.\nOne the other hand, it can also be formulated as a conservation law, vaguely resembling the Euler equations, making it suitable for treatment with methods from convex integration.\n\nIn view of those two frameworks, we will discuss difficulties that arise when trying to answer the question of non-uniqueness coming from the rigidity induced by the curl operator.", "id": "Paper/69238", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69238"}, {"title": " Polya: An Agentic Harness for Teaching Formal Mathematics in Lean ", "webprogram_exclude": "0", "session_ids": ["Session/18190"], "source_sha256": "68c19460b9cd1a599383e38fe1a07f863785c00550e9fc2f54ba394087a72215", "withdrawn": "", "abstract": "Students already use AI to learn, but today's most capable agentic harnesses are built for programming, not teaching. The underlying models are generic, and could in principle tutor with unprecedented personalization, impedance matching a student's rate and style. Here, we describe Polya, a harness designed specifically to teach mathematics with the following components: \n\nFirst, Polya provides a framework for authoring tutorials in Lean, annotated with topics, concepts, and exercises. We have autoformalized tutorials on type theory, topology, order theory, and algebra; a graduate-level topic can be formalized and verified in roughly a day, depending on the subject.\n\nSecond, the Polya server lets authors publish tutorials, extracting concept graphs that link them internally and across every tutorial the server hosts. Students use the graph to navigate topics and set goals; it also frames our estimate of their mastery.\n\nThird, Polya serves exercises drawn from a selected concept subgraph or autoformalized on the fly from the student's progress. While solving, the student has the Lean Infoview and a chat and hint generator conditioned on their full history of solutions and questions. Keystrokes, hint requests, and questions feed an estimate of how well the student understands a concept and, importantly, its neighbors.\n\nPolya is in alpha testing with close collaborators and students and will be released to the community. It places the student at the center of a rapidly evolving ecosystem of formal mathematics tools, with the aim of accelerating their learning of Lean, of formal mathematics, and ultimately of mathematics itself.", "id": "Paper/69239", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69239"}, {"title": " A Mean Value Property for s-harmonic functions ", "webprogram_exclude": "0", "session_ids": ["Session/18283"], "source_sha256": "2074d7cbe3b3fc76d724fdf07446de46149861f8144412f91ba900f2a1e1384d", "withdrawn": "", "abstract": "The fractional Laplacian is a fundamental example of a nonlocal operator that arises naturally in harmonic analysis, probability theory, and partial differential equations. In this work, we present a Mean Value Property for s-harmonic functions, i.e. functions that satisfy $(-\\Delta)^su=0$ for s strictly between 0 and 1, where $(-\\Delta)^s$ is the fractional Laplacian. This work generalizes a recent result by Charro, Lebiedzik, and Raihen on Mean Value Properties for polyharmonic functions.", "id": "Paper/69244", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69244"}, {"title": " Updates from the Mathematical Art Manifesto group ", "webprogram_exclude": "0", "session_ids": ["Session/17986"], "source_sha256": "96c6e74591cda98ae9e3768680ebb9a8e5787c172c98128d281a0eafdae459a3", "withdrawn": "", "abstract": "Since Summer 2025, a group of mathematical artists and supporters from North America and Europe has met virtually each month to discuss mathematical art as Art, drawing on the ideas of art critic and philosopher Arthur Danto who defined Art as embodied meaning in an art theoretic/historic context. Notable recent writers on these issues have included George Hart, Frank Farris, and Edmund Harris. Rather than seeking a single, rigid definition of mathematical art, the group has explored the various practices, intentions, and sources of inspiration that drive the work. These conversations have informed the development of a mathematical art manifesto. This talk will highlight several of our most engaging discussions, present examples of work by group members, and report on the manifesto and the group’s ongoing activities.", "id": "Paper/69245", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69245"}, {"title": " Stochastic modeling for replicating cellular populations with cyclic behavior ", "webprogram_exclude": "0", "session_ids": ["Session/18303"], "source_sha256": "df01f4103da6a565d2c23059168c6fa3b61443d0ab7417d0852165f320338d59", "withdrawn": "", "abstract": "Periodic processes are fundamental to biological systems, from cell division cycles in yeast to circadian rhythms in mammalian cells. Understanding population-level dynamics in these processes has important implications for biological systems.\nIn this work, we present a framework using discrete-time multi-type Markov branching processes to model the dynamics of cellular reproduction in populations undergoing periodic processes. The approach naturally incorporates stochasticity, replication, and measurable biological quantities. Under mild conditions, we establish that these systems converge to well-defined long-term population-level limits. We also show that it is possible to characterize how parameters of the underlying periodic process (estimated from biological observables) influence both the asymptotic behavior and the transient dynamics.\nFinally, we apply this framework to data in the particular cases of the yeast cell cycle and the Malaria parasite intraerythrocytic developmental cycle (IEC), and we observe that the model faithfully reproduces the observed dynamical behaviors.", "id": "Paper/69247", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69247"}, {"title": " Bayesian Curve Reconstruction from Point Cloud Data Using Markov Chain Monte Carlo ", "webprogram_exclude": "0", "session_ids": ["Session/19338"], "source_sha256": "e4bd5243856bc53eba953bf6480dfcad97a432c1bafaa7e40fe5bbafbe8fe375", "withdrawn": "", "abstract": "Point-cloud data routinely captured by modern imaging and sensor technologies provide detailed geometric descriptions of objects and environments, but their analysis is hindered by large data volumes, localization noise, and missing information. In addition, existing point-cloud reconstruction pipelines typically return a single best-fit structure without uncertainty quantification. We introduce a fully Bayesian framework for representing point-cloud data and reconstructing closed curves, in which observed points are modeled as noisy perturbations of latent locations constrained to lie on the underlying curve that is regularized by a non-parametric prior. Posterior inference in our framework is carried out using a series of Markov chain Monte Carlo samplers tailored to point-cloud characteristics. Numerical experiments, including synthetic examples and real-world LiDAR datasets, show accurate reconstructions and quantified uncertainty over the recovered curves.", "id": "Paper/69250", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69250"}, {"title": " Modeling La Crosse Virus in North Carolina and Tennessee: Mosquito Activity and Human Infection ", "webprogram_exclude": "0", "session_ids": ["Session/17841"], "source_sha256": "8f4ac311ebca96a293020a9fe8984106300f08e78b0dd564953f4f7e9d006418", "withdrawn": "", "abstract": "La Crosse Virus (LACV) is a mosquito-borne virus that is spread through the bite of an infected \\textit{Aedes} mosquito. Individuals infected with the virus may develop La Crosse virus-neuroinvasive disease (LACV-ND), but most infections are asymptomatic or unreported. Reported cases primarily occur in individuals under 20 years old, and since 2001, most cases have occurred in western North Carolina and eastern Tennessee. In an effort to understand the dynamics of the virus, specifically from the vector to the human host, we used a system of ordinary differential equations to develop the first model that accounts for inter- and intra-year variability of LACV transmission in mosquito and human populations. Environmental effects on mosquito populations were incorporated using non-decreasing, time-varying functional forms of precipitation and temperature. We parameterized human demographics using population data, and used yearly case data and past seroprevalence studies to estimate human transmission rates and the proportion of reported cases. Sensitivity analysis of six model parameters identified the host-seeking mosquito death rate, immature-to-host-seeking development rate (successful adult emergence), and oviposition rate as having the greatest influence on infected mosquito abundance. Interestingly, the transovarial rate of transmission (proportion of eggs laid with LACV) and mosquito infection parameter had the greatest effect on predicted human cases. Parameter estimates indicated that reported case data could not uniquely identify parameter pairs of transmission rate and reporting proportion, highlighting the need for more reliable seroprevalence data for reducing uncertainty in model calibration.  With more mosquito and seroprevalence data, model uncertainty could be reduced, increasing our understanding of this important vector-borne disease.", "id": "Paper/69253", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69253"}, {"title": " Number theoretic aspects of vertex operator algebras beyond the <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.716ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 1169.4 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">C_2</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-43\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-43\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-32\" x=\"1011\" y=\"-213\"></use>\n</g>\n</svg>-cofinite setting ", "webprogram_exclude": "0", "session_ids": ["Session/18270"], "source_sha256": "4828360cc6fc79a68c3bdac537c73b6daaa1c7dac52a2dfce414b8bb9b047849", "withdrawn": "", "abstract": "We discuss why modularity properties naturally arise for characters of modules for infinite-dimensional Lie algebras, and how through the relation to vertex operator algebras one can push this picture beyond the classical setting, including recent progress in the irrational (i.e. non semi-simple) setting, and without an assumption of a finite number of simple modules.", "id": "Paper/69254", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69254"}, {"title": " MDS subcodes of polynomial evaluation codes ", "webprogram_exclude": "0", "session_ids": ["Session/18388"], "source_sha256": "cfd0f76a01c48652f8f135f3751a5abbbaa3be3302fa859066913efb1ca79afc", "withdrawn": "", "abstract": "Maximum distance separable codes are useful even in situations where linearity of the code is not a requirement of the application. In this talk, we consider certain nonlinear MDS subcodes of evaluation codes, their properties, and how they can be efficiently described even in the absence of linearity.", "id": "Paper/69256", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69256"}, {"title": " From dancing raisins to the chaotic bubblewheel: emergent dynamics of bubble-laden bodies ", "webprogram_exclude": "0", "session_ids": ["Session/17383"], "source_sha256": "2f6274fe6a852c59758f7872456ef77d6a26de322a6600d350c53226a4a82087", "withdrawn": "", "abstract": "Raisins dropped into a glass of carbonated water famously dance: bubbles nucleate upon them, lift them to the free surface, then burst, sending them plummeting, and the process begins anew. Experiments with fixed and freely moving bodies show how the lift from a growing bubble layer develops and saturates in time, and how this couples to the body dynamics to set the system into motion. For larger bodies, thousands of bubbles accumulate along the underbelly and render the body rotationally unstable, while rotation strips them away as they meet the air above. The resulting rotational dynamics include regimes of steady rolling, periodic and aperiodic rocking, chaos, and intermittent capsizing events. Treating the bubble population as a continuum field and projecting onto two modes leads to the generalized Lorenz system and its famed chaotic attractor. Even an extremely small center-of-mass offset can qualitatively change the dynamics, and an offset of a few percent stabilizes the body entirely. The floating experiment is a highly accessible physical realization of the Lorenz system which, owing to continuous gas loss from the fluid to the air above, sweeps slowly and without intervention across a classical bifurcation diagram in time.", "id": "Paper/69259", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69259"}, {"title": " Hermitian rank in ideal powers ", "webprogram_exclude": "0", "session_ids": ["Session/18295"], "source_sha256": "4d1e566572d12ac5b475db7c58e6ea08f48e7718f06027f9adbf3fc7df5187d0", "withdrawn": "", "abstract": "We prove that the (hermitian) rank of $QP^d$ is bounded from below by the rank of $P^d$ whenever $Q$ is not identically zero and real-analytic in a neighborhood of some point on the zero set of $P$ in $\\mathbb{C}^n$ and $P$ is a polynomial of bidegree at most $(1,1)$. This result generalizes the theorem of D'Angelo and the second for bihomogeneous $P$ and Huang's Lemma. The inequality demonstrates that real-analytic multipliers cannot reduce the algebraic complexity of ideal powers. Examples show that no hypothesis can be dropped. As an application, we give a lower bound on the target dimension for a CR map of hyperquadrics depending on the order of contact.", "id": "Paper/69260", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69260"}, {"title": " Data-efficient operator learning and matrix recovery ", "webprogram_exclude": "0", "session_ids": ["Session/18272"], "source_sha256": "de285073921c76d5c74299610047bb944c63ed33e9c402188b125dcd63c8ec2b", "withdrawn": "", "abstract": "Operator learning is a rapidly developing area focused on approximating the solution operators of partial differential equations (PDEs) from finitely many input-output function pairs. However, obtaining this data can be prohibitively expensive, so one hopes to solve this problem using as few input-output pairs as possible. It turns out that this is closely related to the problem of structured matrix recovery from matrix-vector products. We describe some algorithms for recovering various common structures of matrices. We then discuss the extension of these methods to infinite dimensions in the context of learning the Green's function of a uniformly elliptic PDE in 3D. This work provides a theoretical explanation for the observed strong performance of recent deep learning techniques in operator learning, even when there is limited data availability. We also discuss the importance of access to the adjoint operator in this problem, which corresponds to the role of transpose-matrix-vector products in numerical linear algebra.", "id": "Paper/69262", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69262"}, {"title": " Localization in Anderson-type models with non-stationary singular noise ", "webprogram_exclude": "0", "session_ids": ["Session/18292"], "source_sha256": "08a06fa6319ed7cb13162a5ca1afbba8b556bbdeaab3ffefad8a29b39f72e3f0", "withdrawn": "", "abstract": "The Anderson model is a fundamental one in the rigorous study of disordered materials. We will discuss various recent results concerning variants which eschew two simplifying assumptions; regularity and stationarity of the disorder.", "id": "Paper/69268", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69268"}, {"title": " Quadratic linear strands of prime ideals ", "webprogram_exclude": "0", "session_ids": ["Session/17373"], "source_sha256": "9aaee51836c73a8d672fc0a7ad9c8a624417ef5f8a542ba5dce4115f9ef968ec", "withdrawn": "", "abstract": "We prove sharp estimates on the quadratic strand of the resolution of any homogeneous prime ideal in a standard graded polynomial ring over an arbitrary field. Our bounds only depend on the height of the prime ideal, and they are optimal since for every $h \\geq 1$ we show that there exists a prime ideal of height $h$ achieving them. In particular, we show that a prime ideal of height $h$ can contain at most $h^2$ quadratic minimal generators, and that there exists a prime ideal minimally generated by $h^2$ quadrics.", "id": "Paper/69269", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69269"}, {"title": " Zero forcing propagation time intervals and graphs with fixed propagation time ", "webprogram_exclude": "0", "session_ids": ["Session/18207"], "source_sha256": "f2f5385cd141191fb65974e6ec07742d0d920c5346d0d24b983d6936eae4c75d", "withdrawn": "", "abstract": "Zero forcing in a graph refers to the evolution of vertex states under repeated application of a color change rule. Typically the states are chosen to be blue and white, and a forcing set is an initial set of blue vertices such that all of the vertices are blue at the end of the process.  In this context, the propagation time of a set in a graph is the number of iterations of the color change rule required to have all vertices blue, performing independent color changes simultaneously.  Different minimal forcing sets need not have the same propagation time, and we study the realizability of specific  integers as propagation times of minimal forcing sets in graphs for two of the most well-studied color change rules (standard and positive semidefinite). Particular attention is paid to the case where all minimal forcing sets have the same propagation time, and we term this phenomenon fixed propagation time. For each of the two variants, we present a general form of graphs all of which have fixed propagation time equal to one. We conjecture that these are the only such graphs and prove these conjectures for joins of graphs. Families of graphs with longer fixed propagation time for standard forcing are exhibited, and it is shown that such graphs do not exist for positive semidefinite forcing.", "id": "Paper/69271", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69271"}, {"title": " Bayesian Machine Learning Enabled Uncertainty Quantification of Atherosclerotic Cardiovascular Disease Risk Prediction ", "webprogram_exclude": "0", "session_ids": ["Session/19340"], "source_sha256": "09b1662b3712b1da74d294d9e9b726a3306dcd4380d02f7cb089e9a538f52de2", "withdrawn": "", "abstract": "Cardiovascular disease (CVD) risk scores estimate an individual’s future CVD risk and help guide preventive care decisions. Commonly used scores include the Pooled Cohort Equation, QRISK3, SCORE2, and PREVENT.  These risk prediction methods often only provide a point estimate. However, this disregards the inherent uncertainty present in these predictions, such as sampling and parameter estimate uncertainty, which could impact clinical decision making.  While current work has highlighted the need to include uncertainty quantification with CVD risk scores, there is not currently a widely accepted method to do so. To address this research gap, we leverage the PREVENT Equations (10-year risk) and data from the UK Biobank to train a Bayesian Additive Regression Tree Model to predict patients’ 10-year atherosclerotic CVD risk. This Bayesian approach provides not only a point estimate of 10-year atherosclerotic CVD risk but also a distribution of potential scores to represent the uncertainty surrounding the point estimate. We then investigate the differences in uncertainty within different subgroups of the overall UK Biobank population and the shared characteristics of participants with larger amounts of uncertainty. We also discuss different metrics to help quantify the uncertainty that are both mathematically relevant and clinically useful. Lastly, we introduce plans to further apply the model to other potential risk scores and package the trained model for epidemiologists, public health officials, and clinicians.", "id": "Paper/69273", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69273"}, {"title": " Fast operator learning for mapping correlations ", "webprogram_exclude": "0", "session_ids": ["Session/17807"], "source_sha256": "eacd892d53555f91e2a0c4a3af831da3ef775329dd49ec9ffb83270c62bd74fa", "withdrawn": "", "abstract": "We propose a fast, optimization-free method for learning the transition operators of high-dimensional Markov processes. The central idea is to perform a Galerkin projection of the transition operator to a suitable set of low-order bases that capture the correlations between the dimensions. Such a discretized operator can be obtained from moments corresponding to our choice of basis without curse of dimensionality. Furthermore, by exploiting its low-rank structure and the spatial decay of correlations, we can obtain a compressed representation with computational complexity of order $\\mathcal{O}(dN)$, where $d$ is the dimensionality and $N$ is the sample size. We further theoretically analyze the approximation error of the proposed compressed representation. We numerically demonstrate that the learned operator allows efficient prediction of future events and solving high-dimensional boundary value problems. This gives rise to a simple linear algebraic method for high-dimensional rare-events simulations.", "id": "Paper/69274", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69274"}, {"title": " Toward the construction of tensor categories with modularity properties ", "webprogram_exclude": "0", "session_ids": ["Session/17907"], "source_sha256": "4088d56d0a22db54516d1acaa43634391bf2988db1dac866f0351311503c957d", "withdrawn": "", "abstract": "We discuss recent progress toward constructing classes of modules for vertex operator algebras which exhibit modularity type properties for collections of their graded traces and more generalized trace-like $q$-series.  In particular, we discuss progress toward constructing new modular (or quasi-modular) tensor categories.", "id": "Paper/69278", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69278"}, {"title": " Higher Effectivity, toward a notion of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"7.491ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 3225.2 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">(\\infty ,\\infty )</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-221E\" x=\"389\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2C\" x=\"1390\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-221E\" x=\"1835\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"2835\" y=\"0\"></use>\n</g>\n</svg>-topos. ", "webprogram_exclude": "0", "session_ids": ["Session/18210"], "source_sha256": "8fcc12c7f0eca43c0dda786f12812ed91270cfd4b376766fb48f29f7c0e68802", "withdrawn": "", "abstract": "One of the fundamental properties of the category of spaces is the effectiveness of equivalence relations. Toposes, that can be viewed, roughly speaking, as categories that share the well-behaved features of spaces, are required to satisfy it by Giraud’s axioms.\n\nIn this talk, we will introduce an $(\\infty,\\infty)$-categorical analogue of equivalence relations and state a theorem asserting their effectiveness in $(\\infty,\\infty)$-categories. If time permits, we will then use this perspective as  for proposing a notion of $(\\infty,\\infty)$-topos.", "id": "Paper/69279", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69279"}, {"title": " A Nonlocal Approach to Phase-Field Modeling of Solidification ", "webprogram_exclude": "0", "session_ids": ["Session/18377"], "source_sha256": "54558d022d85e20c65f219b1b6ec8009c985796ce4bea9b6242d899c87ff9699", "withdrawn": "", "abstract": "Solidification models of pure materials commonly use phase-field models as a way to track the solid-liquid interface.  In instances where a sharp interface is desired, a classical local phase-field model becomes restrictive because it requires taking the limit of an interfacial width parameter, and how small one can take that parameter is tied to the resolution mesh.  In this talk, we consider a nonlocal alternative, in which the local diffusion operator has been replaced with a nonlocal operator.  Though the natural nonlocal analog for such a system is a nonlocal Allen-Cahn model, we consider a non-mass-conserving Cahn-Hilliard type model that allows a sharp interface to evolve in time.   We will present our efficient discretization scheme as well as validation of our model against analytic solutions of associated sharp-interface Stefan problems.  This work was performed in collaboration with Oak Ridge National Laboratory under an appointment to the Minority Serving Institutions Internship Program (MSIIP) administered by the Oak Ridge Institute for Science and Education (ORISE) for the National Nuclear Security Administration (NNSA) and U.S. Department of Energy (DOE). ORISE is managed by Oak Ridge Associated Universities (ORAU). All opinions expressed in this publication is the author’s and do not necessarily reflect the policies and views of NNSA, DOE, ORISE or ORAU.", "id": "Paper/69282", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69282"}, {"title": " Combinatorics of agreement zero codes ", "webprogram_exclude": "0", "session_ids": ["Session/19339"], "source_sha256": "f33d2b27fa0e5733b6756f40f0b8602b540f987a8ee1013b6030fefca3977598", "withdrawn": "", "abstract": "In this talk, we enumerate sub-codes of Reed-Solomon codes over $\\mathbb{F}_q$, where the number of codewords in a sub-code is $q$, and no two codewords agree in any position. Exact enumeration for any field size $q$ and maximum degree 0,1, and $q-1$ are proven. More general results, such as factors and bounds, for all degrees are found. Finally, exact results for small maximum degree and field size pairs are calculated.", "id": "Paper/69283", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69283"}, {"title": " An Introduction to Boundary Integral Equations ", "webprogram_exclude": "0", "session_ids": ["Session/18367"], "source_sha256": "25ee768f68bf101476d94906535556be80b1d5dc0499b0aa3f71152dee1b498e", "withdrawn": "", "abstract": "We will explore boundary integral equations both theoretically and numerically. Consider a Laplace boundary value problem, say \\(\\Delta u=0\\) for \\(x \\in D\\subset \\mathbb{R}^3\\) and \\(u=f\\) for \\(x\\in \\partial D\\). Green's formula gives us a way of representing the solution as an integral over the boundary. This takes us from a 3D boundary value problem to a 2D boundary integral equation, which is a great numerical reduction.", "id": "Paper/69286", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69286"}, {"title": " Sketching Without the Curse: Linear-Scaling Randomized Algorithms in High Dimensions ", "webprogram_exclude": "0", "session_ids": ["Session/19350"], "source_sha256": "0e93099f98665f894e9299e0ace35ae68d54ebbc25070686df9d2cefe334e931", "withdrawn": "", "abstract": "We introduce the TTStack sketch, a structured random projection tailored to the tensor train (TT) format that unifies existing TT-adapted sketching operators. By varying two integer parameters the block count $P$ and block rank $R$, TTStack interpolates between the Khatri-Rao sketch ($R=1$) and the Gaussian TT sketch ($P=1$). We prove that TTStack can preserve a subspace's geometry with high probability while acting as a linear dimensional reduction map through an Oblivious Subspace Embedding (OSE) property given parameters $R = \\mathcal{O}(d(r+\\log 1/\\delta))$ and $P = \\mathcal{O}(\\varepsilon^{-2})$, or alternatively achieve a more relaxed, yet useful guarantee through an Oblivious Subspace Injection (OSI) property under the more lenient condition $R = \\mathcal{O}(d)$ and $P = \\mathcal{O}(\\varepsilon^{-2}(r + \\log r/\\delta))$ which lends itself to natural parallelization. Both guarantees depend only linearly on the tensor order $d$ and on the subspace dimension $r$, in contrast to prior constructions that are known to suffer from the curse of dimensionality thus requiring an exponential scaling in $d$. This framework directly stablishes quasi-optimal error bounds for the low-rank factorization and randomized TT rounding in both the fixed-rank and fixed-precision regimes.", "id": "Paper/69287", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69287"}, {"title": " A synthetic description of equivariant motivic homotopy theory ", "webprogram_exclude": "0", "session_ids": ["Session/17701"], "source_sha256": "147334622698bc0b12decfde351d357c395e61f6ea6a6b052b6330d9431d1bfd", "withdrawn": "", "abstract": "Work of Pstrągowski and Gheorghe-Isaksen-Krause-Ricka provide a description of (cellular, $p$-complete) motivic homotopy theory over $\\mathbb{C}$ which does not reference algebraic geometry, in terms of what have come to be known as \\emph{synthetic spectra}. This category can be thought as a categorification of the Adams-Novikov spectral sequence, and the aforementioned equivalence provides an explanation for earlier observations which suggested that the Adams-Novikov spectral sequence can be read off from the $\\mathbb{C}$-motivic sphere. \n\nI will discuss joint work with Lucas Piessevaux which shows that many aspects of this story can be generalized in the presence of the action of a finite abelian group, hopefully highlighting phenomena which are not as visible in the non-equivariant setting.", "id": "Paper/69288", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69288"}, {"title": " Sketching Without the Curse: Linear-Scaling Randomized Algorithms for Tensor Trains ", "webprogram_exclude": "0", "session_ids": ["Session/19350"], "source_sha256": "4c188e968a7fb6287b72341e100b5c71a7cabdb77f016d520cbefe311871024e", "withdrawn": "", "abstract": "We introduce the TTStack sketch, a structured random projection tailored to the tensor train (TT) format that unifies existing TT-adapted sketching operators. By varying two integer parameters the block count $P$ and block rank $R$, TTStack interpolates between the Khatri-Rao sketch ($R=1$) and the Gaussian TT sketch ($P=1$). We prove that TTStack can preserve a subspace's geometry with high probability while acting as a linear dimensional reduction map through an Oblivious Subspace Embedding (OSE) property given parameters $R = \\mathcal{O}(d(r+\\log 1/\\delta))$ and $P = \\mathcal{O}(\\varepsilon^{-2})$, or alternatively achieve a more relaxed, yet useful guarantee through an Oblivious Subspace Injection (OSI) property under the more lenient condition $R = \\mathcal{O}(d)$ and $P = \\mathcal{O}(\\varepsilon^{-2}(r + \\log r/\\delta))$ which lends itself to natural parallelization. Both guarantees depend only linearly on the tensor order $d$ and on the subspace dimension $r$, in contrast to prior constructions that are known to suffer from the curse of dimensionality thus requiring an exponential scaling in $d$. This framework directly stablishes quasi-optimal error bounds for the low-rank factorization and randomized TT rounding in both the fixed-rank and fixed-precision regimes.", "id": "Paper/69290", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69290"}, {"title": " Jacob Bernoulli on the Evolute of the Cycloid and Some Interesting Applications ", "webprogram_exclude": "0", "session_ids": ["Session/18373"], "source_sha256": "c0142ffb28dc4a5eb9d3c2b1821925600693a461cec06ce62df1eea50a8280d8", "withdrawn": "", "abstract": "In the June 1692 volume of the \\textit{Acta Eruditorum} Jacob Bernoulli wrote: “I had scarcely submitted to the Editors of the \\textit{Acta} my recent speculation on Cycloids and other curves, when on the following day I received a letter from my Brother [Johann Bernoulli] in Paris, in which he communicated some excellent things pertaining to this topic... all of which I could not read without astonishment, when I considered that neither of us knew anything of the other’s speculations concerning these curves. But these things gave me the opportunity to take up again this material, which had already been set aside.” During this period Johann Bernoulli was working with Guillaume François Antoine, Marquis de l'Hôpital. This talk will consider Jacob Bernoulli’s May and June 1692 \\textit{Acta} papers and the results relating to cycloids, evolutes and caustics. This will also be connected to some of what L'Hôpital later published about the same topics in \\textit{Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes} and some loose connections to twentieth century architecture.", "id": "Paper/69292", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69292"}, {"title": " AI in Crystallography: Mathematics Exposes Artificial Illusions in Material Design ", "webprogram_exclude": "0", "session_ids": ["Session/18241"], "source_sha256": "7f6059c5818ef959bfd69ac2465fed62baa7025862c40bf506c14135ec802a5d", "withdrawn": "", "abstract": "Crystallography is the study of solid crystalline materials. Chemists dream of designing a new material that would change the world. Google’s AI tool, GNoME, tried to predict new materials by generating 2.2 million simulated crystals [1], but failed to recognise thousands of exact duplicates and many more near-duplicates. \n\nThese duplicates had flown under the radar because there are an infinite number of different discrete representations of the same crystal structure. Since the derivation of the 230 space-groups in the 1890s, crystallographers have relied on these symmetry groups to study 3D periodic structures.\nHowever, any experimental noise or thermodynamic atom vibrations break the symmetry. In reality, atoms in crystals have real continuous coordinates and aren’t restricted to a discrete grid. \nTherefore, comparing crystals reliably requires a new geometric approach developed by mathematicians in the last decade, which uses equivalence classes, isometry, invariants, and metrics that change continuously under perturbations. [2] [3]\n\nWe have developed and implemented a white-box algorithm that can generate 2.2 million new-looking crystals in less than 24 hours on a modest laptop with the power of school-level geometry rather than AI. With the press of a single button, anyone can disguise an existing crystal and bypass detections that do not use Lipschitz continuous metrics. Therefore, it is imperative to analyse new creations mathematically to see which are the same and which are different, especially to avoid black-box Artificial Illusions.\n\nUsing geometry to rigorously study real objects is growing beyond just mathematical crystallography and into an emerging field called Geometric Data Science which tackles practical challenges in object recognition and\ndata comparison by converting them into formally stated mathematical problems.\n\n[1] Merchant, A., & Cubuk, E. D. (2023, November 29). Millions of new materials discovered with deep learning. Google DeepMind. \n\n[2] Olga Anosova, Vitaliy Kurlin, Marjorie Senechal. The importance of definitions in crystallography. IUCrJ, v.11 (4), p.453-463 (2024).\n\n[3] Daniel Widdowson, Vitaliy Kurlin. Pointwise Distance Distributions for detecting near-duplicates in large materials databases. SIAM Journal on Applied Mathematics, v.86 (3), p.898-918 (2026).", "id": "Paper/69293", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69293"}, {"title": " Privately Outsourcing Polynomial Computations ", "webprogram_exclude": "0", "session_ids": ["Session/18389"], "source_sha256": "ba3a5c79338b49add2e94871ff3a4500375f072da80798a7230820a47f7111f6", "withdrawn": "", "abstract": "We consider the problem of secure polynomial computation over private data using an untrusted third-party computing service. Building on existing information-theoretic frameworks for privacy-preserving outsourced computation, we investigate extensions that broaden the range of supported computation scenarios while maintaining strong privacy guarantees. We also address scalability issues associated with the storage and management of auxiliary information, and develop an extension that combines information-theoretic and computational tools to reduce this overhead. The resulting framework provides a more flexible and scalable approach to secure computation over private data.", "id": "Paper/69295", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69295"}, {"title": " Singing Math in the Middle West: Purdue engineering and college songs of the Harlequin Club, 1907-1912 ", "webprogram_exclude": "0", "session_ids": ["Session/18373"], "source_sha256": "4c3e5316fa3a32c3c9127545927560b94e94f9cba02cd7a1e5dac61a14b3b4cb", "withdrawn": "", "abstract": "This paper draws attention to the mathematical singing traditions of Purdue University, especially in the early productions of the student-led Harlequin Club. Integrating perspectives on college singing and mathematical student life, it particularly investigates what it meant for the performers to be singing “engineering” at the time. The Harlequin Club followed the example of the MIT Tech Show, an outgrowth of each institution’s transformation of a problematic minstrel tradition into celebrations of college life. In the newly rebranded shows, some “college man” would be embroiled in fair-flung plots, odd locales, and usually romance, all the while singing about distinctive college studies, including mathematics. At Purdue, engineering’s unsteady status came to the fore, as the strangeness of the situations emphasized shifting roles and negotiated relationships. The sheet music cover for the 1909 song “Back to Old Purdue,” though playing on clear nostalgia, was not so centrally about the Purdue student character but rather about someone piratical, with guns smoking and an unusual tower in the background. In the songs, sheet music covers, and related objects, singing traditions indicate the strange expectations placed on college students studying mathematical subjects, especially engineering.", "id": "Paper/69297", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69297"}, {"title": " Reselection in the Game of Best Choice \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18205"], "source_sha256": "0f59175bc5ee2efa913506ee370d3bf6aa10c8229c3b90213e2ee09a5a1dc9f6", "withdrawn": "", "abstract": "In the game of best choice, better known as the secretary problem, an interviewer meets candidates one at a time in random order and must decide immediately whether to hire, with no chance to return to anyone passed over. The classical analysis assumes the candidate rankings are uniformly distributed, which implicitly requires that the interviewer have no influence over the candidate pool.\n\nWe propose a model in which the interviewer instead refines their ranking criteria while interviewing and uses what they learn to improve the pool, a feedback loop we call the reselect step. The resulting distribution on the symmetric group favors permutations in which better candidates tend to arrive later. Our main tool is a permutation statistic we call bottom-to-top maxima, which in the interview story marks a candidate who arrives after everyone ranked below them. We give combinatorial formulas for the distribution in terms of these, recovering a result of Pitman and Stanley in the case of the identity permutation. The distribution itself turns out to go back to Steck in the early 1970s, where it was expressed as a matrix determinant.\n\nWe then solve the model in which a single reselect step occurs after a proportion $y$ of the interviews. The probability of winning under optimal play remains asymptotically $1/e$, but in general no positional strategy attains it. The optimal rule instead compares the current interview position with the next bottom-to-top maximum occurring after the reselect step. We show that the switch from rejecting to accepting always falls between positions $1/e$ and $1/e + (1-1/e)y$.\n\nThis project began at the 2025 REUF workshop at ICERM, and is joint work with Dillon Hanson and Brant Jones.", "id": "Paper/69298", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69298"}, {"title": " Eisenstein series modulo prime powers ", "webprogram_exclude": "0", "session_ids": ["Session/17450"], "source_sha256": "e12572f940a9d7659f0288e567d1bc4be41ffee96a1b3a2f8fc4f03f2d502106", "withdrawn": "", "abstract": "If $p\\geq 5$ is prime and $k\\geq 4$ is an even integer with $(p-1)\\nmid k$ we consider the  Eisenstein series $G_k$ on $\\SL_2(\\Z)$ modulo powers of $p$.\nIt is classically known that for such $k$ we have $G_k\\equiv G_{k'}\\pmod p$\nif $k\\equiv k'\\pmod{p-1}$.\nHere we obtain a generalization modulo prime powers  $p^m$.  In particular we show that, \n modulo powers of  $E_{p-1}$, every such Eisenstein series is congruent modulo $p^m$ to a modular form of weight at most $mp$.", "id": "Paper/69300", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69300"}, {"title": " Being in the right place at the right time: how spatial and temporal covariances determine population growth ", "webprogram_exclude": "0", "session_ids": ["Session/18009"], "source_sha256": "b95553c41811f48d5f1fd80d02139a327dc34ad9950d04c2e754e824bcf8fb28", "withdrawn": "", "abstract": "For linear models of populations living in spatially heterogeneous environments, the long-term growth rate (the dominant Lyapunov exponent) is determined by the time average of the population-weighted mean of the local per-capita growth rates. This average decomposes into a mean effect plus covariance terms: a spatial covariance between where individuals tend to be and how good those places are on average, and a temporal covariance between when individuals are in a place and how good that place is at that moment. In this talk, I use this decomposition to revisit several results on multipatch models in continuous time and to connect them to related work in the literature. For deterministic ODE models, the reduction principle (more dispersal lowers the growth rate) corresponds to dispersal eroding a nonnegative spatial covariance. For stochastic differential equation models with environmental noise in each patch, a second term enters, the variance of the population-weighted local growth rates, which dispersal reduces. The tension between these terms allows dispersal to increase growth rates or to have non-monotonic effects. For piecewise deterministic Markov process models, in which the environment switches randomly between finitely many states, approximations of the growth rate in the slow and fast switching limits show that slower fluctuations generate positive temporal covariances that inflate growth, and that random and periodic fluctuations have different effects at faster time scales. Throughout, I relate these results to the inflationary effect, spatial bet hedging, and reduction principle from the biological literature. Open problems will be highlighted", "id": "Paper/69301", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69301"}, {"title": " Energy-Based Filtration of Alternative RNA Secondary Structures ", "webprogram_exclude": "0", "session_ids": ["Session/17970"], "source_sha256": "7ecd5350eada853c0ab07d852a1f2f254a5fb3e2cab4ca47353393b0de44030b", "withdrawn": "", "abstract": "RNA secondary structure prediction is commonly formulated as an energy-minimization problem under the nearest-neighbor thermodynamic model. However, the minimum-free-energy structure can miss helices present in known structures, motivating the consideration of alternative predictions. We systematically vary the multiloop parameters of the energy model to generate alternative optimal structures and introduce an energy-based filtration to identify a compact set of plausible candidates. The filtration separates the energetic contributions associated with the varied parameters, allowing structures generated under different parameter choices to be compared consistently. Across several RNA families, the resulting ensembles frequently contain structures with improved recovery of known helices while substantially reducing the number of candidates. Compared with Boltzmann sampling, the filtered ensembles provide a more focused collection of alternative helices, particularly among lower-probability helices where sampling produces many competing predictions.", "id": "Paper/69311", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69311"}, {"title": " The Iterated Parabolic Maximum Principle ", "webprogram_exclude": "0", "session_ids": ["Session/19363"], "source_sha256": "0d925c200aba708212a833b14330a90d8f168422ffb2d747fba2ff215df7375d", "withdrawn": "", "abstract": "In this talk, we extend the Iterated Maximum Principle to an Iterated Parabolic Maximum Principle. We thus use this extension to prove existence-uniqueness of viscosity solutions to the parabolic infinite Laplace equation in Grushin-type spaces. We then explore the long-term behavior of these solutions. These results provide a parabolic counterpart to the elliptic theory of infinite-Laplace equations in Grushin-type spaces.", "id": "Paper/69317", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69317"}, {"title": " The Brunn-Minkowski inequality on curved spaces ", "webprogram_exclude": "0", "session_ids": ["Session/17991"], "source_sha256": "e830c1067ec0250a9c3c371c7930d7e15b740bf1422d4c97e6a68c5fbb350ffe", "withdrawn": "", "abstract": "We present recent work on saturation and stability of the Brunn-Minkowski inequality on manifolds with Ricci curvature bounded below.", "id": "Paper/69319", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69319"}, {"title": " Power Domination for Random 4-Regular Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18207"], "source_sha256": "f1fb90308652a8c5180aeb48e4f5c291ac74381dcad09136a92f26e8a6666259", "withdrawn": "", "abstract": "The power domination process is a graph-theoretic process which models the observance of a power network through placement of Phasor Measurement Units. Building on work by Kang and Wormald, we provide an upper bound for the power domination number of random quartic graphs which holds asymptotically almost surely. The proof involves an analysis of a natural algorithm for building such a set via the so-called differential equations method.", "id": "Paper/69320", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69320"}, {"title": " F-singularities of foliations ", "webprogram_exclude": "0", "session_ids": ["Session/17929"], "source_sha256": "7779a2aa83036cffc6136cabf23a076b9efbf108105623739863aaa3c1817c80", "withdrawn": "", "abstract": "We develop a theory of F -singularities of foliations in positive characteristic that naturally contains the classical theory of F -singularities as a particular case and link it to the minimal model program for foliations in positive chracteristic.", "id": "Paper/69322", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69322"}, {"title": " MinRank Problem - SupportMinors Modeling ", "webprogram_exclude": "0", "session_ids": ["Session/18073"], "source_sha256": "d86c62c3d10ca96140425d5ec0618ae209917d16388a4d13dd71057e9e29592a", "withdrawn": "", "abstract": "The MinRank Problem is the computational problem of finding a low-rank linear combination of a given set of matrices. Several cryptographic attacks can be reduced to instances of MinRank. In this talk, I will introduce the SupportMinors Modeling, a recent approach to solving the MinRank Problem. We will discuss the construction of the modeling and the heuristics used to estimate its complexity, as well as the theoretical results that we are able to prove. These results provide a rigorous foundation for some of the complexity estimates underlying the SupportMinors approach.", "id": "Paper/69323", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69323"}, {"title": " Searching for Hard Grid Diagrams of the Unknot ", "webprogram_exclude": "0", "session_ids": ["Session/18384"], "source_sha256": "c333fd278e3ec1945f465959bde8a1903d51cb77034ea429b6294b1ccad6c4c5", "withdrawn": "", "abstract": "Diagrams provide a useful way to represent knots, and different types of diagrams\nadmit different collections of moves that transform one diagram into another. In\nmany settings, this leads to the notion of \\emph{hardness}: whether simplifying a diagram requires first increasing some measure of its complexity. Grid diagrams are one\nsuch type of knot diagram, but many questions under the corresponding Cromwell\nmoves remain unanswered. We study this idea for grid diagrams of the unknot. We introduce grid diagrams of the unknot and the associated Cromwell moves, then discuss results concerning the relationships among these diagrams. These relationships allow us to generate large collections of unknot grid diagrams and search for hard examples. We conclude by presenting newly discovered hard grid diagrams of the unknot.", "id": "Paper/69324", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69324"}, {"title": " Math in the field: Diffusion models and the minimum habitat size for bobwhite quail ", "webprogram_exclude": "0", "session_ids": ["Session/17688"], "source_sha256": "88d2cc873517258415d2670dac05bd490107c47f11939651ca5f72813160f73c", "withdrawn": "", "abstract": "Habitat fragmentation divides continuous habitat into smaller patches separated by a less suitable matrix. For many species, persistence depends not only on demographic processes within a patch but also on movement across habitat boundaries, which may change as local population density increases. In this talk, we develop a reaction–diffusion framework for studying population persistence in fragmented landscapes. The reaction term describes local population growth, while diffusion represents dispersal through space. Particular attention is given to movement at the habitat–matrix interface. We compare boundary conditions representing emigration from a patch with those incorporating density-dependent emigration, in which the tendency to leave increases with crowding. These boundary assumptions can substantially affect the relationship between patch size and population persistence. We apply the framework to northern bobwhite quail to estimate a biologically meaningful critical patch size for persistence. The model is parameterized using movement and demographic rates reported in field studies, supplemented by fitted relationships where direct estimates are unavailable. By comparing predictions under alternative movement assumptions, the analysis provides a mathematical basis for evaluating common conservation rules of thumb and identifying which aspects of edge behavior most strongly influence minimum patch-size recommendations.", "id": "Paper/69325", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69325"}, {"title": " Too Many Crystals: Fast generation of billions of differently looking crystals using geometry ", "webprogram_exclude": "0", "session_ids": ["Session/18078"], "source_sha256": "f3ed7b2ed51e9a7ec22e0883e5b5095aab7aac98a261ba05f372cb57fbb5e3b3", "withdrawn": "", "abstract": "Crystallography is the study of solid crystalline materials. Chemists dream of designing a new material that would change the world. Google’s AI tool, GNoME, tried to predict new materials by generating 2.2 million simulated crystals [1], but failed to recognise thousands of exact duplicates and many more near-duplicates. \n\nDue to experimental noise and thermodynamic vibrations which break the symmetry, atoms in crystals have real continuous coordinates and aren’t restricted to a discrete grid. Therefore, comparing crystals reliably requires a geometric approach using equivalence classes, isometry, invariants, and metrics that change continuously under perturbations. [2] [3]\n\nWe demonstrate a white-box algorithm that can generate 2.2 million new-looking crystals in less than 24 hours on a modest laptop with the power of school-level geometry rather than AI. With the press of a single button, anyone can disguise an existing crystal so that its Crystallographic Information File (CIF) looks completely different and bypasses filters and detections that do not use Lipschitz continuous metrics. Therefore, it is imperative to analyse new creations mathematically to see which are the same and which are different, especially to avoid black-box Artificial Illusions.\n\nUsing geometry to rigorously study real objects is growing beyond just mathematical crystallography and into an emerging field called Geometric Data Science which tackles practical challenges in object recognition and\ndata comparison by converting them into formally stated mathematical problems.\n\n[1] Merchant, A., & Cubuk, E. D. (2023, November 29). Millions of new materials discovered with deep learning. Google DeepMind. \n\n[2] Olga Anosova, Vitaliy Kurlin, Marjorie Senechal. The importance of definitions in crystallography. IUCrJ, v.11 (4), p.453-463 (2024),\n\n[3] Daniel Widdowson, Vitaliy Kurlin. Pointwise Distance Distributions for detecting near-duplicates in large materials databases. SIAM Journal on Applied Mathematics, v.86 (3), p.898-918 (2026)", "id": "Paper/69326", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69326"}, {"title": " Carcinogenesis Timelines in Early- and Late-Onset Cancers and Across Birth Cohorts ", "webprogram_exclude": "0", "session_ids": ["Session/17688"], "source_sha256": "6a1b60c9538f8cd7ce8cc91d91b0f1868fc7f9e0b8bd296a1afd34f4b33c1521", "withdrawn": "", "abstract": "Cancer develops through the process of carcinogenesis, which entails sequential mutations and clonal expansions. Knowing when these events, particularly mutations, occur is crucial for prevention and early detection strategies. This is especially important for early-onset cancers, which have shown a concerning increase in recent years. However, these mutational steps are difficult to observe at the population level, making mathematical modeling particularly valuable.\nWe modeled sequential stages of carcinogenesis using systems of differential equations and used a convolution-based approach to estimate the expected ages at which key transitions occur in breast, colorectal, and thyroid cancers. Model results suggest early-life initiation across all three cancers, while malignant transitions occur significantly earlier in early-onset than in late-onset breast and colorectal cancers. For thyroid cancer, the results do not show a significant difference in the timing of malignant transitions between early- and late-onset cases. We also observed a generational shift toward accelerated progression and earlier malignancy in more recent birth cohorts. The inferred timing of these changes can help guide etiologic investigations and identify age windows relevant to prevention and early detection.", "id": "Paper/69328", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69328"}, {"title": " Agentic Computational Algebra ", "webprogram_exclude": "0", "session_ids": ["Session/18355"], "source_sha256": "d44cbfb40669442bf6c204e9229f7e8a57bdcd9ed66088460958adebf34065fe", "withdrawn": "", "abstract": "We explore the use of AI agents for solving problems in computational algebra. For the problems we consider, the main challenge is not correctness but time: general-purpose algorithms provide rigorous guarantees but can be astronomically slow, and whether a problem is solvable in practice may depend on how a system is posed or which specialized tool is used. We study whether agents can automate these choices while learning from past verified attempts, and whether they can implement a fast reusable solver for known problem families. More broadly, computational algebra provides a useful testbed for agent tool use and memory, since it supplies infinitely many problems with verifiable answers and tunable difficulty. To this end, we describe concrete benchmark families of zero-dimensional polynomial systems with controlled shared structure, and we evaluate agents that can reformulate problems, invoke existing algebra tools, and retain experience across instances. Preliminary experiments show that agents can expand the frontier of solvable problems by discovering and reusing effective reformulations. However, model reasoning and memory maintenance can offset these gains, although compilation can amortize the cost of rediscovery across instances.", "id": "Paper/69333", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69333"}, {"title": " Some Visual Explorations in Number Theory ", "webprogram_exclude": "0", "session_ids": ["Session/17289"], "source_sha256": "7e41ca271e288e3dc0383cdbe1a03368a0ede1a179ac4110babe522782d4a371", "withdrawn": "", "abstract": "Number theory studies rings of integers, class groups, continued fractions, and Diophantine equations, among many others.  Their abstract beauty has (rightly) enthralled us for centuries, but we simply don't draw enough pictures of them.  I'll explore what our very human visual cortex can reveal.", "id": "Paper/69334", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69334"}, {"title": " A Nonlinear Mixed-Effects Approach to Parameter Identifiability in Diabetic Foot Ulcer Healing ", "webprogram_exclude": "0", "session_ids": ["Session/19365"], "source_sha256": "812fce023bbdaa873d1f285571d84a8d78a9a3c3104e0890b42400acd0e80595", "withdrawn": "", "abstract": "Diabetic foot ulcers (DFUs) are among the most common complications of diabetes, and DFUs that fail to close are a leading cause of nontraumatic lower-limb amputation. Standard treatments for DFUs often fail because biochemical processes vary between patients. Mathematical models can analyze these mechanisms, but linking them to individual patients remains challenging. We address this challenge by extending our previous work with a four-equation ODE model from Krishna et al. (2015) that tracks matrix metalloproteinases (in particular, MMP-1); its inhibitor, TIMP-1; the extracellular matrix; and fibroblast density over time. While previous work used cohort-averaged patient data from Muller et al. (2008), the current work curve fits data from 16 individual patients over 12 weeks using nonlinear mixed-effects (NLME) modeling in Monolix with the Stochastic Approximation of Expectation-Maximization (SAEM) algorithm. Parameter identifiability was assessed for each patient by computing coefficients of variation (CVs) for every parameter. Parameters with high CVs were considered unidentifiable and either fixed at nominal values or removed. The model was then refit, producing a reduced model with improved identifiability. Of the eleven rate constants, four (k2, k6, k7, and k10) were found to be practically unidentifiable and were removed by setting them to 0, and one (k3) was fixed at a nominal value, since its individual estimates were nearly uniform across the cohort. One parameter (k9) that ranked poorly by this measure was nevertheless retained, since its estimates spanned nearly three orders of magnitude for several patients and removing it degraded their curve fits. Overall, this work better captures individual variability in DFU patients while identifying a practically identifiable subset of parameters from sparse clinical data. Confidence and prediction intervals were also constructed for the estimated parameters and curve fits. Future work will use the reduced model developed here to pose an optimal design problem for when patient measurements should be taken.", "id": "Paper/69335", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69335"}, {"title": " A Diffusion Framework with Memory for Microfiber Transport in Porous Media ", "webprogram_exclude": "0", "session_ids": ["Session/19337"], "source_sha256": "18c990d19fc3b6b407d5008b1292cbcd6557ee0b7bd489a2bdeafe1aac8ac7e7", "withdrawn": "", "abstract": "Deformable microfibers moving through heterogeneous porous media can experience intermittent trapping and widely varying residence times. Motivated by these processes, we develop a diffusion framework with temporal memory to investigate transport and capture in idealized pore geometries. Within a continuous-time random-walk formulation, memory kernels are constructed from exponential, truncated power-law, gamma, and generalized gamma waiting-time distributions. \n\nThe exponential model provides a memoryless reference, while the other distributions introduce additional flexibility in the waiting-time statistics. We consider a localized initial release in a two-dimensional domain containing multiple circular cavities with absorbing or reflecting boundaries. A Laplace-domain Fourier–Bessel representation accounts for interactions among cavities, and numerical inversion recovers spatial concentration, local breakthrough curves, survival probabilities, and first-passage statistics. The generalized gamma extension introduces independently adjustable shape, scale, and power parameters, with the gamma distribution recovered as a special case. Comparisons examine how waiting-time statistics and boundary configurations influence the timing and distribution of capture. \n\nThis framework connects effective transport memory with idealized pore geometry and provides a basis for studying delayed migration and retention motivated by threadlike microplastics in heterogeneous porous media.", "id": "Paper/69336", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69336"}, {"title": " Categorical Foundations of Compliance for Multi-agent AI Systems ", "webprogram_exclude": "0", "session_ids": ["Session/18324"], "source_sha256": "f388929b45d395089757a964f6bfa65acf786a3cdd906e1c252af93678b480a0", "withdrawn": "", "abstract": "Government, finance, and health-care databases may be modeled as relations whose entries carry combinations of control metadata describing legal basis, secrecy, releasability, and temporal constraints. Individual metadata items form a partially ordered set; the admissible combinations of incomparable policy states are antichains. For such a poset, antichains carry natural operations obtained from unions and intersections of upward-closed sets, yielding a quantale and, in fact, a locale. This gives a mathematically natural way to compose compliance constraints from different sources: when an agentic AI system combines data from multiple agents, the resulting policy can be synthesized by these operations in an associative and distributive manner. The construction is functorial in the underlying partial order, so changes in compliance rules can be analyzed algebraically rather than by ad hoc case checking. This perspective helps predict the effects of policy mutations and exposes vulnerabilities such as privilege-escalation attacks.\n\nThe same framework extends to entitlement hierarchies and to more general notions of access than Boolean visibility, using profunctors between enriched categories. On the applied side, regulatory documents such as intelligence-control and construction-permit regulations have been translated into directed acyclic graphs and ontologies, and antichains have been prototyped as an operational primitive in cloud systems. In realistic settings, optimized graph-analytic implementations in Java and Rust achieve high throughput, demonstrating feasibility in large-scale workflows.", "id": "Paper/69337", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69337"}, {"title": " Scalable Manifold MALA for Large-Scale Bayesian Imaging Inverse Problems ", "webprogram_exclude": "0", "session_ids": ["Session/18446"], "source_sha256": "b04b5178971b85cfbf5cebaf37d8d228ce92cf67ab6f1c565a35ef3f1d2f8836", "withdrawn": "", "abstract": "Bayesian inference provides a principled framework for image reconstruction, enabling not only point estimates but also rigorous uncertainty quantification. For large-scale Bayesian inverse problems, Markov chain Monte Carlo (MCMC) methods are typically employed to sample from the posterior distribution and quantify uncertainty. However, applying advanced MCMC methods, such as the Simplified Manifold Metropolis-adjusted Langevin Algorithm (SMMALA), to high-dimensional imaging problems remains computationally prohibitive and difficult to scale. Although SMMALA achieves improved convergence by exploiting the local curvature of the posterior distribution, it requires the solution of large-scale linear systems at every MCMC iteration. In high-dimensional imaging applications, such as computerized tomography and seismic imaging, performing computations involving large-scale matrices arising from the forward model and solving the resulting linear systems using state-of-the-art approaches lead to significant memory and computational bottlenecks. In this talk, we present scalable implementations of SMMALA that avoid explicit matrix representations, substantially reducing memory requirements while preserving the accelerated convergence properties of geometry-informed MCMC methods. We demonstrate the efficiency and accuracy of the proposed approach for scalable uncertainty quantification in large-scale imaging inverse problems.", "id": "Paper/69338", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69338"}, {"title": " A Kohnen-Zagier Formula in Level 1 ", "webprogram_exclude": "0", "session_ids": ["Session/18276"], "source_sha256": "bbd90ab164db161825c8d1de403f35133a151b1d0eda88c4c742027cda5d06b9", "withdrawn": "", "abstract": "In 1985 Kohnen used the Shimura correspondence to prove a general formula relating the coefficients of half-integral weight modular forms of level $ 4N $ transforming with respect to the theta multiplier   to central values of $ L $-functions for twists of newforms of level $ N $. This generalized previous work with Zagier. In this paper, we prove a Kohnen-Zagier type formula using Yang's Shimura correspondence for powers of the eta multiplier in level $ 1 $, relating the coefficients of half-integral weight modular forms to central values of $ L $-functions for  twists of newforms of level $ 6 $.  To do so we develop some of the theory of modular forms transforming with respect to powers of the eta multiplier and introduce Shintani lifts of level $ 6 $, with Fourier coefficients given in terms of cycle integrals.", "id": "Paper/69339", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69339"}, {"title": " Building and sustaining effective high school modeling teams. ", "webprogram_exclude": "0", "session_ids": ["Session/19005"], "source_sha256": "5aeae37bec62e6be3327b768349041895622488cba396d563d736cc67bc653cc", "withdrawn": "", "abstract": "Fifteen years ago, I began the mathematical modeling program at Adlai E. Stevenson High School. Through the years, our program has evolved from a class project into a sustained approach to preparing students for mathematical modeling competitions. In this talk, I will examine that evolution through three lenses: what I wish I had known at the outset, what we have learned over the past decade, and where I hope to take the program in the next ten years.\nTopics will include team formation, student selection, competition preparation, training timelines, software suggestions, and my evolving role of the teacher as instructor, coach, and facilitator.", "id": "Paper/69340", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69340"}, {"title": " Foundation Tensor Networks Enable One-Shot Ground States of Glassy Systems ", "webprogram_exclude": "0", "session_ids": ["Session/18247"], "source_sha256": "545ff8ba9cce50f49aac77b303c836feb231f1c4e0e30f5a4ff3ff76f5afcee0", "withdrawn": "", "abstract": "Tensor network methods and neural quantum states have revolutionized many calculations in quantum many-body physics. Disordered systems, most notably spin glasses, remain difficult to tackle with either method due to the need to compute the ground state for every realization of the disorder. Foundation neural quantum states attempt to ameliorate this by generalizing to multiple Hamiltonians. However, they, like most variational Monte Carlo methods, are plagued by the need to perform extensive sampling to measure observables. Tensor networks, in contrast, do not have this limitation. In this talk, I will showcase our efforts to develop a hybrid method called foundation tensor networks (FTNs) that trains a foundation model to generate the tensor network representing the ground state in one shot from the parameters of the Hamiltonian.  I will also highlight our application of the method to critical phenomena in quantum spin glasses.", "id": "Paper/69345", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69345"}, {"title": " Comparing Random Population Models ", "webprogram_exclude": "0", "session_ids": ["Session/18095"], "source_sha256": "3aee6225f9fa9ab21d996879cf203e352118ba9db4f4a0923ceb2b2a5d30c489", "withdrawn": "", "abstract": "This work grew out of research conducted at SLMath over the summer with Eddy Kwessi as part of the LATTICE program. Starting from a deterministic population model, there are many mathematically distinct ways to introduce randomness. One may perturb population abundance directly, allow biological parameters to fluctuate randomly from generation to generation, or replace the discrete model by a stochastic differential equation. These choices need not lead to the same long-term predictions. We compare several stochastic formulations of the Beverton-Holt and Ricker population models, using Lyapunov exponents and stochastic growth rates to study stability and persistence. In particular, different formulations can produce different stability behavior and persistence thresholds. Our overall conclusion is that stochasticity is not specified by the amount of noise alone; the mechanism by which randomness enters a model is itself part of the modeling assumption.", "id": "Paper/69346", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69346"}, {"title": " Hyperparameter Optimization of Physics-Informed Neural Networks and Application to Magnetic Triple Arcade Structures in the Solar Corona: Preliminary Report ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "7e022ee012249f266bc8f4b558addc50d28f4b04fa84bc0b237c72090f4fc618", "withdrawn": "", "abstract": "This study investigates the performance of physics-informed neural networks (PINNs) trained on various ordinary and partial differential equations with applications in heliophysics. PINNs are a novel expansion on conventional multilayer perceptron neural networks. The loss function of a PINN is a weighted sum of the output mean squared error (MSE) from training data–which constitutes the total loss function of a classical neural network–and physics-based loss, usually an MSE with respect to a force or energy conservation constraint. We find the optimal combinations of hyperparameters for PINNs tasked with solving a non-periodic first-degree oscillator, the second-degree Van Der Pol (VDP) oscillator, a Soloviev system with a drop-shaped domain, and a triple arcade structure equation. The former two are ODEs, and the latter two are PDE solutions of the Grad-Shafranov (GS) equation governing magnetohydrodynamics (MHD) for 2D solar plasma. We apply a standardized regime of hyperparameters–learning rate, physics-based loss weight, hidden layers, and neurons per layer–to find the optimal combination for each differential equation with respect to their known analytical solutions. The study seeks to extract generalizable conclusions about how PINNs can best be applied to other problems in the field. Notable findings include an extremely high physics-based weighting for the non-periodic first-degree oscillator compared to other equations. We propose that this result is due to the inherent unpredictability of a non-periodic function, making the PINN rely more heavily on physical constraints. The VDP oscillator yields higher optimal learning rates for higher function stiffnesses, contrary to conventional wisdom. Optimal network architectures are consistent across most functions: 4 or 5 hidden layers with 32 or 64 neurons per layer. We propose new research methodologies to be tested in the future for further elucidation of the aforementioned conclusions.", "id": "Paper/69347", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69347"}, {"title": " The mathematical works of Erick Ross ", "webprogram_exclude": "0", "session_ids": ["Session/17450"], "source_sha256": "ca1c6f210086d7df1a66c9f2aa154f867b508123093a36b8c80e77e099d92638", "withdrawn": "", "abstract": "In this talk, we recall some of the works done by Erick Ross, who tragically passed away at the age of 25. His works have involved explicit computations of various objects relating to modular forms, such as works related to trace formulas, the asymptotic behavior of the Hecke operators, and the asymptotic behavior of Fourier coefficients of modular forms.", "id": "Paper/69356", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69356"}, {"title": " Profiling AI Tutor Usage in Introductory Calculus: Behavioral, Academic, and Demographic Correlates ", "webprogram_exclude": "0", "session_ids": ["Session/18262"], "source_sha256": "b0e5bd546c2a4f6a399bb1c41f67a13deae13e6e97621585e641cda11597c992", "withdrawn": "", "abstract": "AI-based tutors are increasingly embedded in college courses, yet usage is rarely uniform: students self-select into different levels of engagement, and the correlates of that variation remain underexplored. This study characterizes AI tutor usage among students (N = 2,475) enrolled in different sections (N = 83) of introductory calculus, with the goal of building descriptive usage profiles that inform modeling of tutor impact on student outcomes. \n\nUsing tutor interaction logs, we classify students into ordinal usage tiers, ranking them by their total course-level engagement with the tutor relative to the distribution of active users. We then characterize each tier along three dimensions: behavioral (engagement with materials and study patterns), academic (aggregated scores and by assignment type), and demographic (self-reported background characteristics). We also report on a companion survey that captures student-reported perceptions of tutor helpfulness and usability, allowing tier-level comparison of subjective experience alongside behavioral and academic indicators.\n\nThese profiles form the foundation of mixed effect models examining whether, and under what conditions, tutor usage is associated with learning and engagement outcomes. We discuss methodological challenges (particularly the risk of selection effects, since usage tier is not randomly assigned) and outline strategies to narrow the space of plausible alternative explanations, including baseline-adjusted comparisons and within-student change measures.\n\nWe tie this work to the broader intelligent tutoring systems literature – scaffolding, adaptive feedback, and self-regulated learning – and consider how tutor interactions and behavior might be refined to better support students across the usage spectrum. Rather than advancing a single causal claim, this work aims to offer a systematic description of who uses AI tutors, how, and in what context – key precursors to targeted claims about tutor efficacy and design.", "id": "Paper/69359", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69359"}, {"title": " A Fourier Sampling Theorem for Persistent Homology ", "webprogram_exclude": "0", "session_ids": ["Session/19358"], "source_sha256": "edb0504fde4ab1806e2d892b833c07a07d574e8924e679bbcea0a32d824290aa", "withdrawn": "", "abstract": "When persistent homology is applied to continuous signals, the necessity of physical measurements imposes fundamental limits on sampling frequency. Given an underlying ideal function, how can prior structural assumptions about the signal be quantified and distilled into a minimal sampling rate to guarantee a desired topological accuracy?\n\nLeveraging foundational tools such as Cohen-Steiner’s stability theorem and the Shannon-Nyquist sampling theorem, we investigate how derivative and functional bounds on an ideal signal translate to guarantees in persistence space. We survey plausible contextual assumptions, such as bounded first and second derivatives, and establish bounds on the bottleneck distance between the true and subsampled persistence diagrams. Finally, because there is a limit to the sampling frequency of any measurement, what is the highest precision with which we can estimate the persistence diagram of a continuous function through subsampling? What are the persistent homology implications of this limitation?", "id": "Paper/69360", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69360"}, {"title": " Parameterization of Invariant tori and their stable/unstable manifolds for Hamiltonian systems ", "webprogram_exclude": "0", "session_ids": ["Session/18065"], "source_sha256": "32ed07c9d97ffa10b66b23053d47f2a6e0c0a41e7cfa36078ded3376f36ff8b6", "withdrawn": "", "abstract": "In Hamiltonian systems, typical motions are either quasi-periodic or chaotic.  Quasi-periodic solutions are associated with stable (i.e. elliptic) invariant tori, and chaotic motions are often understood by studying transverse intersections of stable/unstable manifolds of hyperbolic equilibria, periodic orbits, or invariant tori. The goal of this talk is to explain how the parameterization method is used to compute invariant tori and their attached stable/unstable manifolds in Hamiltonian systems. \n     The parameterization method is a framework for computing invariant objects in dynamical systems by solving an invariance equation via a Newton-like scheme.  For invariant tori, this procedure requires two critical initial steps (1) accurately computing the rotation vector for the torus and (2) finding a reasonable initial approximation of the torus in Fourier space so that the iterative method converges.\n     When the torus is stable, we exploit Weighted Birkhoff Averages (WBA) of time series data to compute the rotation vector and an approximation of the Fourier coefficients of the torus. \n     If the torus is unstable, nearby points diverge exponentially fast in forward and backward time, and time series data is difficult to obtain via direct simulation. Instead, we use the normal form approximation to find an approximate torus and rotation vector near a base invariant object, and then perform numerical continuation to follow family of tori away from the domain of the normal form. For unstable tori, we also apply the parameterization method to compute high-order Fourier-Taylor expansions of the stable and unstable manifolds attached to the torus. \n     This talk will demonstrate the utility of these ideas in the Circular Restricted Three Body Problem (CR3BP), which is a dynamical system describing the motion of a massless particle moving solely under the gravitational influence of two large primaries on circular orbits.", "id": "Paper/69361", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69361"}, {"title": " Relativistic Fluid Dynamics: From Particle Colliders to Neutron Star Mergers ", "webprogram_exclude": "0", "session_ids": ["Session/18300"], "source_sha256": "3109048d7ca74c5324d847f8b559cb479e3ce0589e134295709cba6fad1e57b0", "withdrawn": "", "abstract": "Heavy-ion collision experiments have provided overwhelming evidence that quarks and gluons, the elementary particles within protons and neutrons, can flow as a nearly frictionless, strongly interacting relativistic liquid over distance scales not much larger than the size of a proton. On the other hand, with the dawn of the multi-messenger astronomy era marked by the detection of gravitational waves from a binary neutron star merger, it became imperative to understand how extremely dense fluids behave under very strong gravitational fields. Therefore, two of the most cutting-edge experimental facilities in modern science, the Large Hadron Collider and the Laser Interferometer Gravitational-Wave Observatory, have produced data whose interpretation requires pushing the boundaries of our current understanding of fluid dynamics in the relativistic regime.\n\nIn this talk, I will describe the recent progress that has reshaped our understanding of the onset of relativistic fluid dynamics and its extension to the far-from-equilibrium regime. I will present rigorous results that, under explicit conditions, establish causality and local well-posedness for the two leading theories of relativistic viscous fluid dynamics coupled to Einstein’s equations: Israel-Stewart theory and the Bemfica-Disconzi-Noronha-Kovtun formalism. I will also discuss major open questions concerning the physical and mathematical behavior of relativistic viscous fluids, including the fate of shocks, the relation between breakdown of the fluid evolution and geodesic incompleteness, and the possibility of global well-posed evolution.", "id": "Paper/69364", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69364"}, {"title": " A branching process model for estimating the parameters of telomere shortening using the shortest telomere length. ", "webprogram_exclude": "0", "session_ids": ["Session/18350"], "source_sha256": "07c5d6ff5a19d56c7723c3ee3d13342376df6bb206239658d4b78780a53eded3", "withdrawn": "", "abstract": "In the absence of telomerase, telomeres (which are at the ends of chromosomes) shorten with each cell division, and after a critical number of divisions, the cell becomes senescent, i.e., it stops dividing. Telomere length at each chromosome end is heterogeneous, but previous studies show that a single telomere is sufficient to trigger senescence when first reaching a critical threshold length in Saccharomyces cerevisiae.\n \nIn this work, we aim to estimate the probabilistic parameters of telomere shortening from experimental data using a multitype age-dependent Markov branching process. In our model, we follow the length of the shortest telomere in a telomerase-negative cell population. To fit the parameters, we used distributions of telomere lengths from experiments on Saccharomyces cerevisiae.\n\nWe fitted the expected distribution and number of population doublings predicted by the model to the experimental values. The results show reasonable qualitative and quantitative agreement between the expected and empirical cumulative distributions of telomere lengths and between the expected and empirical numbers of population doublings at given times. The developed model can help estimate the parameters of telomere shortening and improve our understanding of the evolution of telomere lengths.", "id": "Paper/69365", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69365"}, {"title": " An Embroidered (5,4) Hyperbolic Fish Pattern ", "webprogram_exclude": "0", "session_ids": ["Session/18232"], "source_sha256": "77caa3f43ad3c85f24db4f1c3aacd64bea9df49f2b816b2230673f849830c0ac", "withdrawn": "", "abstract": "In the past we have used a computer-controlled embroidery machine to create repeating patterns in the Poincar\\'e disc model of the hyperbolic plane.  We continue this project by by creating a new hyperbolic pattern inspired by M.C.~Escher's Euclidean Regular Division Drawing \\#20.  This pattern has 4-fold rotations at meeting points of the tails and of the dorsal fins of the fish.  We can envision a generalization of this pattern, which we denote (p,q), that has p-fold rotations at the tails and q-fold rotations at the dorsal fins.  Thus Escher's drawing would be described by (4,4) in our notation.  The (p,q) pattern will be a pattern in the hyperbolic plane if (p-2)(q-2) is greater than 4.  Our new pattern is the (5,4) pattern.  It has symmetry group [5.4]+ in Coxeter notation or 542 in orbifold notation.  Our pattern has perfect 5-color symmetry.", "id": "Paper/69366", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69366"}, {"title": " Physics Informed Random Feature Neural Networks for Solving PDEs ", "webprogram_exclude": "0", "session_ids": ["Session/18282"], "source_sha256": "984242362d1d8bef52161c608bc0c5e843e0e0d7a41e52f2774055cb4eb7225e", "withdrawn": "", "abstract": "Machine learning-based partial differential equations (PDEs) solvers have attracted significant attention in recent years. Most progress in this area has been driven by deep neural networks such as physics-informed neural networks (PINNs) and kernel method (such as physics-informed Gaussian Processes).  \nWe introduce a physics-informed random feature method for countering part of the spectral bias which PINN-based solvers are facing for a certain class of PDEs. Random feature method was originally proposed to approximate large-scale kernel machines and can be viewed as a specialized randomized neural network.\nCompared to other state-of-the-art PINN-based solvers which require a large number of collocation points, our proposed method reduces the computational complexity.  \nIn this paper, we develop a rigorous approximation error analysis and derive high-probability error bounds on the $H^1$ norm.\nWe provide extensive numerical tests for verifying our theoretical guarantees on error decay rates, as well as several comparison tests to showcase our claimed capability for combating spectral bias in these deep learning based methods.", "id": "Paper/69368", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69368"}, {"title": " Real Algebraic Overtwisted Contact Structures on <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.576ex\" height=\"2.509ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -934.9 1109.1 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">S^3</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-53\" d=\"M308 24Q367 24 416 76T466 197Q466 260 414 284Q308 311 278 321T236 341Q176 383 176 462Q176 523 208 573T273 648Q302 673 343 688T407 704H418H425Q521 704 564 640Q565 640 577 653T603 682T623 704Q624 704 627 704T632 705Q645 705 645 698T617 577T585 459T569 456Q549 456 549 465Q549 471 550 475Q550 478 551 494T553 520Q553 554 544 579T526 616T501 641Q465 662 419 662Q362 662 313 616T263 510Q263 480 278 458T319 427Q323 425 389 408T456 390Q490 379 522 342T554 242Q554 216 546 186Q541 164 528 137T492 78T426 18T332 -20Q320 -22 298 -22Q199 -22 144 33L134 44L106 13Q83 -14 78 -18T65 -22Q52 -22 52 -14Q52 -11 110 221Q112 227 130 227H143Q149 221 149 216Q149 214 148 207T144 186T142 153Q144 114 160 87T203 47T255 29T308 24Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-53\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-33\" x=\"926\" y=\"513\"></use>\n</g>\n</svg> and Lens Spaces ", "webprogram_exclude": "0", "session_ids": ["Session/17105"], "source_sha256": "a13dccea23b9361a8189843d5d0cf1a029c7cb1795b0bd22e26d8d40b6844789", "withdrawn": "", "abstract": "By Milnor's fibration theorem, it is known that a holomorphic germ \\( f: \\mathbb{C}^2\\to \\mathbb{C}\\) with an isolated singularity at the origin induces an open book decomposition on $S^3$ which is known to support the unique tight contact structure on \\(S^3\\). Therefore, realizing the overtwisted contact structures on \\(S^3\\) algebraically requires leaving the holomorphicity. \nFollowing the extension of Milnor's fibration theorem to real analytic maps, we call an oriented link \\(L \\subset S^3\\) \\emph{real algebraic} if it is the singularity link of a real algebraic map \\(h \\colon (\\mathbb{R}^4, 0) \\to (\\mathbb{R}^2, 0)\\) with an isolated singularity at the origin, i.e. \\(\\mathrm{Crit}(h) = \\{0\\}\\). In this case the argument map defines an open book decomposition which is called \\emph{real algebraic open book}. A contact structure on \\(S^3\\) is \\emph{real algebraic} if it is supported by such an open book.\nWe prove that every overtwisted contact structure on \\(S^3\\)  is supported by a real algebraic open book with planar pages. \n\nWe then extend these constructions to lens spaces, which arise both as quotients of \\(S^3\\) under finite cyclic group actions and as links of cyclic quotient surface singularities. We prove that every lens space \\(L(p,q)\\) carries infinitely many nonisotopic real algebraic overtwisted contact structures, supported by planar rational open books. Moreover, for the lens spaces \\(L(p, p-1)\\), these open books can be chosen to be honest, and every value of the \\(3\\)-dimensional invariant \\(d_3\\) is realized.", "id": "Paper/69369", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69369"}, {"title": " Some Results on the Coefficients of the Interlace Polynomials ", "webprogram_exclude": "0", "session_ids": ["Session/17900"], "source_sha256": "28a523278300468544e80e70effb327e9c111babf4e737d2667fae306cf3773e", "withdrawn": "", "abstract": "The interlace polynomial of a graph may be defined recursively using a graph operation called pivoting. To any computation of an interlace polynomial, we associate a binary tree that we call a pivot tree. Pivot trees extend the known combinatorial interpretation using earlier-sibling-covers to give a combinatorial interpretation of the coefficients of the interlace polynomial of any graph. We use pivot trees to justify some results about interlace polynomial coefficients, and we discuss a related tiling model.", "id": "Paper/69370", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69370"}, {"title": " Representing Per- and Polyfluoroalkyl Substances (PFAS) Molecules for Machine Learning Using Persistent Homology ", "webprogram_exclude": "0", "session_ids": ["Session/18105"], "source_sha256": "2db166039621fc1e64569b5ced7e8d28d4859c2b7cba1f4716842827ef083bae", "withdrawn": "", "abstract": "Per- and polyfluoroalkyl substances (PFAS) are integral to many modern industrial processes, including semiconductor manufacturing, thus motivating efforts to identify alternative molecules with comparable functional performance. Exploration of the relevant chemical spaces, as well as characterization and classification of PFAS and similar compounds, will support such efforts. One approach is to produce representations of PFAS molecules which are compatible with machine learning models. Techniques from topological data analysis, particularly persistent homology, can potentially quantify structural properties which are not easily measured by classical analysis methods. Persistence images are an established tool for converting topological summaries to a format suited for many machine learning algorithms. We demonstrate the use of persistence images for a PFAS classification task. In particular, we consider reproducibility of classification results with respect to low-profile processing choices.", "id": "Paper/69372", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69372"}, {"title": " <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.211ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 521.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">k</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-6B\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Hyperopic Cops and Robber ", "webprogram_exclude": "0", "session_ids": ["Session/18085"], "source_sha256": "d1ba977708178b26d84937d068186d271d83fb394a4579c898d5299da09a5144", "withdrawn": "", "abstract": "A generalization of hyperopic cops and robber, analogous to the $k$-visibility cops and robber, is introduced in this paper. For a positive integer $k$ the $k$-hyperopic game of cops and robber is defined similarly as the usual cops and robber game, but with the robber being omniscient and invisible to the cops that are at distance at most $k$ away from the robber. The cops win the game if, after a finite number of rounds, a cop occupies the same vertex as robber. Otherwise, robber wins. The minimum number of cops needed to win the game on a graph $G$ is the $k$-hyperopic cop number $c_{H,k}(G)$ of $G$.\n\n    In addition to basic properties of the new invariant, cop-win graphs are characterized and a general upper bound in terms of the matching number of the graph is given. The invariant is also studied on trees where the upper bounds mostly depend on the relation between $k$ and the diameter of the tree. It is also proven that the 2-hyperopic cop number of outerplanar graphs is at most 2 and an upper bound in terms of the number of vertices of the graph is presented for $k \\geq 3$.", "id": "Paper/69374", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69374"}, {"title": " Mathematical Modeling of Ice Accretion on a Rotating Aircraft-Engine Spinner ", "webprogram_exclude": "0", "session_ids": ["Session/19343"], "source_sha256": "b686864577e2163904d82539ba239ce8e30704875150a325c18b07c2d5d62363", "withdrawn": "", "abstract": "This work develops a mathematical model for ice accretion on a rotating conical aircraft-engine spinner. Using the lubrication approximation, the thin liquid-water film is described by a reduced form of the Navier-Stokes equations that includes centrifugal forcing from spinner rotation. The model couples water-film transport with incoming droplet collection, freezing, and ice-thickness growth. A thermal balance accounts for convective cooling and the effect of incoming supercooled droplets. The governing equations are nondimensionalized to identify the main parameters controlling film motion and freezing. Theoretical predictions are compared with available experimental results and show good agreement, supporting the model as a useful framework for studying ice growth on rotating spinner surfaces.", "id": "Paper/69378", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69378"}, {"title": " Compatible Path Covers in Robust Zero Forcing Variants ", "webprogram_exclude": "0", "session_ids": ["Session/18207"], "source_sha256": "9d1d79aff382e418dd7f8e0da9eda15f332efc9af1b134789b11c122233719dc", "withdrawn": "", "abstract": "\\begin{abstract}\n   Zero forcing is an iterative graph coloring process studied for its wide array of applications. In this process, the vertices of the graph are initially designated as blue or white, then a dynamic rule alters the color of vertices until a steady-state is reached. The zero forcing number of a graph is the minimum cardinality of a set of blue vertices that results in all vertices in the steady-state. The zero forcing number has motivated the introduction of a host of variants motivated by linear-algebraic or graph-theoretic contexts. Among these are several variants that build robustness into the forcing process, most notably $\\ell$-leaky forcing and $k$-fault tolerance. Each of these robust parameters induces a collection of path covers of the graph whose members satisfy structural conditions compatible with the form of robustness imposed. We describe how these compatible collections of path covers arise in the leaky forcing and fault-tolerant settings, the bounds they place on known values of the robust parameters, and applications of these characterizations.\n\\end{abstract}", "id": "Paper/69379", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69379"}, {"title": " Real modules of Lie superalgebras and Kostant’s cascade ", "webprogram_exclude": "0", "session_ids": ["Session/17666"], "source_sha256": "9f893b35663701dab44a5a7bb0cdc7076d30a3f9037604ebc1591ea911dce238", "withdrawn": "", "abstract": "We provide a concrete classification of irreducible finite dimensional real modules of a wide class of Lie superalgebras that includes the simple ones and all of the real Lie algebras. In the purely even case, we recover classical results that are as old as the works of E. Cartan, Iwahori, Karpelevich, etc., with simpler conceptual proofs. We also establish an apparently new connection with Kostant's cascade of strongly orthogonal roots. This talk is based on joint work with S. Sahi and V. Serganova.", "id": "Paper/69382", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69382"}, {"title": " Modeling cortisol time-scales in a model of emotion regulation ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "cc5580f423f0dd67149d876e6437840982e01ae325e241d2b2b7bc03921112bf", "withdrawn": "", "abstract": "Emotional regulation and maladaptive arousal responses are central to understanding the impact of stress on brain function. In this work, we develop and analyze a mathematical model of prefrontal–amygdala circuitry using Wilson–Cowan population equations to capture the excitatory–inhibitory dynamics underlying emotional control. The model incorporates reciprocal projections between prefrontal pyramidal cells and basolateral amygdala principal neurons, as well as inhibitory microcircuits that mediate feed-forward and feedback suppression. To represent the influence of stress hormones, we augment this neural framework with a cortisol-dependent delay term. Specifically, we implement an integral kernel that encodes the system’s memory of past arousal activity: acute stress is modeled as a sharp kernel emphasizing recent amygdala firing, whereas chronic stress corresponds to a broader kernel integrating over a longer history.\n\nThrough numerical simulations and bifurcation analysis, we characterize the system’s behavior under baseline, acute, and chronic stress conditions. We focus on the emergence of distinct amygdala firing rhythms, their modulation by prefrontal feedback, and the phase transitions between dynamical regimes. Under acute stress, the model predicts transient high-frequency oscillations and rapid return to baseline. In contrast, chronic stress broadens the kernel’s memory, leading to persistent dysregulated rhythms, reduced prefrontal control, and a shift toward pathological attractor states.\n\nFinally, we situate our findings within the empirical literature on stress and brain function, highlighting how the model recapitulates known effects of cortisol on amygdala excitability, prefrontal inhibition, and long-term alterations in emotional regulation. This framework provides a mechanistic bridge between neural circuitry, hormonal modulation, and stress-related changes in brain dynamics, with implications for understanding resilience versus vulnerability in affective disorders.", "id": "Paper/69383", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69383"}, {"title": " Constraints and benefits from visualizing number theoretic objects ", "webprogram_exclude": "0", "session_ids": ["Session/18366"], "source_sha256": "add3a91870ed1151b8da1010745396f188fa6bfbd9ed73fee42c88919f3f2c69", "withdrawn": "", "abstract": "A visualization of a mathematical object should ideally be both interesting and explanatory. To explain something, the visualization should contain information about the object. But to make visual sense, one normally has to lie about what's shown, cheat in the visualization, and/or omit substantial components. In this talk, we'll explore this tension as we examine visualizations of Dirichlet characters, Gauss sums, rational points on varieties, modular forms, and more. Many of these visualizations have appeared on the LMFDB or other expository number theory outlets.", "id": "Paper/69385", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69385"}, {"title": " Foliations of Planar Linear and Polar Systems ", "webprogram_exclude": "0", "session_ids": ["Session/18271"], "source_sha256": "5412b1af99f615f84f421dca8ff17fbadcb494b939f387a9edac8efec53f32d8", "withdrawn": "", "abstract": "The trace–determinant diagram is a standard method to classify equilibria of planar linear systems as nodes, saddles, and foci.  But systems in the same stability class can still behave in different ways.  In this talk, we show how each region of the diagram can be further organized by curves on which a ratio stays fixed.  For nodes, the ratio compares two growth or decay rates; for saddles, it compares expansion and contraction; and for foci, it compares rotation with radial growth or decay.  These curves give a finer picture of the dynamics within each stability class.  Moving along one curve changes the overall time scale while keeping the ratio fixed.  We then develop a similar stability diagram for a broader family of systems written in polar coordinates. The polar system comes from a planar linear system, and the two diagrams are related by a change of variables.  The ideas are accessible in a first course in ODEs and can be explored through phase portraits and computation.", "id": "Paper/69389", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69389"}, {"title": " Restricted Bounds on Parking Functions ", "webprogram_exclude": "0", "session_ids": ["Session/18338"], "source_sha256": "48f3069a22636cd2080b2d869ff2fe9094abe1c9a7cd6472a2c036a0d46daa15", "withdrawn": "", "abstract": "Parking functions represent possible preferences of $n$ cars that enter a one-way street where every car is able to park according to the following parking rules: each car (1) parks in their preferred spot if it is empty, or (2) parks at the next available spot if their preferred spot is filled. \nHere, we explore parking functions where the number of times a spot can be preferred is at most $k$. \nWe describe a bijection between ordered, unlabeled trees and our restricted parking functions, where the number of children each node has corresponds to the number of times a spot appears in the parking function. \nWe also construct a bijection between $k$-paths (a generalized version of Motzkin paths) and our restricted parking functions.", "id": "Paper/69394", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69394"}, {"title": " Manufacturing colimits in higher categories ", "webprogram_exclude": "0", "session_ids": ["Session/18000"], "source_sha256": "10cf5dee7872ffcbf49de4cf6ef68698ec00c43f402a1c9e087e31589ef97e80", "withdrawn": "", "abstract": "There are several models of $(\\infty, n)$-categories as certain presheaves of spaces or sets. In these models limits may often be computed in the underlying presheaf category, while colimits are notoriously difficult to compute. Nevertheless many important results in higher category theory depend on not only knowing that certain colimits of $(\\infty,n)$-categories exist, but also on being able to recognize them via small simple models. Examples occur in Lurie’s approach to the bordism hypothesis, the tangle hypothesis, and variants with singularities or defects. These rely on identifying certain bordism categories via a series of (homotopy) pushouts.\n\nThe goal of this talk is to describe new results that provide a general method/recognition schema for identifying pushouts of $(\\infty,n)$-categories. We hope to illustrate the technique with some simple examples.", "id": "Paper/69396", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69396"}, {"title": " Symplectic extension graphs and Ribet’s lemma ", "webprogram_exclude": "0", "session_ids": ["Session/19356"], "source_sha256": "bc72ebaffee3768bc2a29dde875fae1ded96ae127264778f02256c4a454e4128", "withdrawn": "", "abstract": "In his pioneering paper, Ribet uses Eisenstein congruences to prove the converse to Herbrand's theorem. A key ingredient in his proof is a method of constructing nontrivial extensions of certain characters, commonly known as Ribet's lemma.  In my talk, I will go over Ribet's lemma and its various generalizations. In particular, I will define symplectic extension graphs associated with symplectic representations, and study it by the use of Bruhat--Tits buildings associated with symplectic groups. We obtain a symplectic analogue of a result of Bellaiche.", "id": "Paper/69406", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69406"}, {"title": " The Super Tree Property at Many Cardinals Simultaneously ", "webprogram_exclude": "0", "session_ids": ["Session/18589"], "source_sha256": "4d7c59a85ae09dad6a52a94e21c26994bc0c4f53a95b6c3e4836f51be9dc8b79", "withdrawn": "", "abstract": "The super tree property is a generalization of the tree property closely linked with supercompact cardinals: a cardinal is supercompact if and only if it is inaccessible and has the super tree property. Like the tree property, the super tree property can consistently hold at small cardinals. Forcing the tree property and its generalizations to hold at many small cardinals simultaneously is a long-running project in set theory. In this talk, we will discuss generalizing two results about the tree property to the super tree property: Golshani and Hayut's result that the tree property can hold at many consecutive successors of singular cardinals, and Neeman's construction of a model in which the tree property holds at $\\aleph_n$ for $1<n<\\omega$ and at $\\aleph_{\\omega+1}$ simultaneously.", "id": "Paper/69410", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69410"}, {"title": " Flat covers of simple modules ", "webprogram_exclude": "0", "session_ids": ["Session/18371"], "source_sha256": "5004ee02f8acc19affac03836db766c832afa555125b04555cfd9a5f127a0c2f", "withdrawn": "", "abstract": "We prove that the flat cover of a simple module is indecomposable, with local\nendomorphism ring, over every commutative ring and over every ring finitely generated\nas a module over its centre; in both cases the kernel is the corresponding radical\nmultiple $FJ$ of the covering module.  These results are then applied to\nquasi-coherent sheaves: if a closed point $x$ of a scheme $X$ has a flat-admissible\naffine neighbourhood, the geometric flat cover $p\\colon\\mathcal F\\to i_{x*}\\kappa(x)$\nsatisfies $\\ker p=\\mathcal I_x\\mathcal F$ and $\\mathcal F$ is indecomposable.  At a\nreduced pinched point the cover is the fibre product of the branchwise covers, and its\nkernel their direct sum.", "id": "Paper/69415", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69415"}, {"title": " Using Bayes Factors to Monitor Behavior of Unmanned Platforms ", "webprogram_exclude": "0", "session_ids": ["Session/18024"], "source_sha256": "5cda460fca7fbfdfce4435ab27bacc0f95647a36eb1375fb151e3a6956bf81b1", "withdrawn": "", "abstract": "We derive a Bayesian hypothesis test for analyzing the equality of regression coefficients between two independent data sets. The test is developed with non-local normal-moment (gNAP) priors, which allows for the resulting Bayes factor to be expressed as a function of standardized effect sizes. This allows researchers to evaluate their hypothesis across a range of effect sizes. The Bayes factor has a closed-form marginal likelihood when assuming equal variance across the two datasets. An extension to cases where the variance across the datasets is unknown and not assumed to be equal can be expressed as a one-dimensional integral that can be easily evaluated. A similar low-dimensional numerical integration can evaluate extensions to cases with general covariance structures, like AR(p) data. Simulations show superior evidence accumulation for both a true null and true alternative compared to common default prior choices. An application to data from the Have Remy flight test, a collaboration between Lockheed Martin and the Air Force Test Pilot School in 2025, is discussed. These results show the applicability of the new Bayesian test in the realm of analyzing unmanned platforms in live flight and simulation.", "id": "Paper/69416", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69416"}, {"title": " Pedagogy in Practice: Project‑Based Learning and Student‑Centered Modeling of ODEs and PDEs ", "webprogram_exclude": "0", "session_ids": ["Session/17765"], "source_sha256": "4c613c2e8233ce0209d33371c5c18c7a22842df3a127f8c6904db41e78afeb8f", "withdrawn": "", "abstract": "This presentation examines a student‑centered course on finite‑difference methods for modeling physical systems governed by ODEs and PDEs, emphasizing how project‑based learning and ungrading practices support autonomy, conceptual development, and engagement with applied mathematics. The nonlinear pendulum project serves as the central case study: students construct finite‑difference discretizations, investigate numerical behavior, and relate computational results to the underlying nonlinear dynamics, refining their reasoning through cycles of feedback, revision, and reflective writing. These observations illustrate the broader pedagogical structure of the course, which also includes an experimental heat‑equation inverse problem in which students estimate thermal diffusivity from collected data, as well as an open‑ended final project that invites students to design and analyze a modeling problem of their choosing. The course replaces point‑based grading with portfolio‑based assessment and metacognitive reflection, supported by a PreTeXt‑Plus version under development that integrates interactive examples and opportunities for self‑assessment. The session will conclude with practical guidance for instructors interested in adapting or incorporating similar ODE/PDE modeling projects into their own courses, with attention to scaffolding, feedback design, and student‑centered assessment practices.", "id": "Paper/69418", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69418"}, {"title": " Automated Classification of Homeostasis Structure in Input-Output Networks ", "webprogram_exclude": "0", "session_ids": ["Session/18257"], "source_sha256": "23d2373fb3ce9b8e12a1869bf47cbc8b8189cfd398367331656cff0cba05657b", "withdrawn": "", "abstract": "Homeostasis is widely observed in biological systems and refers to their ability to maintain an output quantity approximately constant despite variations in external disturbances. Mathematically, homeostasis can be formulated through an input–output function mapping an external parameter to an output variable. Infinitesimal homeostasis occurs at isolated points where the derivative of this input–output function vanishes, allowing tools from singularity theory and combinatorial matrix theory to characterize and classify homeostatic mechanisms in terms of network topology. Although the theoretical framework allows homeostasis subnetworks to be identified directly from combinatorial structures of the input–output network without numerical simulation, the required combinatorial enumeration becomes increasingly intractable as network size grows. Moreover, the reliance on advanced graph-theoretic concepts limits its broader accessibility and practical use across disciplines, particularly in biological applications. To overcome these limitations, we develop a Python-based algorithm that automates the identification of homeostasis subnetworks and their associated homeostasis conditions directly from network topology. Given an input–output network specified solely by its connectivity structure and the designation of input and output nodes, the algorithm automatically identifies the relevant graph-theoretical structures and enumerates all homeostatic mechanisms. We demonstrate the applicability of the algorithm across a range of biological examples, including small and large networks, networks with a single input parameter (with single or multiple input nodes), multiple input parameters, and cases where input and output coincide. This wide applicability stems from our extension of the theoretical framework from single-input–single-output networks to networks with multiple input nodes through an augmented single-input-node representation. The resulting computational framework provides a scalable and systematic approach to classifying homeostatic mechanisms in complex biological networks, facilitating the application of advanced mathematical theory to a broad range of biological systems.", "id": "Paper/69419", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69419"}, {"title": " Dynamics of a Discrete-Time Refuge-Mediated Competition Model with an Allee Effect ", "webprogram_exclude": "0", "session_ids": ["Session/18325"], "source_sha256": "9596d0411c195504d4c4681c02bd2d7486cb89ad762148980afe7db32138ecae", "withdrawn": "", "abstract": "We present a discrete-time nonlinear competition model incorporating Allee effects and a refuge. The model describes two competing species, with the weaker competitor having access to a refuge patch that allows it to escape interspecific competition. Within the refuge, individuals are subject to mate limitation, giving rise to an Allee effect. We first analyze the subsystem in the absence of the stronger competitor and establish conditions for local and global stability. We then investigate the full competition model and derive conditions for uniform persistence, demonstrating that access to a refuge can facilitate coexistence despite the presence of an Allee effect. Numerical simulations further illustrate abrupt ecological transitions, including shifts from competitive exclusion of the weaker species to coexistence of both species.", "id": "Paper/69421", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69421"}, {"title": " Seeing Seastars: Characterizing graph powers ", "webprogram_exclude": "0", "session_ids": ["Session/18106"], "source_sha256": "bcf95c5b04473793d4d3e69d16613f45bd6c0b6f16688e4c9b928b5da55a544f", "withdrawn": "", "abstract": "This talk will introduce ``seastars\", i.e. graphs with a particular sort of symmetry that resembles a seastar's arms and central disc.  The motivation for this class of graphs comes from the gluing algebra of graphs.  In the gluing algebra, a seastar is a graph that has been multiplied by itself.  That is, a seastar is a square, cube, fourth power, etc. of a graph in the gluing algebra.  \n\nFamiliar classes of graphs will be classified according to their powers.  In particular, we will show that a cube is not a cube, and a hypercube is not a cube, but a square is a square.", "id": "Paper/69424", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69424"}, {"title": " Collective behavior of active interfacial floaters with competing interactions ", "webprogram_exclude": "0", "session_ids": ["Session/18222"], "source_sha256": "b15d7ed8ad32dbd2fa3a86918a06fabb4e5dc229d275b57deb8a14b7c8fc43d3", "withdrawn": "", "abstract": "The air-water interface offers a tunable setting for exploring competing interactions, where capillary attraction between floating bodies (the so-called \"Cheerios effect\") can be set against the repulsion of embedded magnetic dipoles. We consider small magnetized disks floating at such an interface and driven by an oscillating external magnetic field, which respond by pitching and emitting waves that in turn set them into motion. Guided by companion experiments on both isolated floaters and collections, we develop a series of reduced models aimed at coupling the pitching motion to the resultant propulsion, the orientational preferences of a single surfer, and the collective states that emerge as the number of floaters is increased. These results suggest that the deformed interface provides an ideal and tunable environment for studying hydrodynamically-coupled collections of polar active particles at intermediate length- and time-scales. Ongoing efforts will be discussed.", "id": "Paper/69425", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69425"}, {"title": " Erdős–Falconer Distance Results for Pinned Graphs over Finite Fields ", "webprogram_exclude": "0", "session_ids": ["Session/18369"], "source_sha256": "e375cad1336932169306981035af85f66b9127e73de57c6e93b9f11c12e7cd3c", "withdrawn": "", "abstract": "The Erdős distance problem asks how many distinct distances a finite point set determines; the Falconer version extends this to Hausdorff dimension in the continuous setting. A further extension replaces a pair of points with a graph: fix some vertices as \"pins,\" let the rest range over a target set, and ask how large that set must be for the resulting vector of edge-distances to realize quantitatively many combinations. We report two sets of results on this problem over finite fields. \n\\par First, a quantitative analogue of a recent Euclidean pinned-graph theorem: when each new vertex depends on fewer earlier vertices than the ambient dimension, sufficiently large target sets guarantee that quantitatively many pin choices realizes quantitatively many distance configurations, recovering known single-pin thresholds as a special case. When a vertex depends on too many earlier vertices, we get a weaker, rank-truncated bound instead. Second, complementary mechanisms for distance configurations, including star estimates in dimension $d$ and a two-star construction used to count triangles.", "id": "Paper/69427", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69427"}, {"title": " Covers of curves, Ceresa cycles, and Unlikely intersections ", "webprogram_exclude": "0", "session_ids": ["Session/18263"], "source_sha256": "2a3c31f009ab291311ca91fbae0dcf24680323c0659fed91fce7502fdaa6a6dd", "withdrawn": "", "abstract": "The Ceresa cycle, first studied by Ceresa in the 1980s, is an example of a homologically trivial but algebraically nontrivial cycle on the Jacobian of a smooth curve. While the Ceresa\ncycle of a hyperelliptic curve is always zero, less is known about the set of genus g curves for which the Ceresa cycle vanishes or is torsion.\n\nIn joint work with Padma Srinivasan, Toren\nD’Nelly-Warady, and Tejasi Bhatnagar we consider Ceresa cycles of families of curves with\nmore than one map to an elliptic curve. We leverage dimension reduction techniques from\nclassical algebraic geometry (such as intersection theory) to determine when the Ceresa cycle is torsion via explicit computations of points on an elliptic curve, rather than computing with 1-dimensional subvarieties of the Jacobian.", "id": "Paper/69429", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69429"}, {"title": " Enumerating <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"0.97ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 417.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\ell</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2113\" d=\"M345 104T349 104T361 95T369 80T352 59Q268 -20 206 -20Q170 -20 146 3T113 53T99 104L94 129Q94 130 79 116T48 86T28 70Q22 70 15 79T7 94Q7 98 12 103T58 147L91 179V185Q91 186 91 191T92 200Q92 282 128 400T223 612T336 705Q397 705 397 636V627Q397 453 194 233Q185 223 180 218T174 211T171 208T165 201L163 186Q159 142 159 123Q159 17 208 17Q228 17 253 30T293 56T335 94Q345 104 349 104ZM360 634Q360 655 354 661T336 668Q328 668 322 666T302 645T272 592Q252 547 229 467T192 330L179 273Q179 272 186 280T204 300T221 322Q327 453 355 590Q360 612 360 634Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-2113\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-interval Parking Functions ", "webprogram_exclude": "0", "session_ids": ["Session/18085"], "source_sha256": "837f6a5613ca92ea353b876154c89c36707864e3aa5a847119907756b3f493b4", "withdrawn": "", "abstract": "In 1966, Alan G. Konheim and Benjamin Weiss defined parking functions. \nInterval parking functions were introduced in 2020 by Colaric, Demuse, Martin, and Yin. Here, we specialize to the case of $\\ell$-interval parking functions which are interval parking functions where all cars have a preference interval of length $\\ell$. Inspired by work studying statistics of permutations, we examine equidistribution for the inversion statistic and the major index for $\\ell$-interval parking functions (and general $n$). We include a discussion of results regarding relationships between unit interval parking functions and $2$-interval parking functions, and we pose some problems for future exploration when $\\ell \\geq 3$.", "id": "Paper/69430", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69430"}, {"title": " Königsberg pseudoprimes and related adventures in prime detection ", "webprogram_exclude": "0", "session_ids": ["Session/17808"], "source_sha256": "bf7af8857e3ad08191f79af73c8dab4ec2e89db1a8e0d9e2d2272e992d45c213", "withdrawn": "", "abstract": "In the summers of 2023 and 2024, I guided students through research generalizing Fermat's little theorem: if $p$ is a prime, then $a^p \\equiv a \\bmod p$ for any integer $a$. The generalization extends to matrices: if $p$ is prime, then $\\mathrm{Tr}(A^p) \\equiv \\mathrm{Tr}(A) \\bmod p$ for any square matrix $A$. Both give a composite-ness test: if $n$ has $a^n \\not \\equiv a \\bmod n$ for some $a$, then $n$ is not prime.\n\nDo different matrices give better compositeness tests than other matrices? Yes, and following this computational question led us through a web of higher mathematics explorations. In this talk, we'll describe this work and the role of computation as an onramp to researching math.", "id": "Paper/69431", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69431"}, {"title": " Sectional Curvature Pinching of Two-Step Nilmanifolds ", "webprogram_exclude": "0", "session_ids": ["Session/18290"], "source_sha256": "7ce9c5e2704beceb117d5e8a72760f0d04387be5f8e73bc32dbca178d5b50149", "withdrawn": "", "abstract": "We study the classical problem of sectional curvature pinching in the class of 2-step nilmanifolds, which are necessarily of mixed curvature. We show that the pinching constant of any 2-step nilmanifold lies in the compact interval $[-3, -\\frac{3}{2}]$. The upper bound $-\\frac{3}{2}$ is achieved by the complex Heisenberg group $\\mathrm{Heis}_3(\\mathbb{C})$ with a Ricci soliton metric. The upper bound exhibits rigidity: if a simply connected 2-step nilmanifold $N$ has the pinching constant $-\\frac{3}{2}$, then $N$ admits a Ricci soliton complex Heisenberg group as a totally geodesic subgroup. On the other hand, the lower bound satisfies non-rigidity: any 2-step nilpotent Lie group admits a metric with pinching constant $-3$. This is derived by showing that there is an open neighborhood $U$ of $\\mathrm{Heis}_3(\\mathbb{R})\\times \\mathbb{R}^{n-3}$ in the space of $n$-dimensional 2-step nilmanifolds such that the pinching constant is $-3$ on $U$, and any 2-step nilpotent Lie group $N$ has a metric $g$ such that $(N,g)$ lies in $U$. In fact, if $N$ is not isomorphic to $\\mathrm{Heis}_3(\\mathbb{R})\\times \\mathbb{R}^{n-3}$, then there is a curve $g_t$ of metrics on $N$ with $(N,g_t)\\in U$, showing that there are uncountably many left-invariant metrics on $N$ such that the pinching constant is $-3$.", "id": "Paper/69437", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69437"}, {"title": " Syzygies and Singularities of Secant Varieties of Curves ", "webprogram_exclude": "0", "session_ids": ["Session/18347"], "source_sha256": "e50fed118e46b1da111f7632f10c75a832a1160d92813253784bb630aa014d58", "withdrawn": "", "abstract": "We’ll describe joint work with Wenbo Niu and Jinhyung Park on the singularities and syzygies of the secant varieties of a smooth projective curve, which is embedded by the complete linear system of a very positive degree line bundle.", "id": "Paper/69440", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69440"}, {"title": " Parking Completions and Volumes of Polytopes ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "fffbe435d572f9b27edd42d0ea734a595c4c806de8d066f1fa756684043fb82a", "withdrawn": "", "abstract": "Parking functions correspond with preferences of $n$ cars which enter sequentially to park on a one-way street where (1) each car parks in the first available spot greater than or equal to its preference and (2) all cars successfully park. \nWe generalize parking functions to parking completions: \nwe are given that some cars have already parked in a set of spots, which are indexed in a sequence~$\\mathbf{t}$. \nWe then consider a preference list $\\mathbf{c}$, where $|\\mathbf{t}|$ + $|\\mathbf{c}|$ = $n$. \nIf all cars can park, we say that $\\mathbf{c}$ is a parking completion. \nAdeniran et al.\\ (2020) state an open problem which proposes a connection between the number of parking completions to the volumes of Pitman-Stanley polytopes by explicit computation on small values of $n$. \nHere, we provide a partial solution to this open problem by proving that the set of parking completions is the set of $\\mathbf{x}$-parking functions.", "id": "Paper/69442", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69442"}, {"title": " Minimal nondegenerate extensions of braided fusion categories ", "webprogram_exclude": "0", "session_ids": ["Session/18641"], "source_sha256": "e3402191d417ff728b6aaef2df3fa9a4b5f8c9d59f8eb1e8196a2e6a78f33984", "withdrawn": "", "abstract": "Braided fusion categories live somewhere between commutative and associative algebra: they have an associative tensor product and, like a commutative algebra, a way to exchange aka “braid” objects $X \\otimes Y \\cong Y \\otimes X$, but unlike a commutative algebra, the braiding depends on whether one moves $X$ “over” or “under” $Y$. Braided fusion categories generalize quadratic forms on abelian groups; they control the representation theory of quantum groups; they model quasiparticle excitations in topological insulators; they provide topologically-protected quantum error correction. Many questions from representation theory and quantum many-body physics turn out to boil down to the question of whether, and in how many ways, a given braided fusion category can be extended to one which is nondegenerate—every object braids nontrivially with some other object—in a minimal way—every new object braids nontrivially with some old object. Techniques from group cohomology can reduce this question to one final case, but that case needed new ideas from algebraic topology and higher category theory. This duet talk will overview this subject and explain our recent resolution of the final case.", "id": "Paper/69446", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69446"}, {"title": " Using Transition Path Theory to study state transitions in a model of the Stratospheric Polar Vortex ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "b1e9f3e136b33568d36e35bc0d55dc92735e5c6810cdc2e5e3b283fcd105c67b", "withdrawn": "", "abstract": "The stratospheric polar vortex, an intense circulation of low-pressure and cold air over the winter pole, is critical in driving unusual surface weather patterns, including extreme cold air outbreaks and flooding. Understanding this phenomenon and forecasting the scale and timing of disruptions to the vortex remains a significant scientific challenge with real-world consequences in weather pattern predictions. My research focuses on leveraging stochastic differential equations and transition path theory to investigate the dynamics of variability within stochastic models of the polar vortex. I am applying a rare events algorithm to a three-dimensional minimal contour model, where separate basins of attraction represent strong and weak vortex states. Using this algorithm, I aim to characterize and analyze the transitions between these basins that are indicative of vortex disruptions. This will provide insight into where and why such transitions occur, and how we can better predict them. This approach can significantly improve our ability to forecast vortex disruptions and predict their magnitude and impact. Ultimately, my research seeks to study the transitions between vortex states during extreme vortex disruptions. My research seeks to bridge this gap, offering new mathematical tools and insights for understanding and predicting extreme events in climate systems.", "id": "Paper/69447", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69447"}, {"title": " Superb crystals ", "webprogram_exclude": "0", "session_ids": ["Session/18067"], "source_sha256": "a97b1b2dcdee3644db74f43eb9adcf293e0d3cba87afa850cd00b1d7a0c3c464", "withdrawn": "", "abstract": "Crystals are combinatorial skeletons of certain G-modules. Kashiwara's tensor product rule for crystals gives an elegant combinatorial method for computing the tensor product of the corresponding crystals. Amazingly, in type A, this tensor rule corresponds precisely to the combinatorial product of tableaux using RSK insertion.\n\nDemazure crystals are extremal subsets of crystals that capture the structure of certain B-modules. While the tensor product of Demazure modules does not, in general, admit a filtration by Demazure modules, this does sometimes happen (see Mathieu 1989; Joseph 2003; Kouno 2020). Sadly, even in these cases, then tensor product of the corresponding Demazure crystals often fails to capture this structure.\n\nIn this talk, we'll discuss a generalization of RSK to Kohnert diagrams that suggests the existence of a generalized tensor product for Demazure crystals that should reflect the conjecture by Polo that the tensor product of Demazure modules always admits a filtration by Schubert modules.", "id": "Paper/69449", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69449"}, {"title": " Geometric Structure of Rotation-Invariant Binary Operations and Induced Metrics on Matrix Spaces ", "webprogram_exclude": "0", "session_ids": ["Session/19352"], "source_sha256": "a33f484d341b768b15cef0af3d2f1f4dd3639d50035d815554acb94934bbd4bc", "withdrawn": "", "abstract": "Binary operations invariant with respect to rotations generate natural\ngeometric structures on matrix balls. In this paper, we investigate the\nrelationship between rotation-invariant binary operations, the metric\ntensors generated by them, and isomorphisms between such operations.\nWe first study metric tensors invariant under the left-right action of\nthe orthogonal groups on rectangular matrices. Using singular value\ndecomposition, we reduce the analysis to canonical matrices and describe\nthe corresponding canonical block structure of the metric tensor,\nincluding both distinct and repeated singular values. We then introduce\nrotation-equivariant isomorphisms between binary operations and derive\nthe transformation law relating their generated metric tensors. This\nleads to a block transformation criterion expressed in terms of the\ncanonical metric coefficients and the Jacobian blocks of the\nisomorphism. The criterion provides a direct method for determining how\nthe metric tensor changes when a rotation-invariant binary operation is\ntransformed by a smooth isomorphism. As an application, we study matrix\nEinstein and M\\\"obius additions and show how the metric tensor associated\nwith M\\\"obius addition can be obtained from the Einstein metric through\nthe isomorphism formula. We further investigate scaled Einstein\noperations and the corresponding family of rotation-invariant metric\ntensors, illustrating how these transformations connect Einstein-type\ngeometries with their limiting geometric structures. The results provide\na unified algebraic and differential-geometric framework for studying\nrotation-invariant binary operations, their isomorphisms, and the metric\ntensors they generate on matrix balls.", "id": "Paper/69451", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69451"}, {"title": " Fans Meet Congruences: Fan-Based Meet-Congruences of the Weak Order ", "webprogram_exclude": "0", "session_ids": ["Session/18138"], "source_sha256": "adc592d3a278d9b1fe7984edad6a09ea118df98be1180e2281928919fbca9525", "withdrawn": "", "abstract": "Lattice congruences and quotients of the weak order on a finite Coxeter group have strong geometric properties. In particular, there is a complete fan associated to any lattice quotient of the weak order which is a coarsening of the Coxeter fan. Meet-quotients of the weak order do not necessarily define fans, however when they do, we call them fan-based meet-congruences. In this talk, we will discuss the geometric properties of fan-based meet-congruences of the weak order on a finite Coxeter group. We will also describe the topology of intervals in the fan-based meet-quotients in terms of the faces of the coarsened Coxeter fan. We will briefly mention applications to Bruhat interval polytopes and hypergraphic polytopes. This talk is based on joint work with Nathan Reading.", "id": "Paper/69452", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69452"}, {"title": " Bounding Chain Optimal Cycle Representatives in Complex Networks ", "webprogram_exclude": "0", "session_ids": ["Session/18352"], "source_sha256": "bb28c76b27fac72243c35076fed53e83bb98df5ad5565022ed4e6e7c6be3a6c7", "withdrawn": "", "abstract": "Topological data analysis (TDA) provides a valuable framework for understanding the structure of data, including complex networks, through analyzing cycles. By linking topological features back to cycle representatives in the original data, researchers can gain deeper insights from TDA. However, we show that the standard linear programming methods used to optimize cycles can be inadequate in network data, leading to either unintuitive results or intractable optimization problems due to cycles that remain open within the network structure at the end of a filtration. In response, we propose a novel approach to optimize cycles within a network structure by minimizing the size of bounding chains around these remaining open cycles. We empirically demonstrate the effectiveness of this method on both random networks and real data for getting meaningful topological results.", "id": "Paper/69453", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69453"}, {"title": " Cognitive Similarities in High Dimensional Image Embeddings ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "02698e6a8160888231649aee71beabb9095e034fee8fcf7bc2bf27dfe8d7f9a6", "withdrawn": "", "abstract": "In this poster we consider aspects of similarity in high-dimensional spaces. A common initial step in quantitatively analyzing such similarity is embedding elements in a high-dimensional Euclidean space. In such cases, application of standard measures of similarity such as Euclidean or cosine distance can lead to issues, in particular with regards to norm selectivity. We show that an approach founded on social-based cohesion can excel in mimicking human cognitive similarity.  An important result is an application to large sets of images, wherein an interesting phase transition is observed.", "id": "Paper/69454", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69454"}, {"title": " Legendrian surfaces and Weinstein domains ", "webprogram_exclude": "0", "session_ids": ["Session/17691"], "source_sha256": "8d1e5f664e2b40593b659d6df713e1ed1a93175355c11e7ed79e625658a1cda8", "withdrawn": "", "abstract": "Weinstein manifolds are symplectic manifolds with a compatible Morse handlebody structure that are generalizations of contangent bundles. Currently, we do not have explicit handlebody diagrams for most Weinstein manifolds including cotangent bundles of closed manifolds with dimension greater than 2. In joint work in progress with Laura Starkston and Angela Wu we provide explicit handlebody diagrams various 6-dimensional Weinstein manifolds. We also provide results on isotopies of legendrian surfaces in the boundary of subcritical 6-dimensional Weinstein domains.", "id": "Paper/69456", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69456"}, {"title": " Line Shellings of Geometric Lattices ", "webprogram_exclude": "0", "session_ids": ["Session/18286"], "source_sha256": "fc7bcc28a2098bc7eb0832838851a72c0eec55cf31403e0cf4ae67b11def2273", "withdrawn": "", "abstract": "Inspired by Bruggesser--Mani's line shellings of polytopes, we introduce line shellings for the lattice of flats of a matroid: given a normal complex for a Bergman fan of a matroid induced by a building set, we show that the reverse-lexicographic order of the coordinates of its vertices is a shelling order.  This gives a new proof of Bj\\\"orner's classical result that the order complex of the lattice of flats of a matroid is shellable, and gives a geometric proof of shellability for nested set complexes of matroids.", "id": "Paper/69464", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69464"}, {"title": " Rainbow Numbers of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"3.469ex\" height=\"3.009ex\" style=\"vertical-align: -1.171ex;\" viewBox=\"0 -791.3 1493.6 1295.7\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbb {Z}_{p^k}</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJAMS-5A\" d=\"M39 -1Q29 9 29 12Q29 23 60 77T219 337L410 648H364Q261 648 210 628Q168 612 142 588T109 545T97 509T88 490Q85 489 80 489Q72 489 61 503L70 588Q72 607 75 628T79 662T81 675Q84 677 88 681Q90 683 341 683H592Q604 673 604 666Q604 662 412 348L221 37Q221 35 301 35Q406 35 446 48Q504 68 543 111T597 212Q602 239 617 239Q624 239 629 234T635 223Q635 215 621 113T604 8L597 1Q595 -1 317 -1H39ZM148 637L166 648H112V632Q111 629 110 622T108 612Q108 608 110 608T116 612T129 623T148 637ZM552 646Q552 648 504 648Q452 648 450 643Q448 639 266 343T77 37Q77 35 128 35H179L366 339L552 646ZM572 35Q581 89 581 97L561 77Q542 59 526 48L508 37L539 35H572Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-70\" d=\"M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJAMS-5A\" x=\"0\" y=\"0\"></use>\n<g transform=\"translate(667,-259)\">\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-70\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.574)\" xlink:href=\"#E1-MJMATHI-6B\" x=\"620\" y=\"355\"></use>\n</g>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18338"], "source_sha256": "faf0ebee1fab1773559b249ad3dd8d11cb5a0daa2b3a86520ca1ee3e50ca296f", "withdrawn": "", "abstract": "For any set of integers $S$, we define an exact $r$-coloring to be a surjective map $S\\rightarrow[r]$. Given an equation $eq$, we define the rainbow number $\\text{rb}(S,eq)$ to be the minimum number of colors $r$ such that every exact $r$-coloring of $S$ contains a solution to $eq$ such that each variable in the equation is colored with a distinct color.\n\nWe aim to generalize previous work on $\\text{rb}(\\Z_p,x+y=z^2)$ for $p$ prime, done by the 2025 Fairfield University REU, to $\\text{rb}(\\Z_{p^k},x+y=z^2)$ for $k\\geq 2$.\nWe show that $\\text{rb}(\\Z_{p^2},x+y=z^2)=\\text{rb}(\\Z_{p^3},x+y=z^2)=\\text{rb}(\\Z_p,x+y=z^2)+\\frac{p-1}{2}$ for $p>2$. We also show a lower bound for $\\text{rb}(\\Z_{p^k},x+y=z^m)$ that is linear in p and k, as well as a better lower bound for $\\text{rb}(\\Z_{2^k},x+y=z^2)$. Joint work with Berikkyzy, Danburg, Herlihy, Lundy, and Wang as part of the 2026 Fairfield University REU.", "id": "Paper/69466", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69466"}, {"title": " Modeling Cell Migration with Substrates of Variable Rigidity ", "webprogram_exclude": "0", "session_ids": ["Session/19371"], "source_sha256": "5e65c34c6c696e535003fe0e96f0e8f210ad3ac2d41e53775a6b62f235031e55", "withdrawn": "", "abstract": "Cell migration is fundamental to many biological processes, including the immune response, tissue repair, and embryonic development. Our previous cell migration model simulates a three-dimensional cell migrating across a rigid floor, representing the cell as a network of damped springs (viscoelastic elements). In this work, we extend the model by replacing the rigid floor with a deformable viscoelastic substrate. The extension requires developing a strategy for modeling the 3D substrate, and it allows us to investigate how cell-substrate interactions influence migration behavior.  Specifically, this allows us to consider an experimentally verified “Goldilocks” effect, in which cells exhibit optimal migration on substrates of intermediate stiffness. Ultimately, our work provides the necessary computational framework for investigating how substrate properties influence cell migration.", "id": "Paper/69469", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69469"}, {"title": " On Ruling polynomials of Legendrian links ", "webprogram_exclude": "0", "session_ids": ["Session/18218"], "source_sha256": "3daa9f4f850fac21cde5de2f7aaea2c408ef60ee4b736987216102c1fe7d0467", "withdrawn": "", "abstract": "The ruling polynomial is a Legendrian invariant that is closely related to the augmentation variety of the Legendrian. We characterize all graded and ungraded ruling polynomials, and construct Legendrian links realizing each possible polynomial. The graded augmentation varieties of the Legendrians we construct all have trivial cluster algebra structures. Finally, we construct Legendrian knots admitting $k$ exact Lagrangian fillings with $\\chi(L)=n$ that are pairwise smoothly non-isotopic for $n\\leq 1$, and $k\\geq 0$.", "id": "Paper/69471", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69471"}, {"title": " Rainbow numbers for the equation <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"15.022ex\" height=\"2.843ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -934.9 6467.9 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">x+y=a^{k-1}z^k</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-78\" d=\"M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 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transform=\"translate(5529,0)\">\n <use xlink:href=\"#E1-MJMATHI-7A\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-6B\" x=\"663\" y=\"513\"></use>\n</g>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18338"], "source_sha256": "a0eead7e675d8536879b6702c2fe399eb16e884cc855a4c30ee6c4c6166d7ad3", "withdrawn": "", "abstract": "Given a positive integer $r$, we define an exact $r$-coloring of a set $S$ as a surjective function $c : S \\to [r]$. The rainbow number $\\operatorname{rb}(S, \\mathrm{eq})$ of an equation eq and a set $S$ is the smallest integer $r$ so that any exact $r$-coloring of $S$ admits a rainbow solution to $eq$. In this talk we discuss the rainbow number for the equation $x+y=a^{k-1}z^k$ in $\\mathbb{Z}_n$ for particular $n$ and $k$. We begin with a short proof of a relationship between the rainbow numbers of the equations $x+y=z^k$ and $x+y=a^{k-1}z^k$ in $\\mathbb{Z}_n$. We will then present the value of $\\operatorname{rb}(\\mathbb{Z}_{2p}, x+y=z^2)$ for prime p as well as prove a constructive lower bound on $\\operatorname{rb}(\\mathbb{Z}_{pq}, x+y=z^2)$ when $p,q$ are distinct odd primes. We additionally exhibit a family of counterexamples to a conjecture made by Ansaldi et al. (2024) that $\\operatorname{rb}(\\mathbb{Z}_{p}, x-y=z^k)=\\operatorname{rb}(\\mathbb{Z}_{p}, x+y=z^k)$ for all positive integers $k$. Joint work with Berikkyzy, Danburg, Longin, Lundy, and Wang as part of the 2026 Fairfield University REU.", "id": "Paper/69478", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69478"}, {"title": " Finite generation of cohomology for bosonizations ", "webprogram_exclude": "0", "session_ids": ["Session/17949"], "source_sha256": "8ec93ffedcc97de7ce83fa9c4d182c93acd88891ecf80704bbc7ed4bf354acd0", "withdrawn": "", "abstract": "Finite generation of cohomology is a fundamental problem for finite-dimensional Hopf algebras and, more generally, finite tensor categories. \n\nIn this talk, I will discuss a method for proving finite generation for bosonizations of braided Hopf algebras. The approach uses deformation sequences of algebras and applies more generally to smash products. As applications, we obtain finite generation results for bosonizations of several families of Nichols algebras.", "id": "Paper/69481", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69481"}, {"title": " Quadratic composite operator and it’s applications to biorthogonal Quantum Mechanics ", "webprogram_exclude": "0", "session_ids": ["Session/18383"], "source_sha256": "71c63420ec0bcbd401696493ac7f3272fb75a73e74daa3902fe822c70402725c", "withdrawn": "", "abstract": "In Quantum Mechanics the Hamiltonian of a system is assumed to be Hermitian for physical reasons. However, this requirement has been loosened to allow for non-Hermitian operators, or in finite dimension the matrix representation when we want to model systems that lose information to their environment. There have been different approaches to the so called non-Hermitian or open systems. In this work we will focus on the biorthogonal Quantum Mechanics discussed by D. C. Brody in his 2014 paper. To this end we investigate the role of a generalization of the quadratic composite operator construction first introduced by A. Cerjan, T. Lorin, and F. Vides. We will explore how the quadratic composite operator connects with non-Hermitian problems with an emphasis on approximate joint eigenvectors and how they evolve over time.", "id": "Paper/69486", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69486"}, {"title": " Communicating Mathematics ", "webprogram_exclude": "0", "session_ids": ["Session/18101"], "source_sha256": "613d8ffd9476fe09557472cf7e7d1997b3912a5b9cf30222b5f856c9eb51816d", "withdrawn": "", "abstract": "We will discuss some ongoing experiments with mathematical communication, especially those relevant to recent technological developments.", "id": "Paper/69487", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69487"}, {"title": " Construction of some short exact sequences ", "webprogram_exclude": "0", "session_ids": ["Session/18264"], "source_sha256": "9a55040dddde070651ad4222dbbc4a9923c74c6d886ee969955282f0fb89a0b5", "withdrawn": "", "abstract": "There is a widely-known construction for the almost split sequence terminating in an indecomposable, non-projective module for a finite group. We will show that a similar construction can also be used for a much less widely-known family of short exact sequences coming from Auslander's theory of ``morphisms determined by modules.\"", "id": "Paper/69488", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69488"}, {"title": " When are Newton–Okounkov body bounds of a chemical reaction network at least as good as mixed-volume bounds? ", "webprogram_exclude": "0", "session_ids": ["Session/18257"], "source_sha256": "b4190412d5d33cb5ef1da5efa58b314732b957e28e4d0ea9bf0ffcfc08eb6883", "withdrawn": "", "abstract": "Determining the maximum number of positive isolated steady states admitted by a chemical reaction network is an important and generally difficult problem. One upper bound on this number, called the mixed-volume bound, is obtained from Newton polytopes associated to the network. A second upper bound, introduced by Obatake and Walker, is the Newton--Okounkov body bound. This bound is the self-intersection index of a vector space associated to the network and is computed using a Newton--Okounkov body. In this paper, we characterize the networks for which the Newton--Okounkov body bound is less than or equal to the mixed-volume bound for every \"admissible\" vector space. We call such networks \\emph{full-volume}. Using a criterion of Bihan and Soprunov, we characterize the full-volume property in terms of the proper faces of a polytope we associate to the network. For certain networks without conservation-law equations, we reformulate this condition in terms of the reaction structure of the network, obtaining a characterization based on the sizes of certain subsets of species. On the other hand, for networks with conservation-law equations, we show that the presence of these equations causes many networks to fail to be full-volume.", "id": "Paper/69491", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69491"}, {"title": " Role Extraction in Core-Periphery Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/19366"], "source_sha256": "c7a7ebead07ac80b9e367af6766483fd7da99a9b3173faf24061dc5a234e782a", "withdrawn": "", "abstract": "We study core-periphery detection in undirected, unweighted graphs through the framework of network role extraction, focusing on the Neighborhood Pattern Similarity (NPS) matrix. Unlike methods that directly optimize a prescribed core-periphery objective, NPS identifies structural roles by comparing the neighborhood patterns of vertices. We develop a spectral analysis of NPS for core-periphery graphs and investigate how its recovery performance depends on graph size, the relative sizes of the core and periphery, and edge density. Numerical experiments on synthetic and real-world networks compare NPS with existing core-periphery detection methods and demonstrate accurate and robust recovery, with NPS performing favorably across the networks considered. We also derive a generalized modularity-matrix representation for a direct role-extraction objective, connecting this framework with optimization-based formulations of core-periphery detection. These results provide a matrix-based perspective on both the analysis and detection of core-periphery structure.", "id": "Paper/69493", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69493"}, {"title": " Keller maps and Holonomic <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.924ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 828.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">D</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-44\" d=\"M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-44\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-modules ", "webprogram_exclude": "0", "session_ids": ["Session/18285"], "source_sha256": "cfda1bdbd525fcbc7b5514b921ae9754daefe4f70da9cf4b3673379a6a4359d4", "withdrawn": "", "abstract": "Let $k$ be a field of characteristic $p$ and $R=k[x_1,\\dots,x_n]$. Let $D$ denote the ring of $k$-linear differential operators on $R$. Let $\\varphi:R\\to R$ be a $k$-algebra endomorphism whose Jacobian is a unit in $R$. We show that there is a unique $k$-algebra endomorphism $\\Phi:D\\to D$ such that $\\Phi|_R=\\varphi$ and that the restriction of scalar via $\\Phi$ preserves holonomicity.", "id": "Paper/69495", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69495"}, {"title": " Phase-field modeling of colloid-polymer mixtures in microgravity \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/19343"], "source_sha256": "bc9aae4a1cf39882e2ab3eb66be58a318bb4bf813701ead9b283ce049ca656dc", "withdrawn": "", "abstract": "In a microgravity environment, phase transitions in colloid-polymer suspensions give valuable insight into atomic-scale phase transitions. To explore the effects of fluid viscosity and other system parameters on phase behavior, we present simulation results of a phase-field model that couples a Cahn-Hilliard equation for the colloid concentration with the incompressible Stokes equations to include the effects of hydrodynamic interactions between particles and surrounding fluid in the low-Reynolds number limit. The model also incorporates the dependence of viscosity on the local colloid concentration, which influences the hydrodynamic behavior. We also present experimental results, extracted from images of experiments conducted by NASA on the International Space Station.", "id": "Paper/69496", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69496"}, {"title": " Accelerating Tau Propagation Models with Machine Learning Surrogates ", "webprogram_exclude": "0", "session_ids": ["Session/18007"], "source_sha256": "6e358ba99bde729b1f5337d466762be82b1a13d3df1bcd100cf5fa220e2193b5", "withdrawn": "", "abstract": "Computational models provide a biophysically grounded framework for studying tau protein spread in Alzheimer's disease and other tauopathies. However, parameter inference, a key step in fitting models to empirical data, is typically intractable due to the high computational cost of numerical simulation. Here, we introduce a machine learning framework to accelerate the Network Transport Model (NTM), which simulates tau propagation on the brain's structural connectome. We replace the computationally expensive PDE solver (used to model tau dynamics along connectome graph edges) with five classes of surrogate models: linear regression, symbolic regression, gaussian process (GP), spline interpolate and multilayer perceptrons (MLPs). The MLP surrogate achieved the highest fidelity  ($R^2 > 0.99$) against traditional numeric solvers,  while symbolic regression yielded symbolic expressions relating the model outputs of interest - tau flux and an edge mass correction terms - to nodal state variables and biochemical rate parameters.\nThese surrogates reduced simulation time from hours to minutes ($\\approx60\\times$ speedup), making the thousands of forward simulations required for data-driven parameter inference computationally feasible.", "id": "Paper/69504", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69504"}, {"title": " Some episodes in the history of mathematical education ", "webprogram_exclude": "0", "session_ids": ["Session/18373"], "source_sha256": "fc5d132fa9d9169f8a55d0ca9f632235de16c9398fbe96e423b75142921b53f3", "withdrawn": "", "abstract": "One of the first schools of mathematics can be traced back to the influence of the British Navy in the 1600s. The role of gambling and lotteries played a role in the choice of topics in elementary texts in the 1700s. The very idea of inference– how do you learn from experience – is tied to attempts to mathematize induction in the 1700s. These and other examples involving some very famous names like Isaac Newton, Pierre Simon Laplace, Samuel Pepys (of diary fame), and the French mathematician Condorcet. These and other little known stories will be discussed.", "id": "Paper/69507", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69507"}, {"title": " Combining taxonomies for classification: When are sharks and dolphins similar? ", "webprogram_exclude": "0", "session_ids": ["Session/18024"], "source_sha256": "f83e41af84ce8efc30bf46efa7b86749565731c326d4dc22cb558d8bd83ba493", "withdrawn": "", "abstract": "We present novel methods of fusing taxonomies in an effort to resolve conflicts that arise when designing taxonomies. Current taxonomies are often expert-created structures, which can produce bias towards certain classes. For instance, a taxonomy system for classifying living organisms may look different if the expert used biomes or species relationships. We focus on taxonomies which can be represented as labeled rooted directed trees, also called arborescences. We present methods of fusing arborescences in a way that preserves underlying structure using a set-theoretic perspective. \nHierarchical classification considers class relationships and can give a coarser result if a specific class is unable to be determined. We compare whether fused arborescences improve hierarchical classification compared to the original expert-defined trees. Our findings suggest that these fused graphs show some improvement in metrics such as tree-induced error.", "id": "Paper/69508", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69508"}, {"title": " Optimizing Stellar Subdivisions for Toric Resolution of Singularities ", "webprogram_exclude": "0", "session_ids": ["Session/19356"], "source_sha256": "1c72447a127785105d9c903d147172b6a3e3dd9e8a9b9472ba04eaee7bbdb1a7", "withdrawn": "", "abstract": "Resolution of singularities is a central problem in algebraic geometry, classically studied through Hironaka’s work and its many later developments. Toric singularities admit a combinatorial description in terms of rational polyhedral cones. A cone is smooth precisely when its primitive ray generators extend to a lattice basis, and resolving a toric singularity amounts to subdividing singular cones into unimodular ones. This project studies the optimization problem underlying this process: How can one choose lattice rays so as to minimize the number of stellar subdivisions needed to obtain a smooth subdivision? There is an optimal choice for the 2D case given by Hirzebruch-Jung continued fractions, but beyond that not much is known.\n\nWe formulate cone smoothing as a discrete-geometric search problem on lattice cones. The multiplicity of a cone, given by the lattice index of its ray generators, serves as a measure of singularity. Candidate subdivisions are analyzed using fundamental parallelepipeds, Hilbert basis elements, quotient-lattice structure, and unimodular equivalence of cones. In particular, we establish a canonical form for generating and classifying three-dimensional simplicial cones up to unimodular equivalence, allowing redundant instances to be identified and removed from the search space.\n\nWe have obtained results for several structured classes of cones, including explicit optimal subdivision behavior in special families and computational evidence for broader patterns in ray selection. In particular, in the 3D case, we consolidated results from the literature to prove that selecting rays from a smaller set is sufficient for optimal subdivision.\nTo expand and generalize these results, we develop a learning-based framework that combines graph neural networks with reinforcement learning to study cone smoothing as a sequential decision problem. In this framework, a fan is represented as a heterogeneous graph whose nodes encode cones and candidate lattice rays, while the learning agent predicts which stellar subdivision is most likely to reduce the remaining smoothing complexity. With this novel graph-based reinforcement learning approach, we aim to learn ray-selection policies that produce efficient and optimal smoothings of n-dimensional cones.", "id": "Paper/69509", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69509"}, {"title": " Global existence of classical solutions to the Landau-Fermi-Dirac equation ", "webprogram_exclude": "0", "session_ids": ["Session/18331"], "source_sha256": "60ac81fb1a4afb6c4a9a733e8fa15eeb8ac932c8b8646d8bc100ce09753c423b", "withdrawn": "", "abstract": "In this talk, I will discuss recent work on the Landau-Fermi-Dirac equation, a quantum modification of the classical Landau equation for fermions.  Mathematically, this model encodes the Pauli exclusion principle in a way that yields an $L^\\infty$ bound on the density in phase space \"for free.\"  Our work takes advantage of this to deduce two new a priori estimates that yield the global existence of classical solutions.  In particular, we show that polynomial decay in velocity can be propagated (up to a multiplicative exponential growth factor in time) and that desaturation (the number of fermions per unit space is positive but bounded away the physical maximum) spontaneously occurs.  The combination of these, when paired with the well-developed regularity theory for kinetic equations, yields smooth solutions for all time.", "id": "Paper/69510", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69510"}, {"title": " Enhanced and Anomalous Dissipation in Models of Fluid Flows ", "webprogram_exclude": "0", "session_ids": ["Session/17962"], "source_sha256": "54765270d3b16e1c8b69ed2a386182763e7d43c1779907db63e8eb6db820f2ec", "withdrawn": "", "abstract": "In this talk, we discuss a few constructions that capture mechanisms of enhanced and anomalous dissipation in simplified models. We examine how multiscale structures can drive the effective transfer of energy to progressively smaller scales and study the resulting behavior of the energy dissipation rate in the vanishing viscosity limit. We also discuss what these constructions may suggest about the corresponding problem for the Navier--Stokes equations.", "id": "Paper/69511", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69511"}, {"title": " Evolution of Internal Waves in a 2D Perturbed Cylinder \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18326"], "source_sha256": "56284b1667f2b491560b63a6692f6e75f8fa18a17b8f15adac1a1cede22b1d0e", "withdrawn": "", "abstract": "I will discuss the long-time behavior of solutions to the internal wave equation in a 2D perturbed cylinder with flat ends. The long-time profile of such solutions is analyzed via regularity of solutions to the stationary equation. I will show how to obtain a limiting absorption principle for the stationary equation via a propagation of defect measure argument.", "id": "Paper/69512", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69512"}, {"title": " Topological entanglement of open curves in 3-space and protein structure complexity ", "webprogram_exclude": "0", "session_ids": ["Session/18358"], "source_sha256": "b5226a839fa181620a1f3833c12ee7878b0ca9326b608a4086d75225024299b9", "withdrawn": "", "abstract": "Even though intuitively entanglement is often understood in terms of knotting or linking, many of the filamentous systems in the natural world are not mathematical knots or links.  In this talk, we will introduce a novel and general framework in knot theory that can characterize the complexity of open curves in 3-space. This leads to new metrics of entanglement of open curves in 3-space that generalize classical topological invariants, like for example, the Jones polynomial and Vassiliev invariants. \nWe apply our methods to proteins to understand the interplay between their structures and functions. We show that our proposed quantitative topological metrics based on static protein structures alone correlate with protein dynamics and protein function. \nThe methods and results represent a new framework for advancing knot theory, as well as its applications to filamentous materials, which can be validated by experimental data and integrated into machine-learning algorithms.", "id": "Paper/69513", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69513"}, {"title": " On the <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.202ex\" height=\"1.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -576.1 517.5 721.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\tau</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-3C4\" d=\"M39 284Q18 284 18 294Q18 301 45 338T99 398Q134 425 164 429Q170 431 332 431Q492 431 497 429Q517 424 517 402Q517 388 508 376T485 360Q479 358 389 358T299 356Q298 355 283 274T251 109T233 20Q228 5 215 -4T186 -13Q153 -13 153 20V30L203 192Q214 228 227 272T248 336L254 357Q254 358 208 358Q206 358 197 358T183 359Q105 359 61 295Q56 287 53 286T39 284Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-3C4\" x=\"0\" y=\"0\"></use>\n</g>\n</svg> Invariant for Satellites with (1,1)-Unknot Patterns and 2-Bridge Knot Patterns ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "5183558c21f08f005f88b9c74cd8b383296bdfd6fda0f0603bb2687ecdf67f03", "withdrawn": "", "abstract": "We investigate the $\\tau$ invariant for 2-bridge knots and satellite knots with (1,1)-unknot patterns. Our approach relies on the immersed curve techniques in Heegaard Floer homology—developed by Hanselman, Rasmussen, and Watson around 2016—as well as Chen’s 2019 pairing theorem for satellite knots with (1,1)-patterns. Specifically, we focus on unknot patterns arising from the 2-bridge links with Schubert form $b(2qn+2i,q)$, where $q$ is even and $1 \\leq i \\leq |q|-1$. Using this setup, we compute formulas for the effect of the satellite operation on $\\tau$ for the families where $i=q-1$ and $i=(q+1)/2$. We also contextualize the work of Patwardhan and Xiao (2024) as corresponding to the $i=(q-1)/2$ family. Furthermore, we identify the $i=(q+1)/2$ family as always braided, thereby recovering Eldridge's (2026) formula for this case. By introducing a word representation for immersed curves, we conjecture an algorithmic method to compute $\\tau$ for any satellite with a (1,1)-unknot pattern directly from its Schubert normal form. Finally, for 2-bridge knots, we calculate $\\tau$ using immersed curve pairing with the unknot. This yields a purely geometric computation based on the immersed curve’s twisting behavior, inviting further exploration into connections with the established relationship between $\\tau$ and the signature of 2-bridge knots.", "id": "Paper/69514", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69514"}, {"title": " Cauchy-completions and higher idempotents ", "webprogram_exclude": "0", "session_ids": ["Session/18210"], "source_sha256": "6c6268eeff90ec9af36d83490cdaa1b6a5360fb263623a99a48f8a52357bd705", "withdrawn": "", "abstract": "An enriched category is said to be Cauchy-complete if it admits all absolute colimits: those weighted colimits that commute with every enriched functor. For instance, an ordinary (set-enriched) category is Cauchy-complete precisely iff it is idempotent-complete, an abelian-group-enriched category iff it is both idempotent-complete and additive, and a spectra-enriched ∞-category iff it is idempotent-complete and stable. \nI will extend this notion to enriched (∞,n)-categories and explain how, assuming the cobordism hypothesis, it can be used to construct framed fully extended topological field theories. In particular, it leads to a notion of higher idempotents, also known as condensations in the sense of Gaiotto and Johnson-Freyd. Joint work in progress with David Reutter.", "id": "Paper/69515", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69515"}, {"title": " Admissibility, Stability and Consistency of a Narrow Stencil Method for Approximating Viscosity Solutions of Monge-Ampère-type Equations ", "webprogram_exclude": "0", "session_ids": ["Session/17872"], "source_sha256": "f4ecdb4fae436d5f939d4830e09b14239cae7866f5fbeea255b673c89b7272d2", "withdrawn": "", "abstract": "This talk introduces a stable non-monotone finite difference method for approximating viscosity solutions of fully nonlinear Monge-Amp\\`{e}re-type equations. It develops a notion of local consistency and proves admissibility and stability using novel cut offs. The numerical experiments demonstrate $O(h^2)$ convergence across regularity classes and include: the classical $C^2$ prescribed Gaussian curvature equation, the $C^{1,1}$ optimal transport equation, and the $C^{0,1}$ Alexandrov cone with gradient singularity on the boundary. A numerical moment is introduced inspired by a recent high order method for approximating stationary Hamilton-Jacobi equations. The novel numerical moment uses fourth order stabilizers over the Cartesian and diagonal directions of the local stencil. The Monge-Amp\\`{e}re operator is the canonical example of a fully nonlinear degenerate elliptic PDE and is difficult to directly approximate due to its conditional uniqueness properties.", "id": "Paper/69516", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69516"}, {"title": " Connecting absorbing Markov chains to irreducible ones. Application to the computation of bounds of interesting metrics defined in the latter. ", "webprogram_exclude": "0", "session_ids": ["Session/17976"], "source_sha256": "e5f4166cd4e163cc1d573a1b4f6d13e51f474dc058b500b8fffa9f52e944d030", "withdrawn": "", "abstract": "Siegmund duality connects irreducible and absorbing Markov chains in a very specific way, with a constraint: the irreducible chain must satisfy a specific monotonicity property; the interesting point is that the connection is done through the respective transient distributions. Here, we present a different way of making an association that starts with an irreducible model and builds an associated absorbing one, with specific relationships between properties of both models evolving in steady state.  In the talk, we will illustrate this link with an application, the derivation of bounds of important metrics defined in the irreducible model. This is useful when, for instance, the irreducible model is huge and complex, making impossible to evaluate its steady state distribution and then, the metrics of interest. The illustration will consider queueing models and performance oriented metrics.", "id": "Paper/69518", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69518"}, {"title": " Counting Complexity in Group Theory ", "webprogram_exclude": "0", "session_ids": ["Session/18214"], "source_sha256": "3a867a8d24c18b55d53a1f7f195b2a7cb6aa077b0a3f4e9b4e40672a6558c67b", "withdrawn": "", "abstract": "Determining the computational complexity of counting the number of homomorphisms from one group to another is an interesting question within the field of computational algebra. I will discuss my investigation in the case where the target group is the dihedral group of order 8, i.e. the symmetries of a square. In turn, I will connect this result to the complexity of counting the number of solutions to certain systems of equations. This is joint work with Eric Samperton.", "id": "Paper/69521", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69521"}, {"title": " A graph construction for analysing the parametric asymptotics of Markov processes ", "webprogram_exclude": "0", "session_ids": ["Session/17811"], "source_sha256": "c405e09f0fc8010879c2d8190ff04084c14449cd019326971dc2b48274344064", "withdrawn": "", "abstract": "The linear framework is a graph-theoretic approach to continuous-time, time-homogeneous, finite-state Markov processes, in which a directed graph with labelled edges specifies the infinitesimal generator of the process. Vertices represent states, edges represent transitions and edge labels represent transition rates. The framework allows certain properties of the Markov process, such as its steady-state probabilities and moments of the first passage time distribution, to be expressed as rational functions of the edge labels. Here, we introduce a graph operator that captures the effect of taking a single edge label to infinity, producing what we call an \"asymptotic graph\". We show that, under a broad range of circumstances, the steady-state probabilities, the eigenvalues of the Laplacian matrix, and the moments of the first passage time distribution of the asymptotic graph are precisely the limits of those of the original graph as the corresponding edge label is sent to infinity. We also demonstrate how the asymptotic graph operator commutes with several other graph operators, extending the development of an operator algebra within the linear framework. Together, these results suggest that the asymptotic graph provides a natural context for analysing the behaviour of a Markov process as a single parameter is sent to infinity.", "id": "Paper/69523", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69523"}, {"title": " Clustering and Mean-Variance Optimization in Portfolio Construction ", "webprogram_exclude": "0", "session_ids": ["Session/18328"], "source_sha256": "7713874e39d784ed2658f36eccc76f534adf7954c8dd214cd5366685c9f577ce", "withdrawn": "", "abstract": "This project develops a portfolio construction framework that integrates unsupervised clustering with Modern Portfolio Theory (MPT). A universe of 46 publicly traded U.S. companies across eleven sectors is grouped using K-Means and Self-Organizing Maps (SOM) to identify groups of similar companies. Cardinality constraints are used to determine portfolio size based on improvements in the Sharpe ratio, followed by mean–variance optimization. Portfolio performance is compared with classical MPT, including major market stress periods. Results show that K-Means–MPT generally outperforms SOM–MPT and classical MPT, while both clustering approaches improve diversification and risk-adjusted performance.", "id": "Paper/69528", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69528"}, {"title": " Stability of traveling waves for a reaction-diffusion equation with nonlinear diffusion ", "webprogram_exclude": "0", "session_ids": ["Session/18109"], "source_sha256": "08c52fe2a90858d7d11d5f2525e170538cde3c2e1535fe8b2785e379ad4e97d2", "withdrawn": "", "abstract": "In this talk, I will report on an ongoing project to develop new tools for understanding and quantifying the stability of traveling waves for reaction-diffusion equations, especially in the \"pulled\" and \"pushmi-pullyu\" regime.  This talk will focus on the application of the shape defect function to a nonlinear diffusion model.  It is a preliminary report of ongoing work with Mete Demircigil and Ryan Patterson.", "id": "Paper/69529", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69529"}, {"title": " Singular parametric limits on graphs, dynamical systems, and algebraic varieties ", "webprogram_exclude": "0", "session_ids": ["Session/18303"], "source_sha256": "dddc3ed13ca9911d7ca2e46a21bd52961d2947a1e11f8b426495d055cd71bd74", "withdrawn": "", "abstract": "In previous work, we used graph-theoretic frameworks such as the linear framework and linear compartment models to introduce a graph operator that captures the effect of taking a single edge label to infinity. Such limits arise naturally in biochemical reaction networks when one reaction occurs on a much faster timescale than the others, motivating connections to timescale separation and model reduction. We have previously demonstrated that the resulting “asymptotic graph” provides a natural context for analyzing the behavior of a Markov process and a model’s structural identifiability via the transfer function. In this talk, I consider what this limiting operation can reveal about the dynamical and algebraic geometric structure of the underlying models. In particular, I explore how the dynamics behave in the infinite-parameter limit and what this limit suggests about the geometry of parameter space and a reaction network’s associated steady-state variety. These questions are illustrated through examples of biochemical reaction networks arising from enzyme kinetics.", "id": "Paper/69531", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69531"}, {"title": " The space of d-pleated surfaces and its topology ", "webprogram_exclude": "0", "session_ids": ["Session/17283"], "source_sha256": "567a0cd500998e12c6612a2cffc29ca3c2ccdac59a388e3499f267a5f60d09e4", "withdrawn": "", "abstract": "In this talk, we will discuss joint work with Giuseppe Martone, Filippo Mazzoli, and Tengren Zhang about d-pleated surfaces, which are surface group representations into $\\mathrm{", "id": "Paper/69533", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69533"}, {"title": " Front Propagation for Go-or-Grow Models of Aerotaxis ", "webprogram_exclude": "0", "session_ids": ["Session/18445"], "source_sha256": "54df6d074dfaa083ea3c594760716d61765568381e8a38b1b9a3b6971764f18f", "withdrawn": "", "abstract": "In this talk, I will introduce and analyze two simple models for “aerotaxis,” that is, when organisms follow oxygen gradients.  In particular, we establish well-posedness of a suitable nonstandard notion of weak solutions for both models. Further, we characterize the front location up to $O(1)$-precision in all cases, including the delicate boundary “pushmi-pullyu” case.  This is a joint work with Mete Demircigil.", "id": "Paper/69536", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69536"}, {"title": " Differential Equations Satisfied by Reversed Dickson Polynomial ", "webprogram_exclude": "0", "session_ids": ["Session/18385"], "source_sha256": "f6942e378b39ade7257100b861361ee00ab9f08f89b593dcd933b8a79c49f921", "withdrawn": "", "abstract": "Dickson polynomials constitute an important family of special polynomials with significant applications in algebra, number theory, finite fields, coding theory, and cryptography. It is well-known that the Dickson polynomials of the first kind and second kind satisfy second-order linear homogeneous differential equations. \n\nReversed Dickson polynomials were introduced in 2009 by interchanging the roles of the variable and the parameter of Dickson polynomials. They have mainly been studied in the literature for their permutation behaviour over finite fields, but their differential properties have received comparatively less attention. We investigate differential equations satisfied by the reversed Dickson polynomials of the first kind, the second kind, and the $(k+1)$-th kind.\\\\\n\nThis is a joint work with Neranga Fernando (Knox College).", "id": "Paper/69538", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69538"}, {"title": " Using AI Enabled Homework to Increase Learning Outcomes in a Foundations of Mathematics Course ", "webprogram_exclude": "0", "session_ids": ["Session/18262"], "source_sha256": "842097c5bac91470d2809db19828ad53955eb139e5324b3519199e2a06e1a8b9", "withdrawn": "", "abstract": "The presenters piloted a new AI enabled homework system in their Foundations of Mathematics course. The system allowed for generative AI to join the student-instructor feedback loop and assist in improving student’s homework solutions without compromising student learning. This approach allowed students to use any available generative AI tools and required no specialized interface. The approach can be extended to other courses in the math curriculum. We will share student feedback and instructor observations about the benefits and drawbacks of the approach versus previous semesters without AI. The Foundations course serves as an introduction to proof writing course at the United States Military Academy at West Point.", "id": "Paper/69539", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69539"}, {"title": " Finite Time Blow-Up in a Damped Klein-Gordon Equation ", "webprogram_exclude": "0", "session_ids": ["Session/19363"], "source_sha256": "f78e791457e924af08fae85e623fe54610e213bb0137eeee864dd31d11448c98", "withdrawn": "", "abstract": "We consider a non-linear Klein-Gordon Equation with the introduction of a spatial damping term $a(x)\\in L^\\infty$ where $a(x)$ shares the same sign of $u_{tt}$. We prove, using non conservative energy methods and H. A. Levine's established concavity condition, that under sufficient initial conditions we get finite time blow-up of solutions. Levine's concavity condition utilizes defining an auxiliary function in terms of our solution and showing that such an auxiliary function is bounded below by a function that blows up in finite time.", "id": "Paper/69541", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69541"}, {"title": " Counting Correspondence Colorings ", "webprogram_exclude": "0", "session_ids": ["Session/18360"], "source_sha256": "5000348d01722557496c3869f221f87afd2ef40ee240287c799b1b6551745e80", "withdrawn": "", "abstract": "Introduced by Dvo\\v{r}\\'{a}k and Postle in 2015, correspondence coloring (DP-coloring) is a generalization of list coloring and proper vertex coloring that allows for the color restrictions to vary at each edge of a graph.\nIn this presentation, we focus on the DP color function, introduced by Kaul and Mudrock in 2019, which generalizes the chromatic polynomial of a graph. \nThis function, $P_{DP}(G, k)$, counts the minimum number of valid correspondence colorings of a graph $G$ over all correspondence assignments with list size $k$.\nA central open question about the DP color function is whether this function is a polynomial for large enough $k$.\nThis question has been answered affirmatively for various classes of graphs, including chordal graphs ($P_{DP}(G, k) = P(G, k)$), generalized theta graphs, and recently, bipartite graphs.\nWe introduce a new permutation-based view of correspondence assignments and use this perspective to aid in characterizing certain correspondence assignments that minimize $P_{DP}(G, k)$. \nThis permutation interpretation allows us to provide a counterexample to the conjecture that for every graph $G$, $P_{DP}(G, k)$ is polynomial for large enough $k$.", "id": "Paper/69542", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69542"}, {"title": " On the Tri-plane Crossing Number of Knotted Surfaces ", "webprogram_exclude": "0", "session_ids": ["Session/18384"], "source_sha256": "0da8b7c0bffd02257c0c827c8f5047045e74eaade891846cd1672316ba172383", "withdrawn": "", "abstract": "The tri-plane crossing number is an invariant used to study knotted surfaces in the $4$-sphere, but is difficult to calculate. By generalizing the triple point number obstruction of Gong, Lewis-Monkman, and Osnes '26 and using banded unlink calculus, we obtain novel lower and upper bounds on the tri-plane crossing number for various non-ribbon twist-spun knots. We exhibit a minimal crossing diagram for the $2$-twist spun figure-eight knot, determining its tri-plane crossing number to be 8. This is the second such computation for a non-trivial knotted surface. Additionally, through a counting argument of the number of double circles in a broken surface diagram, we obtain the first known nontrivial lower bound on the tri-plane crossing number of ribbon $2$-knots.", "id": "Paper/69543", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69543"}, {"title": " Systems of Higher Homotopies (part 2) ", "webprogram_exclude": "0", "session_ids": ["Session/18030"], "source_sha256": "b3ca0f4744c01469477fde7d363d01262485aebf31ca82cb135ba77d837ed3f8", "withdrawn": "", "abstract": "In part 2 of the talk, we will introduce the generalized definition of systems of higher homotopies introduced by Kalir, Pollicove, and Watson. We will show how this notion recovers the definition of Eisenbud and Shamash, as well as the notion of an A-infinity module. We will then show how systems of higher homotopies can be used to transfer resolutions in several different settings.", "id": "Paper/69545", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69545"}, {"title": " Semiclassical improvements to density functional theory ", "webprogram_exclude": "0", "session_ids": ["Session/18326"], "source_sha256": "b32931f6870eb625193157daf43d20b97718dd163189ec2ab2431c54cb876ec8", "withdrawn": "", "abstract": "Density functional theory is a standard tool for computing energies (eigenvalues) throughout chemistry and in many parts of physics and materials science. I will present the basics of the subject and then show how semiclassical analysis can improve the accuracy of its results. Specifically, we compensate errors in approximate density functionals using a normalization correction derived from semiclassical spectral asymptotics.", "id": "Paper/69546", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69546"}, {"title": " Telling time with a circadian clock: Signal integration in cyanobacteria ", "webprogram_exclude": "0", "session_ids": ["Session/17972"], "source_sha256": "b61c4b6416fa42780fe39bb41f0d0e3a5819785a40ba7742f82cb915229a6407", "withdrawn": "", "abstract": "A simple circadian clock allows cyanobacteria to align photosynthesis, photoprotection, and metabolism with the Earth’s varying day-night cycles. Recent work models the clock as an encoder–decoder that estimates biologically relevant quantities like time to sunset or future light levels, providing a principled explanation for non-24-hour internal periods and their dependence on seasonal structure and latitude. Building on this mechanism, we simulate the KaiABC oscillator as a limit-cycle attractor near a Hopf bifurcation. By harnessing environmental signals like temperature and solar radiation as inputs to the model, we can chart the oscillator’s trajectory in “clock” phase space. In particular, luminance changes drive shifts in the limit cycle's origin during day-to-night transitions, while temperature scales the oscillation amplitude. This entrainment over time can be modeled as movement between orbits, providing a statistical basis for downstream prediction of crucial physiological variables. The model’s predictive power is enhanced by encoding oscillation nullification at sufficiently low temperatures, informed by experimental observations of lab-strain cyanobacteria. This additional temperature dependence on the bifurcation parameter more clearly captures seasonal variations in clock behavior across climates, prompting further investigation into the wide variety of circadian structures in nature.", "id": "Paper/69547", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69547"}, {"title": " Splitting of equivariant stable h-cobordism spaces ", "webprogram_exclude": "0", "session_ids": ["Session/18217"], "source_sha256": "bdbc5448e6a500d47504e8a4c73aefad58516da98d92507332f774ca3034ed88", "withdrawn": "", "abstract": "A classical and central result in equivariant stable homotopy theory is the tom Dieck splitting of the fixed points of the suspension spectrum of a G-CW complex. In previous work with Malkiewich, we constructed an equivariant A-theory spectrum whose fixed points also exhibit a similar splitting. I will discuss an analogous tom Dieck splitting for the stable space of equivariant h-cobordisms, which allows us to relate it to equivariant A-theory. This is joint work with Goodwillie, Igusa, and Malkiewich.", "id": "Paper/69549", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69549"}, {"title": " Stability Margins of Upper-Ocean Stratification: A Mathematical Diagnostic for Intrinsic Thermal Variability ", "webprogram_exclude": "0", "session_ids": ["Session/19351"], "source_sha256": "c0e3020265b58e248d2d0afd9d9f87d82be46cafda3f08cba8cf8a119b88c867", "withdrawn": "", "abstract": "The upper ocean exhibits thermal variability driven by interactions among vertical mixing, stratification, and nonlinear air sea feedbacks. We develop a minimal three-layer dynamical model to determine when a steadily stratified water column loses stability and develops self-sustained thermal oscillations without external periodic forcing. We analytically establish bounded long-term behavior and a unique stratified equilibrium, and derive a closed-form threshold separating steady and oscillatory regimes. This threshold defines a dimensionless stability margin that measures the distance of a water column from the onset of intrinsic variability. Beyond the threshold, a codimension-two Hopf-Hopf bifurcation organizing point produces quasi-periodic, multi-frequency oscillations through the interaction of vertical mixing and nonlinear thermal feedbacks. To connect the theory with observations, we generate Argo-like temperature–salinity profiles and solve an inverse problem to recover physically interpretable model parameters. The resulting framework provides a mathematical diagnostic for assessing and comparing the stability and intrinsic variability of upper-ocean regimes.", "id": "Paper/69550", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69550"}, {"title": " Regularity of minimizers of functionals with <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"5.082ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 2188.2 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">(p,q)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-70\" d=\"M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-71\" d=\"M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-70\" x=\"389\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2C\" x=\"893\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-71\" x=\"1338\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"1798\" y=\"0\"></use>\n</g>\n</svg>-growth in the Heisenberg group ", "webprogram_exclude": "0", "session_ids": ["Session/19357"], "source_sha256": "f5c84c93361022673e2df594c8ed59e7ef4390da75bf1cf9c2ad5c7406eda7b8", "withdrawn": "", "abstract": "In the Heisenberg group, we discuss the interior Lipschitz continuity of local minimizers of autonomous integral functionals whose energy densities satisfy a $p$-coercivity bound and a $q$-growth bound, where $1<p<q<\\infty$ are subject to an appropriate gap condition.", "id": "Paper/69553", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69553"}, {"title": " A Zero-One Law for One-Shot Analytic System Identification ", "webprogram_exclude": "0", "session_ids": ["Session/18447"], "source_sha256": "0345d616ad577ac97f5b5140d4b2dd93a464106a0df4897d7370840c1d88f730", "withdrawn": "", "abstract": "Equation discovery is an important scientific machine learning task that seeks to determine an unknown equation from solution data. We consider the case where the underlying system has input quantities and is described by an unknown linear combination of known analytic dictionary operators between Banach spaces. We ask which inputs produce solutions that uniquely determine the unknown coefficients. This describes a large class of discovery problems for ordinary and partial differential equations and recovery problems for linearly parameterized structured matrices, where the inputs can include initial conditions, boundary conditions, forcing signals, source terms, and matrix-vector product queries. The unknown coefficients are recoverable precisely when the dictionary operators evaluated on the input—solution pair are linearly independent. We prove a zero-one law for the degenerate set of inputs failing to produce the required linear independence. Either every input is degenerate and the coefficients are not recoverable from any input—solution pair, or the degenerate set of inputs is negligible in the sense that it is Lebesgue null on compact translates of finite-dimensional slices with sufficiently high dimension (a property we call compactly slice-null), and almost every input sampled from any non-degenerate Gaussian measure on input space allows for recovery of the unknown coefficients. We apply this framework to the recovery of matrices, analytic continuous-time dynamical systems, and partial differential equations. For several problem classes we further characterize the degenerate sets and identify deterministic choices of inputs that guarantee coefficient recovery.", "id": "Paper/69555", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69555"}, {"title": " On the representation type of a finite tensor category ", "webprogram_exclude": "0", "session_ids": ["Session/17907"], "source_sha256": "ff1a00df87841440b2a895d07aa28f3dccb2ac1cec8d9bc9e4062fcd8f913ece", "withdrawn": "", "abstract": "Support varieties provide a geometric approach to studying representations of finite-dimensional algebras and, more generally, finite tensor categories. Under suitable finite-generation assumptions on cohomology, these varieties encode homological information such as the complexity of objects and can be used to study representation-theoretic properties of the category.\n\nIn this talk, I will discuss support varieties for finite tensor categories and explain how their geometry can be used to obtain information about representation type. In particular, I will describe how complexity provides criteria for detecting wild representation type and how these ideas extend to module categories.", "id": "Paper/69557", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69557"}, {"title": " Play  and  proof: eliciting linear combinations through sun grids ", "webprogram_exclude": "0", "session_ids": ["Session/18235"], "source_sha256": "6eecdde4b393269046ff816b12d3fb4031a3996bb925551729dd57ca45faaca5", "withdrawn": "", "abstract": "How do you design a problem that elicits linear algebra concepts without using linear algebra? This talk will describe one approach to this issue via a case study of constructing a particular problem. \n\nThe speaker happened (via the arXiv) upon a recreational mathematics paper in number theory that contained \\emph{two sentences} suggesting the use of basic linear algebra in examining a family of examples. Understanding the structure of these examples led to the parts of an Exam Assessing Readiness (EAR) problem for \\{MathILy, MathILy-Er\\}, a pair of selective intensive summer mathematics programs.\n\nThis talk will be suitable both for attendees who want to experience the problem/mathematics themselves and for those who have a pedagogical interest in problem construction.", "id": "Paper/69559", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69559"}, {"title": " Uncrowding Algorithms and Crystal Structures in K-Theoretic Combinatorics ", "webprogram_exclude": "0", "session_ids": ["Session/18067"], "source_sha256": "b9d3c0ff23ca217f6139a85ca6c413babe7606a64695d16d97f97feb4d23f101", "withdrawn": "", "abstract": "Crystal bases provide powerful combinatorial models for representations of quantum groups, with semistandard Young tableaux being the classical type A example. K-theoretic Schubert calculus gives rise to richer families of tableaux, including set-valued and hook-valued tableaux, whose generating functions are stable Grothendieck polynomials and their canonical analogues. In this talk, I will describe how these K-theoretic tableau models can be understood through crystal-theoretic methods. A key tool for understanding these objects is an “uncrowding” operator, which relates more complicated tableaux back to classical ones while preserving structural features. Building on Buch’s uncrowding operator for set-valued tableaux, I will discuss a recent extension to hook-valued tableaux. By studying these operators, we uncover a “hidden” symmetry of hook-valued tableaux through jeu de taquin, using a classical result of Benkart, Sottile, and Stroomer.", "id": "Paper/69562", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69562"}, {"title": " Quasi-Gorenstein morphisms and virtual G smallness ", "webprogram_exclude": "0", "session_ids": ["Session/18025"], "source_sha256": "af07ad8061e2b747de8291be22800c9225b77f5a59ffde90c64806e3dfcdc5fd", "withdrawn": "", "abstract": "A quasi-Gorenstein homomorphism of commutative noetherian local rings, as first defined by Avramov and Foxby, naturally characterizes the Gorenstein property in commutative algebra. In particular, the canonical surjection of a local ring R onto its residue field is quasi-Gorenstein if and only if R is Gorenstein. Moreover, if a local homomorphism R to S is quasi-Gorenstein, then R is Gorenstein if and only if S is Gorenstein. In this talk we will provide a necessary and sufficient condition for a morphism to be quasi-Gorenstein in terms of a Gorenstein variant of virtually smallness. This parallels a result of Briggs, Iyengar, Letz, and Pollitz which classifies locally complete intersection morphisms. This presentation is based on joint work with Zachary Nason and Andrew Soto Levins.", "id": "Paper/69563", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69563"}, {"title": " Combinatorial Properties of Soliton Decomposition Classes ", "webprogram_exclude": "0", "session_ids": ["Session/19366"], "source_sha256": "564369b3cf80f5dc84072f36443cdad0280387e19bf266018d963f853562cdcc", "withdrawn": "", "abstract": "We explore the discrete dynamical system known as ``box-ball evolution” that transforms permutations $w$ into row-strict ``soliton decomposition” Young tableaux $\\mathrm{SD}(w)$. Expanding on the work of Gunawan and other authors, we explore the ``soliton decomposition classes” formed by permutations with the same soliton decomposition, and compare them to the $\\mathrm{P}$ and $\\mathrm{Q}$ classes given by the famous Robison--Schensted correspondence. We introduce a ``soliton recording tableau”, denoted $\\mathrm{SQ}(w)$, and prove that the map from permutations to pairs of tableaux given by $w \\mapsto (\\mathrm{SD}(w), \\mathrm{SQ}(w))$ is well-defined and injective. We also discuss the problem of finding ``moves” on permutations that preserve their soliton decomposition, generalizing known results about Knuth moves and developing a new algorithm for computing soliton decompositions.", "id": "Paper/69568", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69568"}, {"title": " Systems of Higher Homotopies (Part 1) ", "webprogram_exclude": "0", "session_ids": ["Session/18030"], "source_sha256": "87879438061178fddef47f64e86110e893e364eda6f5173f2de203277ebccb75", "withdrawn": "", "abstract": "Eisenbud and Shamash define a family of endomorphisms called a system of higher homotopies to construct free resolutions across quotients by regular sequences. They demonstrate that these systems exist even in the absence of differential graded (DG) module structures. Recent work by Briggs, Cameron, Letz, and Pollitz connects this construction to a generalized notion of Koszul duality. In this talk we will review the constructions of Eisenbud and Shamash as well as their connection to Koszul duality through (curved) DG coalgebras and twisting morphisms.", "id": "Paper/69571", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69571"}, {"title": " Modeling the effects of pericyte control of capillaries on blood flow and oxygenation in the retinal microcirculation ", "webprogram_exclude": "0", "session_ids": ["Session/18122"], "source_sha256": "0cea2292c278f1f6eef811ab9f1471c1d649695a75f0413f61e914c27cfd721f", "withdrawn": "", "abstract": "The retinal microcirculation supplies blood and oxygen to the cells responsible for vision,\nand vascular impairments are involved in the progression of eye diseases such as\nglaucoma. In addition to the control of microvascular blood flow that takes place in the\nsmooth-muscle-surrounded upstream arterioles, blood flow in retinal microvascular networks\nis also regulated downstream by pericytes -- contractile cells wrapped around the\nwalls of capillaries. Here, an established theoretical model of a compartmental retinal\nmicrovascular network is extended to investigate the role of pericyte-mediated control of\ncapillary diameters. This capillary regulation is modeled using a wall mechanics framework\nanalogous to that used for smooth muscle cells in the arterioles. Pericyte tone is\ndescribed by a nonlinear sigmoidal function that incorporates constrictive responses to\nmyogenic tension and endothelin-1 and dilatory responses to nitric oxide and adenosine.\nChanges in pericyte tone alter capillary diameter and resistance, thereby influencing capillary\nblood flow and oxygen delivery. A Krogh cylinder model is used in the arteriolar,\ncapillary, and venular compartments to simulate oxygen transport. Model results suggest\nthat disruption of signals moderating capillary pericyte tone can lead to sustained capillary\nconstriction, reduced perfusion, and impaired oxygen delivery. These results imply a\nnon-trivial contribution of pericyte-mediated capillary blood flow regulation to the overall\nability of the retina to regulate blood flow, with impairments in capillary flow regulation\npotentially contributing to glaucomatous damage.", "id": "Paper/69578", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69578"}, {"title": " Uubs, suubs, and the <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"3.133ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 1349 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathsf {TA}</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJSS-54\" d=\"M36 608V688H644V608H518L392 609V0H288V609L162 608H36Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJSS-41\" d=\"M183 181Q183 179 152 91T118 0H28L154 346L280 693Q281 694 333 694H385L511 349Q636 4 638 2Q638 0 584 0H530L464 183H184L183 181ZM324 606Q319 578 292 492T238 332T210 256Q210 254 324 254T438 255L429 281L419 308Q409 336 395 378T365 465T339 551T324 611V606Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJSS-54\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJSS-41\" x=\"681\" y=\"0\"></use>\n</g>\n</svg> degrees as theory spectra ", "webprogram_exclude": "0", "session_ids": ["Session/18589"], "source_sha256": "62041783a8d1807f75a5b8d27b0431a2998ad83eaf029c7f18f6cfdc47f5da79", "withdrawn": "", "abstract": "A pair of results from Andrews and Knight (2013) and Andrews et al. (2017) show the $\\mathsf{TA}$ degrees (degrees of nonstandard models of true arithmetic) to be the spectrum of an atomic theory, but not the spectrum of any $\\omega$-stable theory. Exploring which sorts of theories (superstable, stable, etc.) can have the $\\mathsf{TA}$ degrees as their spectrum led us to consider the uniform upper bounds (uubs) and subuniform upper bounds (suubs) of the arithmetic sets as theory spectra. This produced examples of theory spectra which are spectra of superstable, atomic theories, but not spectra of small theories, a division not previously witnessed by theory spectra. We discuss these results and their relation to our ongoing efforts to clarify which sorts of theories can have the $\\mathsf{TA}$ degrees as their spectrum.", "id": "Paper/69581", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69581"}, {"title": " What Counts as Mathematical Work? Student views of their Parents’ occupations and the Social Boundaries of Mathematics ", "webprogram_exclude": "0", "session_ids": ["Session/17853"], "source_sha256": "da05c32d0670b6db19e2b25a87ef247288b616e1eed12ed448705df73755e59a", "withdrawn": "", "abstract": "What counts as mathematical work, and who gets to decide? This paper examines 707 survey responses from Algebra II students in the US-Mexico Borderlands Region, who described their mothers’ and fathers’ occupations and rated, on a five-point scale, the extent to which each job aligned with STEM. Rather than treating these ratings as attempts to reproduce an official STEM taxonomy, we interpret them as acts of classification revealing students’ implicit philosophy of mathematics.\n\nPreliminary analysis suggests that students recognize STEM most readily when work displays visible markers of technicality, such as machinery, electricity, engineering, computers, specialized tools, or formal credentials. Yet mathematical practices often become invisible when embedded in ordinary work. Students describe parents handling money, maintaining inventories, measuring materials, preparing taxes, managing schedules, or calculating quantities while assigning those occupations only low or moderate STEM ratings. Caregiving and domestic work are especially revealing: students may describe such labor as difficult or indispensable while locating it near the non-STEM end of the scale.\n\nThese patterns suggest a distinction between mathematics as practice and mathematics as socially recognized identity. Quantification, measurement, spatial reasoning, or data management may occur without the work being named “mathematical,” while occupational titles or technological artifacts may serve as warrants for STEM status despite little articulated mathematical content.\n\nWe propose that STEM operates not as a binary natural kind but as a locally negotiated, graded category shaped by visibility, institutional status, technological imagery, and familiar prototypes. The findings raise a wider philosophical question: if mathematical activity can be present without being recognized as mathematics, then the boundaries of mathematics are not merely disciplinary or logical, but also social, linguistic, epistemic, and lived within family life.", "id": "Paper/69582", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69582"}, {"title": " Cellular Homology of Watertight Models, II ", "webprogram_exclude": "0", "session_ids": ["Session/18323"], "source_sha256": "38a8015557c5323600f0746490afe91e226e4e35aa848b6eb27951490efa4f63", "withdrawn": "", "abstract": "Watertightness of Computer-aided design (CAD) models is a widely desired\nproperty, yet often lacks a formal definition. In part I, we proposed a formal\ndefinition of watertightness using CW complexes. We then introduce the notion\nof sheet decompositions as a framework for efficient computation of verifying\nwatertightness. We present several homological properties of our sheet decomposition. In particular, we prove that sheet decompositions preserve top homology while significantly decreasing the size of the CW complex. Since we define\nhomology over the integers we pose verification of watertightness of a mesh as\nsolving an integer linear program (ILP) on the corresponding sheet decomposition. With efficient computation in mind, we show methods for computing the\nsheet decomposition and verifying watertightness. We show several computational examples demonstrating the efficiency of our method. For meshes with\nup to 1.1 million triangles, our framework computes the sheet decomposition in\nunder 8 seconds and verifies watertightness by solving the ILP in less than a\nsecond.", "id": "Paper/69584", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69584"}, {"title": " Environmental Drivers and County-Specific Forecasting of Valley Fever in California ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "70f251565049012a19e5d3d1f53c341f4ab0355b5291a7c8a0206e296630a1c9", "withdrawn": "", "abstract": "Valley Fever (\\emph{coccidioidomycosis}) is a fungal respiratory disease whose incidence is influenced by environmental conditions. Strong seasonality, irregular surges, and delays of up to two years in public case reporting complicate timely forecasting and public health planning. This study evaluated whether environmental data alone could forecast monthly county-level incidence and whether models trained separately for each county better preserve local patterns than models trained on geographically aggregated data.\n\nWe analyzed county-month observations from 2001–2024 across eight California counties using 11 meteorological, soil, air-quality, wildfire, and pesticide-related predictors. Aggregate time series were constructed using monthly means or medians across counties. Preliminary experiments used seasonal autoregressive integrated moving average models with exogenous variables (SARIMAX), while final comparisons evaluated county-specific and aggregate long short-term memory (LSTM) networks against linear regression baselines. Performance was measured using root mean squared error (RMSE) over six-month walk-forward test periods from 2016–2024. We also used repeated permutation feature importance to evaluate environmental predictors across models with and without wildfire acreage.\n\nCounty-specific LSTMs outperformed aggregate LSTMs in all eight counties, reducing mean RMSE by approximately 55\\%. Linear regression achieved lower RMSE in four counties; however, county-specific LSTMs more consistently captured seasonality, temporal variation, and incidence peaks. Feature importance varied geographically, while wildfire showed positive predictive importance in only five of eight counties. These findings indicate that environmental signals do not transfer uniformly across California and that county-specific modeling better preserves localized disease and environmental patterns.", "id": "Paper/69587", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69587"}, {"title": " When Full Coordination Is Not Yet Possible: Making Meaningful Progress ", "webprogram_exclude": "0", "session_ids": ["Session/17971"], "source_sha256": "6a8303fb2dd24cb59677469087aeb120b0ea87cf98e8737f9074d5ff4a26eab0", "withdrawn": "", "abstract": "Coordinating multiple sections of undergraduate mathematics courses requires balancing consistency in student experiences with academic freedom and practical implementation constraints. At Northern Illinois University, I coordinate several mathematics courses, and in this talk, I share the progressive changes we have implemented, including greater alignment of learning objectives and assessments, common syllabi and pacing, shared online homework, and structured exam retakes in Trigonometry. Some of these efforts have been accompanied by encouraging student outcomes and passing rates, while broader coordination remains challenging because of differences in instructional practices and in how common course structures are implemented across sections. I also reflect on the challenges, setbacks, and lessons learned while working toward stronger coordination and greater consistency across sections.", "id": "Paper/69588", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69588"}, {"title": " Analogies Between Soliton Decomposition and the Robinson–Schnested Correspondence ", "webprogram_exclude": "0", "session_ids": ["Session/18241"], "source_sha256": "6cd07fd3ce0d7bdb24d252824d6f7ac9195c0070540bd175e9a917a2a680ad14", "withdrawn": "", "abstract": "In this talk, we introduce the discrete dynamical system known as ``box-ball evolution” that transforms permutations $w$ into row-strict ``soliton decomposition” Young tableaux, denoted $\\mathrm{SD}(w)$. Following the work of Gunawan and other authors, we explore the ``soliton decomposition classes” formed by taking all permutations with the same soliton decomposition tableau, and compare them to the $\\mathrm{P}$ and $\\mathrm{Q}$ classes given by the famous Robison-Schensted (RS) correspondence.\n\nAs part of our work, we introduce a ``soliton recording tableau”, denoted $\\mathrm{SQ}(w)$, that acts analogously to the recording tableau $\\mathrm{Q}$ in the RS correspondence. We prove that the map from permutations to pairs of tableaux given by $w \\mapsto (\\mathrm{SD}(w), \\mathrm{SQ}(w))$ is well-defined and injective. We also discuss the problem of finding ``moves” on permutations that preserve their soliton decomposition class, proving some partial results and a new algorithm for computing soliton decompositions.", "id": "Paper/69591", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69591"}, {"title": " Fractals and coastlines: from anti war research to fractal geometry ", "webprogram_exclude": "0", "session_ids": ["Session/18554"], "source_sha256": "364ad8ee8ec90ce4c5338d83843f3a9d6b1a4c89ff0062d629fef78aca472ce2", "withdrawn": "", "abstract": "In the 1940s, Lewis Fry Richardson (1881-1953) faced a complication in his research on the lengths of borders and coastlines. Richardson, a British mathematician and meteorologist, was studying the relationship between border length and propensity for war. This was part of a larger project, driven by his Quaker upbringing and pacifist values, to mathematically model the causes of war with the hopes of preventing future wars. However, Richardson could not get consistent results for the lengths of the frontiers that he studied, a variation of measurements that is now referred to as the “coastline paradox.” Richardson wrote about his challenges in an article that was posthumously published as “The Problem of Contiguity” in 1961. This article was taken up by Benoit Mandelbrot (1924-2010); Mandelbrot’s 1967 paper “How Long is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension” directly borrowed Richardson’s charts and equations. In this talk, I examine the narrative of Richardson’s research, in his own words and as taken up by Mandelbrot. Richardson developed his coastline research as one aspect of his anti-war research, which stemmed from a lifelong commitment to pacifism, and he researched both borders and coastlines. While Mandelbrot frequently credited Richardson for influencing him (somewhat of a rarity for Mandelbrot), he did not carry the same political commitments that Richardson had, nor did he discuss Richardson’s broader project of pacifist mathematics. As I situate the work of these mathematicians amidst their varied material tools, physical locations across the United States and Britain, political commitments and inspirations, and institutional contexts, I attend to how mathematicians intentionally or unintentionally position themselves and their work across different political and mathematical landscapes.", "id": "Paper/69592", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69592"}, {"title": " False discovery control in repeated analyses of biobank data ", "webprogram_exclude": "0", "session_ids": ["Session/18314"], "source_sha256": "92847f4763eb4f6e7d9ca399b984e3a4142bf1abb7cf8911fc680cbe31531624", "withdrawn": "", "abstract": "Repeated analyses of biobank data can alter the statistical support and clinical interpretation of earlier discoveries. We examine how a discovery list can retain previous declarations while controlling false discoveries across releases. For a fixed family of hypotheses, we use e-values and closed testing to construct a retained list that includes all current e-BH discoveries based on the same nondecreasing evidence. Calibration of the terminal null evidence yields control of the expected maximum false discovery proportion over time.\n\nIn simulations, closure increased power relative to the underlying Gaussian evidence procedure, while an anytime p-value method remained more powerful in the main setting. Heavy-tailed errors inflated false discoveries for Gaussian evidence even under correct variance specification. An analysis of protein-disease associations across four FinnGen releases showed turnover in reported discoveries and a modest increase in retained associations through closure. An inherited change in angioplasty coding affected both coronary cases and atrial fibrillation control exclusions. The findings show how the choice of reporting rule depends on evidence calibration and why repeated analyses should record current association evidence alongside the clinical definition and basis of each earlier declaration.", "id": "Paper/69595", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69595"}, {"title": " Combinatorial Hodge Index Theorem for Polytopes ", "webprogram_exclude": "0", "session_ids": ["Session/19366"], "source_sha256": "a7ea72a5301952c4597e586279256f7557dac86974dfa025454d1d22f8791b04", "withdrawn": "", "abstract": "One advantage of toric varieties is that they carry an associated fan/polytope, which acts as a combinatorial blueprint, allowing one to find combinatorial formulas for their invariants. This yields results not only in algebraic geometry, but also in the study of polytopes. However, not every polytope can be associated to a toric variety, so to remedy this, Barthel-Brasselet-Fiesler-Kaup threw away the geometry and introduced \"combinatorial intersection cohomology\" for an arbitrary fan that is not in general the blueprint for a toric variety. In doing so, BBFK open the door to studying more general convex polytopes such as those whose combinatorial type does not contain polytopes with all rational coordinates. Using their combinatorial intersection cohomology framework, I will give a purely combinatorial proof (one that does not refer back to the geometry after passing to the fan) of the formula for the intersection cohomology signature of a (possibly non-simplcial) complete toric variety, proved by Maxim-Schuermann geometrically with mixed Hodge modules.", "id": "Paper/69596", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69596"}, {"title": " How Mathematical Scientists Use and View AI: The PIMS Survey on Mathematics and AI ", "webprogram_exclude": "0", "session_ids": ["Session/18190"], "source_sha256": "7575f848a2958a75ee77349c2d8e4adb9d107b4af916ea208e1652f6232f8bed", "withdrawn": "", "abstract": "In 2026, AI systems produced a plethora of mathematical results, including some that are quite prominent, like the disproof of a 1946 Erdős conjecture, and claimed advances on several long-open problems. These developments were quickly followed by public debate within the mathematical community, including the Leiden Declaration on Artificial Intelligence and Mathematics (which at the time of this abstract submission has over 4000 signatures), and a (separate) statement by twenty-five Fields medalists warning that the goals of AI companies and the goals of the mathematical community are misaligned. Between these poles, what do working mathematical scientists actually do with AI, and what do they think of it? We report early results from the PIMS Survey on Mathematics and AI, a confidential survey of faculty, postdocs, and graduate students across the thirteen PIMS member and affiliate institutions, fielded from August 2026. It measures task-level use, attitudes and worries, skill and support needs, perceived norms, views on credit and authorship, and agreement with recommendations from the Leiden Declaration. We present what the data say about adoption, the attitudes and practices of mathematical scientists, differences by career stage and field, and what the community wants from its institutes.", "id": "Paper/69601", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69601"}, {"title": " Schubitopes are not Ehrhart positive ", "webprogram_exclude": "0", "session_ids": ["Session/18308"], "source_sha256": "1c7ff542eead89e0cdc03573615fcf4bf172fdcdd36b7fa8a5e56b5718dcaae7", "withdrawn": "", "abstract": "Schubitopes are a family of generalized permutahedra that includes the Newton\npolytopes of both Schubert polynomials and Demazure characters of $GL_n$. Monical, Tokcan,\nand Yong conjectured that Schubitopes are Ehrhart positive. We exhibit a counterexample\nto this conjecture, a Schubitope whose Ehrhart polynomial contains a negative coefficient\nin its monomial expansion.", "id": "Paper/69609", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69609"}, {"title": " Using Zero Forcing to Determine Maximum Nullity: An Application to Diamond Rectangle Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18146"], "source_sha256": "a0c25266b9b7116a5a61c04c9dd43665a00696b8ae2d44668cb7372460c5d366", "withdrawn": "", "abstract": "Zero forcing is a graph coloring process that was introduced as a combinatorial tool for studying the minimum rank and maximum nullity of symmetric matrices described by a graph. In particular, the maximum nullity of a graph is bounded above by its zero forcing number. In this talk, based on joint work with students, we use this connection to determine the maximum nullity of Diamond rectangle graphs, a family of induced subgraphs of the two-dimensional grid. We construct a zero forcing set that gives an upper bound on the zero forcing number and combine this with a lower bound on maximum nullity obtained from an edge covering. These bounds coincide giving an exact formula for both the maximum nullity and the zero forcing number of the family.", "id": "Paper/69613", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69613"}, {"title": " Euclidean actions on higher categories ", "webprogram_exclude": "0", "session_ids": ["Session/18209"], "source_sha256": "b21cf57387e4e196e68ce55afb83d7bbf84d914124fa0e4d78f25bf2501f2096", "withdrawn": "", "abstract": "In this talk, I will discuss evidence supporting the following conjecture, which is supported by the cobordism/tangle hypothesis and by factorization homology.  \n\nConjecture.  \nThe continuous group O(n) acts on the category of n-categories.", "id": "Paper/69619", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69619"}, {"title": " Set Theory and Wright’s Normality Conjecture for AW*-Algebras ", "webprogram_exclude": "0", "session_ids": ["Session/18382"], "source_sha256": "84cdf2d6e6bb117a113b2761378f620665dc161af80b499c63a7bc1ae5ca8940", "withdrawn": "", "abstract": "We discuss set-theoretic forcing techniques in operator algebras. In particular, we explain how Boolean-valued model techniques were used in a proposed solution to a conjecture of Wright on normality of AW$^*$-algebras. We also discuss progress on the monotone completeness conjecture using forcing techniques and transfinite induction.", "id": "Paper/69620", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69620"}, {"title": " A geometric approach to the density of rank-metric codes ", "webprogram_exclude": "0", "session_ids": ["Session/18388"], "source_sha256": "fe26ccb591e5b99ea66baec3951f7a971bea3290ee31fda5797995b7a2130b33", "withdrawn": "", "abstract": "We apply tools from algebraic geometry to study, for fixed $m,n,k,\\delta$, the asymptotic density as $q\\to\\infty$ of $k$-dimensional linear rank-metric codes $\\mathcal{C}\\subseteq\\mathbb{F}_q^{m\\times n}$ with minimum rank distance at least $\\delta$. This builds on significant recent interest in density questions for MRD (maximum rank distance) codes. Our results recover the known cases in which the density tends to $0$ or $1$ and determine the limit in the cases where it was previously unknown.  More generally, we study the asymptotic proportion of linear sections of geometrically irreducible projective varieties over finite fields that have no $\\mathbb{F}_q$-rational points.", "id": "Paper/69621", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69621"}, {"title": " The algebraic topology of bridge multisections ", "webprogram_exclude": "0", "session_ids": ["Session/18344"], "source_sha256": "bd62e441eb2d9cd293483711057f723315880419b15ba6caf1ed656ba93ce8fd", "withdrawn": "", "abstract": "Various algebraic-topological invariants, such as group trisections, torsion, and twisted homology, have been computed from multisection diagrams. We continue this program in the setting of bridge multisections of codimension-two submanifolds, computing further invariants, including ones related to the second homotopy group.", "id": "Paper/69623", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69623"}, {"title": " Strong convergence and graph products of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.852ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 1228 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">C^{\\ast }</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-43\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2217\" d=\"M229 286Q216 420 216 436Q216 454 240 464Q241 464 245 464T251 465Q263 464 273 456T283 436Q283 419 277 356T270 286L328 328Q384 369 389 372T399 375Q412 375 423 365T435 338Q435 325 425 315Q420 312 357 282T289 250L355 219L425 184Q434 175 434 161Q434 146 425 136T401 125Q393 125 383 131T328 171L270 213Q283 79 283 63Q283 53 276 44T250 35Q231 35 224 44T216 63Q216 80 222 143T229 213L171 171Q115 130 110 127Q106 124 100 124Q87 124 76 134T64 161Q64 166 64 169T67 175T72 181T81 188T94 195T113 204T138 215T170 230T210 250L74 315Q65 324 65 338Q65 353 74 363T98 374Q106 374 116 368T171 328L229 286Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-43\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-2217\" x=\"1094\" y=\"513\"></use>\n</g>\n</svg>-algebras ", "webprogram_exclude": "0", "session_ids": ["Session/18381"], "source_sha256": "04b2da6870ffc170ffbf81bc45a56a9a47f56e73909f1334bb86dce5fb2beff7", "withdrawn": "", "abstract": "Graph products interpolate between free products and tensor products, with a graph specifying which vertex algebras commute. We study the preservation of finite-dimensional approximation properties under this construction.\n\nIn this talk, I will explain how reduced graph products of exact tracial MF $C^{\\ast}$-algebras remain tracial MF, and how graph products preserve the PMF property for groups, without assuming residual finiteness. The proofs use random matrix models that respect the commutation relations prescribed by the graph and converge both in moments and in operator norm. I will outline the construction and explain how strong convergence yields the desired approximation properties.\n\nThis is joint work with Nicholas Sweeney.", "id": "Paper/69625", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69625"}, {"title": " Unitary Cohomology of Semisimple Groups ", "webprogram_exclude": "0", "session_ids": ["Session/18121"], "source_sha256": "bed7464bb8a7bfb81d2e06dc6e44a6e8556e8853d9346af55789ef599b319fce", "withdrawn": "", "abstract": "Cohomology of unitary representations naturally arises in many contexts such as Kazhdan's property $(T)$, Matsushima's formula for the cohomology of a locally symmetric space, and more recently higher property $(T)$. Vogan and Zuckerman gave a full description of the cohomology of irreducible unitary representations of simple Lie groups. In particular, there are only finitely many representations with non-vanishing cohomology and the cohomology is finite-dimensional. I will discuss joint work with Bader, Gorfine, and Sauer describing the cohomology of (possibly) reducible unitary representations. The cohomology $H^q(G;V)$ is a topological vector space that is not necessarily Hausdorff. The reduced cohomology $\\overline{H}^q(G;V) = H^q(G;V)/\\overline{\\{0\\}}$ is described by containment of the Vogan-Zuckerman representations, while the torsion cohomology $\\mathring{H}^q(G;V) = \\overline{\\{0\\}}$ is related to weak containment of the Vogan-Zuckerman representations. We show that the first degree where torsion cohomology does not vanish goes to infinity with the dimension of the symmetric space, as opposed to property $(T_n)$ which the group only possesses up to a degree proportional to the rank.", "id": "Paper/69627", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69627"}, {"title": " SPINET: Sheaf Protein Inverse Folding Network ", "webprogram_exclude": "0", "session_ids": ["Session/19371"], "source_sha256": "e9227e130e9e819776d66ea78310c60edd19a3a3f7d462a3f2cc71462526a3d7", "withdrawn": "", "abstract": "Inverse folding seeks an amino acid sequence that will adopt a given protein structure. Most existing methods operate on static structures or conformational ensembles, without explicitly modeling protein motion over time. Because these dynamics are closely tied to function, incorporating them into inverse folding could enable the design of sequences with targeted dynamic and functional properties. Here we introduce SPINET, a spatiotemporal sheaf neural network that infers protein sequences from molecular dynamics trajectories. At each time step, SPINET represents the protein as a cellular sheaf over a residue interaction graph. Learnable restriction maps, conditioned on node and edge features, project neighboring residue representations into shared edge stalks, where their discrepancies drive sheaf-based message passing. A recurrent neural network then aggregates these spatial representations across time before predicting the amino acid sequence. On proteins from the mdCATH and ATLAS datasets, SPINET outperforms existing methods in sequence recovery and structural similarity, evaluated by folding predicted sequences with ESMFold and comparing them with ground-truth structures. These results highlight cellular sheaves as a promising framework for modeling dynamic geometric relationships in protein design.", "id": "Paper/69628", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69628"}, {"title": " The <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.487ex\" height=\"3.009ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -1150.1 640.4 1295.7\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\overline {\\partial }</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2202\" d=\"M202 508Q179 508 169 520T158 547Q158 557 164 577T185 624T230 675T301 710L333 715H345Q378 715 384 714Q447 703 489 661T549 568T566 457Q566 362 519 240T402 53Q321 -22 223 -22Q123 -22 73 56Q42 102 42 148V159Q42 276 129 370T322 465Q383 465 414 434T455 367L458 378Q478 461 478 515Q478 603 437 639T344 676Q266 676 223 612Q264 606 264 572Q264 547 246 528T202 508ZM430 306Q430 372 401 400T333 428Q270 428 222 382Q197 354 183 323T150 221Q132 149 132 116Q132 21 232 21Q244 21 250 22Q327 35 374 112Q389 137 409 196T430 306Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-AF\" d=\"M69 544V590H430V544H69Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-2202\" x=\"24\" y=\"0\"></use>\n<g transform=\"translate(23,532)\">\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-AF\" x=\"-70\" y=\"0\"></use>\n<g transform=\"translate(244.2978504270688,0) scale(0.22317505996324485,1)\">\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-AF\"></use>\n</g>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-AF\" x=\"372\" y=\"0\"></use>\n</g>\n</g>\n</svg>-Neumann problem in a family of domains ", "webprogram_exclude": "0", "session_ids": ["Session/17887"], "source_sha256": "14bec841ff6978d7eead7f070ea846046ebb7643c350a51c103ccb7f1d3b0818", "withdrawn": "", "abstract": "The classical work of Kohn and Nirenberg studies the boundary regularity of solutions to non-coercive boundary value problems, of which the $\\overline{\\partial}$-Neumann problem is a prototypical example. Roughly speaking, they show that a compactness estimate implies the global regularity of solutions and a subelliptic estimate guarantees the local regularity. How do these results extend to families of boundary value problems? \n\nHamilton shows that if there is a family of elliptic boundary value problems depending smoothly on a parameter and uniform persuasive estimates hold (which imply uniform subelliptic estimates), then the family of solution operators also depends smoothly on the parameter. We deal with the compactness estimate in families. We show that if a family of $\\overline{\\partial}$-Neumann problems depends smoothly on a parameter and uniform compactness estimate(s) hold, then the family of solution operators also depends smoothly on the parameter. For us, the parameter encodes the deformation of the complex structure, the underlying hermitian metric, and the volume form.", "id": "Paper/69633", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69633"}, {"title": " Infinite staircases in Hirzebruch surfaces ", "webprogram_exclude": "0", "session_ids": ["Session/17105"], "source_sha256": "71b5fbd4b5e08b1428c7f95e63d6d339e807cf1432836a7b7ae8f71ddab08538", "withdrawn": "", "abstract": "This talk will trace the development of work on infinite staircases in ellipsoid embedding functions for Hirzebruch surfaces, beginning with the collaboration of Bertozzi, Holm, Maw, McDuff, Mwakyoma, Pires, and Weiler at WiSCon 2019. Their work initiated a series of projects that led to a classification of infinite staircases in these surfaces. I will describe this classification, highlighting the recursive families of embedding obstructions and the symmetries that organize them, as well as the geometric constructions that produce matching embeddings. The talk will cover the original WiSCon paper and subsequent developments, including my joint work with McDuff, Weiler, and Pires.", "id": "Paper/69639", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69639"}, {"title": " Starting a Mathematics Pedagogy Course for Graduate Students: Implementation and Impact ", "webprogram_exclude": "0", "session_ids": ["Session/18091"], "source_sha256": "dd4076e1c5341334b4d4b43bbf94d7383ee1f7bcec68314181eff5de8dfd450c", "withdrawn": "", "abstract": "In this talk I will share the process of implementing a mathematics specific pedagogy course for graduate students at an R1 research institution. In Spring 2023, I organized a pedagogy reading course for first year graduate students in pure and applied math at UC Davis. The course has continued to run every year and is now institutionalized as a mathematics pedagogy course instead of a generic reading course. Existing literature informed the decision to use a flipped format, with participants completing readings outside of class and then discussing how to apply the readings to TAing and teaching courses at UC Davis. \nThe second part of this talk will be about the impact of this pedagogy course. After completing the course, students shared that they felt more equipped to teach their own math courses as the instructor of record and had new ideas about what it means to be an effective instructor. Furthermore, these graduate students made real changes to their teaching work because of this pedagogy course, including shifting away from a pure lecture format to incorporate active learning in the classroom.", "id": "Paper/69640", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69640"}, {"title": " Boundary spectral data for <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"7.339ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 3159.8 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">K_X(D)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-58\" d=\"M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-44\" d=\"M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-4B\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-58\" x=\"1201\" y=\"-213\"></use>\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"1552\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-44\" x=\"1941\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"2770\" y=\"0\"></use>\n</g>\n</svg>-twisted Higgs bundles ", "webprogram_exclude": "0", "session_ids": ["Session/19350"], "source_sha256": "8094247eb43d77640a05d5eda567d98e573d0ac6771bb169d6935e928263c7d6", "withdrawn": "", "abstract": "Let \\(X\\) be a smooth projective curve, \\(D\\) an effective divisor, and \\(V=K_X(D)\\). We study \\(V\\)-twisted Higgs bundles through their spectral curves \\(\\Sigma_a\\subset \\operatorname{Tot}(V)\\), with emphasis on fixing spectral data along \\(D\\). If \\(\\rho_D\\) denotes the restriction map on the Hitchin base, then\n$$ \\ker(d\\rho_D)_a=\\bigoplus_i H^0(X,V^i(-D)), $$\nand its image under the Kodaira--Spencer map records the local deformation directions of a singular spectral curve that remain available after imposing the boundary condition. The boundary restriction packages invariant polar data at \\(D\\); for reduced \\(D\\) and regular-semisimple residues, this is compatible with the residue data governing the Bottacin--Markman Poisson leaves of the meromorphic Higgs moduli space. Under natural cohomological interpolation hypotheses, the constrained deformation map yields local versality criteria at prescribed isolated singularities. We then compare these directions with regularity criteria for relative fine compactified Jacobians of rank-one torsion-free sheaves. In the nodal case, the condition has a graph-theoretic formulation in terms of separating versus nonseparating edges of the dual graph for nodes lying over \\(D\\). Thus boundary conditions in the Hitchin system are reflected simultaneously in Poisson geometry, local deformation theory, and compactified Jacobians.", "id": "Paper/69642", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69642"}, {"title": " Particle Transport in the Express Lane: Bypassing Complex Histories with Generative Monte Carlo ", "webprogram_exclude": "0", "session_ids": ["Session/19344"], "source_sha256": "47e1b66e4ba038a95d7c815417729592223d9bb4ade70d5522097a03514a0d9e", "withdrawn": "", "abstract": "Monte Carlo (MC) methods for linear Boltzmann transport incur computational cost through both the number and complexity of particle histories. Increasing the number of histories improves statistical accuracy according to the familiar $N^{-1/2}$ convergence rate, while more complex histories provide no analogous accuracy-cost trade-off: they must simply be resolved correctly. This becomes particularly consequential in optically thick media, where particles may undergo many scattering events before leaving a region.\n\nGenerative Monte Carlo (GMC) replaces these expensive local random walks with samples from the resulting probability distributions. A conditional generative model directly samples the net outcome of each cell traversal instead of resolving the full scattering history.\n\nWe demonstrate that GMC accurately reproduces scalar-flux solutions while retaining the characteristic $N^{-1/2}$ statistical convergence of MC. Whereas conventional MC becomes increasingly expensive with the number of scattering events, GMC replaces each local scattering history by a constant-cost sample, independent of its complexity, promising substantial speedups over standard MC in optically thick regimes. We discuss current extensions and the broader use of generative models as constant-cost stochastic kernels within MC algorithms.", "id": "Paper/69644", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69644"}, {"title": " Ascending, Bridge, and Unknotting Numbers of Knotted Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18087"], "source_sha256": "c64660baf1d678fe6c013e5404b842160492e815e9a7f6202b7eddd7726d6e30", "withdrawn": "", "abstract": "In this talk, we introduce two important quantities for virtual and welded spatial graphs, called the ascending number and the bridge number. We prove that a lower bound for the ascending number can be established in terms of the bridge number. This relationship provides a way to compare different notions of unknotting virtual and welded spatial graphs by crossing changes, and reveals a connection between these two measures of complexity. This is joint work with Puttipong Pongtanapaisan and Ritikaa Singhal.", "id": "Paper/69648", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69648"}, {"title": " Threshold Dynamics of a Discrete-Time SIS Epidemic Patch Model with Saturated Incidence ", "webprogram_exclude": "0", "session_ids": ["Session/19359"], "source_sha256": "7fd46b037213ab950437324460c4ae64d47a9bf815d5fd8bcd14a372cd64a1f9", "withdrawn": "", "abstract": "We investigate a discrete-time susceptible-infected-susceptible (SIS) epidemic model in a patchy environment with saturated incidence and population movement. Susceptible and infected individuals are allowed to disperse among interconnected patches, while the total population is conserved. We first analyze the corresponding single-patch model. We establish a sharp threshold dynamics: when the basic reproduction number is at most one, the disease-free equilibrium is globally asymptotically stable, whereas when it exceeds one, the model admits a unique endemic equilibrium that attracts every positive solution. We then extend the analysis to the multi-patch system. Under appropriate assumptions on the dispersal matrices, we investigate how disease transmission, saturation, and the movement of susceptible and infected individuals among patches determine global disease extinction or persistence. These results provide a mathematical framework for understanding the combined effects of nonlinear transmission and spatial movement on the long-term dynamics of discrete-time epidemic systems.", "id": "Paper/69649", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69649"}, {"title": " Beyond the Textbook: Infusing Research and Real-World Applications into Math Curriculum ", "webprogram_exclude": "0", "session_ids": ["Session/18144"], "source_sha256": "b7e805a077e2e4a4533346595b03b87e80ed4adf720a632b44e7b75e7d3fb984", "withdrawn": "", "abstract": "In this talk, I will share strategies and ideas for incorporating mathematical research, authentic real-world applications, and creative paranormal scenarios into the undergraduate curriculum. Examples will include ways that ideas from my research in knot theory can be made accessible to students, as well as applications designed to implement techniques learned in class. For some students, creative writing and unusual paranormal scenarios can provide another way to engage with ideas and make otherwise abstract concepts more approachable and memorable.", "id": "Paper/69651", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69651"}, {"title": " Rational Vector Spaces Done Relevantly ", "webprogram_exclude": "0", "session_ids": ["Session/18589"], "source_sha256": "2c62eafbacc5e67015641058ee901d8a9fc588b8d8b1de7790933fb766a799b5", "withdrawn": "", "abstract": "Relevant logics are those for which, roughly, it is not possible to go from some collection of premises to some unrelated conclusions. Robert Meyer in the 1970's and in later work by Weber, Slaney, and others studied various ways in which we might study mathematics or fragments thereof using a relevant logic, but the arithmetic and set theory studied there are classically very complicated theories. The theory of vector spaces over the rational numbers is classically much simpler. Specifically, it enjoys such properties as quantifier elimination, strong minimality, $\\omega$-stability, and they have countably many countable models. Adapting a proof of Badia and Tedder on the failure of quantifier elimination for algebraically closed fields over any logic $\\mathbf{L}$ between $\\mathbf{B}$ and $\\mathbf{RM}$, we show an analogous result for rational vector spaces. The proof also shows the existence of a non-minimal model, by giving us a definable subset which is neither finite nor cofinite in any sense of the word. Furthermore, up to a notion of isomorphism of these structures, there are continuum many countable models. A similar trick lets us embed a non-trivial linear ordering, showing that these are unstable, even over $\\mathbf{RM}$.", "id": "Paper/69652", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69652"}, {"title": " Khovanov-Type Graph Homologies: Structures and Relations ", "webprogram_exclude": "0", "session_ids": ["Session/17105"], "source_sha256": "256040a0048c2100144e48da986b58546a67265eee6a68b092f76a21c668a11d", "withdrawn": "", "abstract": "The chromatic polynomial is a classical graph invariant that counts proper colorings. Its categorifications, known as chromatic homology theories, uncover additional algebraic and topological structure that is invisible at the level of the polynomial itself. I will describe several manifestations of this structure and the relations among them, including connections with configuration spaces, Khovanov link homology, broken-circuit constructions, Hochschild homology, and spanning trees.", "id": "Paper/69655", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69655"}, {"title": " Fixed point theory for renormali ", "webprogram_exclude": "0", "session_ids": ["Session/18364"], "source_sha256": "6037b259f0f85a23a107ab2501b4c9dec6daca273ab1375b0f4269227a31e704", "withdrawn": "", "abstract": "I will report on some ongoing work on the application of fixed point theory to the functional renormalization group of quantum field theory.", "id": "Paper/69656", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69656"}, {"title": " Evaluating the Effects of MRI Perturbations and Data Augmentation on 3D Brain Tumor Segmentation ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "800f0a6b962e543134c6024d4a1471d322e3b5e176f27a2b7ac2aa9415c75f8c", "withdrawn": "", "abstract": "Deep learning models can accurately segment brain tumors in clean MRI scans, but their performance may decline when the scans are affected by noise, blur, reduced resolution, or other imaging artifacts. We evaluated the robustness of a 3D SegResNet model and whether training augmentation based on perturbed images could improve the model's performance. The model was trained on $484$ labeled cases from the Medical Segmentation Decathlon Task01 BrainTumour dataset using four modalities and a $70/20/10$ training/validation/test split. Performance was assessed with Dice scores for tumor core, whole tumor, and enhancing tumor.\n\nWe tested Gaussian and Rician noise, Gaussian blur, low resolution, contrast changes, bias field, ghosting, and motion at five severity levels. Perturbations were added before or after intensity normalization to examine their interaction with preprocessing. The baseline model achieved a mean Dice score of $0.8403$ on clean images. At severity $5$, bias field reduced mean Dice to $0.2764$, with consistent declines across all tumor regions. Low resolution reduced mean Dice to $0.6974$, with enhancing tumor being the most sensitive region. Motion and ghosting severely degraded performance, whereas contrast changes, Gaussian noise, and foreground-only Rician noise had relatively small effects. Pre-normalization blur was more harmful than post-normalization blur, indicating that preprocessing influenced measured robustness.\n\nWe then trained an augmented model in which half of the training samples received one randomly selected bias-field, low-resolution, or Gaussian-blur perturbation at severity levels $1-4$; level $5$ was held out for testing. At severity $5$, augmentation increased mean Dice from $0.2764$ to $0.7635$ for bias field, from $0.6820$ to $0.7949$ for pre-normalization blur, and from $0.6974$ to $0.7257$ for low resolution. It also generalized to unseen motion and ghosting, increasing mean Dice from $0.1684$ to $0.6601$ and from $0.2293$ to $0.5940$, respectively. Within this model and dataset, reliability depended on both the type of MRI degradation and its interaction with preprocessing, while the augmentation model improved robustness without changing the model architecture.", "id": "Paper/69658", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69658"}, {"title": " Effective equidistribution of some parabolic flows ", "webprogram_exclude": "0", "session_ids": ["Session/18313"], "source_sha256": "8246450f4a152e193e6a7189f60098a512fdd3287b0e963f56414be013774da0", "withdrawn": "", "abstract": "I will present results on the effective equidistribution of some parabolic flows. In particular, I will discuss how effective equidistribution of parabolic flows can be lifted to extensions in principal bundles, and give some examples where the results apply.", "id": "Paper/69659", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69659"}, {"title": " Dehn filling in complex hyperbolic 3-space ", "webprogram_exclude": "0", "session_ids": ["Session/18361"], "source_sha256": "10a01be5d4b9f906b0c2abad499090de1c2d17742921c78164bba110c40da77f", "withdrawn": "", "abstract": "Let $\\Gamma$ be the fundamental group of a finite-volume hyperbolic $d$-manifold $M$. When $d = 2$, then the holonomy representation $\\rho:\\Gamma \\to PO(d,1)$ is flexible; it has many discrete faithful deformations, giving the Teichm\\\"uller space of $M$. When $d = 4$, seminal work of Garland--Raghunathan implies that $\\rho$ is locally rigid, meaning it has no deformations at all. The $d = 3$ case occupies a fascinating middle ground: the deformations of $\\rho$ form Thurston's hyperbolic Dehn filling space, and are the source of most of our examples of hyperbolic structures on closed 3-manifolds. In this talk, we discuss upcoming work with Jeff Danciger, showing that one can find \"Dehn filling spaces\" inside the $PU(3,1)$-character variety of certain $PO(3,1)$ lattices. These Dehn filling spaces give rise to numerous examples with surprising properties; our construction shows that there are convex cocompact groups in $PU(3,1)$ with \"exotic\" limit sets, and that global rigidity can dramatically fail for many locally rigid discrete subgroups of $PU(3,1)$.", "id": "Paper/69664", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69664"}, {"title": " Rotation Number Plateaus for Nonlinear Cocycles ", "webprogram_exclude": "0", "session_ids": ["Session/17960"], "source_sha256": "81be7d2549d661550de0b917145e290dac5ba42c2aa63a794ce14faee69aafc1", "withdrawn": "", "abstract": "Given a cocycle of orientation-preserving circle homeomorphisms over an ergodic base, one can, after choosing a family of lifts, define a rotation number. A natural question is when this rotation number is locally constant under perturbations and what values it can take on such plateaus. A classical example comes from the projectivization of linear Schrödinger cocycles. In this setting, plateaus of the rotation number correspond to uniform hyperbolicity, while the Gap Labeling Theorem imposes algebraic restrictions on their values, described by the corresponding Schwartzman group.\n\nIn this talk I will discuss extensions of this picture beyond the linear setting. We consider general circle cocycles over an ergodic base and ask what dynamical mechanisms can produce plateaus of the rotation number and what algebraic restrictions their values must satisfy. I will first give an overview of known results for circle cocycles and then focus on random dynamical systems on the circle. In this setting, we introduce a property that replaces uniform hyperbolicity and obtain algebraic constraints on the values of the rotation number associated with plateaus. This is joint work with Anton Gorodetski.", "id": "Paper/69665", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69665"}, {"title": " Deep Learning Approaches for Restoring Turbulence-Degraded Images ", "webprogram_exclude": "0", "session_ids": ["Session/19345"], "source_sha256": "b6c0177d73340a7b95894148386544efb513e2a70781fd05c7275cb9af2584b9", "withdrawn": "", "abstract": "Atmospheric turbulence can introduce blur and geometric distortion into images captured over long distances, making reliable restoration challenging. This talk examines how two deep-learning approaches—generative adversarial networks and Transformers—respond to different levels of turbulence degradation. Using image sequences with corresponding clean references, the models are evaluated across multiple image-quality ranges rather than through a single aggregate score. The comparison reveals that model performance depends strongly on the severity of the degradation: adversarial models are more effective for heavily distorted inputs, whereas Transformer-based methods provide stronger restoration when the original scene retains more structural information. These observations illustrate why selecting a restoration method should account for the condition of the input data and provide practical insight into the strengths and limitations of each architecture.", "id": "Paper/69669", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69669"}, {"title": " Reductions of Certain Well-Poised Hypergeometric Character Sums ", "webprogram_exclude": "0", "session_ids": ["Session/17450"], "source_sha256": "b4caa5726088800a25215506b3a28dba9ab19ffa7cfa7c6c981bdb629848a66b", "withdrawn": "", "abstract": "Whipple’s classical reduction formulas express well-poised hypergeometric series either as products and quotients of gamma values or as such gamma factors multiplied by hypergeometric functions, usually of smaller length. Building on earlier work of Greene, McCarthy, and Li--Long--Tu, we establish finite field analogues of three very well-poised identities corresponding to $_4F_3(-1)$, $_5F_4(1)$, and $_6F_5(-1)$. We show that the associated $\\ell$-adic Galois representations as constructed by Katz and Beukers--Cohen--Mellit are reducible, and we explicitly identify one of their constituents in a manner reflecting the corresponding Whipple decompositions. As applications, we obtain new explicit modularity results for hypergeometric Galois representations.", "id": "Paper/69670", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69670"}, {"title": " Superselection theory for 2D braided quantum spin systems via Connes fusion ", "webprogram_exclude": "0", "session_ids": ["Session/18385"], "source_sha256": "377befb39e372c81441136e65d010305d0f28eb34666a5d9b73846f076a10d97", "withdrawn": "", "abstract": "Given a net of operator algebras $\\mathcal{A}$ on a poset $\\mathcal{P}$, its category $\\mathsf{SSS}$ of superselection sectors consists of representations of $\\mathcal{A}$ satisfying a certain superselection criterion originating from algebraic quantum field theory. Using localized endomorphisms, it was shown in [arXiv:2410.21454] that $\\mathsf{SSS}$ is canonically a braided monoidal category whenever $\\mathcal{P}$ satisfies certain geometric axioms. Using ideas from the work [arXiv:1812.04470] on conformal nets, we show that an equivalent braided monoidal structure on $\\mathsf{SSS}$ can be constructed without localizing by using the Connes fusion tensor product of Hilbert space bimodules over von Neumann algebras. As an application, we prove that the category of superselection sectors associated to the 2D braided quantum spin system constructed from a unitary braided fusion category $\\mathcal{B}$ in [arXiv:2506.19969] is equivalent to $\\mathsf{Hilb}(\\mathcal{B})^{\\rm op}$, the opposite of the unitary ind-completion of $\\mathcal{B}$, as braided monoidal categories.", "id": "Paper/69681", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69681"}, {"title": " CHURP: A Framework for Fully Unsupervised Analysis of Birdsong ", "webprogram_exclude": "0", "session_ids": ["Session/19371"], "source_sha256": "989ae1ae16dac76f99c9be38932e2ea78c47a5cdb650449246f6b181ee755b42", "withdrawn": "", "abstract": "Birdsong is a model for studying the acquisition and development of language. Manually parsing hours of song into its basic units, syllables, is a major bottleneck that slows down birdsong research and can introduce bias. To address this issue, we present CHURP, a fully unsupervised framework for the segmentation and classification of birdsong syllables. CHURP utilizes a hybrid convolutional-LSTM autoencoder to encode audio spectrograms into latent trajectories that exhibit loop-like structures corresponding to discrete syllables. The trajectories are segmented based on their spatial deviation from a quiet ambient baseline and are subsequently encoded using time-augmented path signatures, which capture the geometric and temporal dynamics of each vocalization. The embedded syllables are then clustered with HDBSCAN to identify unique groupings and infer a dictionary of syllable types. Compared to the current state-of-the-art unsupervised model, TweetyBERT, CHURP distinctly isolates syllables from background noise, achieving significantly lower frame error rates and higher Jaccard Index—indicating closer agreement with ground-truth syllable durations. Furthermore, CHURP demonstrates strong accuracy in recovering the underlying syntactic structure of the songs by inferring syllable transition probability matrices based on the relative frequencies of ordered pairs of syllables occurring in sequence.", "id": "Paper/69685", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69685"}, {"title": " On Negami’s beautiful formula for graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17900"], "source_sha256": "b945aec4fb8376e4a1de06643a4d5bd1b1a8b5d1ecbf8af80eafa8c952174ee9", "withdrawn": "", "abstract": "Negami introduced a three-variable graph polynomial $f(G;t,x,y)$ characterized by a uniform deletion–contraction rule in which the variables $x$ and $y$ record contraction and deletion, while $t$ records the number of surviving components. Its state-sum expansion contains the Whitney and Tutte polynomials as specializations and leads to a general splitting formula for a graph expressed as the union of two edge-disjoint subgraphs meeting in a prescribed set of vertices. We give a self-contained account of this construction, emphasizing the combinatorial meaning of the partition-lattice matrix that occurs in the splitting formula.", "id": "Paper/69688", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69688"}, {"title": " Supermassive: Massively Parallel Aerospace Simulation and Test & Evaluation for sim2real AI ", "webprogram_exclude": "0", "session_ids": ["Session/18024"], "source_sha256": "2abf7787047f0787bd3fadd18484b7ea12a24050e06bf336a72fcc5da210d768", "withdrawn": "", "abstract": "The accelerating integration of artificial intelligence into joint force operations demands a rigorous, repeatable process for creating autonomous agents that can reason, plan, and act across the full spectrum of missions. We couple high-fidelity synthetic Test & Evaluation environments with GPU accelerated simulation in Supermassive to generate, train, and test AI agents capable of sense-make-act cycles in complex, multidomain scenarios. Domain randomization and reinforcement learning pipelines are employed to train agents in Supermassive for specific mission sets, enabling rapid iteration with automated Test & Evaluation of generalization and safety. We successfully demonstrate our agents in live flight on the X-62A VISTA (F-16D).", "id": "Paper/69689", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69689"}, {"title": " Pipe Dream Rectification and Dual RSK Correspondence ", "webprogram_exclude": "0", "session_ids": ["Session/19321"], "source_sha256": "b0d05473d2684fdf1e5ed757b9588cbb7f24983a527d9afe1752c60c91601707", "withdrawn": "", "abstract": "We prove Dennin's conjecture that his variant of dual RSK correspondence is symmetric when restricted to biGrassmannian permutations. For a binary matrix $A$, let $A^\\dagger$ denote its transpose-complement, and let $\\operatorname{ins}(A)$ and $\\operatorname{rec}(A)$ denote its insertion and recording tableaux. We prove that $\\operatorname{ins}(A^\\dagger) = \\overline{\\operatorname{rec}(A)}$, where the bar denotes the natural complement of the recording tableau. Our proof uses rectification of super pipe dreams and a downward induction on suffixes of $A$.", "id": "Paper/69692", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69692"}, {"title": " Using Generative AI to Accelerate Outcomes-Aligned LMS Course Development ", "webprogram_exclude": "0", "session_ids": ["Session/18092"], "source_sha256": "dc2af4aea8461623d8e8df81127803864119ef472428629e4c9ba161c5d4115d", "withdrawn": "", "abstract": "The rapid emergence of generative artificial intelligence (AI) has created new opportunities for faculty to design and develop online courses more efficiently while maintaining alignment with evidence-based instructional practices. This presentation describes the development of an undergraduate educational technology course using generative AI as a collaborative instructional design partner. Although grounded in a specific course, the methods and lessons learned are transferable across disciplines.\n\nThe project focused on using AI to develop outcomes-aligned learning experiences within a learning management system (LMS). Generative AI assisted with organizing content, drafting module overviews, developing learning activities, creating discussion prompts, generating assessments, and aligning instructional materials with course learning outcomes. Rather than replacing faculty expertise, AI served as a tool for rapid development, refinement, and continuous improvement.\n\nThis presentation outlines a practical framework for integrating AI into course design workflows, including effective prompting strategies, faculty review processes, and methods for ensuring pedagogical quality and academic integrity. Particular attention is given to maintaining alignment among learning outcomes, instructional activities, and assessments while addressing challenges related to accuracy, accessibility, and content verification.\n\nThe session concludes with lessons learned and recommendations for faculty interested in incorporating AI into online course development while preserving instructional quality and promoting student success.", "id": "Paper/69697", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69697"}, {"title": " Tutte polynomial of clique sums and <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.211ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 521.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">k</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-6B\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-sums ", "webprogram_exclude": "0", "session_ids": ["Session/17900"], "source_sha256": "834be7c4d406eac224c86f45d79dc36a0de3620930ebb42fcb2e9bfa49b573ab", "withdrawn": "", "abstract": "We study the behavior of the Tutte polynomial under the graph operations of clique sums and $k$-sums by first clarifying the relation between the splitting formula and clique sums and $k$-sums. We then derive the direct-sum product formula and give explicit matrix formulas for clique sums across an edge and a triangle, as well as for the corresponding $2$-sums and $3$-sums obtained by deleting the common clique edges. The formulas provide recursive methods for computing the Tutte polynomial of graphs assembled along small complete separators.", "id": "Paper/69698", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69698"}, {"title": " Higher-order Schauder estimates for elliptic equations with coefficients singular along a manifold of codimension <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"3.616ex\" height=\"2.343ex\" style=\"vertical-align: -0.505ex;\" viewBox=\"0 -791.3 1556.8 1008.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\geq 2</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2265\" d=\"M83 616Q83 624 89 630T99 636Q107 636 253 568T543 431T687 361Q694 356 694 346T687 331Q685 329 395 192L107 56H101Q83 58 83 76Q83 77 83 79Q82 86 98 95Q117 105 248 167Q326 204 378 228L626 346L360 472Q291 505 200 548Q112 589 98 597T83 616ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-2265\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-32\" x=\"1056\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/17947"], "source_sha256": "bb16e157248252627ade34ae2d28ca8a8967d40dc7408e5fdee11350baa7a62f", "withdrawn": "", "abstract": "In this talk, I will present higher-order Schauder estimates for a class of elliptic equations in divergence form subject to the homogeneous conormal boundary condition on a flat submanifold $S$ of co-dimension $n \\geq 2$. The principal coefficients become singular at $S$ with a rate of blow-up comparable to $\\mathrm{dist}(\\cdot,S)^a, a \\in (-n,0)$. Our results complement the $C^{0,\\alpha}$ and $C^{1,\\alpha}$ estimates obtained by [Cora-Fioravanti-Vita, 2025]. Joint work with Hongjie Dong and Stefano Vita.", "id": "Paper/69708", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69708"}, {"title": " Stochastic Dynamics and Stability of a COVID-19 Compartmental Model ", "webprogram_exclude": "0", "session_ids": ["Session/19343"], "source_sha256": "47f480330807289a512ad37f594ef035343f1b537b667a1b13416267b295ae73", "withdrawn": "", "abstract": "We investigate how random fluctuations influence the dynamics of a compartmental model for COVID-19 transmission. Stochastic simulations illustrate variability among sample paths, while empirical means, variances, and histograms characterize their distributions. The stochastic behavior is examined against the deterministic drift and interpreted in light of local stability and the basic reproduction number. Bifurcation analysis then explores how the dynamics change as model parameters vary.", "id": "Paper/69710", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69710"}, {"title": " Real 2-blocks in quasi-simple groups ", "webprogram_exclude": "0", "session_ids": ["Session/17832"], "source_sha256": "ba71e80aabc04484391cd45af283d84522080f7457079c2a7ab4e8bae1b3ee1c", "withdrawn": "", "abstract": "We determine which quasi-simple groups have a nonprincipal real 2-block; that is, a nonprincipal 2-block whose associated set of irreducible characters is stable under complex conjugation. As a consequence, we show that the Mathieu group $M_{22}$ is the only simple group not possessing a nontrivial irreducible Brauer character of quadratic type, answering a recent question of Gow and Murray.", "id": "Paper/69712", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69712"}, {"title": " New structure for Villadsen algebras of the first type ", "webprogram_exclude": "0", "session_ids": ["Session/18382"], "source_sha256": "cfa3b2f6703d0de9127efc4acba5c5e81de65c492ce5c04f159f0722ac3bb4ad", "withdrawn": "", "abstract": "We establish two main results concerning the comparison theory of positive elements in approximately homogeneous $C^*$-algebras with diagonal maps. The first is a partial computation of the Cuntz semigroup which sheds light on and gives structure to the rank problem. This is realized via an embedding of the semigroup formed by dimension functions at finite stages mapped through the inductive limit. The second is a construction of an AH algebra that obstructs the classification of $*$-homomorphisms from $C_{0}((0,1])$ to an arbitrary $C^*$-algebra of stable rank one. In particular the AH algebra exhibits failure of uniqueness of lifts.", "id": "Paper/69713", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69713"}, {"title": " Optimal Execution Problems with a SPDE Model of the Limit Order Book ", "webprogram_exclude": "0", "session_ids": ["Session/17781"], "source_sha256": "42a2fda4156e7b3869a17220e1f929cb8d77fc07a48b869b320d67a9aa48eadc", "withdrawn": "", "abstract": "We develop a mean field game framework for optimal execution in which the\ninteraction among traders is mediated by the dynamics of the limit order\nbook. The bid- and ask-side order densities are modeled by\ninfinite-dimensional stochastic partial differential equations, with\naggregate trading activity affecting the order book and, through market\ndepth, the mid-price dynamics. We formulate the corresponding finite-player\noptimal execution game and derive its mean field limit in the presence of\ncommon noise. Under suitable conditions, we establish the existence and\nuniqueness of a mean field equilibrium. We also provide a numerical\nillustration of the equilibrium dynamics. Finally, we show that the mean-field equilibrium strategies yield an $\\epsilon_N$-Nash equilibrium for the\nfinite-player game, with $\\epsilon_N=O(N^{-1/2})$.", "id": "Paper/69715", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69715"}, {"title": " Applications of Dowker complexes for relational data analysis in cancer biology ", "webprogram_exclude": "0", "session_ids": ["Session/18105"], "source_sha256": "3a8ffdcee1b9cfe9492e7886633f4b851161759db7c26b2f3f54d92084a1f7f9", "withdrawn": "", "abstract": "Standard methods in topological data analysis, such as persistent homology (PH), are typically focused on the analysis of data consisting of a single entity (e.g., cells or molecular species). State-of-the-art data collection techniques now generate exquisitely detailed multispecies data, prompting a need for methods that can examine and quantify the relations among them. Such heterogeneous data types arise in many contexts, including biomedical imaging, geospatial analysis, and species ecology. Here, we present Dowker persistent homology as an effective tool for capturing relations between two distinct data types. I will present recent applications to both simulated (Stolz et al., 2024) and experimental tumor microenvironments (Yoon et al., 2024), demonstrating its usefulness in relational analysis of multispecies spatial data.", "id": "Paper/69716", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69716"}, {"title": " AI as a scientific instrument in ophthalmology: discovery, deployment, and open problems for mathematicians ", "webprogram_exclude": "0", "session_ids": ["Session/18190"], "source_sha256": "3eeb35419ebdf69cb45a6debb76cbc9dcead58afb684d6b50af010bd3e3401a7", "withdrawn": "", "abstract": "Retinal fundus images carry information beyond the signs diagnosticians are trained to recognize. Neural networks can serve not only to automate diagnosis but as instruments of discovery: in our own work, a network trained to classify patient sex led us to retinal features that differ by sex and that experts had not learned to see. This talk turns from discovery to clinical deployment and the problems it leaves open. Diabetic retinopathy, a leading cause of blindness in working-age adults, is graded on a five-level ordinal scale, which screening reduces to a binary decision: refer, or rescreen in six to twelve months. Deep networks now match specialists at this task and several products have regulatory clearance, yet clinical uptake is limited, and one obstacle is mathematical. A network returns a single score for referable disease, and its training distribution differs from the one it meets in practice: clinics differ in cameras, populations and prevalence, deployment differs from regulatory validation, and all of these drift over time. Clinical use requires an uncertainty estimate with each prediction, a principled rule for deferral to a human grader, and guarantees under such shifts. A second family of problems arises in segmentation, where networks delineate anatomical structures and lesions from which clinical measurements are derived. The ground truth is itself uncertain: annotators draw different boundaries, so the reference a model is trained and evaluated against is a choice rather than a fact, and architectures trained on the same reference disagree. How should annotators’ masks be combined, and should the reference be a single mask or a distribution? How should the outputs of several models be fused? And since clinical measurements depend nonlinearly on these boundaries, what is the appropriate distribution over them, and how does it carry through to the measurements? Drawing on our own work, I will state these problems concretely for this audience.", "id": "Paper/69718", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69718"}, {"title": " Wiener Criterion at <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.324ex\" height=\"1.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -576.1 1000.5 721.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\infty</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-221E\" x=\"0\" y=\"0\"></use>\n</g>\n</svg> for Degenerate Elliptic Equations ", "webprogram_exclude": "0", "session_ids": ["Session/18342"], "source_sha256": "e253c4e5a41ea292a52efb510cdd0f2cc1a0e85e8fc5e3104cee2fb9dbdce0a7", "withdrawn": "", "abstract": "In this talk, I present recent progress on the topic of well-posedness of the Dirichlet problem in the class of bounded solutions for linear degenerate elliptic equations in arbitrary open sets in dimension $n \\geq 2$. More specifically, the weight of the ellipticity is assumed to induce a measure that is doubling and satisfies the weak (1,2) Poincar\\'e inequality. We report on a dichotomy for the solvability of the Dirichlet problem expressed in terms of the behaviour of the associated capacity. If the full-space capacity is trivial, then bounded solutions of the Dirichlet problem are always unique (provided the underlying set is Greenian). Otherwise, a Wiener test at $\\infty$ determines the uniqueness of bounded solutions.", "id": "Paper/69721", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69721"}, {"title": " Combinatorial & Algebraic Invariants of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.07ex\" height=\"2.009ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -576.1 460.5 865.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">q</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-71\" d=\"M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-71\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-simplicial Arrangements ", "webprogram_exclude": "0", "session_ids": ["Session/18384"], "source_sha256": "2ed65b0db661807a3a9c2bcb04c702e022642399cc2429d582b26390d944bf60", "withdrawn": "", "abstract": "The characteristic polynomial of an arrangement of hyperplanes in a vector space is a polynomial in $t$ with a simple combinatorial description. Similar to how the chromatic polynomial of a graph gives counts of proper colorings, the characteristic polynomial of an arrangement over a finite field gives the count of points in the space not lying on any hyperplane. Recently, Nian, Tsujie, Uchiumi, and Yoshinaga introduced a family of hyperplane arrangements over finite fields, parameterized by graphs and simplicial complexes. They conjectured that (a) these arrangements’ characteristic polynomials in $t$ are actually specializations of a polynomial in $q$ and $t$, where $q$ is the cardinality of the finite field, and (b) the chromatic polynomial of a graph can be recovered from the associated arrangement’s characteristic polynomial via a suitable limit. They proved this, e.g., for arrangements associated to graphs that are either chordal or triangle-free. This talk will describe counterexamples to Conjecture (a), give methods to construct more examples satisfying Conjecture (a), and show that Conjecture (a) implies Conjecture (b).", "id": "Paper/69726", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69726"}, {"title": " The Rubey Lattice and Random Pipe Dreams ", "webprogram_exclude": "0", "session_ids": ["Session/18067"], "source_sha256": "efe01a409797a6bd516b5f19182817e01faeb3e8c88102f54fc70f46a8d5f162", "withdrawn": "", "abstract": "Schubert polynomials can be defined as generating functions for\nreduced pipe dreams. Chute and ladder moves connect the reduced pipe\ndreams for a fixed permutation.  Assaf–Schilling and\nGold–Milićević–Sun have used these moves to study crystal structures\non these objects. In 2011, Martin Rubey generalized these moves and\nconjectured that the induced poset is a lattice. We prove this\nconjecture. Our proof introduces a new family of move operators,\ndefined as composites of generalized ladder moves and described\nexplicitly by swaps along the boundary of a partition shape. These\noperators yield recursive formulas for joins and meets in what we call\nthe Rubey lattice.  We also construct an injective map from reduced\npipe dreams to tableaux on the diagram of the permutation. Under this\nmap, the lattice order corresponds exactly to entrywise comparison of\ntableaux, giving an explicit criterion for comparability. The tableau\nconstruction also yields an exact formula for the maximum length of a\nchain and upper and lower bounds on the number of reduced pipe dreams,\nequivalently the sum of the coefficients of the corresponding Schubert\npolynomial. Finally, we describe a Markov process on reduced pipe\ndreams that converges to the uniform distribution, providing a tool\nfor studying their statistics.\n\nThis talk is based on joint work with Connor McCausland and Clare\nMinnerath. An independent proof of Rubey’s conjecture was obtained\nsimultaneously by Axelrod-Freed, Defant, Mularczyk, Nguyen, and Tung.", "id": "Paper/69731", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69731"}, {"title": " Complex Dynamics and Chaos Control in a Discrete Predator–Prey Model with Fear and Immigration ", "webprogram_exclude": "0", "session_ids": ["Session/19351"], "source_sha256": "cfb3f2786517fd97be68f10e0c93336f258468a6d22688b94fb011290cdf2314", "withdrawn": "", "abstract": "This work studies a discrete predator–prey model incorporating a square-root functional response, fear effect, and prey immigration. Analytical conditions for period-doubling and Neimark–Sacker bifurcations are established at the coexistence equilibrium. Numerical simulations and maximal Lyapunov exponents reveal transitions from stable coexistence to periodic, quasiperiodic, and chaotic dynamics. Finally, OGY and state-feedback control methods are applied to stabilize chaotic populations. The results demonstrate how fear and immigration shape ecological stability and complex population behavior", "id": "Paper/69732", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69732"}, {"title": " Finding Order in Chaos: Comparing Lyapunov Exponent Estimation Methods ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "904645b347643c44a95dbdd4de59de6a169a724f27aab7d563027e401d0a96d3", "withdrawn": "", "abstract": "The mathematical study of chaos theory analyzes deterministic dynamical systems for which two solutions with nearby initial conditions diverge unpredictably. Such unpredictability can be assessed numerically with the Lyapunov exponent. A dynamical system with at least one positive Lyapunov exponent is called \"chaotic\". We consider the double pendulum, a well-known dynamical system governed by a system of nonlinear ODEs, as a platform on which to study an approach for characterizing chaos by Lyapunov exponents via machine learning (ML) techniques.\n\nBennetin's algorithm is considered the \"gold standard\" for calculating the Lyapunov spectrum, the set of Lyapunov exponents characterizing a multidimensional dynamical system. The method is be reliable but computationally intensive.  We use the spectrum calculated by this method together with the time series for the state of the pendulum for a set of initial positions of the two masses and zero initial velocity as training data. The time series are the two angular positions and two angular velocities of the pendulums as functions of time.\n\nHerein we apply standard and convolutional neural network to learn the Lyapunov spectrum from the time series of the angular positions. The goal of this work is to assess the efficacy of the ML models in estimating the Lyapunov spectrum from time series data. The training, validation and test sets include deterministic and chaotic dynamics of the double pendulum.  While the training will be computationally costly, the prediction will be highly efficient. We will also explore the generalizability of the method to double pendulums with different parameters (lengths and masses). The poster will report on our findings, as well as directions for further research.", "id": "Paper/69737", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69737"}, {"title": " The Abstract Algebra of Friendship Bracelets ", "webprogram_exclude": "0", "session_ids": ["Session/19340"], "source_sha256": "111a05aa9a7cceaa8f33e2ef9fcad2023d724f8249e32616d9e7b2cc368d0f92", "withdrawn": "", "abstract": "Friendship bracelets are composed of four primary types of knots which further decompose into two types of half-knots. With the construction of a carefully defined isomorphism, we can relate these knots to the algebraic group $\\mathbb{Z}_2 \\oplus \\mathbb{Z}_2$ to explore their structure. Moreover, we can take these algebraic properties of these knots to influence and inspire new designs for friendship bracelets. This talk briefly outlines the algebraic properties of friendship bracelet knots, describes the creative process for two bracelet patterns, and details potential future work in algebraic combinatorics.", "id": "Paper/69738", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69738"}, {"title": " Rational Functions with Large Iterated Monodromy Groups ", "webprogram_exclude": "0", "session_ids": ["Session/17755"], "source_sha256": "b9ac46118611af9cebe834c353a11d7c9cf95f0ba9054d9505e620a4334aab4e", "withdrawn": "", "abstract": "For a rational function $f$ over a field $k$, the Galois group of the tower of fields generated by iterated preimages of a point acts on the resulting tree of preimages, giving arithmetic and geometric arboreal Galois representations of $f$ --- dynamical analogues of the Galois representations attached to torsion of abelian varieties. As in Serre's open image theorem, a central question is how large the image of such a representation can be, and what obstructs it from being as large as possible.\n\nUnder the assumption that the geometric monodromy group contains the iterated wreath product of alternating groups --- a hypothesis guaranteed for broad families of polynomials by recent work of K\\\"onig, Neftin, and Rosenberg --- I will present a criterion for determining whether the geometric arboreal representation is surjective onto the full automorphism group of the tree, and if not, giving a description of the image. I will also show that the geometric representation differs from the arithmetic representation by index at most two, with this discrepancy being determined by the index at the first level at which surjectivity fails. The argument rests on a general dichotomy for fractal subgroups of automorphism groups of rooted trees.", "id": "Paper/69742", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69742"}, {"title": " Heuristic Algorithms for Zero Forcing and Zero Forcing Reconfiguration Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18241"], "source_sha256": "5f3f1bd48d53c9ecea5783fb8fc5b9d388db5122754d050330b84820c0835b41", "withdrawn": "", "abstract": "Zero forcing is a coloring process on a graph where an initial set of colored vertices propagates throughout the graph according to a color-changing rule. A vertex set is called zero forcing if coloring the set eventually results in the entire graph being colored. Finding a minimum zero forcing set is often impractical for large graphs, so in this project we propose heuristic methods for finding small zero forcing sets and generating large collections of distinct small zero forcing sets. We use these collections to investigate the structure of zero forcing reconfiguration graphs and run computational experiments on several families of graphs and real-world networks.", "id": "Paper/69743", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69743"}, {"title": " Statistical and Spatial Assessment of Drought Impacts on Maize Yield in Northern Nigeria: An Integrated Artificial Neural Network and Multiple Linear Regression Approach ", "webprogram_exclude": "0", "session_ids": ["Session/19338"], "source_sha256": "4af43e9c44e2336310663c78a08298ce9c5ef6f8f031fd9d5dcd1a11ea9f7b24", "withdrawn": "", "abstract": "Drought is a major abiotic stress affecting maize production in Sub-Saharan Africa, with rainfall shortages contributing 44\\% to 58\\% grain yield decline in West and Central Africa. Drought ensues when rainfall shortage causes hydrological discrepancies and alters land productive structures. Rainfall influences maize growth and harvests, particularly where irrigation is not practicable. In northern Nigeria, rainfall is unpredictable and often insufficient for viable crop production. Drought indices are used for the detection, classification, and control of drought conditions.\n\nThis study presents an integrated statistical and spatial assessment of drought impacts on maize yield across the 17 states of Northern Nigeria using Artificial Neural Networks (ANN), Multiple Linear Regression (MLR), and spatial analysis. Observed annual data from 1993 to 2018 on the Reconnaissance Drought Index (RDI), Palmer drought indices (SCPDSI, SCPHDI, and SCWLPM), and maize yield (tonnes) were analyzed. MLR models were evaluated using 70\\%, 80\\%, and 90\\% training sets. ANN models were assessed using sigmoid, hyperbolic tangent, and rectified linear unit (ReLU) activation functions, 1--3 hidden layers, and 70\\%, 80\\%, and 90\\% training sets. Mean Squared Error (MSE) was used to evaluate model performance.\n\nMLR results showed regional differences. FCT recorded the lowest MSE (0.7788234) in the North-Central region at 90\\% training, Borno recorded 0.7240276 in the North-East at 80\\%, and Kebbi recorded 0.8029484 in the North-West at 70\\%. For ANN, most states achieved their lowest MSE using ReLU, while MSE generally increased as training percentage increased. Spatial analysis showed regional differences in maize yield, with Kwara, Yobe, and Sokoto recording the lowest yields in the North-Central, North-Eastern, and North-Western regions, respectively. Overall, Yobe had the lowest maize yield. \n\nThe findings demonstrate the importance of integrating statistical, neural network, and spatial approaches for assessing drought impacts and maize yield variability.The results provide insights into regional differences in drought related agricultural impacts and demonstrate the potential of integrated statistical and computational methods for supporting data-driven agricultural planning in drought-prone regions.", "id": "Paper/69744", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69744"}, {"title": " Origami as applied recreational mathematics ", "webprogram_exclude": "0", "session_ids": ["Session/18235"], "source_sha256": "2ca9dab6892d7a7f1f570418fe1bf3824299e6453225b359c4c328f6b0e66c5b", "withdrawn": "", "abstract": "Applications of origami, the art of paper folding, are currently hot research topics in physics, engineering, and architecture. This research is often inspired by recreational origami questions. This talk will present multiple examples of research mathematics that has arisen from origami problems. Teaser: Given a maze and a path through that maze, can you fold a path-shaped piece of paper into a compact pile so that, if the pile were placed at the start of the maze and a certain crease unfolded, the rest of the paper would rigidly unfold by snaking precisely through the maze without colliding with the walls?", "id": "Paper/69746", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69746"}, {"title": " Effect of Graph Gluing on Consensus in Networked Multi-Agent Systems ", "webprogram_exclude": "0", "session_ids": ["Session/19360"], "source_sha256": "c1e74ccb29c985d71faee47853ca0af944699413e8102d47d7fdecea87e23c2c", "withdrawn": "", "abstract": "In this talk, we will examine how bridge and interface gluing of graphs affect the convergence rate of consensus dynamics.  We will discuss preliminary theoretical results, followed by simulations.", "id": "Paper/69747", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69747"}, {"title": " Applications of Free Resolutions to Neuroscience ", "webprogram_exclude": "0", "session_ids": ["Session/18318"], "source_sha256": "4d289b8c53187451be34c145f8ad4f72c05ea02f71c419bf930386d7c576f2b4", "withdrawn": "", "abstract": "Neurons provide a mechanism for a brain to convert external signals into an internal world model. To better understand the transition from external signal to internal model, one can study patterns of neuron firing. Specifically, if one monitors $n$ neurons and records which neurons fire simultaneously, they can represent the firings patterns as elements of $\\mathbb{F}_2^n$. The collection of all observed firing patterns can be viewed as a variety and thus studied using tools from commutative and homological algebra. In this talk, we give a brief survey of the transition from neuron firing to classifying families of neural codes using properties of free resolutions.\n\nThis talk covers joint work with Rebecca R.G., Alexandra Seceleanu, and Nora Youngs.", "id": "Paper/69748", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69748"}, {"title": " Sparse Spectral Methods for Solving Multiscale Parabolic PDEs ", "webprogram_exclude": "0", "session_ids": ["Session/18273"], "source_sha256": "63ddb751ee875e342950e70434dcf7a8cb6c80b6910ab20fd798455e676a6eff", "withdrawn": "", "abstract": "We discuss sparse spectral methods for solving multiscale parabolic PDEs, first proposed by Ingrid Daubechies, Olof Runborg, and Jing Zou in 2007, with a particular focus on the diffusion equation with a nonconstant diffusion coefficient. We show how to obtain runtime improvements by exploiting the structured coupling among Fourier modes of the associated elliptic operator induced by the Fourier sparsity of the diffusion coefficient. This structure allows a potentially high-dimensional problem to be decomposed into smaller independent subproblems. Crucially, these invariant subspaces induce structured Fourier support in the eigenfunctions of the elliptic operator. In the eigenfunction expansion of the parabolic solution, modes associated with small eigenvalues decay more slowly over time and therefore dominate the solution over longer time scales. Our analysis uses this structured Fourier support to obtain an efficient approximation of the long-time solution using only a small subset of the full spectrum. We discuss convergence and error analysis in Sobolev norms.  We also discuss ongoing efforts to extend the methods to several multiscale and high-dimensional problems.\n\nThis talk is based on joint work with Craig Gross/Grosch (MSU) and Mark Iwen (MSU).", "id": "Paper/69749", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69749"}, {"title": " The Kolmogorov Problem for the Nonlinear Diffusion Equation ", "webprogram_exclude": "0", "session_ids": ["Session/18342"], "source_sha256": "7bcd86471d0b81b45f780aefc52d34a08673cdd94b31a8fe89a10d731593c40f", "withdrawn": "", "abstract": "We consider the Dirichlet problem for the nonlinear diffusion equation in arbitrary open sets with non-compact boundaries. We establish sharp condition for the backward uniqueness of the bounded weak solutions expressed in terms of the growth rate of the size of the domain as $t\\downarrow -\\infty$.", "id": "Paper/69750", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69750"}, {"title": " Weaving, Jacquard, and Mathematics ", "webprogram_exclude": "0", "session_ids": ["Session/18234"], "source_sha256": "912c88b775ae46e40b40f62da8ed164acea26f3413d0ac7badfe44c577b4c8f9", "withdrawn": "", "abstract": "When the Jacquard loom was invented over 200 years ago, it transformed the weaving industry in Europe.  Later, it served as an inspiration for the first computer programs.  This talk will explore that relationship and other ways that weaving is connected to mathematical ideas taught in classrooms today.", "id": "Paper/69751", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69751"}, {"title": " Stream differential rings, an algebraic framework for stream differential equations. ", "webprogram_exclude": "0", "session_ids": ["Session/19342"], "source_sha256": "f2fee05192590443a85d587b0ad3168395f134255cffae3df03e07fa099c829c", "withdrawn": "", "abstract": "Rutten's coinductive stream calculus studies infinite streams using coalgebraic methods. In this talk, an algebraic abstraction of infinite streams with convolution product is proposed. A \\emph{stream differential ring} (SD-rings) is a triple $(R,d,x)$, where $R$ is a commutative ring, $x\\in R$, and $d:R\\to R$ is an additive map satisfying $d(x)=1$, $d(1)=0$, and the twisted Leibniz rule $d(ab)=a\\,d(b)+b\\,d(a)-x\\,d(a)d(b)$. The key structural map $\\epsilon(a)=a-xd(a)$ is a ring homomorphism with values in $ker$ $d$, which behaves as a head map motivated by the fundamental theorem of stream calculus. This map naturally makes $d$ an $\\epsilon$-derivation. We discuss analogues of several notions from differential algebra, including differential ideals, radical and prime differential ideals, differential polynomial rings and their associated solution sets. In particular, the radical of an SD-ideal is again an SD-ideal without assuming that $\\mathbb{Q} \\subseteq R$. The theory of SD-rings also shows a natural $x$-adic flavor. Moreover, extending the stream derivative to the polynomial ring $R\\{Y\\}$, we study nonlinear stream differential equations of the form $Ad(\\sigma)^n=U$ algebraically, where $A$ plays a role similar to an initial or separant. The talk aims to outline a possible algebraic framework for stream differential equations.", "id": "Paper/69753", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69753"}, {"title": " Independence Polytopes: a Novel GPT Application ", "webprogram_exclude": "0", "session_ids": ["Session/18334"], "source_sha256": "532dc6f6bc5ac50022455b20fe412beb367c43a6806dc958b2ec2bf25880d62b", "withdrawn": "", "abstract": "We apply a representation-theoretic result of Garver, Patrias, and Thomas (GPT) to give an equivariant bijection between lattice points in dilations of independence polytopes of nu-Tamari lattices and certain order polytopes under a piecewise generalization of rowmotion.  In this special case, GPT recovers Hillman Grassl", "id": "Paper/69757", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69757"}, {"title": " Computational Analysis of Wing Venation and Cell Domain Patterns in the Grasshopper  Arphia conspersa  ", "webprogram_exclude": "0", "session_ids": ["Session/19371"], "source_sha256": "c327745aa732629c0f62b268e646c864e37cba0d565062abc8aa1bed6219a1ec", "withdrawn": "", "abstract": "Insect wings are a remarkable achievement of evolution, being lightweight, strong, durable, and flexible. This is made possible by the presence of ``wing veins’’, the thickened, structure-like elements embedded within the wing surface, which divide the wing into domains. Here, we study a collection of over 4000 grasshopper wings of the species \\textit{Arphia conspersa} collected across Colorado during the 1970’s, which are now stored in the Chicago Field Museum. We describe a computational pipeline to extract vein geometry from wing images, and we analyze morphological features, such as vein thickness and domain circularity. This collection includes geographical, ecological, and morphological information about each specimen, and we examine how these aspects are correlated with wing geometry. We also explore the capabilities of reaction-diffusion systems to model wing structures, and recreate the morphological features seen in the collection.", "id": "Paper/69758", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69758"}, {"title": " Automated Discovery ", "webprogram_exclude": "0", "session_ids": ["Session/17911"], "source_sha256": "1cd5c5e01d6384c4a3f90b5e250b62fd14514ac7bd9107aa3955f3ed2820ed5c", "withdrawn": "", "abstract": "Zero forcing is a graph propagation process with connections to minimum rank, controllability, and combinatorial optimization. We describe how the automated discovery system TheoX, together with its LittlePaul conjecturing module, uses graph registries, automated conjecture generation, counterexample search, and proof-oriented reasoning to study zero forcing and related processes. We present several discoveries arising from this workflow, including constructive polynomial-time upper bounds, forcing rules based on dependency matchings and local structure, and neighborhood-local forcing parameters with sharp behavior on important graph classes. We also discuss unresolved conjectures that survived extensive computational and theoretical attacks. Beyond graphs, the same forcing philosophy leads to rank-limited reconstruction on simplicial complexes, syndrome propagation in quantum information, and local propagation and stopping-set questions in quiver and crystal-melting models. These examples illustrate how automated conjecturing can do more than search for isolated inequalities: it can suggest new definitions, reveal common mechanisms across fields, and generate research problems that remain meaningful after human scrutiny.", "id": "Paper/69763", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69763"}, {"title": " The Rubey Lattice ", "webprogram_exclude": "0", "session_ids": ["Session/18334"], "source_sha256": "6b22c9a7e6ef1d3b946c9e9d23bb5d2d2a8f4a8166e46b6a191b01aa873abd56", "withdrawn": "", "abstract": "For each permutation $w$, we consider the set $\\mathrm{PD}(w)$ of reduced pipe dreams for $w$, partially ordered so that cover relations correspond to (generalized) chute moves. Settling a conjecture of Rubey from 2012, we prove that $\\mathrm{PD}(w)$ is a lattice. To establish this result, we provide a global description of the partial order on $\\mathrm{PD}(w)$ by showing that $\\mathrm{PD}(w)$ is isomorphic to a poset consisting of objects called \\emph{Lehmer tableaux}. In addition, we prove that $\\mathrm{PD}(w)$ is a semidistributive polygonal lattice whose polygons are all diamonds or pentagons and that it satisfies the HH property.  We show additional properties when the permutation avoids the patterns 12543 and 21543, settling another conjecture of Rubey.\n\nThe lattice proof is from joint work with Colin Defant, Hanna Mularczyk, Son Nguyen, and Kathrine Tung. An independent proof was simultaneously given by Sara Billey, Connor McCausland, and Clare Minnerath.", "id": "Paper/69764", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69764"}, {"title": " An Asymptotic Upper Bound For Counting Fiven Numbers ", "webprogram_exclude": "0", "session_ids": ["Session/19361"], "source_sha256": "4e34c6f3c0692fe561ff56f2de518de19d52c50bb1555171bb30b344247d4a54", "withdrawn": "", "abstract": "In this talk, we give an asymptotic upper bound for the number of Fiven (Factorial-Niven) numbers. A Niven number is a number that is a multiple of its digital sum. Dalenberg and Edgar defined a Fiven number as a number that is a multiple of its digital sum using the digits from its representation in factorial-base notation. The upper bound presented here for the asymptotic frequency of Fiven numbers was derived by closely following the methods first used by Cooper and Kennedy and later by DeKoninck and Doyon and others for their derivations of asymptotic bounds for base-10 and other fixed-base Niven numbers.", "id": "Paper/69765", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69765"}, {"title": " From Cell to Canopy: Bridging Mathematical Physiology and Ecosystem Ecology ", "webprogram_exclude": "0", "session_ids": ["Session/17988"], "source_sha256": "e7ea8517b5b8083ac77dae4a20eee1249cbd32b7ca1e1ccbc50bea36b4d90883", "withdrawn": "", "abstract": "The emerging science of ecological forecasting combines observational data with mathematical models to predict short-term future ecosystem states with computed uncertainties. Systems where ecological forecasts are applied range from living organisms (such as tick populations), phenological states, or soil processes. For many of these forecasts, process-based ecosystem models are utilized because they apply foundational physical and biological principles (e.g., photosynthesis and respiration). Many of Jim Keener’s contributions to mathematical biology focused on cellular and human physiology, the core modeling principles also extend to the construction of process-based ecological models. This talk situates ecological forecasting at the intersection of statistics, mathematical biology, uncertainty quantification, and parameter estimation, while outlining future directions for ongoing research. Ultimately, Jim’s vigor and enthusiasm for translating physiological modeling concepts into ecosystem ecology provided a foundational inspiration for my career.", "id": "Paper/69766", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69766"}, {"title": " Engaging Graduate Teaching Instructors in Quantitative Reasoning to Support Precalculus Students’ Mathematical Modelling ", "webprogram_exclude": "0", "session_ids": ["Session/18088"], "source_sha256": "3732ae06c2697b2d058fe31d183e97a75befdccd894ad102a0948360c84bd7a3", "withdrawn": "", "abstract": "The Mathematical Association of America (MAA) has repeatedly called for greater emphasis on modeling and connections among representations of functions (CUPM, 1989, 2004, 2015), yet curriculum developers and instructors have received limited guidance in responding to these calls.  Research in mathematics education has identified key conceptions and reasoning abilities that support students in constructing analytic and graphical models of how quantities in a problem context are related and vary together (e.g., Thompson, 2011; Moore & Carlson, 2012). A foundation for such modeling is students’ development of a personal image of the quantities in a context, including how they are related and how they vary together (Moore & Carlson, 2012; Carlson et al., 2002). The Conventions for Supporting Quantitative Reasoning (Carlson et al., 2024) are designed to support the meaningful emergence of variables, expressions, and formulas (O’Bryan, 2019, 2025), as well as graphs that represent how two conceptualized quantities vary together (Moore & Thompson, 2016). Previous research indicates that supporting Graduate Teaching Instructors (GTIs) in developing more conceptually oriented, student-centered instructional goals and practices is complex. Our study investigates GTIs’ quantitative reasoning (QR) and their use of the conventions for quantitative reasoning while teaching using a conceptually based precalculus curriculum. The interventions also included pre-semester training, a weekly seminar focused on conceptual understanding of the curriculum materials with accompanying assignments, daily reflection immediately following instruction, and reflection after viewing recordings of their lessons. The talk will present the results and impact of these supports on GTIs’ quantitative reasoning and instruction, along with the results from analyzing the impact of students’ quantitative reasoning on their ability to construct meaningful function models.", "id": "Paper/69767", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69767"}, {"title": " When Life gets knotty: Two-dimensional cellular automata based on knot mosaics ", "webprogram_exclude": "0", "session_ids": ["Session/18234"], "source_sha256": "0cdf4f4c210d86f1cbbcc19fd6c3abf59a67b8be72eebe67aa7ba85dfd93b644", "withdrawn": "", "abstract": "Previous work has used cellular automata to represent knotwork which proceeds\nin one direction, such as braids and knitted cables. This one-dimensional system,\nhowever, is not suitable for many other types of knotwork. This work in progress\nexplores the possibility of a two-dimensional system which is capable of representing\nmany more kinds of knots, including those used in macram\\'e. The tile set used in\nthis system is taken from the knot mosaics invented by Lomonoco and Kauffman,\nwhich have been shown to faithfully represent all tame knots and tangles.", "id": "Paper/69769", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69769"}, {"title": " Amenability and hyperfiniteness ", "webprogram_exclude": "0", "session_ids": ["Session/18561"], "source_sha256": "9e335037a98350a1785cbccc150655b5ef41f117fca8f3385e89a7ba8a562456", "withdrawn": "", "abstract": "Amenability is a finite approximation property of groups, introduced by von Neumann. It has seen widespread applications in many areas of mathematics, in particular in the ergodic theory of discrete groups. Ornstein and Weiss showed that every measurable action of an amenable group on a probability space enjoys, almost everywhere, an even stronger finite approximation property known as hyperfiniteness. A longstanding open problem, known as Weiss's Question, asks whether it is necessary to discard this set of measure zero, that is, whether every Borel action of an amenable group is hyperfinite. We will survey current progress on this question, as well as various related questions in settings beyond amenability and groups.", "id": "Paper/69773", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69773"}, {"title": " Structure of products of vector subspaces in a field extension ", "webprogram_exclude": "0", "session_ids": ["Session/18230"], "source_sha256": "402a8632628894ef560ecb6716dcdd78571e3546f4f348605eaf852467d7709d", "withdrawn": "", "abstract": "Let \\(L/F\\) be a finite field extension. For nonzero \\(F\\)-subspaces \\(S,T\\subseteq L\\), write\n$$\nST=\\operatorname{span}_F\\{st:s\\in S,\\ t\\in T\\}.\n$$\nHow small can \\(\\dim_F(ST)\\) be, and what does small dimension reveal about the structure of \\(S\\) and \\(T\\)?\nWe present a Kneser-type theorem in a framework that unifies vector-space dimension and cardinality through a compatible modular matroid structure. In the field-extension setting, the theorem recovers the canonical inequality\n$$\n\\dim_F(ST)\\geq\n\\dim_F(SH)+\\dim_F(TH)-\\dim_F(H),\n$$\nwhere \\(H=\\{x\\in L:xST\\subseteq ST\\}\\) is the stabilizer field of the product space. This formulation highlights the role of subspaces invariant under multiplication and requires no separability assumption.\nWe then investigate critical pairs, for which product dimension is unusually small. We describe a recursive structural theory involving intermediate fields, subspaces spanned by geometric progressions, and higher-dimensional configurations with controlled intersections under multiplicative translates. In particular, we characterize the one-step growth condition \\(\\dim_F(S+aS)=\\dim_F(S)+1\\) through an invariant component and a geometric-progression block. A central tool is a multiplicative polarity that extends the dimension-complementing behavior of orthogonal complements to the matroidal setting.\n\nThis is joint work with Jozsef Losonczy.", "id": "Paper/69774", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69774"}, {"title": " Modeling Population-Level Dynamics of  C. difficile  Transmission Between the Hospital and Community ", "webprogram_exclude": "0", "session_ids": ["Session/18220"], "source_sha256": "3c30aeae1cb0d8292f602ef409dc1a62fefd655034b8009362b1e60d9f200399", "withdrawn": "", "abstract": "\\textit{Clostridioides difficile} (\\textit{C.~difficile}) infections remain a leading cause of infectious diarrhea in the United States. Classified as an urgent public health threat by the Centers for Disease Control and Prevention (CDC), \\textit{C.~difficile} infections are commonly acquired in hospital settings, where the disease is transmitted through spores that persist on contaminated surfaces. However, recent data demonstrate a significant increase in community-acquired cases. The literature suggests that this increase may be partly attributed to interactions involving individuals carrying the pathogen as they leave healthcare settings and enter the community. This study develops an ordinary differential equation compartmental model to analyze the transmission dynamics of \\textit{C.~difficile} between a hospital and a local community and applies Optimal Control Theory to evaluate the efficacy of various mitigation strategies in both the community and the hospital. The results provide insight into effective strategies for controlling the spread of \\textit{C.~difficile}.", "id": "Paper/69775", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69775"}, {"title": " Combinatorial proofs for identities involving the number of missing integers in partitions ", "webprogram_exclude": "0", "session_ids": ["Session/17968"], "source_sha256": "b2cf7da40cc6b30d2fd047c52784879921499be4013e184d92cd74876ef2b1d2", "withdrawn": "", "abstract": "A missing integer of a partition $\\lambda$ is a positive integer less than the largest part that does not appear as a part. In their recent paper, Bhoria, Eyyunni, and Santra studied the number of partitions and overpartitions of $n$ with a fixed number of missing integers, establishing generating functions, identities, and congruences. In this talk, we provide combinatorial proofs of several of their results.", "id": "Paper/69777", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69777"}, {"title": " Harnessing Discrete, Multiscale Modeling and Topological Data Analysis to Forecast Stem Cell Behavior ", "webprogram_exclude": "0", "session_ids": ["Session/18039"], "source_sha256": "bd5081ee6a31ec379d165ef232f3d7f1cffbf6fa4ed7ecf8325427d053bb3f8d", "withdrawn": "", "abstract": "Individual stem cells process information from their environment through biophysical and biochemical cues in order to determine their cell fate (i.e., the germ layer into which they will differentiate). However, cell autonomous decision-making does not fully account for the organizational features associated with developmental patterning. In this work, we investigated the role of intercellular/intracellular signaling and morphogen-based chemotaxis in the context of cell fate decisions. Along with \\textit{in vitro} experiments, we developed an ensemble of multiscale, agent-based models which represent key mechanisms (e.g., signaling and cell division) using discrete mathematical models (e.g., Boolean networks and Markov chains, respectively). The goal of this type of modeling is to connect the local interactions with the population-level patterning that we observed in microscopy images. We also used persistent homology to generate multiscale, topological descriptors (i.e., persistence landscapes) from both microscopy images and model simulations. By comparing descriptors from \\textit{in vitro} and \\textit{in silico} experiments, we were able to perform model selection and to improve model predictions of emergent organization under a variety of differentiation conditions.", "id": "Paper/69778", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69778"}, {"title": " The Geometry of Rare Transitions over Periodic Boundaries ", "webprogram_exclude": "0", "session_ids": ["Session/18008"], "source_sha256": "f6ec37289537e4709f3376dd796583b4dba7865d169d3638cf7477ad9f2cec3c", "withdrawn": "", "abstract": "Noise-induced tipping (N-tipping) occurs when random fluctuations drive transitions from one (meta)stable state to another, often as a rare event. In this talk, we present techniques for determining Most Probable Escape Paths (MPEPs) in Stochastic Differential Equations (SDEs) over periodic boundaries, using a dynamical systems approach suited to the intermediate noise regime. Our framework computes MPEPs by locating intersections of stable and unstable manifolds of invariant sets in a Hamiltonian system derived from the Euler-Lagrange equations of the Freidlin-Wentzell (FW) functional. The Maslov index identifies which critical points of the FW functional are local minimizers, clarifying how noise interacts with the deterministic flow. The Onsager-Machlup functional, treated as a perturbation of the FW functional, then provides a selection mechanism to pick out the MPEP. We illustrate our approach and compare theoretical predictions with Monte Carlo simulations in the Inverted Van der Pol system and a carbon cycle model.", "id": "Paper/69782", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69782"}, {"title": " Promoting Confidence in Patient-Specific Finite Element Models of the Vascular System Through Uncertainty Quantification ", "webprogram_exclude": "0", "session_ids": ["Session/18309"], "source_sha256": "3d9e82185b22a6cd6aea0563775c4a5c32e02c6f81724584336f2c740669cd47", "withdrawn": "", "abstract": "Patient-specific computational models of the cardiovascular system are increasingly used in clinical decision-making, surgical planning, medical device design, and regulatory evaluation. We incorporated advancements in uncertainty quantification (UQ) in a series of studies to evaluate variability in computational simulation outputs of the fluid and solid coronary artery biomechanical environments due to model input uncertainty. Probability density functions were fit to population-derived or patient-specific values and sampled, with temporal variability in time-varying parameters characterized and incorporated into the UQ framework using principal component analysis. Idealized and patient-specific coronary artery computational models of the fluid and solid domains were constructed and solved in the finite element software suite, FEBio, to predict fluid wall shear stress and tissue first principal stress. Parameter-to-model-output emulators were constructed via polynomial chaos expansion using the UQ software, UncertainSCI. Results highlight the considerable variability in predicted mechanical metrics due to input parameter uncertainty, particularly the impact of patient-specific versus population-derived data and the propagation of temporal variability in time-varying model inputs to model predictions. Collectively, these findings underscore the importance of integrating UQ into patient-specific modeling workflows to quantify predictive confidence, while emphasizing the need for coupled computational pipelines, robust data structures, and scalable computing resources to facilitate efficient implementation and enable translation of uncertainty-aware modeling to clinical applications.", "id": "Paper/69784", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69784"}, {"title": " S^{2}-PINNs: Stochastic Separable Physics-Informed Neural Networks ", "webprogram_exclude": "0", "session_ids": ["Session/18280"], "source_sha256": "5f020b5984795c4a27c226a089698b0c1f4aa4d02ea1629cf1f9cc1a7b700df0", "withdrawn": "", "abstract": "Uncertainty quantification (UQ) for random partial differential equations (PDEs) is ubiquitous in computational science and engineering. However, classical spectral solvers for this class of problems face the curse of dimensionality, and existing neural solvers often ignore the stochastic structure that makes moments and calibration tractable. We introduce a stochastic separable physics-informed neural network, dubbed S$^{2}$-PINNs, that represents the solution $u(t,\\mathbf{x},\\mathbf{Z})$ of a random PDE with a learnable Gaussian spatial dictionary, Fourier temporal features, and a generalized polynomial chaos (gPC) stochastic bases, coupled by a low-rank Canonical Polyadic (CP) tensor decomposition core. The method is trained with a hybrid strong-form and gPC-projected residual loss. Our theoretical analysis establishes that the separable class is dense in $L^2$ under mild conditions, and the projected residual corresponds exactly to a stochastic Galerkin constraint. Furthermore, we show that mini-batch projection coefficients are logarithmically dependent on the number of gPC modes, and that orthogonality penalty controls the conditioning of the learned spatial dictionary. Using four manufactured random PDE benchmarks, we show that S$^{2}$-PINN outperforms six baselines in terms of mean and variance accuracy, as well as calibration, while using significantly fewer parameters. Further evaluations on non-manufactured Poisson and Darcy problems, a diffusion scaling study of higher random dimensions, and two stochastic inverse problems reveal the generalization capabilities of the proposed structure. Together, these results support stochastic separability as an effective design principle for physics-informed neural UQ.", "id": "Paper/69787", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69787"}, {"title": " Characterizing Linear Relaxations of the Trilinear Monomial’s Graph via Volume ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "09af00c5972d413bd759e1414db95ad6cb2160402050eac58cac50964c6d8093", "withdrawn": "", "abstract": "Solving difficult mixed integer nonlinear programs via a spatial branch and bound (SBB) algorithm requires effective convex outer approximations of nonconvex sets. In this framework, complex problem formulations are often decomposed into simpler library functions whose relaxations are then composed to build relaxations of the overall problem. Given its computational complexity, tuning SBB to improve run time as much as possible is necessary. In principle, SBB’s efficiency is dependent on the quality of the convexification methods used to approximate the graphs of the library functions.\n \nThe trilinear monomial, $f=x_1x_2x_3,\\;x_i\\in[a_i,b_i]$, serves as one such fundamental library function, appearing frequently as a building block across diverse applications. Understanding the tightest convex relaxation of the trilinear monomial isn’t only beneficial to optimization problems in which a function itself is a trilinear monomial, but also problems with functions that can be decomposed using the trilinear monomial as a library function. \n\nTo improve the runtime of SBB, we want to compare the tightness of the different linear relaxations of the trilinear monomial using volume as a criterion. By definition, the convex hull provides the tightest possible relaxation and thus, serves as a benchmark for evaluating alternative relaxations. In this work, we present the convex hull’s volume via six distinct formulae that together characterize all possible parameter configurations. \n\nWe additionally consider other linear relaxations of the trilinear monomial. While the alternative relaxations may not offer the tightest approximation of the trilinear monomial’s graph, their representations may be less computationally expensive to optimize over compared to the convex hull.", "id": "Paper/69788", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69788"}, {"title": " Universal approximation in topological vector spaces ", "webprogram_exclude": "0", "session_ids": ["Session/19358"], "source_sha256": "4ca8fd2895b62f0f8caea4f487c2b802f369b2ba52691cf3ab1010dedb2eee44", "withdrawn": "", "abstract": "In this talk, I will present results on the approximation of continuous maps between topological vector spaces (TVSs) by neural networks over a compact. I will consider the case of continuous maps between locally convex TVSs, where an explicit formula for a partition of unity on a compact is given in terms of seminorms, and the case of non-locally convex TVSs, where additional assumptions on the topological dimension of the compacts need to be considered. In both approaches, Katetov's extension theorem is used to reduce the problem to the approximation of a map that is uniformly continuous on the whole domain TVS.", "id": "Paper/69797", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69797"}, {"title": " Removing a Long Cycle in Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18339"], "source_sha256": "4cd15eca8bafcf25ef480abfdb87823d5fa3653b5f2024df1c3f552706dd59c2", "withdrawn": "", "abstract": "Thomassen proved that every $(s+3)$-connected graph $G$ contains a cycle $C$ such that $\\kappa(G-V(C))\\ge s$. Further, he proved that every $(s+t-1)$-connected graph $G$ of minimum degree at least $g(s,t)$, its vertex set can be partitioned into two sets $S$ and $T$ such that the subgraphs $G[S]$ and $G[T]$ have connectivity at least $s$ and $t$, respectively. In this paper, we prove that every $(s+1)$-connected graph with minimum degree at least $\\frac{3s}{2}+2m-3$ contains a cycle of length at least $m$ whose removal remains $s$-connected. Our proof leads to a polynomial algorithm for finding such a long cycle in every $(s+1)$-connected graphs.", "id": "Paper/69798", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69798"}, {"title": " Synthesis of Single-Qudit Circuits in Dimensions 3 and 5 ", "webprogram_exclude": "0", "session_ids": ["Session/19338"], "source_sha256": "ad7b31c88c9218d3a48f858e0630cd989754f0c072c22c0f1e3cf901abc1f15c", "withdrawn": "", "abstract": "Efficient synthesis of fault-tolerant quantum circuits is of key interest for compiling quantum algorithms onto near-term and future quantum hardware. Higher-dimensional ``qudits\" offer an alternative to two-dimensional qubits that can reduce circuit complexity through the use of single-qudits for certain multi-qubit operations. To efficiently synthesize single-qudit circuits, we utilize the Clifford + T gate set, a generalization of a popular paradigm for qubit circuits, to qutrit (dimension 3) and ququint (dimension 5) circuits. We additionally utilize the qutrit Clifford + R gate set. Both sets consist of Clifford gates, which can be implemented on many error-correcting codes, and either the T or R gate, which are implementable through well-established magic-state distillation and injection techniques.\n\nWe first implement and test a recently published algorithm for single-qutrit circuit synthesis using the Clifford + R set, which efficiently approximates arbitrary rotation gates via Householder reflections. We confirm this algorithm's optimal scaling of R gates with synthesis precision, then adapt the architecture to single-qutrit and single-ququint circuits. We do this by building search lattices of cyclotomic field embeddings to find candidates that we then decompose into circuits over the Clifford + T gate set, thereby broadening the algorithm's applicability with existing error-correcting codes. By exploring these generalizations to higher dimensions, this work advances the use of fault-tolerant qudit circuits as quantum hardware evolves for long-term applications of quantum computing.", "id": "Paper/69800", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69800"}, {"title": " Atkin–Lehner quotients of the Deligne–Rapoport model of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"6.851ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 2949.9 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">X_0(N)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-58\" d=\"M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4E\" d=\"M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-58\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-30\" x=\"1171\" y=\"-213\"></use>\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"1282\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-4E\" x=\"1671\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"2560\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/17903"], "source_sha256": "3e14201812c8c58a0ff1e5e7639f2b83226e46bebd1b79ed2af9901883f36639", "withdrawn": "", "abstract": "Semistable models of the modular curve $X_0(N)$ have been extensively studied following works of Deligne--Rapoport, Katz--Mazur, et al. Meanwhile, Atkin--Lehner quotients of $X_0(N)$ are also of moduli theoretic significance and provide an important family of examples for computing rational points using the quadratic Chabauty algorithm. In this work, we construct semistable models of Atkin--Lehner quotients of $X_0(N)$ for square-free $N$ by taking the corresponding quotients of the Deligne--Rapoport model of $X_0(N)$. We describe the special fiber of the models explicitly. This is joint work with Lea Beneish.", "id": "Paper/69801", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69801"}, {"title": " Analysis of a twisted Bose-Einstein Markov chain with applications to sampling Catalan structures ", "webprogram_exclude": "0", "session_ids": ["Session/19370"], "source_sha256": "f918b7a20538f6965937b3a51b5b11c2e802fb93de32a617367c6ae375a09c4f", "withdrawn": "", "abstract": "The Burnside process uses a group action to sample combinatorial objects modulo symmetry. We analyze a twisted Bose-Einstein Markov chain and use it to construct rapidly mixing samplers for Catalan structures. We give explicit transition kernels and stationary distributions for the labeled chain and its lumping to occupancy configurations, identify the chain with a symmetric Dirichlet cut-and-paste process, and determine its second-largest eigenvalue. For a fixed twisting parameter, our upper and lower bounds show that the mixing time is $\\Theta(\\log n)$ when the number of boxes grows as a fixed positive power of the number of balls. In the untwisted case, this resolves a conjecture of Diaconis. Applying the analysis to Burnside chains on parking functions and labeled Dyck paths yields algorithms for sampling increasing parking functions and Dyck paths approximately uniformly, with logarithmic mixing times. The talk will emphasize the group-action construction and its combinatorial applications. This is joint work with J. E. Paguyo.", "id": "Paper/69802", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69802"}, {"title": " Matrix Riccati Equations in Optimal Control, A Differential Transform Method Approach ", "webprogram_exclude": "0", "session_ids": ["Session/19337"], "source_sha256": "cebf66f37a35e4aa81f483dad612a4a3ed7b7e6fed25404252218ded904047ee", "withdrawn": "", "abstract": "Abstract: The Matrix Riccati Equation(MRE) named after the mathematician Jacopo Francesco Riccati serves as a mathematical bridge between linear dynamics and optimal performance. The MRE is an essential tool for solving the Linear Quadratic regulator(LQR), in which the goal is to minimize a quadratic cost function subject to a linear dynamic. Unfortunately, there is no general way of solving the Matrix Riccati Equation despite the many fields to which it applies. While the scalar Riccati equation has been studied thoroughly, matrix Riccati equation of which scalar Riccati equations is a particular case, is much less investigated . In this presentation, I will talk about an overview about The Matrix Riccati Equation , how we can use technique(change of variable or Differential transform) from the scalar Riccati equation as a blueprint to solve the MRE and then apply this solution to Optimal Control.", "id": "Paper/69803", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69803"}, {"title": " Making the MBRG: Engaging Undergraduate Students in Mathematical Biology Research ", "webprogram_exclude": "0", "session_ids": ["Session/18205"], "source_sha256": "ff6683388df67a81fd4fdc239b518c42c7516ba9d5aadcea50e620f9bf9513ae", "withdrawn": "", "abstract": "In my first five years as a pre-tenure faculty member, I have been fortunate to collaborate with undergraduate student researchers on a range of projects in mathematical biology. In this talk, I will discuss how the MathBio Research Group (MBRG) was established at Lewis University, where much of this work began, and how this research program has continued to my current position at Villanova University, and through collaborations with students at other institutions and the Summer@ICERM program.\n\nOur research uses mathematical and computational models to investigate biological systems, with a focus on infectious disease dynamics, particularly \\emph{Clostridioides~difficile} transmission. We began with ordinary differential equation and agent-based models of transmission in hospital settings and subsequently extended this work to long-term care facilities and transmission between healthcare settings. More recently, our work has expanded beyond healthcare settings to consider \\emph{C.~difficile} transmission in localized communities, incorporating factors such as environmental contamination, antibiotic use, and population age structure. Across these projects, undergraduate student researchers have contributed to literature reviews, model formulation, computational implementation, sensitivity analysis, and interpretation and communication of results.\n\nI will highlight results from this progression of models and discuss how research questions can evolve naturally as students contribute new ideas and extensions. I will also share strategies for designing projects that are mathematically meaningful and accessible to undergraduates, while building a sustainable, collaborative research program at a primarily undergraduate institution.", "id": "Paper/69804", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69804"}, {"title": " Analyzing Random Walks on <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.583ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 681.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">L</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4C\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-4C\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Isogeny Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18073"], "source_sha256": "20f5a35846233a46ccd6b2a85ee0df7a01cde69ba6cf5a8c38d780afb02ba564", "withdrawn": "", "abstract": "The \\emph{supersingular isogeny problem} asks the solver to take a uniformly random pair of supersingular $j$-invariants in $\\overline{\\mathbb{F}}_p$ and compute an isogeny between the corresponding elliptic curves. This problem is the core hardness assumption for supersingular isogeny cryptography, and many isogeny-based cryptosystems rely on a restricted version of it. If we restrict the degree of the isogeny to be a power of a single prime $\\ell$ (or, more generally, to have only prescribed prime divisors), we can reframe the isogeny problem as a pathfinding problem in a graph.\n\nAssociated to each pair of primes $p \\neq \\ell$, there is a directed out-regular multigraph $G_p(\\ell)$ of degree $\\ell+1$ whose vertices correspond to supersingular $j$-invariants in $\\overline{\\mathbb{F}}_p$ and whose edges correspond to equivalence classes of $\\ell$-isogenies between them. Fixing a prime $p$ and a finite set of primes $L = \\{\\ell_1, \\ldots, \\ell_k\\}$ not containing $p$, one can form the $L$-isogeny graph $G_p(L)$ by summing the adjacency matrices of $G_p(\\ell_1), \\ldots, G_p(\\ell_k)$; this new graph captures all the information of the individual graphs $G_p(\\ell_i)$, as well as the interactions between the different primes $\\ell_i$.\n\nIt is well known that the graphs $G_p(\\ell_i)$ are all Ramanujan: they have optimally large spectral gaps for their size, and random walks on them exhibit rapid mixing to the stationary distribution. One interesting question is whether (and how) these properties transfer to $L$-isogeny graphs.\n\nWe will begin by showing that the Benjamini--Schramm limit of the sequence of $L$-isogeny graphs $(G_p(L))_p$ is a rooted product of trees, and use this to prove that asymptotically the graphs $G_p(L)$ fail to be Ramanujan in the spectral sense. We will then relate this fact to known counts of certain types of cycles in $L$-isogeny graphs. We will finish by discussing the behavior of random walks on $G_p(L)$, in terms of self-collisions and hitting times for special regions of the graph from a uniformly random root.", "id": "Paper/69805", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69805"}, {"title": " Minority Representation and Optimization in Computational Redistricting After Louisiana v. Callais ", "webprogram_exclude": "0", "session_ids": ["Session/19338"], "source_sha256": "39c12e70b22d1c49d41642a67182e3dd951095ccf63b4139ca7a2c0db28a77fb", "withdrawn": "", "abstract": "The Supreme Court’s ruling in \\textit{Louisiana v. Callais} has raised new questions about detecting racial gerrymandering and its effect on minority representation. Answering these questions requires flexible sampling methods to target distributions shaped by policy-driven desiderata, rather than relying on spanning-tree weighted ensembles. In this talk, we discuss two recent applications of the marked edge walk (MEW), a recent Metropolized MCMC algorithm for sampling redistricting plans, to questions raised by the new legal standard. First, we use parallel tempering to sample ensembles of realistic Republican gerrymanders across eight southern states, investigating the ruling’s effect on minority representation. Second, we use simulated annealing to directly optimize districting plans towards target objectives, outperforming the state of the art on several problems. These results demonstrate that Metropolized sampling allows the field of computational redistricting to investigate a broader range of research questions than previous methods allowed.", "id": "Paper/69809", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69809"}, {"title": " An Introduction to Fuchsian Groups Via Triangles and Quaternion Algebras ", "webprogram_exclude": "0", "session_ids": ["Session/18241"], "source_sha256": "f6715d7d9ddfd3b0f3c6e5101db6327ea4ac8f0212b1f3293b4318a27812fad7", "withdrawn": "", "abstract": "Any compact surface can be obtained from either the sphere, the Euclidean plane, or the hyperbolic plane as the quotient by a group action. From Euclidean and spherical geometry, we only obtain the torus, sphere, and Klein bottle, while all others are derived from the hyperbolic plane. With infinitely many of these surfaces coming from hyperbolic geometry, we turn our attention to the groups that form them, known as \\textit{Fuchsian groups}.\\\\\n\n\tWe study Curtis T. McMullen's construction of Fuchsian groups from ``torsion'' triangles using his moduli space of all triangles. Our focus is on an explicit description of the quaternion algebra associated to an artbitrary torsion triangle. We investigate how the quaternion algebra's structure relates to the Galois orbit of the triangle, the algebra of the resulting Fuchsian group, and how this affects the geometry of the resulting quotient surface.", "id": "Paper/69810", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69810"}, {"title": " Modeling Within-Season Vaccine Effectiveness Against Drifting Influenza A and B: A Two-Strain Immune-Ladder Framework ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "a4eecb18d119dc837c84f900dc26ee891d6c28035e5f59e4ccb1916c92bf1fb3", "withdrawn": "", "abstract": "Seasonal influenza vaccines are formulated months in advance from\nsurveillance-based strain predictions. However, genetic drift of the circulating strains, together with waning vaccine- and\ninfection-acquired immunity, may erode vaccine effectiveness (VE) as the\nseason progresses. We formulate a deterministic compartmental model of\ntwo co-circulating strains, Influenza A and Influenza B. Protection conferred by vaccination and\nprior infection is represented as an explicit graded immune ladder\nsubject to a waning process, and susceptibility at each rung is scaled by\na strain-specific antigenic-mismatch parameter. The model is calibrated to within-season surveillance and vaccine\neffectiveness data to assess how vaccine-strain mismatch and immune waning jointly shape the trajectory of VE over a season.", "id": "Paper/69812", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69812"}, {"title": " ORCAS: One-Round-Cheating Adaptor Signatures ", "webprogram_exclude": "0", "session_ids": ["Session/18307"], "source_sha256": "9ea7b19afaf900fe832ac234c7cd637080385cd66ea6130c107bc4e722d72e1d", "withdrawn": "", "abstract": "An adaptor signature extends an existing digital signature scheme with the ability to generate \\emph{pre-signatures}, signature-like objects which can later be converted into true signatures in exchange for revealing a secret. Adaptor signatures can replace on-chain scripts for blockchain applications such as \\emph{atomic swap}—ensuring fair play when two users wish to exchange goods. This talk considers how to construct adaptor signatures for the isogeny-based signature scheme CSI-FiSh. Of the two prior constructions, the first (Tairi \\emph{et al.}, FC 2021) has slow pre-signing and large pre-signatures compared to CSI-FiSh, while the second (Jana \\emph{et al.}, CANS 2024) removes the pre-signing overhead at the cost of modifying the signature scheme itself. Our construction, ORCAS, leverages the multiple repetitions in CSI-FiSh signatures to achieve optimal pre-signature sizes, fast pre-signing in many settings, and compatibility with standard CSI-FiSh.", "id": "Paper/69814", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69814"}, {"title": " Geogebra Applets in MYMathApps Calculus ", "webprogram_exclude": "0", "session_ids": ["Session/18092"], "source_sha256": "4f092f5b7c9a3f9f472e9cf3f14947727b53a31a029cd4e81e378856d4ccfad4", "withdrawn": "", "abstract": "MY Math Apps Calculus is an online text for a 3 semester calculus course for STEM students which emphasizes 3D visualization and interactivity. It is free for JMM attendees at https://mymathapps.com/ using the purchase code JMM27. In the last two years, several Geogebra applets have been added to MYMACalc to supplement the interactivity. I will show the tutorials for Properties of Sine and Cosine Curves, Properties of First & Second Derivative Graphs, and Average Value of a Function. The Geogebra tutorials are much easier to write than the previous tutorials which used Sage-Math or ThreeJS.", "id": "Paper/69819", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69819"}, {"title": " Symplectic alternating color algebras ", "webprogram_exclude": "0", "session_ids": ["Session/19342"], "source_sha256": "684fa2b8253321afc50aed2c210d9e00459cbe7d30e61ff43f7050c577d4ba0d", "withdrawn": "", "abstract": "Let \\(F\\) be a field. A symplectic alternating algebra over \\(F\\) is a symplectic vector space \\(V\\), equipped with an alternating bilinear product such that\n\\[\n(u\\cdot v,w)=(v\\cdot w,u).\n\\]\nThese algebras arose naturally from the study of powerful \\(2\\)-Engel \\(3\\)-groups.\n\nIn this talk, we introduce symplectic alternating color algebras. They extend the classical theory to\na color graded settings defined using a bicharacter.\nWe discuss some of their basic structure and constructions, as well as their possible group theoretic connections.\nThis is joint work with Kenneth Price.", "id": "Paper/69820", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69820"}, {"title": " Parametric and Universal Thouless Invariants in Matrix Product States ", "webprogram_exclude": "0", "session_ids": ["Session/17925"], "source_sha256": "e0e59077cdec3c328a4791770978fc12e1cd8247e11903c962a19cfab390140f", "withdrawn": "", "abstract": "Thouless pumping is a well-studied topological phenomenon found in quantum spin chains. In a typical Thouless pump, a spin chain protected by a compact symmetry $G$ undergoes a periodic evolution in which charge is transported down the chain, with the amount of charge transported each period being a quantized topological invariant, valued in the Pontryagin dual $\\widehat{G}$ of the symmetry group. Since the system is periodic, it may be regarded as a parametrized family of states with the circle acting as the parameter space. In this talk, I will generalize the Thouless pumping invariant to an invariant for families of injective matrix product states parametrized by an arbitrary topological space $X$, taking values in the first degree \\v{C}ech cohomology group $H^1(X;\\widehat{G})$. Moreover, I will show how any Thouless invariant can be obtained as a pullback of a single universal \\v{C}ech class on a classifying space for $G$-symmetric injective matrix product states.", "id": "Paper/69821", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69821"}, {"title": " Tensor Network Methods for Many-Body Schrodinger Dynamics: Recent Progress and Open Challenges ", "webprogram_exclude": "0", "session_ids": ["Session/18247"], "source_sha256": "95d80c2e448d5c074f1332ac73be787920dbb4be4a737e59ffe5f1363adcb4a0", "withdrawn": "", "abstract": "While tensor networks are frequently used for simulations of high-dimensional or many-body dynamics of quantum systems, there is much room for improvement since the tensor ranks grow quickly under generic initial conditions and drives. This rank-growth issue is even a major motivation for the development in quantum computers and simulators. The high dimensionality of the problem has also led to a common practice of taking small time steps, even for problems with slow dynamics. I will highlight recent progress in making tensor-based quantum time evolutions more efficient from multiple directions. By embracing stable evolution methods, one can take large time steps in high dimensional problems when the dynamics is appropriate. Then, to handle the rank-growth issue, one can explore alternate dynamics protocols that still access physically relevant information. The overall picture gives optimism that tensor methods could enable long-time and high-precision calculations of specific properties of large many-body systems.", "id": "Paper/69822", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69822"}, {"title": " Computational Characterization of Mean Arterial Pressure Trajectories After Spinal Anesthesia for Cesarean Delivery ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "2d41cd19db8cad6d1ecbdc79eac58c3ca0414a00d302f7ca2d733f31100ffa7e", "withdrawn": "", "abstract": "Spinal anesthesia is commonly used for cesarean delivery but can cause maternal hypotension through sympathetic blockade from intrathecal bupivacaine. Phenylephrine is frequently used to prevent or treat this hypotension, yet patient responses vary, making individualized blood pressure management challenging. In this interim retrospective analysis, we used unsupervised clustering to identify data-driven patterns in maternal mean arterial pressure trajectories following spinal anesthesia. We analyzed intraoperative time-series data from 137 cesarean delivery cases. Trajectories were aligned to bupivacaine administration, resampled to 1-second intervals, interpolated, adjusted for phenylephrine administration, smoothed, and normalized to each patient’s pre-spinal baseline. We compared four clustering algorithms across different distance metrics, when applicable. Dynamic time warping with k-means and three clusters produced the best separation (silhouette score 0.2478), followed by agglomerative clustering with cosine distance (0.2282). Clusters differed primarily in recovery after the blood pressure nadir rather than the magnitude of the initial decline. We further evaluated early cluster prediction using a multilayer perceptron and support vector classifier, with and without TimesFM feature extraction. The best model achieved 0.568 validation accuracy on 37 held-out patients, with a binomial standard error of approximately eight percentage points. These findings are exploratory because cluster membership may reflect baseline hemodynamics, spinal anesthesia response, clinician-directed phenylephrine administration, and preprocessing choices. This work demonstrates the potential of unsupervised clustering to characterize heterogeneity in maternal blood pressure trajectories after spinal anesthesia. Further validation is needed to assess cluster stability, generalizability, and whether early trajectory features predict clinically meaningful hypotension patterns. Ultimately, this approach may support clinician-in-the-loop decision-making for individualized vasopressor management. (X. Zhang and A. Pulugurtha contributed equally to this work)", "id": "Paper/69823", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69823"}, {"title": " Level Aspect Bounds for Twisted Shintani Zeta Functions ", "webprogram_exclude": "0", "session_ids": ["Session/18335"], "source_sha256": "04c9442e3d51acb87d872275bf16fc39ef2d5640d9d2614c36cb8b239a80a6b7", "withdrawn": "", "abstract": "For a prime $p>3$, let $\\chi_p=(\\frac{\\cdot}{p})$ be the primitive quadratic character modulo $p$. We present progress towards subconvexity of Shintani zeta functions $\\xi^\\pm(s)$ twisted by $\\chi_p$ in the level aspect. We also discuss the more general setting where we twist $\\xi^\\pm(s)$ by a quadratic character with squarefree conductor $q$ co-prime to 6.", "id": "Paper/69826", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69826"}, {"title": " Models of Elliptic Curves with Maximal 2-adic Image Subject to a Rational 2-Isogeny ", "webprogram_exclude": "0", "session_ids": ["Session/18380"], "source_sha256": "1a7c86d61b040caa11d8e432252c14e601e9ef0e621f905e35fa44666532ebfb", "withdrawn": "", "abstract": "Let $E$ be a non-CM elliptic curve defined over $\\mathbb{Q}$. We present models of curves that have 2-adic image as large as possible, given the constraint that they have a rational 2-isogeny. These curves are known to be generic, and one of the aims of this talk is to make that fact explicit. Our techniques make use of modular curves and their $j$-maps, as well as classification results on isogeny-graphs that have appeared in the literature recently.", "id": "Paper/69830", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69830"}, {"title": " Obstruction to Decomposable Exact Lagrangian concordance ", "webprogram_exclude": "0", "session_ids": ["Session/18218"], "source_sha256": "8e4624e48b1a08700498f9ff9e918f5fcf6e55003f837268d66f0e2a73d769ed", "withdrawn": "", "abstract": "Exact Lagrangian cobordisms between Legendrian knots impose an interesting, but still not fully understood, relation on Legendrian knots. In particular, endoconcordances of a Legendrian knot can be used to construct infinitely many exact Lagrangian fillings of certain Legendrian knots.\n\nThere are several known “elementary” building blocks for Lagrangian cobordisms, which are smoothly realized by the attachment of 0- and 1-handles. A fundamental question is whether every pair of nonempty Legendrian knots that are related by a connected exact Lagrangian cobordism can also be related by a decomposable cobordism, namely, a cobordism obtained as a composition of these elementary building blocks.\n\nDimitroglou Rizell and Gołovko made a breakthrough by constructing non-decomposable Lagrangian concordances between stabilized Legendrian knots, and subsequently modified their construction to obtain concordance between Legendrian fillable knots via satellite operations. In this talk, we introduce an augmentation-based obstruction to decomposability for exact Lagrangian concordances between non-stabilized Legendrian knots.", "id": "Paper/69831", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69831"}, {"title": " Examining Changes in Metacognitive Learning Strategies Across Introductory Mathematics, Statistics, and Calculus-Based Physics Courses ", "webprogram_exclude": "0", "session_ids": ["Session/18091"], "source_sha256": "5ff3b9caa844750b3408a6cd8fa11a5b1aa5376125a100a9ca7ea261a4c356ad", "withdrawn": "", "abstract": "Effective study strategies are essential for success in introductory mathematics, statistics, and calculus-based physics courses. This study examined students’ responses to semester-long metacognitive programming that promoted research-based strategies and reflection on study habits. Pre- and post-surveys showed shifts in strategy use, including increased self-testing.", "id": "Paper/69832", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69832"}, {"title": " Using AI and computational visualization to teach Linear Algebra ", "webprogram_exclude": "0", "session_ids": ["Session/18225"], "source_sha256": "18ef3a2be5afb5c2d303f1f53438b7377d9133dcf9225e49b1b2373798ac160d", "withdrawn": "", "abstract": "Linear algebra is a foundation for many engineering and natural science disciplines. However, students often struggle to understand its abstract concepts through traditional theoretical instruction. Project-based and programming-focused learning can improve conceptual understanding, but technical programming challenges may prevent students from fully engaging with the mathematics. AI tools can help reduce these barriers by making it easier for students to create visual models and explore mathematical ideas through computation. This approach connects abstract linear algebra concepts to clear and intuitive geometric representations. This work presents examples from a linear algebra course, including the use of linear transformations and probability to generate different fern patterns, and singular value decomposition (SVD) in applications such as Proper Orthogonal Decomposition (POD), Principal Component Analysis (PCA), and data compression. The examples are implemented in MATLAB and Python. These activities demonstrate how computational and AI-assisted tools can help students visualize abstract concepts, develop a deeper understanding of linear algebra, and connect the subject to applications in data science, engineering, and scientific computing.", "id": "Paper/69833", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69833"}, {"title": " On the Density of Primes with Isomorphic Group Structures in Isogeny Classes of Elliptic Curves ", "webprogram_exclude": "0", "session_ids": ["Session/18076"], "source_sha256": "69453ae0271dfbb35197331e271a085d08ba20d054034687728d7b53e820ba7f", "withdrawn": "", "abstract": "Let $\\mathcal{E}$ be an isogeny class of elliptic curves defined over $\\mathbb{Q}$. We calculate the density of primes $p$ for which all elliptic curves $E \\in \\mathcal{E}$ have isomorphic group structures over $\\mathbb{F}_p$. This question was recently answered in the case where the isogeny class has size 2, with the elliptic curves connected by a rational 2-isogeny. We extend these ideas to larger isogeny classes, using recent classifications of $2$-adic and $3$-adic images associated to isogeny graphs over $\\mathbb{Q}$, together with inclusion-exclusion and results on the degrees of division fields of elliptic curves.", "id": "Paper/69835", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69835"}, {"title": " Coupled continuity equations for constant scalar curvature Kähler metrics ", "webprogram_exclude": "0", "session_ids": ["Session/18337"], "source_sha256": "fbcb9565b186d890c6bd4be0f7a1ae5c777b6c5bd4d1b7f8f3cd8d731333a100", "withdrawn": "", "abstract": "We will discuss a coupled system of elliptic equations whose critical points are a pair $(\\alpha,\\omega)$, where $\\omega$ is a constant scalar curvature K\\\"ahler (cscK) metric and $\\alpha$ is an $\\omega-$harmonic form. The system was inspired by the works of Chen-Cheng and Li-Yuan-Zhang and adapted to the continuity equation setting using the framework of La Nave-Tian. We demonstrate smooth convergence of solutions to the coupled system in the case where the first Chern class is negative, as well as in the setting of Riemann surfaces.", "id": "Paper/69838", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69838"}, {"title": " Regularization and Singular Limits in Nonlinear PDEs of Compressible Fluid Dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/18050"], "source_sha256": "b51022dc6d15d2681d8afea8a4c4c7d3b639edccdcc94e7e6e3d4ab427bf1c6a", "withdrawn": "", "abstract": "We will discuss recent advances in the analysis of singularity formation, suppression, continuation, and stability, as well as related singular limits, for nonlinear PDEs arising in compressible fluid dynamics. Particular attention will be given to the Euler, Navier-Stokes, Euler-Poisson, and Euler-Riesz equations, and to the mathematical mechanisms governing the emergence, regularization, and evolution of singular behavior of solutions in these PDEs.", "id": "Paper/69841", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69841"}, {"title": " Nilpotent Lie Groups with Constant Adjoint Rank: Algebraic and Geometric Properties ", "webprogram_exclude": "0", "session_ids": ["Session/18290"], "source_sha256": "83054ad886fda011ec90bfcaea6903429222c961786a45730c0460287c4cebf3", "withdrawn": "", "abstract": "A two-step nilpotent Lie algebra is said to have \\emph{constant adjoint rank} if all adjoint maps $\\operatorname{ad}_X$ for noncentral elements $X$ have the same rank.  We discuss the properties, structure, and classification of constant adjoint rank nilpotent Lie algebras.  We identify infinitely many of these that admit soliton inner products.", "id": "Paper/69842", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69842"}, {"title": " The Gray tensor product of presentable <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.446ex\" height=\"1.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -576.1 622.5 721.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\omega</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-3C9\" d=\"M495 384Q495 406 514 424T555 443Q574 443 589 425T604 364Q604 334 592 278T555 155T483 38T377 -11Q297 -11 267 66Q266 68 260 61Q201 -11 125 -11Q15 -11 15 139Q15 230 56 325T123 434Q135 441 147 436Q160 429 160 418Q160 406 140 379T94 306T62 208Q61 202 61 187Q61 124 85 100T143 76Q201 76 245 129L253 137V156Q258 297 317 297Q348 297 348 261Q348 243 338 213T318 158L308 135Q309 133 310 129T318 115T334 97T358 83T393 76Q456 76 501 148T546 274Q546 305 533 325T508 357T495 384Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-3C9\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-categories ", "webprogram_exclude": "0", "session_ids": ["Session/18000"], "source_sha256": "fb6c53278a2db35fc58fd7881453b268f2fa2d2c827276f58cc7f28b4cbb467a", "withdrawn": "", "abstract": "For each $n \\leq \\omega$, we construct a monoidal closed structure on $n \\mathrm{Pr}$ which deserves to be called the “presentable Gray tensor product”. We show that for each $m \\leq n \\leq \\omega$, $m \\mathrm{Pr}$ is an algebra over $n \\mathrm{Pr}$. In particular, taking $m < n = \\omega$, we deduce that $\\omega \\mathrm{Pr}$ is not the zero category, answering a question of Stefanich.", "id": "Paper/69843", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69843"}, {"title": " The Segre Invariant on Surfaces ", "webprogram_exclude": "0", "session_ids": ["Session/19350"], "source_sha256": "163fbbb79822b765c10ebbd184fa64a7a8093c6c6ee5f68e7432771f3416e31f", "withdrawn": "", "abstract": "The $k$th Segre Invariant of a vector bundle $E$ on a curve is the maximal degree of a rank $k$ subbundle of $E$. This induces a stratification of the moduli space of vector bundles and is well studied. Much less is known for vector bundles on surfaces. In this talk, we study the stratification induced by the first Segre invariant on $\\mathbb{P}^2$. Specifically, for each Chern character $\\xi$, we compute the Segre invariant of the general sheaf in $M_{\\mathbb{P}^2}(\\xi)$, and we determine all the integers that arise as the Segre invariant of a sheaf in $M_{\\mathbb{P}^2}(\\xi)$. We'll also discuss partial results / ongoing work on the same problem for abelian surfaces.", "id": "Paper/69845", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69845"}, {"title": " Oruga Flow Polytopes and Lattices of Circular Permutations ", "webprogram_exclude": "0", "session_ids": ["Session/18334"], "source_sha256": "8f2fc37d00721ab4239a3c3ef3e34c0a70589c9ee3d53251be04f667251cd5b9", "withdrawn": "", "abstract": "The set of all flows on a given directed acyclic graph gives a polytope called the `flow polytope.' For every such graph $G$ we may obtain a unimodular triangulation of the associated flow polytope by assigning to $G$ a structure called a `framing.' The simplices of this triangulation carry a lattice structure whose Hasse diagram is the dual graph of the triangulation. For the `oruga graphs,' two of these lattices are isomorphic to known lattices of permutations: the weak order and the lattice of circular permutations described by Abram, Chapelier-Laget and Reutenauer. We show that this connection to permutations holds for all framings.  Specifically, for each framing, the associated lattice structure can be expressed naturally in terms of circular permutations of the vertices of a certain tree. This also generalizes the `cycle graph' construction given by Lam and Postnikov in their work on alcoved polytopes.", "id": "Paper/69850", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69850"}, {"title": " Proof and Pictures : Formalizing the Braid Groups ", "webprogram_exclude": "0", "session_ids": ["Session/18208"], "source_sha256": "47160bad6b142b1fdb120cd76f4dfaf4b9aba6f9cbf4ee1b2996cabbb8e45660", "withdrawn": "", "abstract": "Due to braids' clear physical interpretation, images and diagrams have long played a role in both topological and algebraic proofs. And for almost equally as long, retractions and more rigor have followed. \n\nWe present a formalization in Lean (an interactive theorem prover) centering on definitions of braid groups and a solution to their word problem due to Patrick Dehornoy. This was not a mere translation problem. The proof relies heavily on a specific (rectangular) form of van Kampen diagram, which required a novel definition and proof of connection to the word problem.\n\nFar from closing the chapter of intellectual back-and-forth, the formalization and an accompanying interactive widget grant us license to explore -- and visualize -- new theorems, proofs, and conjectures, all with safe, enforced boundaries on correctness and rigor.", "id": "Paper/69855", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69855"}, {"title": " Finding Input-Output Equations for Linear Compartmental Models with Prescribed Orders ", "webprogram_exclude": "0", "session_ids": ["Session/18319"], "source_sha256": "db768d1a939f6d4322be837fd139df6d977fb62d68c41ee9a6f9eab976a991ab", "withdrawn": "", "abstract": "Linear compartmental models are linear systems of ODEs\nthat are determined by a graphical structure $G$. A common\nquestion that arises when performing parameter estimation\nis whether the parameters in our model can be recovered\nuniquely from perfect input-output data (i.e. data from\nvariables we can measure). One way to assess this is by\nstudying the coefficients of input-output equations, which\nare usually obtained via differential elimination. In this\ntalk, we discuss a linear algebra-based algorithm that allows us to compute ”nice” sets of input-output equations\nthat have prescribed orders for the derivatives that appear\nin the input-output equations. Furthermore, we will discuss conditions on $G$ to assess whether a particular set of prescribed orders can be obtained in our set of input-output equations.", "id": "Paper/69856", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69856"}, {"title": " Symmetry from Ordered Nonlocal Mean Curvature ", "webprogram_exclude": "0", "session_ids": ["Session/18377"], "source_sha256": "47f8386b9d058f2aa1c276a4262de0f1955f26f5add7b001bf03905a27d45fef", "withdrawn": "", "abstract": "The classical ordered mean-curvature problem asks whether monotonicity of mean curvature in one direction forces a hypersurface to be symmetric. We investigate its counterpart for nonlocal mean curvature defined by integrable interaction kernels. In contrast with classical curvature, this notion remains meaningful for sets with very limited boundary regularity. We prove that, under appropriate geometric and kernel assumptions, a bounded, connected set whose nonlocal mean curvature is ordered in one direction must be symmetric across a hyperplane orthogonal to that direction. The proof employs a variational argument for the nonlocal perimeter to reduce the curvature inequality to an equality at paired boundary points. We then develop a general version of Alexandrov's moving-plane method to establish symmetry from the pairwise curvature equality.", "id": "Paper/69857", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69857"}, {"title": " Broken Symmetry in Horse Locomotion: Phase-Locked Models and Individual Gait Signatures ", "webprogram_exclude": "0", "session_ids": ["Session/18222"], "source_sha256": "6e145e019dc081c9694b367f2c96100e1aa53f9162392b4ebe6ccf5ba96de72d", "withdrawn": "", "abstract": "Quadrupedal gaits are often introduced as ideal patterns. Walk and trot can be described by the relative phases among four limbs. Anyone who knows a barn, however, knows that real horses do not move like idealized horses. Their rhythms, head motion, and even their asymmetries can be individual.\n\nWe begin with a reduced coupled-oscillator model of walk and trot. Mapping hoof-on events to stride-normalized phases on the circle puts the model and measurements in the same coordinates. The measured phases cluster near the theoretical patterns, but they also contain limb-specific and stride-to-stride departures that an exactly phase-locked model misses.\n\nWe then look at inertial-sensor measurements from three off-the-track Thoroughbreds trotting on a lunge line in both directions. We compare left and right duty factors and limb ranges of motion, along with diagonal advanced placement and vertical displacement symmetry. Every horse was significantly asymmetric in at least one measure, but not in the same way. The affected measures and limb pairs differed from horse to horse.\n\nIn a separate longitudinal dataset, these asymmetries, together with gait timing and limb-angle waveforms, allowed us to identify most enrolled horses months to years later. No enrolled horse was mistaken for another. Asymmetry is therefore not simply noise to remove or evidence of lameness. It can be part of an individual and persistent signature.\n\nThis project also became an interactive app and lesson plan in which students use real horse data to explore phase relationships, broken symmetry, and identification. Horses provide a familiar and surprisingly rich setting for introducing dynamical systems, circular data, and classification.", "id": "Paper/69858", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69858"}, {"title": " Toilet Paper Math ", "webprogram_exclude": "0", "session_ids": ["Session/18212"], "source_sha256": "b3dd18bd324a5ff2e9df240a0913a517873b8682b6f7954779415669b734b7bf", "withdrawn": "", "abstract": "I will present several questions involving toilet paper, which prompt great Math Circle discussion and use real toilet paper as a manipulative. Talking about toilet paper is great for getting people out of their comfort zone. I start with: \"There are 3 kinds of people in the world: Those who crumble their toilet paper: The Crumblers. Those who repeatedly fold their toilet paper in half: The Halvers. And those who repeatedly fold a portion from one end: The Enders.\" The first question is for everyone. The second question is for the Enders. And the third question is for the Halvers. These topics and more are discussed in an article with Dave Auckly in \"Inspiring Mathematics: Lessons from the Navajo Nation Math Circles\".", "id": "Paper/69861", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69861"}, {"title": " Discrete groups acting ergodically on the boundary ", "webprogram_exclude": "0", "session_ids": ["Session/18362"], "source_sha256": "3304466345ed8960523eaf94d68037d389318ff90fa6ed3b70ce10a02910ef52", "withdrawn": "", "abstract": "We construct examples of infinite covolume discrete subgroups in G = SO(n,2)  (n \\geq 3) which act ergodically on the Furstenberg boundary of G, addressing a question  of Margulis for G = SO(n,2), n>2.\n\nThe examples arise from lattices in SO(n,1) and their deformations inside G. More important than the actual examples, we describe a new way of studying these deformations of lattices, which relate them to deformations of the smooth (left multiplication) action of SO(n-1,1) in the finite volume quotient SO(n,1)/\\Gamma. This correspondence allows us to use powerful tools from smooth dynamics. Some potential applications of the correspondence are understanding local rigidity of these groups inside G, and lower bounds on critical exponents of hyperbolic manifolds with totally geodesic boundary.", "id": "Paper/69866", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69866"}, {"title": " Is it Real? Optimal Control of an SIR-Type Model of Misinformation through Educational Campaigns ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "ddd51e635d536397d5e724de58f06c5e8f9ccac2a3f18b316c8bbe8e9b7fe2ff", "withdrawn": "", "abstract": "In today's world, misinformation spreads across social media faster than journalism and public discourse can correct it, with real costs to public health and social cohesion. We formulate an SIR-type compartmental model with three populations: susceptible individuals S(t), critically literate individuals C(t), and misinformed individuals M(t), together with a time-dependent educational intervention E(t) that transfers individuals from both S and M into the critically literate compartment. We establish positivity and boundedness of solutions and derive the misinformation-free equilibrium and the control reproduction number, whose threshold governs the local stability of that equilibrium. A Sobol sensitivity analysis identifies the transmission rate as the dominant driver of misinformation prevalence, and model parameters are calibrated to real rumor cascades from the PHEME Twitter dataset using a physics-informed neural network (PINN). Applying Pontryagin's Maximum Principle, we derive the optimal campaign and prove its existence under both quadratic (continuous) and linear (bang-bang) costs, solving each optimality system by a forward-backward sweep. Both strategies nearly eliminate the outbreak, reducing peak misinformation by 98.0 and 98.8 percent respectively, but they differ sharply in effort: the continuous campaign never exceeds 13 percent of maximum intensity and achieves its reduction using 58 percent of the total effort of the bang-bang campaign, making it the more cost-effective strategy for campaign design.", "id": "Paper/69870", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69870"}, {"title": " Strong and Weak Solutions for a Multiscale Interface Coupling of PDEs and ODEs ", "webprogram_exclude": "0", "session_ids": ["Session/18351"], "source_sha256": "f432839c1361567b7a62ee3a69d3f8ff5b3367d963730576f0038c0950a0a32d", "withdrawn": "", "abstract": "We consider a heterogeneous system which consists of a (locally accurate) 3D descriptive model of fluid flowing through deformable porous media equations, coupled with a systemic 0D lumped model of the remainder of the circulation, where the fluid flow through a vascular network is described via its analogy with a current flowing through an electric circuit. In this talk, we present new results on wellposedness of strong and weak solutions for this multiscale interface coupling.", "id": "Paper/69872", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69872"}, {"title": " Geometric Transitions and Moduli Spaces of Sheaves over Calabi-Yau Varieties ", "webprogram_exclude": "0", "session_ids": ["Session/18268"], "source_sha256": "5f0e548a7907900a5a734eb5f4eeb3999645d30774f4aee775a31f026d280956", "withdrawn": "", "abstract": "In this talk we will discuss recent progress in the study of combined deformation spaces of stable sheave over Calabi-Yau Varieties. Recent results in heterotic string theory have shown that there are invariant properties of such moduli spaces that survive across topology changing transitions in Calabi-Yau manifolds. In particular we will study how classes of slope stable, holomorphic vector bundles can be \"extended\" through conifold transitions of Calabi-Yau manifolds (binational contractions followed by smoothing). Such correspondences are linked to moduli spaces of Higgs bundles over complex surfaces via heterotic/F-theory duality.", "id": "Paper/69873", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69873"}, {"title": " Heterogeneous Nonlocal Models: From Interior Dynamics to Boundary Behavior ", "webprogram_exclude": "0", "session_ids": ["Session/18378"], "source_sha256": "925ccb24ef4ae3ede3c53e3f1a60290d5ca3bc286d02994f7531fb815e0cfba9", "withdrawn": "", "abstract": "Nonlocal models have emerged as a powerful framework for describing phenomena that classical continuum mechanics struggles to capture in applications such as fracture, damage, phase transitions, and image discontinuities. By relying on integral operators, nonlocal systems admit low-regularity and discontinuous solutions without the need for ad hoc enrichments. \nIn this talk I will present basic nonlocal formulations for elasticity, diffusion, conservation laws, as well as some geometric aspects for studying curvature for boundaries that lack (classical) $C^2$ regularity. \n\nA central theme will be the role of heterogeneity and boundary interactions, modeled through spatially varying operators and nonlocal boundary conditions. For these systems, I will discuss recent analytical results (including in the nonlinear regime) obtained with students and collaborators. Particular emphasis will be placed on the limiting behavior of heterogeneous nonlocal systems as the interaction horizon tends to zero. In this regime, we identify the corresponding local (differential) models, clarify their physical interpretation, and highlight open problems and future directions motivated by applications in continuum mechanics, biology, image processing, and beyond.", "id": "Paper/69874", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69874"}, {"title": " Why You Should Teach Rings First in Abstract Algebra: The Case of Associativity ", "webprogram_exclude": "0", "session_ids": ["Session/18068"], "source_sha256": "abe225b83348e1b1db8d99afcdf0a1b6e22b4d50eef1c5c5a177a333d03fb685", "withdrawn": "", "abstract": "The associative property is a persistent but often overlooked difficulty for students in abstract algebra. Teaching groups first, especially with unfamiliar binary operations like the composition of symmetries of an equilateral triangle, can further obscure the role of associativity in algebraic structures. Multiple studies have found that at least half of students completing a group theory course are not able to demonstrate whether an operation is associative and are not able to distinguish the associative property from the commutative property. In this study I compare two introductory abstract algebra courses, one groups-first and one rings-first, taught by the same professor using the same course materials. The rings-first sequence leveraged the familiarity of the integers as a starting example of a ring. My analysis shows that this approach allowed students to attend to the structural significance of often-overlooked properties including associativity, and supported these students to substantially outperform their groups-first peers on validated assessment questions concerning associativity and commutativity.", "id": "Paper/69877", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69877"}, {"title": " Player-wise sketch-and-project for quadratic minimax problems ", "webprogram_exclude": "0", "session_ids": ["Session/17908"], "source_sha256": "dfd5e4413e3f219471a5ce1be2edc1ec392f717a1a77e47f7ac9d3a4a04016e5", "withdrawn": "", "abstract": "In this talk, we develop a randomized player-wise sketch-and-project (SP) framework for solving quadratic minimax problems. In the scheme, each player performs a projection onto a random sketch of its own stationary equations, while holding the opponent’s current iterate fixed. This design preserves the player-wise structure and exploits only partial player information in each update, which alleviates the computation burden of forming and processing the full system. We establish linear convergence for the proposed algorithm under structural assumptions that balance player curvature against cross-player coupling. Joint work with Nicolas Loizou.", "id": "Paper/69884", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69884"}, {"title": " Model selection for dynamical systems in the sparse-data, large-library regime ", "webprogram_exclude": "0", "session_ids": ["Session/18319"], "source_sha256": "796b34568576e1b8846bb35b36f0857b90b54f648dfb1500675b4ae74bcb9348", "withdrawn": "", "abstract": "Data-driven discovery algorithms for dynamical systems, such as SINDy and its variants, recover governing equations by selecting a few active terms from a library of candidates. When data is limited, or the library is large due to insufficient knowledge about the system, the library can exhibit collinearity, resulting in a setting where many competing structures fit the data equally well. We develop a method to select among these structures, and show that the margin between the true system and its decoys is a key quantity for determining whether the true system can be recovered. The method has two interacting parts: (1) given a number of terms $k$, a best-subset search returns the $k$ terms that best fit the data, and (2) sweeping $k$ produces a residual curve whose elbow determines how many terms the model should have. We test our method on ODEs, PDEs, and delay equations in the low-data, large-library regime and find that it recovers the correct structure despite high collinearity in the library, which often causes other thresholding-based methods to fail. The method also produces a confidence metric for the recovered structure, providing a way to identify models for systems where data is scarce or the underlying structure is poorly known.", "id": "Paper/69886", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69886"}, {"title": " Extremal Projector for The Virasoro Algebra ", "webprogram_exclude": "0", "session_ids": ["Session/18372"], "source_sha256": "d698639aed04c443e27a872e38a0973059816c40d62f02313ca89662b765b59f", "withdrawn": "", "abstract": "Extremal projectors are among the most powerful and algebraically subtle constructs in modern Lie theory, representation theory, and mathematical physics. \n\nFormally, an extremal projector is an element lying in a completed rational extension of the universal enveloping algebra $\\widehat{U}'(\\mathfrak{g})$ that projects any module from the BGG category $\\mathcal{O}$ onto its subspace of highest-weight vectors. Their existence and uniqueness (as formal series) are established for a broad range of Lie (super)algebras, quantum groups and Kac-Moody algebras.\n\nIn a 1997 paper, Sophie Chemla conjectured the existence of an extremal projector for the Virasoro algebra. We prove Chemla's conjecture in the affirmative by providing an explicit construction of this operator via an iterative computation of its formal series coefficients.", "id": "Paper/69889", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69889"}, {"title": " Emergence in Directed Networks is Bounded by Boundary-Crossing Paths ", "webprogram_exclude": "0", "session_ids": ["Session/19345"], "source_sha256": "1034123bf1fe1eb05a64e60a1b61a74609bd9e4f156ab9fa4be1f90b74fdd6c0", "withdrawn": "", "abstract": "We propose a rigorous, computable notion of emergence for finite directed graphs. An observation is a graph operator Phi (a bounded graph power, a threshold, or a quotient by a partition), and two subsystems interact by adjoining a prescribed set of cross-edges. Emergence is the discrepancy between observing the joined system and joining the observed parts: the edges present in the observed whole but absent from the combined views of the parts. Our main theorem bounds it combinatorially: for observations built from paths of length at most L, the number of emergent edges is at most the number of simple paths of length at most L that cross the interaction boundary and are preserved by the observation. The proof assigns each emergent edge a distinct crossing path as witness, attributing every instance of emergence to a specific route through the cut. We characterize when the bound is tight, show that emergence requires an observation able to resolve a route rather than a single edge, and confirm the theory by exact path enumeration on standard network models.", "id": "Paper/69890", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69890"}, {"title": " An Unconditionally Stable, Energy-Preserving Finite Element Method with Adaptive Filtering for Geotactic Bioconvection ", "webprogram_exclude": "0", "session_ids": ["Session/18220"], "source_sha256": "fd5f34645ebc58d41d5c304e6d3eb34a518b533e2c8499acb5d9c49902382b9c", "withdrawn": "", "abstract": "Geotactic bioconvection describes the large-scale flow patterns that arise in suspensions of swimming microorganisms exhibiting negative geotaxis. Such systems arise in applications including microbial transport, bioreactor design, and microfluidic systems. The organisms preferentially swim upward and accumulate near the upper surface, creating a top-heavy density distribution that becomes unstable and drives convection. At sufficiently large bioconvective Rayleigh numbers, the resulting flow can exhibit complex, chaotic dynamics analogous to those observed in thermal convection with high Rayleigh number.\n\nAccurate simulation of this regime requires resolving the coupled Navier--Stokes and microorganism concentration equations over long time intervals, making direct numerical simulation on sufficiently fine meshes computationally expensive. We introduce a spatially adaptive Leray-$\\alpha$ regularization for geotactic bioconvection designed to reduce the computational cost of simulations with under resolved mesh. The convecting velocity is obtained through an adaptive differential filter that introduces regularization primarily in regions where additional stabilization is needed.\n\nWe develop a finite element discretization that preserves key structural properties of the underlying bioconvection model, including microorganism mass conservation and the kinetic energy structure. We also analyze the effect of the filter parameters and present numerical experiments in both moderate and high Rayleigh number regimes. The results demonstrate that the adaptive filtered model can reproduce important long-time dynamics of substantially finer unfiltered simulations while using considerably coarser spatial resolution.", "id": "Paper/69892", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69892"}, {"title": " Simultaneous non-vanishing of central values via Rankin-Cohen brackets ", "webprogram_exclude": "0", "session_ids": ["Session/17450"], "source_sha256": "a2b31f70c7d43d8a19863ac96aad1b34b12b6f293eea4a50b167374c0d03d31c", "withdrawn": "", "abstract": "In this talk I will present a new result on the simultaneous non-vanishing of quadratic twists of central values of L-functions for arbitrarily large sets of Hecke eigenforms.", "id": "Paper/69898", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69898"}, {"title": " Arithmetic intersections on non-split Cartan modular curves ", "webprogram_exclude": "0", "session_ids": ["Session/17903"], "source_sha256": "8f16c7f6e032e38a86e891836abd3d54f4f433137ef4be26562514c5936b5093", "withdrawn": "", "abstract": "Take two elliptic curves with complex multiplication over a number field, each equipped with a level structure preserved by all endomorphisms. At which primes $p$ does there exist a isomorphism between the elliptic curves mod $p$ that preserves the level structures? This question was answered for $\\Gamma_0(N)$ level structure (that is, for elliptic curves with a designated cyclic order $N$ subgroup) by Gross, Kohnen, and Zagier in 1987. A key step in their proof is showing that an isomorphism mod $p$ determines embeddings of the (quadratic) CM orders into a common (quaternion) Eichler order. In this talk, we will discuss what changes in the argument when we replace $\\Gamma_0(N)$ with the normalizer of a non-split Cartan subgroup. This is joint work with Elie Studnia and Jan Vonk.", "id": "Paper/69899", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69899"}, {"title": " On the Spread of Graphs in Euclidean Spaces ", "webprogram_exclude": "0", "session_ids": ["Session/19354"], "source_sha256": "45858853a71bce75fa3c3924224e7389b48995708691a76eeb2966c9a5d69ee5", "withdrawn": "", "abstract": "Let $\\Gamma(G,d)$ denote the set of all mappings from the vertex set, $V(G)$ of a graph $G$ into $\\mathbb{R}^d$, where $d$ is a positive integer. \nWe define the \\textit{spread function} of $G$ in dimension $d$ by\n\\[g(G,d) = \\inf\\limits_{\\alpha\\in \\Gamma(G, d)} \\frac{\\max\\limits_{x\\sim y} |\\alpha(x) - \\alpha(y)|}{\\min\\limits_{x\\sim y} |\\alpha(x) - \\alpha(y)|}.\\] \n\nEquivalently, by restricting ourselves to the set $\\Phi(G,d) \\subset \\Gamma(G,d)$, consisting of all mappings $\\phi: V(G)\\to \\mathbb{R}^d$ such that the distance between any two adjacent vertices $x\\sim y$, is at least $1$.\nUnder this normalization, the spread function is the infimum, over all mappings in $\\Phi(G,d)$, of the  maximum distance between adjacent vertices. \n\nIn this work, we investigate metric embeddings of graphs into Euclidean spaces of varying dimensions, and study bounds and exact values of the spread function for selected graphs. \nBy leveraging chromatic number and homomorphism, we derive general theorems that yield sharper bounds and more efficient computations of spread function.\n\n\n  \\medskip\n\n  Keywords: metric graph embeddings, graph embeddings, spread function, chromatic number", "id": "Paper/69900", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69900"}, {"title": " Smooth and stable Euler implosions ", "webprogram_exclude": "0", "session_ids": ["Session/17822"], "source_sha256": "0f55394003701a1c76250bb970512f316cb9f0ffc24d5e23cda1d2285f5310f7", "withdrawn": "", "abstract": "In this talk, we will discuss recent developments in the study of imploding singularities in the compressible Euler equations and their connections to singularity formation in other equations. We will then present a new class of smooth implosions for the non-isentropic compressible Euler equations and quantitatively characterize the stability of the corresponding profiles under both radially symmetric and non-radial perturbations. This is joint work with Steve Shkoller and Vlad Vicol.", "id": "Paper/69901", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69901"}, {"title": " On the combinatorics of orthogonal Gaussian polynomials ", "webprogram_exclude": "0", "session_ids": ["Session/17968"], "source_sha256": "1fb4825e1e748c54e4ec52d2f27b9ed6f510d786d57bebe13213fc689274031f", "withdrawn": "", "abstract": "In a recent work of Krattenthaler, Kronholm, and Marsh, they studied the Gaussian polynomials ${n+m\\brack m}$ from an orthogonal point of view and proved their generating function for $m$ up to $6$. In this talk, we will treat these vertical generating functions from a combinatorial perspective. We will first present a bijection which explain the connection between partitions inside an $n\\times m$ box and partitions counted by those vertical generating functions. After that, we will investigate the congruence property of those vertical generating function. We shall take $m=4$ as an example and show the congruence property mod any odd prime number $\\ell$. A crank that witness these congruence will also be given. And, through our bijection, we can show that this crank is equivalent to those that witness the congruences of the Gaussian polynomials from the horizontal point of view.", "id": "Paper/69902", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69902"}, {"title": " Syzygies of pointed curves in weighted projective space ", "webprogram_exclude": "0", "session_ids": ["Session/18219"], "source_sha256": "88e4a625c0832b5982146bd5da4b506ae8339800eb929a54924b9cfc4ee8b8dc", "withdrawn": "", "abstract": "A strictly ample line bundle induces an embedding of a smooth curve $C$ into a weighted projective space. We discuss the syzygies of embeddings by strictly ample line bundles of the form $O_C(dP)$ for $P$ a point on $C$, including bounds on the degrees of nonvanishing Betti numbers and a weighted version of Green's $N_p$ conditions.", "id": "Paper/69903", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69903"}, {"title": " Multiple Transmission Pathways and Disease-Nutrient Feedbacks in an Oak Wilt Model ", "webprogram_exclude": "0", "session_ids": ["Session/19359"], "source_sha256": "0d01b3fffb0196500e5592383437406d300cca13a4ead05866080905e5870322", "withdrawn": "", "abstract": "Oak wilt spreads through two distinct pathways: belowground transmission through root connections and vector-mediated transmission that can establish new infection centers. To investigate how these pathways interact with nutrient-disease feedbacks, we extend a disease-mediated nutrient dynamic framework to include both nutrient-dependent host-to-host transmission and vector-mediated transmission. The model couples susceptible and infected host biomass with nutrient cycling and uncontaminated and contaminated vector abundance. Using bifurcation analysis, we examine how nutrient availability and vector abundance influence disease invasion, persistence, and long-term dynamics. Our results show that increasing vector abundance produces only a small change in the nutrient threshold for disease persistence but substantially alters the stability of the endemic state. In particular, higher vector abundance narrows the range of nutrient availability that supports sustained oscillations and, at a fixed nutrient level, can shift the system from persistent oscillations to damped oscillations and eventually to a stable endemic state. We also explore how changes in key transmission processes can inform potential disease management strategies. These results highlight how multiple transmission pathways and disease-nutrient feedbacks jointly shape oak wilt persistence and long-term dynamics.", "id": "Paper/69906", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69906"}, {"title": " Invariant differential forms on polyhedral spaces ", "webprogram_exclude": "0", "session_ids": ["Session/18297"], "source_sha256": "4173a5c3b5c2cf928d9522b6cacc83183f2eb1d2834f16528d72092750294b73", "withdrawn": "", "abstract": "Let $K$ be a number field with ring of integers $\\mathcal{O}_K$. We study the cohomology of the general linear group $\\mathrm{GL}_n(\\mathcal{O}_K)$ by relating it to the cohomology of its locally symmetric space $X$. Specifically, by Voronoi's reduction theory, the space $X$ admits a $\\mathrm{GL}_n(\\mathcal{O}_K)$-invariant decomposition into polyhedral cones, which allows us to describe a cone-by-cone algebraic compactification of the quotient space $X/\\mathrm{GL}_n(\\mathcal{O}_K)$. Using this construction, we find new non-zero cohomology classes of $\\mathrm{GL}_n(\\mathcal{O}_K)$, via differential forms on the quotient space $X/\\mathrm{GL}_n(\\mathcal{O}_K)$ induced from the stable cohomology of the group. This is based on work in progress, joint with Francis Brown and Melody Chan.", "id": "Paper/69907", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69907"}, {"title": " New results on the distribution of orders in number fields ", "webprogram_exclude": "0", "session_ids": ["Session/18335"], "source_sha256": "de95e314d510162a81c731a1c300ab4f5ebcd7fc9cd105c794f84dc2889ade49", "withdrawn": "", "abstract": "In this talk I will present some new results on the distribution of orders in number fields.", "id": "Paper/69908", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69908"}, {"title": " Nonstandard discretization and Integration factors in tracking Advection dominated Contaminant transport ", "webprogram_exclude": "0", "session_ids": ["Session/17765"], "source_sha256": "9a55aef1dbf1b3f2fb2cd9ea28b7f69bd75fb82b72179a2d21111336109007ac", "withdrawn": "", "abstract": "Chemical and microbial contamination of water is extremely harmful for public health. Therefore, it is important to understand how contaminants are transported in waterbodies if one is to devise remediation strategies. This presentation will show how differential equation models are constructed to study contamination of waterbodies making use of laboratory and field data. Further, we will demonstrate how concepts such as “integration factor” and “nonstandard discretization” could be employed in computing the exact concentration profile for advection dominated contaminant transport.", "id": "Paper/69909", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69909"}, {"title": " Controlled Generation with Diffusion and Flow Models: A Variational Approach to Inverse Problems and Image Inversion ", "webprogram_exclude": "0", "session_ids": ["Session/18293"], "source_sha256": "7cceff7d0183d57b315037bb5be6bd0b0103c68c4571083d3fe825075e7f37df", "withdrawn": "", "abstract": "This talk presents a unified variational framework for solving inverse problems and image inversion using diffusion and rectified-flow priors. Building on Mitter and Newton’s variational approach to nonlinear estimation, we formulate both tasks as optimal control problems for generative dynamics. For diffusion inverse problems, the objective combines observation fidelity with a relative-entropy cost on path space. Its optimal controlled process realises the posterior path measure under suitable conditions. For image inversion, the corresponding objective balances reconstruction fidelity against the energy required to alter the reference flow, producing a controlled trajectory that reconstructs a given image and supports subsequent editing.\n\nThe nonlinear dependence of the score and velocity fields on the state makes these control problems computationally challenging. We use first-order variations to linearise the dynamics locally and quadratic approximations to the cost. This procedure yields a sequence of local linear–quadratic Gaussian control problems for stochastic diffusion dynamics and their deterministic counterparts for rectified flows. Differential dynamic programming provides numerical solutions through backward value recursions and forward trajectory updates.\n\nWe evaluate the framework on image editing using PIE-Bench dataset and on inverse problem we use FFHQ dataset. The competitive results across these tasks illustrate how a common variational control framework can support posterior inference, image reconstruction, and controlled generation.", "id": "Paper/69910", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69910"}, {"title": " Hypoelliptic Differential Operators and Nilpotent Lie Groups ", "webprogram_exclude": "0", "session_ids": ["Session/18256"], "source_sha256": "627af148034aed94e95efc9e6f3ab7a755f87f9cd66e25834f695ca3fd402e28", "withdrawn": "", "abstract": "It is a classic result that if a twice continuously differentiable function is harmonic, then it must be infinitely differentiable. This regularity property of harmonic functions is reflected in a basic analytic property of the Laplacian, namely that it is elliptic. There has been recent interest in studying hypoelliptic differential operators which generalize this regularity property of the Laplacian, and the proper study of such operators requires use of the representation theory of nilpotent Lie groups. We will provide a new family of first order hypoelliptic differential operators one can associate to any nilpotent Lie group. Moreover, the construction can be generalized to filtered manifolds providing nontrivial examples of hypoelliptic differential operators with non-vanishing Fredholm index. This is joint work with Andres Franco Valiente.", "id": "Paper/69912", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69912"}, {"title": " Regular polyhedra over finite fields ", "webprogram_exclude": "0", "session_ids": ["Session/17903"], "source_sha256": "1d7c72d59c660931c83a5e16f616b21d89f3dd89cf2113b4c77c226218116396", "withdrawn": "", "abstract": "In \\textit{Esquisse d'un Programme}, Grothendieck introduced a notion of regular polyhedra over finite fields and asked for a classification.  In this talk, we will explain his definition and how it fits into the modern theory of polytopes.  Then we will answer his question by relating these polyhedra to triangular modular curves, simultaneously computing some new cases of monodromy groups of triangular modular curves.", "id": "Paper/69915", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69915"}, {"title": " A Banking Stress Test Case Study for Teaching Regression Modeling ", "webprogram_exclude": "0", "session_ids": ["Session/19341"], "source_sha256": "3d7fdf254cc54b98568ff2410762f252c7ecc27c45c852c1a225e87f6e0c3061", "withdrawn": "", "abstract": "Bank stress testing provides a practical example for teaching regression modeling.  In this case study, students work with quarterly historical data from a hypothetical commercial bank and examine pre-provision net revenue (PPNR), an important measure used in the stress-testing process.  The data include PPNR as well as several of its components and related financial variables.  Students first explore the data and identify factors that appear to be important in explaining changes in PPNR. They then develop regression models, compare different model choices, and use the selected variables to forecast PPNR for future periods. As part of the project, students are also asked to interpret their results and discuss possible recommendations based on the model.  The project is designed to help students see how regression can be used in a realistic financial setting.  This case study was previously published in PRIMUS as part of the article ``Integrating Real-World Data into Actuarial Science Teaching: Examples and Challenges.\"", "id": "Paper/69919", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69919"}, {"title": " Advancing Neural Network Performance through Emergence-Promoting Initialization Scheme ", "webprogram_exclude": "0", "session_ids": ["Session/18354"], "source_sha256": "caf97a4d21de40b0c398fae3220fdd52a14eec378103b56638e264e1b1e15055", "withdrawn": "", "abstract": "Emergence in machine learning refers to the spontaneous appearance of complex behaviors or capabilities that arise from the scale and structure of training data and model architectures, despite not being explicitly programmed. We introduce a novel yet straightforward neural network initialization scheme that aims at achieving greater potential for emergence. Measuring emergence as a kind of structural nonlinearity through derived functors, our method adjusts the layer-wise weight scaling factors to achieve higher emergence values. This enhancement is easy to implement, requiring no additional optimization steps for initialization compared to GradInit. We evaluate our approach across various architectures, including MLP and convolutional architectures for image recognition and transformers for machine translation. We demonstrate substantial improvements in both model accuracy and training speed, with and without batch normalization. The simplicity, theoretical innovation, and demonstrable empirical advantages of our method make it a potent enhancement to neural network initialization practices. These results suggest a promising direction for leveraging emergence to improve neural network training methodologies.", "id": "Paper/69920", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69920"}, {"title": " Constitutive Surrogates for Differentiating Black-Box Flux Relations ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "25ad96837d6164984e04c017fc7cf89928497214a55ff78ad04d9f212d6bb8d4", "withdrawn": "", "abstract": "The finite element method (FEM) is a numerical discretization technique used to find approximate solutions to partial differential equations (PDEs). Oftentimes, the governing constitutive law of a given PDE system is nonlinear. In the linearization step, FEM solvers require the law's derivatives; the quality of these derivatives directly affects the solver's accuracy and rate of convergence. When the constitutive law is not available as an analytic closed-form expression, its derivatives are difficult to evaluate. In this project, we consider a thermal flux model given by a deterministic black-box oracle and approximate its derivatives by fitting differentiable local surrogates. We primarily investigate Gaussian processes for their variance estimates and adaptive posterior updates, which are well suited to iterative refitting in the black-box setting. Additionally, we explore the effects of (1) physically informed monotonicity constraints on derivative accuracy and (2) random feature methods on model scalability. In detailed numerical experiments, we show that Gaussian processes with monotonicity constraints and random Fourier feature approximations to the covariance kernel are effective derivative providers for FEM.", "id": "Paper/69921", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69921"}, {"title": " More about deformation of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.741ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 749.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">F</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-46\" d=\"M48 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H742Q749 676 749 669Q749 664 736 557T722 447Q720 440 702 440H690Q683 445 683 453Q683 454 686 477T689 530Q689 560 682 579T663 610T626 626T575 633T503 634H480Q398 633 393 631Q388 629 386 623Q385 622 352 492L320 363H375Q378 363 398 363T426 364T448 367T472 374T489 386Q502 398 511 419T524 457T529 475Q532 480 548 480H560Q567 475 567 470Q567 467 536 339T502 207Q500 200 482 200H470Q463 206 463 212Q463 215 468 234T473 274Q473 303 453 310T364 317H309L277 190Q245 66 245 60Q245 46 334 46H359Q365 40 365 39T363 19Q359 6 353 0H336Q295 2 185 2Q120 2 86 2T48 1Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-46\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-regularity ", "webprogram_exclude": "0", "session_ids": ["Session/17929"], "source_sha256": "14bfdf131ee3835185686b71d5f2c900556340183075517c4e9b381bf856c5a2", "withdrawn": "", "abstract": "Let $(R, \\mathfrak{m})$ be an $F$-finite local ring of characteristic $p>0$ and $f\\in \\mathfrak{m}$ a nonzerodivisor. Under what conditions on $R$ does strong $F$-regularity of $R/fR$ imply strong $F$-regularity of $R$ itself? \n\nSingh (1999) constructed families of rings of characteristic $p \\geq 3$ for which $R/fR$ is a strongly $F$-regular surface but $R$ is not even $F$-pure, showing that $F$-regularity need not deform in odd characteristic; the case of characteristic $2$ has remained open. We construct rings of every positive characteristic, including characteristic $2$, for which $R/fR$ is a toric (hence strongly $F$-regular) surface and $R$ is not $F$-pure. \n\nAdditionally, we give sufficient conditions for strong $F$-regularity to deform from $R/fR$ to $R$, including a result which holds only in characteristic $2$: if $p=2$, the embedding dimension of $R$ is at most $5$, and $R/fR$ is strongly $F$-regular, then $R$ is strongly $F$-regular. Our examples show that these positive results are essentially optimal.", "id": "Paper/69922", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69922"}, {"title": " On an ancient stacked pancake solution to mean curvature flow ", "webprogram_exclude": "0", "session_ids": ["Session/17691"], "source_sha256": "69f0ca7f47c73e562550867794a8ae4ae24c73075f32d642e10f6bce99f7a54f", "withdrawn": "", "abstract": "After giving a brief survey of ancient solutions and their importance in the mean curvature flow I’ll discuss a new solution to MCF, qualitatively corresponding to the “stacking” of two ancient pancakes, constructed in a recent joint work with Louis Yudowitz.", "id": "Paper/69924", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69924"}, {"title": " The monodromy of compact Lagrangian fibrations ", "webprogram_exclude": "0", "session_ids": ["Session/18268"], "source_sha256": "3d97549a93666886dac5cf6af4f6bfe3d26a65f67d450c36b8afedae9068449a", "withdrawn": "", "abstract": "We analyze the monodromy of the local system underlying holomorphic Lagrangian fibrations $f: X \\to B$, where $X$ and $B$ are compact K\\\"ahler manifolds. In the case where $X$ is a primitive symplectic variety and $f$ is not isotrivial, we show that the local system is irreducible over $\\mathbb{C}$. As an application, we consider the Hitchin fibration $h: \\mathcal{M}_\\mathrm{Dol}(C, r) \\to \\mathbb{A}^N$ on the moduli space of Higgs bundles $\\mathcal{M}_\\mathrm{Dol}(C, r)$, for $C$ a smooth curve of genus $g \\geq 2$. We show that in this setting, the local system underlying $h$ is also irreducible over $\\mathbb{C}$.", "id": "Paper/69930", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69930"}, {"title": " Artificial ReLU Networks’ Discrete and PL Morse Decompositions ", "webprogram_exclude": "0", "session_ids": ["Session/18007"], "source_sha256": "af678e35b72c6bde5477d900b904fe6aa545bb671e0d1a60773f06c71bb96752", "withdrawn": "", "abstract": "ReLU neural networks (multilayer perceptrons) decompose their input space into polyhedral complex with particular combinatorial characteristics derived from oriented matroids of their layers' affine functions. This characterization is useful for encoding topological properties of a given network function, and we discuss its theoretical properties, its utility in accessing PL and Discrete Morse measures of function complexity, and issues surrounding its computation, especially in the presence of regions on which the function is constant.", "id": "Paper/69932", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69932"}, {"title": " Favorite problems from the UWM Math Teacher Circle ", "webprogram_exclude": "0", "session_ids": ["Session/18212"], "source_sha256": "11a20b282f28710ea994fc9bf3a0020c570a62cf4a5e120caecaeb4bd8246d8f", "withdrawn": "", "abstract": "The UWM Math Teacher Circle gives teachers time and space to collaborate across schools while engaging with challenging problems and authentically doing mathematics. Participants develop their identities as mathematical thinkers by experiencing the challenges and rewards of exploring new ideas, asking questions, reasoning, and building understanding with others. Our goal is to strengthen teachers’ mathematical identities in ways that influence their classroom practice and, in turn, support stronger mathematical identities among their students. In this talk, we briefly describe our approach to organizing and sustaining a Math Teacher Circle and share some of our favorite activities.", "id": "Paper/69935", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69935"}, {"title": " Demographic Stochasticity in a Discrete-Time Stage-Structured Model for Tree-of-Heaven ", "webprogram_exclude": "0", "session_ids": ["Session/19370"], "source_sha256": "fe7728acd3121afa6fd595ed421a8cad05d8717667455aef50cc7b08f8682bcd", "withdrawn": "", "abstract": "We develop a stage-structured stochastic model for tree-of-heaven (Ailanthus altissima). In the model, each individual belongs to one of four life-history stages: seed, seedling, root sprout, or reproductive adult. We incorporate stage-specific survival and development together with density-dependent sexual reproduction through seeds and clonal reproduction through root sprouts. We estimate the model parameters using reported life-history properties of tree-of-heaven. We derive the basic reproductive number, \\mathcal{R}_0, to characterize population extinction and persistence. We incorporate demographic stochasticity by modeling individual survival and stage transitions using multinomial distributions and reproduction using Poisson distributions. We investigate stochastic variability and the effects of different life-history stages on population establishment. We also discuss corresponding stage-specific control strategies. This modeling framework can be applied to other invasive plant species to study their population dynamics and management.", "id": "Paper/69936", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69936"}, {"title": " Algorithmic Classification of Quasi-Homogenous Calabi-Yau Fourfold Singulariities ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "b3a50dffdf2b8541e71b677ff6c9a043fb2065ddb83efb90bcf25d930b7ca255", "withdrawn": "", "abstract": "Through geometric engineering, mathematicians can generate quantum field theories from singularities. However, writing down all mathematically valid singularities quickly becomes a tedious classification problem. This project studies a computationally manageable class of quasi-homogeneous Calabi–Yau fourfold singularities. I first classify isolated, invertible hypersurfaces in five complex variables built from Brieskorn–Pham, chain, and loop blocks. Quasi-homogeneity allows us to convert each polynomial into a linear system whose solution yields their rational scaling weights. Then, a positivity condition on the weights allows us to easily test their admissibility. By using a Python algorithm that searches for valid finite and infinite cases through studying limits where certain exponents become arbitrarily large, we can find all infinite families of the three classes. The algorithm yielded 133 Brieskorn–Pham infinite families, 23 chain families, and 10 loop families up to cyclic symmetry. The second part of the paper is a natural extension of the classification from hypersurfaces, which are defined by one equation, to singularities defined by multiple equations. When these equations define a complete intersection with an isolated singular point, they are called  isolated complete intersection singularities (ICIS). Both cases utilize the same basic principles: variables have weights, equations have degrees, and the holomorphic volume form has weight ∑︁wi − ∑︁dj. A similar admissibility test arises in this case, but the main difficulty lies in determining whether a singularity is isolated .For a hypersurface, this can be studied using a single gradient, but for an ICIS, the partial derivatives form a larger Jacobian matrix. Rather than checking the matrix directly at every point, I use a theorem by C. T. C. Wall that allows us to test whether a given set of weights and equation degrees can support an isolated complete intersection through a finite set of tests on subsets of variables. Because these tests depend only on the integer weights and equation degrees, they can be implemented directly in Python. This gives a practical way to extend the classification from hypersurfaces to complete intersections.", "id": "Paper/69945", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69945"}, {"title": " Rational degree of Boolean functions ", "webprogram_exclude": "0", "session_ids": ["Session/18090"], "source_sha256": "9719766b03952ccd9c8062ebfbe6d51141308b4ce81021b2e18852e9084bb0f7", "withdrawn": "", "abstract": "The degree $\\deg(f)$ of a Boolean function $f\\colon \\{0,1\\}^n \\to \\{0,1\\}$ is the minimum value of $\\deg(p)$ such that $p$ is a real polynomial and $f = p$ on $\\{0,1\\}^n$. The rational degree $\\mathrm{rdeg}(f)$ of $f$ is the minimum value of $\\max(\\deg(r),\\deg(s))$ such that $p,q$ are real polynomials and $f=r/s$ on $\\{0,1\\}^n$. Clearly, $\\mathrm{rdeg}(f) \\leq \\deg(f)$ as can be seen by taking the denominator $s$ to be $1$. On the other hand, it is unclear whether $\\mathrm{rdeg}(f)$ could be much smaller than $\\deg(f)$.\n\nWe prove that $\\deg(f) \\leq \\widetilde{O}(\\mathrm{rdeg}(f)^3)$ for every Boolean function $f$. This resolves the second of the three open problems stated by Nisan and Szegedy, and attributed to Fortnow, in 1994.", "id": "Paper/69956", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69956"}, {"title": " From Training Ground to Transfer Window: Advising an MCM Team on Real-World Financial Modeling ", "webprogram_exclude": "0", "session_ids": ["Session/18066"], "source_sha256": "e5543ab0b2bccd33244b0babed59c7c7f9af385cf5b31d4f020755469fc6c2cf", "withdrawn": "", "abstract": "As the faculty advisor of Team 2600072, a [Finalist] in the 2026 MCM (Problem D), I will reflect on guiding a team through a financial modeling problem with clear real-world relevance. Professional football clubs are businesses that must allocate limited capital across competing uses while managing risk, revenue uncertainty, and regulation. My students built a dynamic decision model for VfL Wolfsburg that linked investment, on-field performance, revenue, and financial reserves in a feedback loop, and used Pareto optimization to balance short-term returns against long-term sustainability. They extended the model to include the Bundesliga's 70 percent squad cost limit, price elasticity in ticket pricing, and injury risk. These questions of capital allocation, regulatory constraints, pricing, and risk management are the same questions faced by firms and financial decision-makers far beyond sports.\n\nOur preparation rested on three pillars: modeling training (standard models, their principles, and when each applies), programming training (building model frameworks in MATLAB, Python, or C++), and visualization training (producing clear, complete figures). Students also studied many past winning papers. During the contest, the team reviewed every problem before choosing one, then fixed a solution framework early. After the contest, they launched a public website forecasting European football results and compared the forecasts with end-of-season outcomes.\n\nThe contest was an intense and rewarding experience. It taught the students to work under pressure, divide tasks, and communicate complex ideas clearly, and it showed them that financial models must be tested against real data. For me as an advisor, it strengthened my focus on problem framing, honest discussion of assumptions, and follow-up projects that connect mathematics to real financial decisions. I will discuss what worked, what was challenging, and how the experience shaped both my students and my teaching.", "id": "Paper/69958", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69958"}, {"title": " Computational Resolution of Index Form Equations in Quintic Number Fields ", "webprogram_exclude": "0", "session_ids": ["Session/19355"], "source_sha256": "244d242daaee5d72e33c8020430651ce732632a3540c8bd56d5330f9aca2cd65", "withdrawn": "", "abstract": "Let $K$ be a number field of degree $n$ and $\\mathcal O_K$ be its ring of integers. An \\emph{index form equation} seeks all primitive $\\alpha\\in\\mathcal O_K$ such that the index of the order generated by the power basis $\\{1, \\alpha, \\dots , \\alpha^{n-1}\\}$ in $\\mathcal O_K$ is equal to some constant. One application of index form equations is determining whether a field is monogenic, i.e., if $\\mathcal O_K$ can be generated by one element over $\\mathbb Z$. This is equivalent to the index of the resulting power basis being $1$. Currently, there is no efficient fully general method for determining or verifying whether a given number field is monogenic, or for solving index form equations. In their 1999 paper \"Index Form Equations in Quintic Fields\", Gaál and Györy explained an algorithm to solve such equations in degree-$5$ number fields. We present a working and optimized implementation of this algorithm in SageMath, using it to establish the monogeneity of certain quintic number fields in LMFDB where this was previously uncomputed.", "id": "Paper/69981", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69981"}, {"title": " The Generalized Volterra Signature ", "webprogram_exclude": "0", "session_ids": ["Session/18332"], "source_sha256": "ee8bf2b0e55afce619eb3527f042a9573bd2c67839411accdc3330fb3d0850fe", "withdrawn": "", "abstract": "In this paper, we introduce the generalized Volterra signature \\(\\gvsig(\\bX)\\) of a path \\(\\bX\\), extending the classical Volterra signature introduced in [Hager, Harang, Pelizzari \\& Tindel, arXiv:2603.04525, 2026], which extends Lyons' path signature to the Volterra setting. We establish a new algebraic structure to encode the generalized Volterra signature. We also establish a generalized Chen's identity and the shuffle product of signature components for the geometric Volterra signature \\(\\geovsig(\\bX)\\). The shuffle product for the Volterra signature is the first of its kind and allows us to formulate a universal approximation theorem for geometric Volterra signatures. We also provide efficient computational schemes for the generalized Volterra signature. This framework is useful for non-Markovian and memory-dependent problems. We show its effectiveness using both synthetic and real financial data.", "id": "Paper/69984", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69984"}, {"title": " An Extracurricular Training Blueprint for SCUDEM and MCM/ICM Modeling Teams ", "webprogram_exclude": "0", "session_ids": ["Session/19005"], "source_sha256": "4bdab93d759373c3affc96f6a8b61307cdd9ccf9ef29d61ce58a67872b5495d9", "withdrawn": "", "abstract": "The Student Challenge Using Differential Equations Modeling (SCUDEM) and the Mathematical/Interdisciplinary Contest in Modeling (MCM/ICM) are two opportunities for undergraduate students to work on teams to solve real-world problems with mathematical modeling. I will present an extracurricular training blueprint that we are currently using at the University of Florida to help prepare students for participating in these contests. Students attend a variety of hour-long training sessions, which can be scaled up or down depending on how many faculty advisors and graduate student mentors are available to help volunteer their time. I will share tips on what has worked and what hasn’t worked for us so that others can use our framework as a baseline for starting or modifying their own modeling contest training program.", "id": "Paper/69987", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69987"}, {"title": " State-Space Learning and Uncertainty Quantification under Partial Observation in Guam Water-Quality Data ", "webprogram_exclude": "0", "session_ids": ["Session/18280"], "source_sha256": "9b93e6fe43a97db78e65401215a5f8147b34a70294660dfe5ebffb5e0a8a19a3", "withdrawn": "", "abstract": "Environmental monitoring data are often incomplete across variables, locations, and time, creating challenges for understanding the dynamics of the underlying system. This talk examines partial observation in long-term Guam water-quality monitoring data and its implications for state-space learning and uncertainty quantification. We consider how patterns of available and unavailable measurements affect the information that can be extracted from environmental observations and how partially observed measurements can be related to latent system states through state-space models. Observation availability is considered as a time-varying component of the measurement process, allowing us to examine differences across sampling regimes. The study explores approaches for characterizing observation patterns, estimating hidden states, and representing uncertainty when environmental variables are not consistently observed. Particular attention is given to how different forms of partial observation may influence state inference and subsequent prediction. Using Guam water-quality monitoring as a motivating application, this work provides an empirical setting for investigating uncertainty-aware learning in partially observed environmental systems.", "id": "Paper/69990", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69990"}, {"title": " A Nonlinear Cantilever Beam in Kutta-Joukowski Flow ", "webprogram_exclude": "0", "session_ids": ["Session/18283"], "source_sha256": "863a3db180b2e1c125c1736b416a45667fa7b94d9b1679cd4a28559ef339cab1", "withdrawn": "", "abstract": "In this talk, we consider a nonlinear cantilever beam interacting with an inviscid potential flow through Kutta-Joukowski boundary conditions. The coupling introduces a boundary trace term that is not naturally controlled by the energy of the system, creating a central difficulty even at the linear level. We first establish well-posedness for a simplified linearized system using semigroup methods. The full Kutta-Joukowski coupling is then recovered as an admissible boundary perturbation by exploiting a hidden trace regularity of the flow potential.\n\nWe next incorporate a physically derived quasilinear stiffness nonlinearity associated with large beam deflections. Since this nonlinearity cannot be treated as a locally Lipschitz perturbation of the linear generator, a more delicate construction is required. We introduce a regularized system with strong structural damping, construct solutions through a fixed point argument, and derive higher order estimates that are uniform in the regularization parameter. Passing to the limit yields local in time strong solutions for the original nonlinear flow-beam system.", "id": "Paper/69991", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69991"}, {"title": " Operator learning for Mixture Ensemble in Generative Data Assimilation ", "webprogram_exclude": "0", "session_ids": ["Session/17919"], "source_sha256": "9d1fcd59a935c9eca9bf25300f24c27963218046bdd77695c9fd12a237b50e6e", "withdrawn": "", "abstract": "Characterizing the non-Gaussian posterior in partially-observed nonlinear systems remains a central open challenge in data assimilation (DA). The Ensemble Kalman Filter (EnKF) relies on Gaussian assumptions and empirical tuning, while particle filters suffer the curse of dimensionality as state dimension grows. Recent score-based domain adaptation methods require supervised training on ground-truth posterior samples, limiting generalizability where true posteriors are unavailable. No existing method jointly achieves non-Gaussian posterior characterization, scalability, and applicability to general high-dimensional nonlinear systems.\n\nWe propose $\\Omega$ (\\textbf{O}perator-based \\textbf{M}ixture \\textbf{E}nsemble for \\textbf{G}enerative \\textbf{A}ssimilation), a hybrid DA framework integrating Conditional Gaussian Nonlinear System (CGNS) surrogate modeling, unsupervised residual operator learning, annealed Langevin sampling, and Gaussian mixture posterior reconstruction. For each EnKF ensemble member, the CGNS surrogate serves as the forecast model and yields a closed-form Gaussian conditional posterior for unobserved variables, exact under continuous observations and a principled approximation otherwise. Remaining non-Gaussianity is corrected by a residual operator trained unsupervised via Denoising Score Matching on CGNS ensemble members, requiring no ground-truth trajectories; this operator and annealed Langevin Monte Carlo act on the observed and conditioned-mean variables rather than in unobserved space. Corrected means parametrize analytic Gaussian draws, yielding a Gaussian mixture posterior that approximates the full non-Gaussian joint posterior without weight degeneracy.\n\nValidated on the Topographic and Dyad models and on Lorenz-96 (via a fitted surrogate CGNS), $\\Omega$ consistently outperforms EnKF and CGNS-only baselines in posterior accuracy and variable recovery while remaining tractable in high dimensions.", "id": "Paper/69992", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69992"}, {"title": " Radiative Decay of Edge States in a Time-Forced SSH Model ", "webprogram_exclude": "0", "session_ids": ["Session/18443"], "source_sha256": "a68e713b7682d461f1ccb8c9388b88a5d6dc8d6e439688fde47aaef65123b410", "withdrawn": "", "abstract": "We study the effect of time-periodic forcing on the edge state of the semi-infinite Su–Schrieffer–Heeger (SSH) model, a 1D tight-binding model. Numerical simulations and an asymptotic expansion demonstrate that if the frequency of forcing is in resonance with the continuous spectrum of the unforced Hamiltonian, then on a time scale proportional to the inverse square of the forcing amplitude, the edge state decays in amplitude due to the radiation of its energy into the bulk. A proof is work in progress, and makes use of a new dispersive decay estimate for the time-evolution induced by the Hamiltonian.", "id": "Paper/69993", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69993"}, {"title": " On Sum-Freedom of Binary Power Functions ", "webprogram_exclude": "0", "session_ids": ["Session/18311"], "source_sha256": "c151f21c0e96b0d9c76f0bbb56383a39ac14cbedf8417be27de540d3838d97b2", "withdrawn": "", "abstract": "A function from $\\Bbb F_{2^n}$ to $\\Bbb F_{2^n}$ is said to be {\\em $k$th order sum-free} if the sum of its values over each $k$-dimensional $\\Bbb F_2$-affine subspace of $\\Bbb F_{2^n}$ is nonzero. C. Carlet recently introduced this notion as a generalization of almost perfect nonlinear (APN) functions, and the latter are precisely the 2nd order sum-free functions. The APNness of the Welch function $f(x)=x^{2^m+3}$ on $\\Bbb F_{2^{2m+1}}$ was a long-standing conjecture before it was resolved by H. Dobbertin. We give an alternative proof for this result, which leads to a more general algebraic question. We also investigate the 3rd order sum-freedom of the Welch function and power functions of algebraic degree three. We formulate a conjecture about the 3rd order sum-freedom of the power functions of algebraic degree three, which is supported by strong numerical evidence.", "id": "Paper/69997", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69997"}, {"title": " Optimal release of sterile males in the sterile insect technique for Anopheles mosquitoes ", "webprogram_exclude": "0", "session_ids": ["Session/17688"], "source_sha256": "6b3ddbd1cd1d4063c122a3579302118b4e614ea80b67dff37e37c81b180ff4e7", "withdrawn": "", "abstract": "The sterile insect technique (SIT) is a promising strategy for controlling malaria-transmitting Anopheles mosquitoes, but its practical implementation hinges on identifying release protocols that are both effective and resource-efficient. In this talk, I present a mathematical framework for optimizing time-dependent releases of sterile male mosquitoes within a biologically structured population model incorporating nonlinear mating dynamics and life-cycle stages. A key feature of the model is the emergence of an Allee effect induced by mate-finding limitations, creating a threshold below which the wild population collapses naturally. Building on this, I formulate a free-horizon optimal control problem that minimizes the total number of sterile males released while ensuring the population is driven below this threshold. Unlike classical approaches with a fixed terminal time, our formulation uses a state-dependent stopping time corresponding to threshold crossing. I discuss analytical and numerical challenges arising from the geometry of the threshold manifold and the coupling between control intensity and time to elimination. We show that not only do adaptive release strategies can substantially reduce total releases compared to standard protocols, but I show the emergence of so-called singular arc controls as the optimal control solutions. Finally, I explore how mechanisms such as introducing a competing species may further improve SIT efficiency.", "id": "Paper/69999", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/69999"}, {"title": " Forbidden Pairs and Repeated Colors in Friends-and-Strangers Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "76852cba22159645e5d417d7f46e7a84ec9e416665b9c84553fcb149b14f06dd", "withdrawn": "", "abstract": "Given two graphs $X$ and $Y$ on $n$ vertices, the friends-and-strangers graph $\\FS(X,Y)$ has as its vertices configurations of the vertices of $Y$ on the vertices of $X$, where two configurations are adjacent when they differ by swapping two tokens that occupy adjacent vertices of $X$ and are adjacent in $Y$. We let $X$ denote the position graph, where edges mark adjacent positions, and $Y$ the friendship graph, where edges mark friendships. Friends-and-strangers graphs were introduced by Defant and Kravitz and generalize several token-swapping and reconfiguration problems. Previous work has studied both their connectivity and their diameter. In this paper, we study friendship graphs obtained from deleting a sparse graph of forbidden pairs from the complete graph. We determine a sharp maximum-degree condition on the position graph that guarantees connectivity, and prove quadratic bounds on component diameter when the forbidden pairs form a matching. When every token has at most two forbidden partners, we prove a diameter bound of $\\binom{n}{2}+O(n)$ under a minimum-degree condition. We also show that, at the sharp threshold for connectivity, exchanging a single forbidden pair may require quadratically many swaps. We also study cyclic token swapping with repeated colors and determine the   diameter for arbitrary color multiplicities. For a perfect matching of forbidden pairs on a cycle, we establish a formula for the distance between configurations and construct pairs that are quadratically far apart in every connected component.", "id": "Paper/70002", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70002"}, {"title": " Behavior of Solutions in a Multi-Patch Epidemic Model with Saturated Incidence ", "webprogram_exclude": "0", "session_ids": ["Session/19351"], "source_sha256": "64f5861bc324ceb0a85beaa3f11c6db92a1716c1a60c3a5ed3c66b817c762e09", "withdrawn": "", "abstract": "This study investigates the behavior of solutions in a multi-patch epidemic model with a saturation incidence mechanism. When the disease-induced fatality rate is nonzero, we establish that solutions of the model asymptotically approach disease-free equilibria. In contrast, when the disease-induced fatality rate is zero, the model exhibits more complex dynamics. In particular, although the saturation effect reduces the basic reproduction number, $\\mathcal{R}_0$, it may also induce a backward bifurcation of the endemic equilibrium curve at $\\mathcal{R}_0=1$.\n\nUnder suitable assumptions on the model parameters, we provide a detailed analysis of the global dynamics of solutions in relation to the value of $\\mathcal{R}_0$. We further examine the asymptotic profiles of endemic equilibria as the population dispersal rates approach zero, providing insight into the effects of limited movement between patches on disease persistence. Finally, numerical simulations are presented to illustrate and support the theoretical results.", "id": "Paper/70004", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70004"}, {"title": " Dickson Polynomials and Self-reciprocal Polynomials ", "webprogram_exclude": "0", "session_ids": ["Session/17756"], "source_sha256": "a34ac38a1f9f81ded95ced1844e7cfcef839a5c159ef638b692d11271ce76137", "withdrawn": "", "abstract": "Dickson polynomials of the first kind were introduced by Leonard Eugene Dickson in the 1890s in the context of investigating polynomials that induce permutations of finite fields. They have many notable algebraic properties and are widely used in cryptography, coding theory, and polynomial research. The introduction of Dickson polynomials of the (k+1)-th kind in 2012 unified earlier approaches and offered new insights into their behavior over different algebraic structures. Self-reciprocal polynomials are polynomials whose coefficients form a palindrome. They play an important role in coding theory, as well as in the development of efficient factorization algorithms. In this work, we investigate self-reciprocal polynomials arising from Dickson polynomials. We give a complete classification of self-reciprocal polynomials over the ring of integers and Z_p, where p is a prime different from 3. We also present our current work in characteristic 3.", "id": "Paper/70005", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70005"}, {"title": " Vector balancing and nonlinear PDE ", "webprogram_exclude": "0", "session_ids": ["Session/17991"], "source_sha256": "5657defa11f184388afaece3a012f151cec02b15415cfe0679dbd6b6efd39798", "withdrawn": "", "abstract": "In a vector balancing problem one deals with a fixed family of vectors in Euclidean space, and the objective is to find signs for each vector in the family so that the sum of the vectors weighted by those signs has small norm (typically, small sup norm). I will describe recent works with Vlad Kobzar relating this class of problems with nonlinear elliptic PDE, in particular mean curvature flow and Monge-Ampere equations.", "id": "Paper/70006", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70006"}, {"title": " Eisenstein series and zeta functions of prehomogeneous vector spaces ", "webprogram_exclude": "0", "session_ids": ["Session/18335"], "source_sha256": "1b036e09a9b7939854fbbf649357def3cd5db4fdebb05777e4d0c6afc3b66abd", "withdrawn": "", "abstract": "I will speak on constructions of zeta functions of prehomogeneous vector spaces and generalizations coming from periods of Eisenstein series.", "id": "Paper/70009", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70009"}, {"title": " Beyond Consistency: Building Course Coordinators and Cultures of Continuous Improvement ", "webprogram_exclude": "0", "session_ids": ["Session/18250"], "source_sha256": "10353a1f5a1e321e39180689ea8e2da1171591046c0d7c8e58e7e9cc89621e33", "withdrawn": "", "abstract": "Course coordination is often focused on ensuring consistency across multiple sections of a course, but its long-term success depends on developing the people and processes that sustain it. This presentation examines two complementary aspects of effective course coordination: onboarding and mentoring course coordinators, and fostering a culture of continuous improvement that responds to evolving student needs. Drawing on experiences from a large first-year STEM course, I will share approaches to developing course coordinators, supporting instructor collaboration, and creating structures that encourage ongoing innovation in teaching and learning. Reflections on successes, challenges, and lessons learned will frame a broader discussion of how course coordination can evolve beyond consistency toward continuous improvement.", "id": "Paper/70010", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70010"}, {"title": " Your Life in Numbers: An Exploration from Content-Centered Mathematics to Context-Centered Mathematics ", "webprogram_exclude": "0", "session_ids": ["Session/19349"], "source_sha256": "f82669c16de01b3ad981f120c2130ef8b424eda1f9abded276e7e9c91ae6baeb", "withdrawn": "", "abstract": "Students frequently enter mathematics classrooms believing that mathematics is a collection of formulas and procedures disconnected from their lives. Rather than organizing learning exclusively around traditional mathematical topics, this presentation focuses on a course that situates mathematics in familiar, meaningful contexts. This presentation will share the design and philosophy of Your Life in Numbers, a course created by the presenter to answer the question: “How can we design experiences that allow students to discover where mathematics already exists in their lives?”. \nThe presenter will share examples of interdisciplinary learning activities and strategies for connecting mathematical concepts to students' lived experiences. Participants will consider how similar approaches can be incorporated into existing mathematics courses without requiring a complete curriculum redesign or a new course. The session will challenge the educators to reconsider a familiar student question, “When will I ever use this?” as the starting point for learning and to design learning experiences in which students discover the answer for themselves. The presenter will discuss the survey results collected in this course.", "id": "Paper/70011", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70011"}, {"title": " Vietoris–Rips Contractibility for Dense Subsets of Finite-Dimensional Normed Spaces ", "webprogram_exclude": "0", "session_ids": ["Session/18072"], "source_sha256": "ed54ad7a36bc63b65613718fe6f403861731f34be50bf3b307e8e09bf0e4955c", "withdrawn": "", "abstract": "Let $Y$ be a $\\delta$-dense subset of a finite-dimensional normed space $X$. We prove that the open Vietoris--Rips complex $\\operatorname{VR}_{<}(Y;r)$ is contractible whenever $r>\\delta/(1-J_{\\mathrm{fin}}(X))$. Here $J_{\\mathrm{fin}}(X)$ is the normalized finite Jung constant, namely the supremum of circumradius divided by diameter over finite subsets of positive diameter. The proof uses the canonical isometric embedding of $X$ into a hyperconvex normed space, where $\\operatorname{VR}_{<}(Y;r)$ is the nerve of an equal-radius open-ball cover.\n\nApplying this result to lattices gives explicit contractibility bounds. In $(\\mathbb{Z}^n,\\ell_1)$, we show that the open Vietoris--Rips complex is contractible for $r>\\max\\{n,n(n-1)/2\\}$, and the closed complex is contractible for $r\\geq\\max\\{n,n(n-1)/2\\}$. This asymptotically halves the leading term of Zaremsky's previous bound $n^2+n-1$. Our method also gives explicit bounds for $(\\mathbb{Z}^n,\\ell_p)$ for all $1\\leq p\\leq\\infty$, recovering the optimal closed-complex bound $r\\geq 1$ when $p=\\infty$. For a general locally finite $\\delta$-dense subset $Y\\subset X$, a separate closed-cover argument proves that $\\operatorname{VR}_{\\leq}(Y;r)$ is contractible whenever $r\\geq\\delta/(1-J_{\\mathrm{fin}}(X))$.", "id": "Paper/70012", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70012"}, {"title": " Learning Under Limited Information: Hidden States, Uncertainty, and Dynamical Systems ", "webprogram_exclude": "0", "session_ids": ["Session/18280"], "source_sha256": "b4b7c1b3dd98bd0db37588d8e756e69abb7a44122a3daad1b1e10e0fdf46aba4", "withdrawn": "", "abstract": "Real-world systems are never fully accessible through observations. Measurements may be incomplete, sparse, indirect, delayed, or noisy, leaving important states and dynamics hidden from direct observation. This talk considers Learning Under Limited Information (LULI) as a conceptual perspective for understanding how intelligent systems learn, infer, predict, and make decisions when access to the underlying reality is fundamentally limited. We discuss how limited information gives rise to hidden states and latent dynamics, how these hidden aspects create uncertainty, and how different research traditions address different parts of this common challenge. In particular, we connect classical state estimation and state-space modeling with representation learning, uncertainty-aware learning, and scientific AI. For dynamical systems, this perspective highlights the importance of reasoning jointly about what is observed, what remains hidden, and what can be inferred reliably from available information. This perspective provides a common language for connecting state estimation, modern machine learning, and uncertainty-aware reasoning in dynamical systems where the underlying state is only partially accessible.", "id": "Paper/70014", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70014"}, {"title": " Inference under model uncertainty: from gravitational waves to the transient sky ", "webprogram_exclude": "0", "session_ids": ["Session/18300"], "source_sha256": "2fe732155ac60a14f34ddc41288df42ff76dbce15cc267fed8491cd16e98fe12", "withdrawn": "", "abstract": "Bayesian inference for gravitational-wave transients rests on two models we do not fully trust: the noise and the signal. This talk follows what happens as each is relaxed. First, we replace the Gaussian noise assumption behind standard gravitational-wave likelihoods with heavy-tailed alternatives, obtaining posteriors that remain robust to non-stationary and glitch-contaminated data. Second, we drop the waveform model altogether and reconstruct the signal as a sum of an unknown number of wavelets, a trans-dimensional Bayesian problem in which the dimension of the parameter space is itself inferred. Reversible-jump MCMC is the natural tool, but its dimension-changing moves are notoriously inefficient. We show that normalizing flows trained to propose these moves, combined with an exact Metropolis–Hastings correction, accelerate convergence by large factors while preserving the target posterior, and we characterize when learned proposals help and when they do not. The method applies unchanged across domains: we demonstrate it on LIGO data (GW150914), simulated LISA massive black hole binaries, and non-astrophysical time series.", "id": "Paper/70018", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70018"}, {"title": " Quantum Error Correction Using Low-Density Parity-Check Codes ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "38951a90b041afcdb761f484134d0c84c3d27d686f0c6ef28f3d5e2baa5abc77", "withdrawn": "", "abstract": "The most powerful computers of today are limited in their ability to balance efficiency with information retention,  a limit which quantum computers can overcome. Realizing this potential, however, requires quantum error correction to protect fragile information from unavoidable noise. We tackle this problem by introducing a new construction of quantum low-density parity-check (QLDPC) codes. By using permutations induced by Dickson polynomials, a well studied class of functions the interest of which modern applications have renewed, we construct codes with both high girth and low lifting factors that allow for efficient information recovery.  Our new algebraic construction method builds quantum and classical codes that demonstrate a $25 \\%$ improvement in logical error rate and $20 \\%$ reduction in cycle count relative to prior research, providing promising advancements toward practical quantum computers.", "id": "Paper/70019", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70019"}, {"title": " Density of list- and correspondence-critical graphs ", "webprogram_exclude": "0", "session_ids": ["Session/16805"], "source_sha256": "1d5de484325bb4077249e188a4ed8c2cd5c560bf6873f3480a5fa0a9a2fcb099", "withdrawn": "", "abstract": "A graph G is list $k$-critical if G is not $(k-1)$-list-colorable, but every proper subgraph of $G$ is $(k-1)$-list-colorable. In this talk, we ask the following question: How large must the average degree of a list $k$-critical graph be? Every list k-critical graph has minimum degree at least $k-1$ and hence average degree at least $k-1$. Surprisingly, previous work has been unable to improve this lower bound by any constant, with the previously best lower bound being only $k - 1 + \\Omega(2/k)$.\n\nIn this talk, we will show that for all $k ≥ 4$, every list k-critical graph has average degree at least $k - 1 + 1/28$, giving the first constant improvement to the trivial lower bound. As a corollary, we obtain the following improvement to Brooks' theorem: For all $d ≥ 3$, if G has no $K_{d+1}$ subgraph and has maximum average degree at most $d + 1/28$, then G is d-list-colorable.\n\nAll of these results hold in the setting of correspondence coloring (DP-coloring) as well.", "id": "Paper/70024", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70024"}, {"title": " Ballon-Power Car: Mathematical Model for the Motion of a Toy Car ", "webprogram_exclude": "0", "session_ids": ["Session/18271"], "source_sha256": "7978b9228c99b271dd0bec1c67b5a8000862af2721d165f87d70428ddf913f69", "withdrawn": "", "abstract": "A balloon-powered car provides a simple experimental system for investigating the dynamics of a variable-mass air-propelled vehicle. The motion of the car results from the conversion of the elastic potential energy stored in an inflated balloon into the kinetic energy of translational motion. As the balloon deflates, the pressure and effective diameter of the balloon change, resulting in a time-dependent propulsive force. At the same time, the aerodynamic drag acting on the car varies with its velocity and with the changing geometry of the balloon.\nWe formulate a mathematical model of the car's motion in terms of a system of nonlinear ordinary differential equations describing the coupled dynamics of balloon deflation and vehicle translation. The model incorporates the time-dependent thrust generated by the escaping air, aerodynamic resistance, and the changing diameter of the balloon. The principal model parameters are estimated from experimental measurements obtained using a toy balloon-powered car. The study demonstrates how a simple physical system can serve as a tractable model problem for nonlinear dynamical systems and provides a framework for connecting mathematical modeling, parameter estimation, and experimental validation.", "id": "Paper/70026", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70026"}, {"title": " How many times can a tree achieve maximum eigenvalue multiplicity? ", "webprogram_exclude": "0", "session_ids": ["Session/18227"], "source_sha256": "866c32a3ef31c745362fb2b8b96033e5e3989ddfd86bf40951124a5eb822ec5e", "withdrawn": "", "abstract": "Consider a simple graph $G$ and the class of symmetric matrices whose off diagonal zero-nonzero pattern agrees with the adjacency matrix of $G$, but whose diagonal is unrestricted. The inverse eigenvalue problem for graphs asks what multisets of eigenvalues can occur for matrices in this class.  In this talk we present a novel decomposition of a tree into a set of vertices and paths, which serves as a tool for characterizing matrices achieving maximum multiplicity.  We use this condition to prove some general results about the number of eigenvalues that can simultaneously achieve the maximum multiplicity.", "id": "Paper/70028", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70028"}, {"title": " Enriching teaching and learning experiences via AI Assistants ", "webprogram_exclude": "0", "session_ids": ["Session/18262"], "source_sha256": "61c49a717afe84592f05917193f5cb0282a651537a60f1b40de63ebd3fd78874", "withdrawn": "", "abstract": "AI Assistants, as part of the instructional team in Calculus classes, can enrich teaching and learning experiences by helping instructors and TAs in various ways so that they can focus better on students' needs. In addition, they can be a venue for instructors to provide better education based on their principles and values. In this talk, I'll explain the benefits, risks, and the development process of such educational tools.", "id": "Paper/70029", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70029"}, {"title": " Fourier-ratio decay, generalized Salem estimates, and additive structure ", "webprogram_exclude": "0", "session_ids": ["Session/19336"], "source_sha256": "562b0e84cf4b33f57fd029b9d99a3faf5570f7822d6828cb9a1f27ad06f1fdfe", "withdrawn": "", "abstract": "The Fourier-ratio decay exponent \\(\\kappa\\) measures the power-scale concentration of the Fourier transform of a family of sets in \\(\\mathbb Z_N^d\\). Since its definition involves the Fourier \\(\\ell^1\\) norm, it can be difficult to estimate directly. In this talk, I will explain how higher Fourier moments provide an alternative way to control \\(\\kappa\\). If a family \\(S_N\\subset\\mathbb Z_N^d\\) with support-size exponent \\(\\alpha\\) is uniformly \\((p,s)\\)-Salem for some \\(p>2\\), then\n\n$$\n\\kappa(\\{1_{S_N}\\})\n\\leq\n\\frac{\\alpha p(1-2s)}{2(p-2)}.\n$$\n\nWhen \\(p=4\\), the relevant Fourier moment is determined by the additive energy of \\(S_N\\). This gives quantitative bounds for \\(\\kappa\\) from energy estimates. At the opposite endpoint, maximal \\(\\kappa\\) forces nearly maximal additive energy; the Balog–Szemerédi–Gowers theorem then yields a large subset with subpolynomial doubling. I will conclude with a related obstruction for finite-group extension estimates. This is joint work with Alex Iosevich and Zhihe Li.", "id": "Paper/70030", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70030"}, {"title": " Noncommutative Entire & Meromorphic Functions ", "webprogram_exclude": "0", "session_ids": ["Session/18256"], "source_sha256": "b113e44a4bf50762dd8cbcf6798a95274d69c0ca6051b733e6aef5c297e2c4c5", "withdrawn": "", "abstract": "This talk focuses on a natural generalization of the ring of entire functions to the noncommutative (NC) setting. Namely, we simply define a NC entire function to be a power series with infinite radius of convergence. In analogy with the single variable setting (where the ring of entires is a Bezout domain), the ring of NC entires is a semifir, and this allows us to construct its universal skew field of fractions. We will discuss recent developments that show this universal skew field of fractions is a skew field of ``global” NC meromorphic functions, as well as applications to free probability and several remaining open questions. This project is joint work with Robert Martin and Eli Shamovich.", "id": "Paper/70031", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70031"}, {"title": " A hierarchy of blood vessel models ", "webprogram_exclude": "0", "session_ids": ["Session/17757"], "source_sha256": "326081011c2f67741e3bed2352e06787b5e999c6ebb87f239b09332fa0113fce", "withdrawn": "", "abstract": "I will describe a family of models describing blood perfusion through a tissue surrounding a thin blood vessel. The models will be a 3D-3D Darcy—Stokes model, a 3D-1D Darcy—Poiseuille model, and a 1D model using Green’s function. In the 1D model, the exterior blood pressure is given by an explicit Green’s function involving the interior blood pressure while the interior satisfies a 1D integrodifferential equation that incorporates the effects of the exterior pressure and the vessel geometry. The 3D-3D model is the most detailed model while the 1D model is the easiest to approximate numerically. I will show that the models are well-posed. Further, I will show that the 1D model and the 3D-1D models are good approximations of the more detailed 3D-3D model by proving a convergence rate between the three models as the radius of the vessel converges to zero.", "id": "Paper/70034", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70034"}, {"title": " Winning Within the Rules: A Dynamic Decision Model for Football Club Resource Allocation ", "webprogram_exclude": "0", "session_ids": ["Session/18066"], "source_sha256": "a64ba7d8748547d426f3666033c96efc5d5ec9ef4a5d425a4cc7dc61284b8b63", "withdrawn": "", "abstract": "How can a football club chase trophies without going broke? In Germany's Bundesliga, that question comes wrapped in unusual constraints: the \"50+1 rule\" that keeps clubs under member-majority ownership, and a 70 percent squad-cost limit that enforces financial discipline. Using VfL Wolfsburg as our case study, we modeled how a club should divide a limited budget across four competing levers—transfers, wages, academy investment, and business operations—while pursuing two goals that often pull in opposite directions: winning matches and staying financially sustainable.\n\nWe started with a foundational market model linking three drivers of a club's trajectory: on-field performance, financial reserves, and the evolving value of its academy. This produced baseline allocation recommendations. Because real football never stands still, we then layered in four dynamic factors—transfer-market strategy, Bundesliga regulation and league expansion, ticket-pricing optimization, and injury-impact management—each studied for how it tips the balance between competitiveness and revenue.\n\nWe integrated everything into what we call the PITCH Center System: a dynamic decision framework built on multi-objective (Pareto) optimization. Instead of forcing a single \"best\" answer, it maps the trade-offs between performance and profit, then does two things—predict an optimal budget split for the upcoming season, and suggest real-time adjustments as the club's situation changes mid-season.", "id": "Paper/70043", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70043"}, {"title": " The Second Vanishing Theorem in Ramified Mixed Characteristic ", "webprogram_exclude": "0", "session_ids": ["Session/18318"], "source_sha256": "81e801fb83ba88916bcd5fa6024dceddd33453b34666912cd4b31b88976aeb0b", "withdrawn": "", "abstract": "Local Cohomology, since its introduction, has served as an important invariant for com-\nmutative rings and their modules. They furthermore provide the local model for relative\ncohomology groups for schemes. As with all cohomology theories, vanishing theorems are\nwidely sought after, and for local cohomology a classical theorem of Grothendieck states\nthat all local cohomology vanishes past the dimension of the ring. Hartshorne-Lichtenbaum\nvanishing tells us when local cohomology vanishes at the dimension of the ring, and for\nvanishing one below the dimension of the ring we arrive at the Second Vanishing Theorem.\nWe highlight our proof of the Second Vanishing Theorem in the final unknown case for regular\nlocal rings, that being the case of ramified mixed characteristic rings, and give a few applications of this result. The methods work in equicharacteristic, and we show\nhow we can reduce the unramified case to the ramified case as well, yielding a unified proof\nof the Second Vanishing Theorem in all characteristics. Our proof involves the use of formal schemes and a result proven by Gabber which is false in unramified mixed characteristic, providing a potential path for further results on local cohomology in general, as well as in ramified mixed characteristic.", "id": "Paper/70044", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70044"}, {"title": " Modularity of Correlators for Heavy Heisenberg Algebras ", "webprogram_exclude": "0", "session_ids": ["Session/18270"], "source_sha256": "1e1b0e291c81839829b64ba3e0aac11253c6566f8f2a72b4d13a1ae12039d4d0", "withdrawn": "", "abstract": "Zhu famously proved the modular invariance of correlation functions for elements in rational $C_2$-cofinite vertex operator algebras. In joint work with Keller, we proved that correlation functions with zero modes inserted also satisfy nice modular transformation properties. Of special interest are  the so-called ``zero mode correlators\", which are correlation functions with zero modes but no vertex operators inserted. Miyamoto proved that the generating function for zero mode correlators of a weight 1 vector is a Jacobi form of weight 0. In this talk we discuss recent progress in generalizing Miyamoto's result. (Based on joint work with Christoph A. Keller.)", "id": "Paper/70047", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70047"}, {"title": " Cohomology of Handlebody Torelli Groups ", "webprogram_exclude": "0", "session_ids": ["Session/18297"], "source_sha256": "beadc5a242c52fa78c95beec82c0b9961f1f5c14b5dd7e57d2344593d690aac2", "withdrawn": "", "abstract": "We begin by introducing the Torelli subgroup of the mapping class group of a surface and outlining known results about its low-dimensional cohomology. We then present recent work extending these results to a Torelli subgroup of the mapping class group of a handlebody.", "id": "Paper/70048", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70048"}, {"title": " Viscosity Estimation for Navier-Stokes Equations ", "webprogram_exclude": "0", "session_ids": ["Session/18258"], "source_sha256": "fc7a2559c3e4a526659fbecbca67a2c29977cb47589021e0bc73b69fb52d4f67", "withdrawn": "", "abstract": "Convergence in parameter estimation classically requires “persistency of excitation,” which is a non-degeneracy condition on a trajectory-dependent signal. In the context of identifying the unknown viscosity from spectral observations in the two-dimensional Navier–Stokes equations for incompressible fluids, I will present an excitation condition that is computable, verifiable a apriori, and sharp with respect to scaling. Our approach employs a data assimilation methodology to account for an unknown initial state, through which candidate viscosities are selected by minimizing the loss between the low-mode observations of the fluid velocity and low-mode projection of a nudging-based filter that assimilates these observations.", "id": "Paper/70050", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70050"}, {"title": " Bartnik mass of apparent horizon in non time symmetric setting ", "webprogram_exclude": "0", "session_ids": ["Session/18266"], "source_sha256": "283d3a9fb87047f7ec593c8502bb633989e2340ef9105b618440bcefc3d88250", "withdrawn": "", "abstract": "We construct initial data sets realizing prescribed Bartnik data for apparent horizons in the non-time-symmetric setting and glue them to asymptotically flat exteriors while preserving the strict dominant energy condition throughout the collar. As an application, we consider a Bartnik data induced by a Kerr horizon and construct admissible asymptotically flat extension satisfying strict dominant energy and no apparent horizon condition with the ADM-mass strictly less than the mass of the corresponding Kerr spacetime. This provides a potential obstruction to the Bartnik conjecture concerning the realization of Bartnik mass by stationary vacuum extensions.", "id": "Paper/70052", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70052"}, {"title": " Threshold Dynamics for Dispersive Spin Models ", "webprogram_exclude": "0", "session_ids": ["Session/18385"], "source_sha256": "6f2b31fafceb040c0d22a435b11d1bd1d8bde0383df65ad8e790676932089a1f", "withdrawn": "", "abstract": "The asymptotics of solutions of quantum spin models, such as the Klein-Gordon and NLS equations in a magnetic field, are closely related to the spectral theory of their associated Hamiltonians. In this talk, we give exact profile solutions for some modeling equations. Moreover, we review recent progress on threshold dynamics for the solitary waves that are trajectories from invariant manifolds for the initial profile state.  Our method relies on a modified Lyapunov functional combined with an analysis of the underlying linearization operators.", "id": "Paper/70056", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70056"}, {"title": " Uniformly Lipschitz and Cascading Nonexpansive Mappings on the Unit Ball of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.845ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 1225 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\ell ^{\\infty }</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2113\" d=\"M345 104T349 104T361 95T369 80T352 59Q268 -20 206 -20Q170 -20 146 3T113 53T99 104L94 129Q94 130 79 116T48 86T28 70Q22 70 15 79T7 94Q7 98 12 103T58 147L91 179V185Q91 186 91 191T92 200Q92 282 128 400T223 612T336 705Q397 705 397 636V627Q397 453 194 233Q185 223 180 218T174 211T171 208T165 201L163 186Q159 142 159 123Q159 17 208 17Q228 17 253 30T293 56T335 94Q345 104 349 104ZM360 634Q360 655 354 661T336 668Q328 668 322 666T302 645T272 592Q252 547 229 467T192 330L179 273Q179 272 186 280T204 300T221 322Q327 453 355 590Q360 612 360 634Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-2113\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-221E\" x=\"590\" y=\"513\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/17782"], "source_sha256": "6048fd266f0be30ba57fe53e4dd18fa803d06d5a1608b24354f3a0f65faecddf", "withdrawn": "", "abstract": "Goebel and Kirk showed in a uniformly convex space there exists a $k_0 > 1$ such that any uniformly Lipschitz self-mapping on a closed, bounded, convex set, whose uniformly Lipschitz constant $k$ is such that $k < k_0$, has a fixed point. We’d like to see if there’s an analogous result for the unit ball of $\\ell^{\\infty}$. We build multiple examples showing that if such a $k_0$ exists, then $k_0 \\leq 2$. One of these examples is also cascading nonexpansive and can be constructed so that its Lipschitz constant can be made as close to $1$ as we’d like, hence close to nonexpansive.", "id": "Paper/70057", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70057"}, {"title": " Privacy-Preserving Matrix Computation in the Single-Server Setting ", "webprogram_exclude": "0", "session_ids": ["Session/18307"], "source_sha256": "146a63034368ee73b6a36732f5631b21f55ddae18b829fbbf404c0228201492d", "withdrawn": "", "abstract": "We consider privacy-preserving outsourced matrix computation in a single-server setting, where a user seeks to delegate computationally intensive operations involving sensitive data to a potentially untrusted server. In contrast to many existing secure distributed matrix multiplication approaches, which rely on multiple non-colluding servers, we investigate privacy guarantees that remain meaningful even when the computation is performed by a single server.\n\nOur focus is on the tradeoff between privacy and efficiency. We develop a framework that exploits algebraic structure in the underlying data and computation to reduce the computational burden on the user while providing tunable statistical privacy guarantees. The resulting approach offers a new perspective on lightweight privacy-preserving outsourced matrix computation and on the tradeoffs between privacy strength and computational efficiency.", "id": "Paper/70065", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70065"}, {"title": " Two-primary <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.066ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 889.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">K</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-4B\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-theory of two-point configuration spaces of complete bipartite graphs ", "webprogram_exclude": "0", "session_ids": ["Session/19356"], "source_sha256": "7782d79e2b8ed1eec264c7c48e459e6a17d0644001d1bd4d75d845b35a67f0d7", "withdrawn": "", "abstract": "Consider the unordered two-point configuration spaces of the complete bipartite graphs given by $X_{a,b}=\\text{UConf}_2(K_{a,b})$ for constants $a, b \\ge 3$ defined by \n\\[\n    \\text{UConf}_2(X_{a,b})=\\{\\{x,y\\}\\subset X_{a,b} \\hspace{0.1cm} | \\hspace{0.1cm} x\\neq y\\}\n\\]\nWe derive the real and complex topological K-theory of $X_{a,b}$. To do so, we first use the Ko-Park computation of the first and second homology of the graph braid groups $H_1(X_{a,b};\\mathbb{Z})$ and $H_2(X_{a,b};\\mathbb{Z})$. Thus, from there, we use the integral Bockstein homomorphisms to show that the cup-square map $H^1(X_{a,b},\\mathbb{F}_2)\\xrightarrow{} H^2(X_{a,b},\\mathbb{F}_2)$ has rank 1. Thus, using the results of the classification of stable real and complex vector bundles over two-dimensional complexes, we obtain\n\\[\n    \\widetilde{KO}^0(X_{a,b})\\cong \\mathbb{Z}/4 \\oplus (\\mathbb{Z}/2)^{(1-a)(1-b)+\\mu}, \\hspace{0.3cm} \\widetilde{KU}^0(X_{a,b})=\\mathbb{Z}^\\mu \\oplus \\mathbb{Z}/2\n\\]\nwhere \n\\[\n\\mu=\\binom{a+b}{2}-ab(a+b-2)+\\frac{ab(a-1)(b-1)}{2}-1+(a-1)(b-1)\n\\]", "id": "Paper/70066", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70066"}, {"title": " Time-like geodesics in a unit signature (1,2) hyperbolic spacetime staircase-metric (SCM) manifold ", "webprogram_exclude": "0", "session_ids": ["Session/19352"], "source_sha256": "d60b6dbb9f91c740a3f64aada504fa36ac2d53a6b0dcb3d20aff901c84db3e02", "withdrawn": "", "abstract": "Following a brief introduction to staircase metric (SCM) geometry and its accompanying methodology, we extend earlier work (on a particular signature (1,1) non-contractible and overall negative curvature spacetime manifold) to a signature (1,2) case, which is a natural extension of the (1,1) manifold via rotation.  Specifically, we study the time-like geodesics in this spacetime 3-manifold.  Further, we identify such geodesics in the manifold that are also closed.  This at least mirrors the set of such time-like geodesics in the (1,1) case.", "id": "Paper/70068", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70068"}, {"title": " Coarse-to-Fine Conditional Diffusion for Sparse Darcy Inversion with Differentiable GPU Multigrid ", "webprogram_exclude": "0", "session_ids": ["Session/19322"], "source_sha256": "9078376a34ed55b23ecd2eac2b3dd060d12095e491021e2af26d8f42d32cf595", "withdrawn": "", "abstract": "We study recovery of permeability $k=e^m$ from sparse observations of the solution to the Darcy equation $-\\nabla\\cdot(k\\nabla u)=f$. A two-stage conditional Elucidated Diffusion Model generates log-permeability fields using sensor data and the known source. The coarse estimate is interpolated onto the fine grid and supplied as an additional condition to the second model. Fine-stage training mixes true and predicted coarse fields to account for imperfect estimates at inference.\n\nWe evaluated the method on 5,000 test cases with log-permeability sampled using Gaussian fields of varying variance and correlation length. Reconstruction proceeds from $32\\times32$ to $128\\times128$ with 500 observations per case. Selecting the best of 20 candidates by comparing their forward solutions with sensor measurements reduced the median relative $\\ell^2$ errors from 20.6% to 16.9% for permeability and from 7.03% to 4.05% for the PDE solution, relative to using a single candidate. Stratified errors were largest for short correlation lengths and high log-permeability variance.\n\nTo support these computations, the PDE backend uses piecewise linear finite elements and GPU multigrid in NVIDIA Warp for data generation, candidate evaluation and physics guidance. Manufactured-solution tests recover second-order $L^2$ and first-order $H^1$-seminorm convergence. In smooth-coefficient benchmarks, we observed six or seven V-cycles across meshes with up to 16.8 million degrees of freedom. In a directional derivative check, differentiation through fixed V-cycles agreed with centred finite differences. However, additional guidance using gradients of observation mismatch did not improve overall median accuracy under the tested settings. We also outline an extension to incompressible Navier-Stokes flow.", "id": "Paper/70070", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70070"}, {"title": " Incidence toric ideals and three-point functions ", "webprogram_exclude": "0", "session_ids": ["Session/18253"], "source_sha256": "25f82fb12830036dbb8df6e6ee9bfb8d680f9169df0eedd0aeefb5dbc37af7fa", "withdrawn": "", "abstract": "Motivated by three-point functions from conformal field theory, we study these from a combinatorial and topological perspective via incidence toric ideals. These ideals arise naturally in the context of incidence matrices of simplicial complexes. In this setting, the generators of these toric ideals admit combinatorial interpretations as null $t$-designs and topologically as balanced orientable normal pseudomanifolds without boundary. This is joint work with Barbara Betti, Thiago Holleben, and Flavio Salizzoni.", "id": "Paper/70071", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70071"}, {"title": " Using Path Bundles to find PSD Forcing Sets with Desired Structural Properties ", "webprogram_exclude": "0", "session_ids": ["Session/18207"], "source_sha256": "84b839c52202c19cc20d04c39b6a921c282d153c83de02df12d3f9159853e51e", "withdrawn": "", "abstract": "Recent work has identified a new substructure called path bundles which are induced by positive semidefinite (PSD) forcing processes.  In addition to being induced by PSD forcing processes, path bundles provide considerable information about PSD forcing.  In particular, they act as analogs to the reversals of standard forcing, identify induced subgraphs for which a PSD forcing set is a standard forcing set, and are mechanisms for finding additional PSD forcing sets.  Once introduced, we demonstrate how these tools have been used for recent results ranging from properties of reconfiguration graphs to a new characterization of claw-free graphs utilizing zero forcing variants to a connection between PSD forcing and rigid linkages.", "id": "Paper/70072", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70072"}, {"title": " Conformal Einstein Flow, Geometrization of 3-Manifolds, and Cosmological Implications ", "webprogram_exclude": "0", "session_ids": ["Session/19365"], "source_sha256": "8817996c55229b02a5ef23a073de38a0cad195f275f41e72629a7bea04a893bd", "withdrawn": "", "abstract": "We show that      the         dynamical  Hamiltonian formulation of the Einstein field equations can be reduced to  a free   unconstrained  dynamical system   with a  time-dependent     monotonically decreasing  Hamiltonian $H_{\\rm reduced}=\\tau^3\\int_M\\varphi^6d\\mu_\\gamma    $ where $\\tau={\\rm tr}_gk$, $\\varphi=\\varphi(\\gamma,p^{TT})$ is the Lichnerowicz transforming conformal factor, and whose global infimum   on the   reduced phase space is given by $ (\\frac{3}{2}(-\\sigma(M)))^{3/2}$, where the $\\sigma$-constant of $M$  has direct topological significance. Since this reduction involves transforming the\n constrained {\\it physical variables} $(g,\\pi)$\n to the \n free  unconstrained    \n {\\it conformal variables}  $(\\gamma, p^{TT})$,    we refer to the resulting reduced dynamical system as    {\\bf conformal Einstein flow}. \n \n We apply this flow to  the   five Bianchi types that correspond to the Thurston types {\\it Nil, Sol}, $H^2\\times R$,   $\\widetilde{SL(2,R)}$, and $H^3$. Using   known solutions   in each of these cases, we  find by explicit computation that in the first four cases,   the volumes collapse to zero and the model either pancakes collapse to a 2-manifold,   barrel collapses to a 1-manifold, or in the case of {\\it Nil}, totally collapses  to a point. In each of these cases, the collapse occurs with bounded curvature,  precisely as occurs in the theory of  collapsing Riemannian manifolds.  \n However, in the hyperbolic case where       $\\gamma$ is hyperbolic and $p^{TT}=0$, the resulting pair is a fixed point for the conformal Einstein flow and thus the volume does not collapse.\n \n A plausible scenario suggested by these results is that \nunder the  conformal Einstein flow, in the Thurston decomposition of a closed 3-manifold with the above five components, the hyperbolic geometric components overwhelming dominate the spatial volume as the universe expands and that the actual evolving metric on $M$ naturally tends to flow toward a locally homogeneous and isotropic metric on each of the volume-dominating components. In this scenario, the conformal Einstein flow provides a dynamic  mechanism to explain the observed fact that the universe seems to be locally homogenous and isotropic.\nExtrapolating even further, the conformal Einstein flow may provide a naturally given dynamic mechanism, as opposed to Ricci-Pereleman flow, for the geometrization of closed 3-manifolds.", "id": "Paper/70074", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70074"}, {"title": " On the homology of two-step nilpotent Lie algebras indexed by trees ", "webprogram_exclude": "0", "session_ids": ["Session/18286"], "source_sha256": "99192736b3e8c3778e6b257589d7b78f69db9e58683bccfc0089d68a3c90f0a3", "withdrawn": "", "abstract": "Dani and Mainkar constructed, for each graph $G$, a two-step nilpotent Lie algebra, i.e., a Lie algebra $L_G$ satisfying $[L_G,[L_G,L_G]] = 0$.  In this talk, we will examine the homology of $L_G$, for when $G$ is a tree. We give explicit computation of the homology for the case of certain families of graphs. For the case when $G$ is a star, we give an $S_n$-module structure of the homology as well.", "id": "Paper/70076", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70076"}, {"title": " (Re)Inventing the Wheel: Standard-based grading when the LMS does not provide sufficient support ", "webprogram_exclude": "0", "session_ids": ["Session/19341"], "source_sha256": "db6ee57e1c99934169c1d8a3cfeadd1d2e6e12a6cc7fcd3381f34b8cb6351a8b", "withdrawn": "", "abstract": "Standard-based grading can provide students with meaningful information about individual progress toward their learning goals, but implementation can be challenging when the learning management system does not adequately support it. I will share my experience implementing standard-based grading in MA 34100 (Foundations of Analysis), an introductory proof-writing course at Purdue University. \n\nBecause D2L Brightspace does not provide a suitable standard-based gradebook, I developed a separate gradebook using Microsoft Lists. The system allows the instructor and teaching assistant to view and edit all students' grade entries while allowing each student to view their own entries without editing them. I will describe the design of this system and reflect on the practical challenges of maintaining a gradebook outside the LMS to make an alternative grading system workable. \n\nThe technical implementation is only part of the challenge. Students accustomed to conventional grading schemes need clear guidance to understand what standards-based grades represent, how their progress is recorded, and how they can use this information to guide their learning. I will discuss how I have introduced and communicated the grading system to students and reflect on potential areas of improvement. I will conclude with practical lessons for instructors implementing alternative grading systems---successful implementation requires both workable technical infrastructure and clear communication that makes the grading system transparent to students.", "id": "Paper/70077", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70077"}, {"title": " A Gutzwiller trace formula for singular potentials ", "webprogram_exclude": "0", "session_ids": ["Session/17804"], "source_sha256": "1bf2c39154c644afbcba3fc71fcdfdb4f1da9aa0ffb2b7eba60a677085b92bf5", "withdrawn": "", "abstract": "We discuss extending the Gutzwiller trace formula, which relates the regularized trace of the solution operator for a semiclassical Schrödinger propagator to dynamical data of the corresponding Hamiltonian dynamics, from the case of smooth potentials to that of conormal potentials with derivative discontinuities across some hypersurface. We show, in addition to a main term as expected from classical dynamics, that there is a subleading contribution\nfrom dynamics associated to “branching” Hamiltonian trajectories that are allowed to reflect from the hypersurface of potential singularity. We discuss the computations behind the trace formula, some variational calculus needed to make sense of the dynamical quantities appearing in the formula, and an explicit 1-dimensional example whose eigenvalues have explicit asymptotics that demonstrate the contributions from the branching trajectories.", "id": "Paper/70078", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70078"}, {"title": " Gorenstein graded Möbius algberas are Koszul ", "webprogram_exclude": "0", "session_ids": ["Session/18318"], "source_sha256": "4e880ef12dcb7731153780651e7e6739b765d1edc5e99e736cdc3f1999100b66", "withdrawn": "", "abstract": "The graded M\\\"obius algebra of a matroid is an algebra encoding the combinatorics of its lattice of flats. In 2016, Maeno and Numata showed that the graded M\\\"obius algebra of a matroid is Gorenstein if and only if the matroid is modular. Joint with Jason McCullough, we show that modular matroids have Koszul graded M\\\"obius algebras by showing that their defining ideals have a quadratic Gr\\\"obner basis, and we show that the graded M\\\"obius algebras of nearly all affine geometries are quadratic.", "id": "Paper/70082", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70082"}, {"title": " Cohomology-free vector fields have zero entropy ", "webprogram_exclude": "0", "session_ids": ["Session/18313"], "source_sha256": "c8eff23055e041ca66099ea6c3896f7d4b649ce7029846036bd06ac74d7aaf4c", "withdrawn": "", "abstract": "A vector field X on compact manifold M is called cohomology-free if it has the property that the action of the Lie derivative $L_X$ on smooth functions $C^\\infty(M)$ has range a codimension 1 subspace of all smooth functions.\nI will explain a proof that such a vector field has zero topological entropy.", "id": "Paper/70083", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70083"}, {"title": " Discrete in tiem data assimilation for the 3D Navier-Stokes equation. ", "webprogram_exclude": "0", "session_ids": ["Session/17757"], "source_sha256": "05045e04e0e6f09bb32e48019c702a5675441a7116b9d154629fe947e4d42052", "withdrawn": "", "abstract": "We study a data assimilation algorithm for the three-dimensional Navier–Stokes equations using observations that are available only at discrete times and at limited spatial resolution. Under suitable conditions on the observation resolution, sampling interval, and nudging parameter, we show that the data-assimilated system admits a unique global regular solution. We then prove that the assimilated solution synchronizes with the reference solution at the observation times, up to the observational error. As a consequence, the same conditions provide a regularity criterion for the three-dimensional Navier–Stokes equations based solely on discrete-in-time, spatially coarse observations.", "id": "Paper/70085", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70085"}, {"title": " Classifying caps in affine geometry of 8 dimensions ", "webprogram_exclude": "0", "session_ids": ["Session/18241"], "source_sha256": "717a47df8abca85e4a054c1c9dc5a17727f3d73e215a2e99ca9c7817065a27be", "withdrawn": "", "abstract": "\\begin{abstract}\nThe card game \\emph{Quads} models the affine geometry $\\mathrm{AG}(8,2)$ of\ndimension~$8$ over the field $\\mathbb{F}_2$. Each card is a point of\n$\\mathrm{AG}(8,2)$, and a \\emph{quad} is a $4$-element subset of points\nthat sum to the zero vector. The main goal of the game is\nto find quads until the deck is cleared. The objects of our interest are \\emph{caps},\nquad-free subsets of $\\mathrm{AG}(8,2)$.  We consider the problem of classifying caps in dimension~$8$ up to a\n\\emph{type}. After giving a precise definition of\ncap type, we present a set of proved theorems that substantially reduce the number of types\nrequiring individual consideration. For caps of larger size, we\nintroduce a mapping between quad-free sets and binary error-correcting\ncodes. We are going to present the way such correspondance will let us utilize the results from coding theory in order to classify caps of sizes too high for direct analysis. Finally, we are going to present Quads with Friends, an online web application adapting EvenQuads, a card game created by Association for Women in Mathematics that celebrates women in mathematics and makes the affine geometry intuitive. \n\\end{abstract}", "id": "Paper/70087", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70087"}, {"title": " Beyond Structure: How Curriculum and Pedagogy Shape Outcomes in Co-Requisite Statistics ", "webprogram_exclude": "0", "session_ids": ["Session/18236"], "source_sha256": "b0e105ee4bedddcae0fddbca021a3374ea470c7d71c3079289bfc0fea311a8b1", "withdrawn": "", "abstract": "Co-requisite remediation has substantially increased completion of college-level math requirements by allowing students to bypass developmental prerequisite courses and instead receive just-in-time support alongside college-level content. While the structural benefits of co-requisite models are well established, less is known about how curricular and pedagogical choices within that structure affect student outcomes. This study is among the first to isolate the impact of curriculum and instruction on student success within co-requisite mathematics.\n\nFunded by IES and conducted in partnership with Dallas College, this study compares outcomes and experiences of students in co-requisite statistics courses taught using Statway — a curriculum built on active, collaborative pedagogy and rich, authentic contexts — against sections using traditional curriculum and instruction. The study spanned 8 semesters across 7 campuses, 1,861 students, and 41 faculty, using a QED design, along with a cost analysis.\n\nFindings show that Statway students earned significantly higher course grades and were roughly half as likely to receive a DFWI grade. These benefits held consistently across incoming math knowledge, race, gender, and Pell eligibility. Cost analysis further showed that Statway was less expensive to implement than traditional instruction, despite additional investment in professional development, largely due to reduced faculty preparation time. These findings suggest that within co-requisite structures, instructional approach is not incidental — it is a significant lever for improving equity and success in college mathematics. As co-requisite models become standard practice nationally, this study offers evidence that curricular and pedagogical choices, specifically those emphasizing active, collaborative engagement with authentic contexts, can meaningfully extend the benefits of the co-requisite model itself.", "id": "Paper/70092", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70092"}, {"title": " Modeling the Interactions Between Zero-Day Options and Underlying Markets Using Joint Limit Order Book Data ", "webprogram_exclude": "0", "session_ids": ["Session/18124"], "source_sha256": "655bcc2580240d58f161437fc7c60143f26fafc7e36d58e2f1cdd233f2c049fa", "withdrawn": "", "abstract": "We propose a framework to quantify intraday cross-market interactions between zero-days-to-expiration (0DTE) options and their underlying exchange-traded funds (ETFs) using event-level data. A joint limit order book model is developed to estimate event intensities, such as order arrivals, cancellations, and trades, via a multivariate Hawkes process. We find statistically significant cross-market excitation and strong same-market clustering, with interactions that are asymmetric and highly time-varying over the trading day. Distinct patterns in interaction strength are observed around macroeconomic announcements. The framework further identifies microstructure-level drivers of cross-market excitation, allowing different event types to be decomposed, quantified, and compared in terms of their contributions to cross-market dynamics.", "id": "Paper/70093", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70093"}, {"title": " A Fourier Ratio Refinement of Spectral Synthesis on Finite Abelian Groups ", "webprogram_exclude": "0", "session_ids": ["Session/19336"], "source_sha256": "d41b9cc961744d21950d725f7be440d9c3fc767f522f7ae21a510ba81b9a0a7a", "withdrawn": "", "abstract": "We study asymptotic spectral synthesis on (\\mathbb Z_N^d): when does a uniform Fourier (\\ell^p) bound force the largest Fourier coefficient to tend to zero as (N\\to\\infty)? We use the unitary Fourier transform and counting-measure norms. For functions supported on sets of size (N^{\\alpha+o(1)}), we show that Fourier concentration, quantified by a Fourier-ratio exponent (\\kappa), improves the admissible range of (p). Our estimates use the Fourier ratio of either the function or its support indicator, with the latter applying uniformly to arbitrary weights on the support. We construct examples showing that the resulting finite critical exponent is sharp as a universal bound determined by (\\alpha) and (\\kappa).\n\nWe then examine how symmetry and arithmetic structure yield stronger results for specific families. For paraboloids in dimension (d\\ge2), synthesis at the universal critical exponent fails along odd primes but holds along powers of a fixed odd prime. Along products of all odd primes up to a growing bound, synthesis extends to a larger endpoint. These families have the same support-size and Fourier-ratio exponents, illustrating the additional role of arithmetic structure. This is joint work with Alex Iosevich and Ke Yu.", "id": "Paper/70095", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70095"}, {"title": " ICC groups with property (T) which are not properly proximal ", "webprogram_exclude": "0", "session_ids": ["Session/18383"], "source_sha256": "6f77c4d27e77f20c6ea0a0ece2efeff81a0eaa1d069db7840c1b70ac76a4528f", "withdrawn": "", "abstract": "Proper proximality was introduced by Boutonnet, Ioana, and Peterson to extend boundary methods in the study of group von Neumann algebras beyond the setting of biexact groups. In this talk, I will present ICC groups with Kazhdan's property (T) which are not properly proximal, answering a question of Peterson. These examples are also finitely generated linear groups. Since ICC groups with property (T) are non-inner amenable, they answer negatively the question of Boutonnet, Ioana, and Peterson whether every non-inner amenable finitely generated linear group is properly proximal.", "id": "Paper/70098", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70098"}, {"title": " Orbit closures for subgroups of the mapping class group acting on the character variety ", "webprogram_exclude": "0", "session_ids": ["Session/18121"], "source_sha256": "2c91c749c137ff80080495709dd0230c5bcf457e8550d998a4d284916705fc3c", "withdrawn": "", "abstract": "A subgroup $\\Gamma$ of the mapping class group of a compact orientable surface S is called ``algebro-geometric'' if it arises as the monodromy of a quasi-projective family of Riemann surfaces.\nConsider a compact Lie group K and corresponding character variety $X:=Hom(\\pi_1(S),K)/K$ which parametrizes isomorphism classes of representations to $K$.\nThe character variety $X$ carries an action of the mapping class group, and hence its subgroups. In this talk, I will discuss results establishing some properties of orbit closures of algebro-geometric subgroups. Such orbit closures are in particular manifolds (with singularities and orbifold points) and have additional geometric properties.", "id": "Paper/70101", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70101"}, {"title": " A Combinatorial Bicategory for Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18381"], "source_sha256": "3afcdf0f8053eec84a2ebbfc536b97472a98c65d9fbfb288ed3288c388609b18", "withdrawn": "", "abstract": "I will introduce graph modules, a combinatorial object that computes the K-theory of a graph algebra and of its AF core. From these I build a bicategory of graph bimodules: a simple, combinatorial bicategory of graphs in which isomorphism entails Morita equivalence of the corresponding graph algebras. I will show how the elementary graph moves are realized as graph bimodules, and make  connections with the KK-theory of graph algebras.", "id": "Paper/70102", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70102"}, {"title": " Structure-preserving generative models ", "webprogram_exclude": "0", "session_ids": ["Session/18273"], "source_sha256": "4da2e75015951ba5f0599c146803808fad8b69ea8b0f59921bf06f3fe4675a3e", "withdrawn": "", "abstract": "In generating images for scientific problem-solving and discovery, conventional integral probability metrics for evaluating generative models are uninformative. Instead of matching the target distribution, we often care about accurately matching the distribution of certain observables/features, which may in turn help us infer the interactions among the components\nof the generated random variable. In this work, we characterize how such meaningful features\nfor downstream tasks may be preserved by diffusion models, even when the generated distribution is inaccurate due to learning errors.", "id": "Paper/70103", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70103"}, {"title": " Third Order Mock Theta Functions and Partition Ranks ", "webprogram_exclude": "0", "session_ids": ["Session/18333"], "source_sha256": "b7684d82807671d3719b67982b34f56cf94094c4f8bb7609a7d12518e102676e", "withdrawn": "", "abstract": "Zwegers connected Ramanujan's mock theta functions to real-analytic modular forms of weight $\\frac{1}{2}$. Frank Garvan and the speaker recently gave a proof of Zwegers' theorem for the third order mock theta functions without using Watson's transformation results, obtaining new identities for $\\omega(q)$ and $f(q)$. In this talk, we show that these identities are equivalent to identities in Ramanujan's Lost Notebook. We also explain their connections to the $M_2$-rank of partitions without repeated odd parts and the Dyson ranks of partitions and overpartitions. This is joint work with Frank Garvan.", "id": "Paper/70104", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70104"}, {"title": " Lessons Learned in Implementing a Motivation Intervention in an Undergraduate Pre-calculus Course: Innovations in Recruitment and Data Collection ", "webprogram_exclude": "0", "session_ids": ["Session/18200"], "source_sha256": "154b5aa4390358fd9ad2cebb2968dabdc7c3125d11e260178c2df4e28133c0dc", "withdrawn": "", "abstract": "Being successful in pre-calculus courses is significant for students pursuing mathematics and other STEM degrees and careers. Our team implemented a quasi-experimental multi-group study to encourage first-year college students to reflect on their efforts and reshape any maladaptive attributions of failure using an attribution retraining intervention program. Our goal was to encourage academic success and persistence through reflective activities. The control group received useful information on various campus resources. One intervention group received attribution retraining, and a second intervention group received attribution retraining and additional self-reflection prompts about their exam performance using exam wrappers (i.e., reflective activities focused on how time was spent preparing for exams, and how one can prepare for the next assessment). \n\t\nThe intervention has been implemented for three semesters at a four-year university. Our goal was to recruit greater than 1,000 students from pre-calculus across three cohorts and from 42 pre-calculus sections. Data were collected from three surveys: pre, mid, and post. The project has been a significant undertaking requiring cooperation from course instructors and significant buy-in from student participants. We will present three lessons learned, and innovations pursued: 1. Challenges and strategies working with a large group of instructors when carrying out recruitment and implementation efforts. 2. Innovations in recruitment approaches that leverage human and technology-assisted efforts (e.g., multiple class visits and personalized text messaging and emails). 3. Best practices in implementation, the reflective course activities, and evaluation metrics in a math class. We will also present preliminary effects of the intervention on motivation, causal attributions, and math achievement.", "id": "Paper/70105", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70105"}, {"title": " Interlace Polynomials of Eyeglasses Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18206"], "source_sha256": "d044a033a88224d17f2bf2bf957e49a5b8c8e079bb701538aa6e1a03978c5e53", "withdrawn": "", "abstract": "The eyeglasses graph is a graph that has two cycles connected by a path. We present the interlace polynomial of the eyeglasses graph giving explicit formulas, special values, and behavior of coefficients. We also discuss the interlace polynomials of similar families of graphs.", "id": "Paper/70106", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70106"}, {"title": " A New Lower Bound for the “L” Problem With Four Colors ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "4898db717fa1b93f54b5b5197e7efba2986fce651d34018593fe0982cc6d67a4", "withdrawn": "", "abstract": "Consider a discrete $n \\times n$ integer grid where each point is colored using one of $k$ colors. An L is a set of points $\\{(i,j),(i,j+t),(i+t,j+t)\\}$ contained in the grid with $t>0$. An L is monochromatic if all three of its points share the same color. By the Gallai--Witt theorem, for each positive integer $k$, there exists a least integer $n_k$ such that every $k$-coloring of an $n_k \\times n_k$ grid contains a monochromatic L. In 2023, Canakci et al. used SAT solvers to give a lower bound for a 3-coloring. In 2025, Mammel, Smith, and Yerger provided a theoretical lower bound for any $k$. Using a local search algorithm with periodic restarts, we establish a new lower bound that improves upon the theoretical bound.", "id": "Paper/70108", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70108"}, {"title": " Design of MDP Convolutional Codes and Maximally Recoverable Codes Through the Lens of Matrix Completion ", "webprogram_exclude": "0", "session_ids": ["Session/18388"], "source_sha256": "73ff1eaa51c2d9e34e18970e9c6d50b250f779d8a5ea738b9be1d5aa9f1c3e80", "withdrawn": "", "abstract": "The matrix completion problem provides a unifying lens through\nwhich many fundamental problems in coding theory can be viewed.\nIn this paper, we investigate Locally Recoverable Codes (LRCs) with\nMaximal Recoverability (MR) in the framework of matrix completion.In par-\nticular, we present techniques that are general enough to provide con-\nstructions for MR and other types of codes. A common feature of our code\nconstructions is the sparsity of their generator matrices and the prop-\nerty that a large number of the entries of the generator matrices are\nelements of a small subfield of a larger extension field.", "id": "Paper/70109", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70109"}, {"title": " Mean Dimension and the Radius of Comparison of Crossed Product C*-Algebras ", "webprogram_exclude": "0", "session_ids": ["Session/18382"], "source_sha256": "4a734dfd7b04d5f8c74731feebee5823f99a8dde33944f82ba640476bd213495", "withdrawn": "", "abstract": "For a finite CW complex $K$, shift-invariant subsets of $K^\\mathbb{Z}$ are important examples of minimal systems with positive mean dimension. In this talk, we define block-type subshifts and prove $\\text{rc}(C(X)\\rtimes\\mathbb{Z})=\\frac12\\text{mdim}(X,\\text{shift})$ for them. For particular examples of block-type subshifts, such as those constructed by Lindenstrauss and Weiss, we compute the Elliott invariant and provide examples of non-isomorphic crossed products with the same Elliott invariant. We also show that in these particular examples, $C(X)\\rtimes\\mathbb{Z}$ contains an orbit breaking subalgebra isomorphic to a Villadsen algebra of the first kind.", "id": "Paper/70111", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70111"}, {"title": " Weyl alternation sets and the Bruhat order ", "webprogram_exclude": "0", "session_ids": ["Session/18138"], "source_sha256": "2412e8bea691e2753eb8aada8aa763b8246d6bfde11b92ef74794f17b871a8ee", "withdrawn": "", "abstract": "Given integral weights $\\lambda$ and $\\mu$ of a simple Lie algebra $\\mathfrak{g}$, Kostant's weight multiplicity formula gives the multiplicity of the weight $\\mu$ in the irreducible representation with highest weight $\\lambda$ as an alternating sum over the Weyl group $W$ of the Lie algebra whose terms involve a vector partition function. The Weyl alternation set $\\mathcal{A}(\\lambda,\\mu)$ is the set of elements of the Weyl group that contribute nontrivially to Kostant's weight multiplicity formula. We study the poset structure of these sets under the Bruhat order on $W$ and show that every Weyl alternation set $\\mathcal{A}(\\lambda, \\mu)$ is a (possibly empty) order ideal.", "id": "Paper/70112", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70112"}, {"title": " Obstructing Binary Goldbach Representations of Even Numbers ", "webprogram_exclude": "0", "session_ids": ["Session/17106"], "source_sha256": "5c4464f6e72c7e073921498ad7db83c12d7999cbb1de3272bee97ebe119da81d", "withdrawn": "", "abstract": "This paper aims to construct an algorithm that minimizes a portion of prime numbers that are disregarded in order to maximize the amount of even natural numbers that cannot be represented as the sum of two primes. It discovers that there exists infinitely many even numbers, such that their sums of two pairs is bounded by a certain function of the maximum even number. The paper finds that by taking an arbitrary prime number, we can take a specific subset of the prime number's modular set that contains all but two of its residues, we can remove an infinite set of prime numbers of density zero such that infinitely many even numbers cannot be decomposed into two remaining prime numbers.", "id": "Paper/70113", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70113"}, {"title": " Weighted Gaussian Poincaré Inequalities: Sharp Stability, Caffarelli-Kohn-Nirenberg Inequalities, and Applications ", "webprogram_exclude": "0", "session_ids": ["Session/18265"], "source_sha256": "099ecfc70a010f792d2005d75c40f8cddda84a81240ed19909feb2f715abc9c6", "withdrawn": "", "abstract": "We introduce a new family of weighted Gaussian $L^2$-Poincar\\'{e}-type inequalities with explicit sharp constants and optimizers, together with corresponding sharp $L^2$-gradient stability estimates. This family substantially extends the classical Gaussian Poincar\\'{e} inequality. To address the singular nature of the weights, we develop a new approach based on generalized Laguerre polynomial expansions, spherical harmonic decompositions, and a Kelvin-type transform. As an application, we obtain a complete characterization of the stability of the $L^2$-Caffarelli-Kohn-Nirenberg (CKN) inequalities, establishing sharp stability estimates throughout the full parameter range, together with corresponding stability results for the associated stability inequalities. We further establish weighted $L^p$-Poincar\\'{e} inequalities for all $p>1$ and derive sharp stability estimates for the $L^p$-CKN inequalities for $p \\geq 2$ throughout the full parameter range for which the sharp constants and optimizers are known. We also present applications to the second-order Heisenberg uncertainty principle, including a simpler proof of its stability estimate and an improved stability result for curl-free vector fields. Finally, we establish a family of sharp fractional-order CKN inequalities together with their corresponding sharp stability estimates. This talk is based on joint work with Guozhen Lu, Nguyen Lam, Nguyen Van Hoang.", "id": "Paper/70115", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70115"}, {"title": " Engaging Students through Collaboration: Exploring the Fibonacci Nim Game ", "webprogram_exclude": "0", "session_ids": ["Session/17961"], "source_sha256": "98f538ccdd41d9602a4645e29030cf4524f87f48203b53d54c78d55a8e0b59e3", "withdrawn": "", "abstract": "Math outreach programs provide opportunities for students to experience mathematics beyond the traditional classroom with intend to develop positive attitudes toward math problem-solving. This presentation will highlight one of the hands-on projects used during various outreach programs at surrounding high schools. It will demonstrate winning strategies for solving Nim game and connection with Fibonacci numbers. We explore student engagement and collaboration through the use of the Fibonacci Nim game, a two-player mathematical game in which players strategically remove objects from a pile according to changing constraints.\n\nThis project is designed to provide opportunities for high-school and undergraduate students to learn about one of the interesting and fascinating properties of the Fibonacci numbers (the Zeckendorf representation) and to emphasize critical thinking in developing strategies for solving various Nim games. At the end, some of the feedback about this project that the participating students provided on the post-survey will be shared.", "id": "Paper/70116", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70116"}, {"title": " Paths in <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"5.168ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 2225.2 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">(3,3)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-33\" x=\"389\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2C\" x=\"890\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-33\" x=\"1335\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"1835\" y=\"0\"></use>\n</g>\n</svg>-tournaments ", "webprogram_exclude": "0", "session_ids": ["Session/18360"], "source_sha256": "b3bfaa72d7bd5171b90b03260ae51f16b462cc7b5b6d38bf298d4b92f07df3c6", "withdrawn": "", "abstract": "It is well known that every tournament contains a spanning path.  We study a generalization to \\emph{fully directed hypergraphs}, where each edge comes with a total ordering of its vertices.  For $0\\le k\\le r!$, an \\emph{$(r,k)$-tournament} is a fully directed hypergraph such that each set of $r$ vertices spans $k$ edges. A $(2,1)$-tournament is just a conventional tournament.  Let $f(n,r,k)$ be the minimum, over all $(r,k)$-tournaments $G$ with $n$ vertices, of the maximum size of a (tight) path in $G$.  In our language, the statement that every tournament has a spanning path becomes $f(n,2,1)=n$.  \n\nIn this talk, we focus on $(3,3)$-tournaments.  We show that $\\Omega((\\log n)^{1/2 - o(1)}) \\le f(n,3,3) \\le O(\\log n)$.  This is joint work with Richard C. Devine.", "id": "Paper/70117", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70117"}, {"title": " Enumeration of Arithmetical Structures on Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17943"], "source_sha256": "99c4b82be20cadcc7548079b9973242c685f0601ccb250cb155cbe8d89875e21", "withdrawn": "", "abstract": "Arithmetical structures on graphs are positive integer vertex labelings satisfying certain divisibility and coprimality conditions. Their enumeration connects graph theory with classical combinatorial sequences, including the Catalan numbers. In this talk, we will survey enumeration results and open questions for several families of graphs. We will then turn to an extremal question: among connected graphs with a fixed number of vertices, which have the fewest arithmetical structures? We will present new results concerning the role of path graphs as minimizers.", "id": "Paper/70118", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70118"}, {"title": " The ACCTION Project: Utilizing a Documentary Film as a Virtual Reverse Site Visit ", "webprogram_exclude": "0", "session_ids": ["Session/18200"], "source_sha256": "d54268567ce60696a02d2522cb4912752080e192e8f844eb36ff685314edfaca", "withdrawn": "", "abstract": "Mathematics education at the community college level often faces barriers to implementing active learning due to faculty resistance, logistical challenges, and a lack of authentic, scalable professional development. The NSF-funded ACCTION (Advancing Community College Teaching and Innovations to Overhaul Norms) project at Randolph Community College addresses this gap by utilizing a highly unique deliverable: a documentary film.\n\nThis presentation explores the development of the ACCTION documentary as a \"virtual reverse site visit.\" Rather than relying on abstract descriptions, this immersive medium invites a diverse audience—instructors, students, administrators, and policymakers—to virtually step inside a reformed community college classroom. It allows these critical decision-makers and stakeholders to witness exactly how to implement active learning methodologies while intimately experiencing the student perspective. By capturing the authentic, and often challenging, transition from passive lecture to student-centered active learning in Precalculus Algebra, the film serves as an innovative tool for broad dissemination. We will detail the methodology behind engineering a specialized Active Learning Space equipped for broadcast-quality data capture, allowing for the observation of unscripted peer-to-peer discourse and genuine student engagement.\n\nFurthermore, this talk will discuss the theoretical framework of using visual media to influence faculty perspectives. Documenting the real-time application of strategies—such as the Building Thinking Classrooms framework—provides educators with a tangible model of pedagogical transformation. By visualizing both the reduction of student math anxiety and the instructor's transformative journey, the documentary aims to overcome institutional inertia. Attendees will gain insights into how leveraging audiovisual media and narrative storytelling can serve as a powerful catalyst for widespread pedagogical reform and scalable professional development in the mathematical sciences.", "id": "Paper/70119", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70119"}, {"title": " Complex Stochastic Gradient Descent and Directional Bias in Reproducing Kernel Hilbert Spaces ", "webprogram_exclude": "0", "session_ids": ["Session/17718"], "source_sha256": "13673b4aa8bfc6145ff981c14e336313f31153e6ed6389a7c19c69537be58b49", "withdrawn": "", "abstract": "Stochastic Gradient Descent (SGD) is a known stochastic iterative method popular for large-scale convex optimization problems due to its simple implementation and scalability. Some objectives, such as those found in complex-valued neural networks, benefit from updates like in SGD and Gradient Descent (GD) with a newly defined ``gradient'' that allows for complex parameters. Complex variants of the SGD/GD methods have already been proposed, but convergence guarantees without analyticity constraints have not yet been provided. We propose a variant of SGD (complex SGD) that allows for complex parameters, and we provide convergence guarantees under assumptions that parallel those from the real setting. Notably, these results extend to GD, and with the same set of assumptions, we demonstrate that known directional bias results extend from the real to the complex setting for general regression problems. We also provide empirical results demonstrating the efficacy of the complex SGD in sample kernel regression problems with complex reproducing kernel Hilbert spaces.", "id": "Paper/70120", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70120"}, {"title": " Circulations of Life – Geometrically and Polar ", "webprogram_exclude": "0", "session_ids": ["Session/17091"], "source_sha256": "3d1c6c5f2ac2fc6d0aa240b28fae22e4d361682ed610f6429acca3ab53d8fdff", "withdrawn": "", "abstract": "The course of life can be seen in cycles and circulations, including some people’s beliefs of birth and rebirth, but also as a combination of linearity and cyclicity in spirals and other curves that can be described in polar coordinates. Two solo dance pieces explore both options – geometrically through the conic sections, and through diverse polar curves generated by a Mathematica program", "id": "Paper/70121", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70121"}, {"title": " Come learn about MSRI-UP ", "webprogram_exclude": "0", "session_ids": ["Session/18166"], "source_sha256": "31b88ff6539450f48e684ff6d766940244ac213769100828af0c4aca81de34b5", "withdrawn": "", "abstract": "In celebration of the 20th cohort of MSRI-UP, this session highlights the program’s history, core structure, and key metrics of success. Attendees will gain valuable insights into the design and impact of this long-running Research Experience for Undergraduates (REU). This interactive talk is designed both for prospective student participants and for faculty members who currently run (or are interested in launching) their own REU programs. The presentation will conclude with an open Q&A session.", "id": "Paper/70122", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70122"}, {"title": " Implementing Building Thinking Classrooms in Precalculus Algebra: Early Outcomes from the ACCTION Project ", "webprogram_exclude": "0", "session_ids": ["Session/18199"], "source_sha256": "da561638d1b1170e6bb2d990886ad75bb02a123a2a5b6120de50fcd7da2af259", "withdrawn": "", "abstract": "The transition from passive lecture-based instruction to student-centered active learning is often hindered by a lack of discipline-specific, ready-to-implement curriculum. The NSF-funded ACCTION (Advancing Community College Teaching, Innovations to Overhaul Norms) project addresses this challenge through a collaborative partnership led by Randolph Community College and Chandler-Gilbert Community College (CGCC). With CGCC playing a pivotal role in curriculum design, the project is developing and piloting specialized Open Educational Resources (OER) explicitly tailored for Precalculus Algebra.  \n\nThis presentation highlights the early outcomes of integrating the Building Thinking Classrooms (BTC) framework into community college mathematics. We will explore the practical application of active learning strategies, including the use of vertical non-permanent surfaces and strategically designed, high-cognitive-demand tasks that balance procedural fluency with deep conceptual understanding. Because we are currently piloting these newly developed OER materials in 5 classrooms across 3 colleges, we will bring preliminary empirical results directly to the discussion.\n\nFurthermore, this session will detail our methodology for assessing these pedagogical shifts in real-time. By utilizing the Observation Protocol for Active Learning (OPAL) and the Mathematical Sophistication Instrument (MSI), we are actively measuring how targeted instructional redesigns reduce student math anxiety and foster authentic mathematical discourse. Finally, we will highlight how these live classroom implementations are being captured in a documentary film to provide a scalable, visual model for systemic reform in undergraduate STEM education.", "id": "Paper/70128", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70128"}, {"title": " ON THE DIAMETERS OF EXACT DISTANCE SQUARE GRAPHS ", "webprogram_exclude": "0", "session_ids": ["Session/19354"], "source_sha256": "c18d89d8497a26bf7c54eed57a1143196d531c51fbe3d3dffc9a092de84b827e", "withdrawn": "", "abstract": "Let $G$ be a connected graph with diameter $n \\ge 3$. The exact distance square graph, denoted by $D_2(G)$, is formed by adding an edge between any two vertices $u, v \\in V(G)$ if and only if their shortest path distance in $G$ is exactly $d_G(u, v) = 2$. The relationship between $\\operatorname{diam}(G)$ and $\\operatorname{diam}(D_2(G))$ has been the subject of recent conjectures in structural graph theory [1, 2]. \n\nThis work rigorously resolves two outstanding problems regarding these diameter bounds. First, we prove a recent conjecture [1], establishing the universal upper bound that $\\operatorname{diam}(D_2(G)) \\le n + 2$. Second, we resolve an open problem [1] by explicitly constructing a specific graph class partitioning the vertex set to demonstrate that for an odd diameter $n \\ge 3$, the absolute minimal diameter of $D_2(G)$ evaluates strictly to $\\lfloor n/2 \\rfloor + 1$. \n\nFurthermore, we explore the sharpness of the upper bound for arbitrary odd diameters $n > 3$ [2]. To analyze this sharpness, we formulate a novel intersection metric, $e$, defined as the size of the intersection between the vertex set of a chosen diametric path $P$ in $G$ and the cycle-extended diametric set $(P_c)^{\\#2}$ in $D_2(G)$. By establishing intermediate parity lemmas for $n>3$---specifically that $(k-1) \\le e$ for odd $n$, and $k-2 \\le e$ for even $n$ (where $k = \\operatorname{diam}(D_2(G))$)---we provide an explicit algebraic formulation that bounds the exact distance squared graph's diameter and achieve sharp inequalities in both odd and even cases, unlike the paper [2] which only had sharpness for the even case.\n\n\\vspace{1em}\n\\noindent \\textbf{References} \\\\\n{[1]} arXiv:2403.07646 [math.CO] \\\\\n{[2]} arXiv:2501.01575 [math.CO]", "id": "Paper/70131", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70131"}, {"title": " Spatial distribution, competition, coexistence, and range limits in ecology ", "webprogram_exclude": "0", "session_ids": ["Session/18325"], "source_sha256": "64fd457d6f873381ca1238de434f6e2215496814b137c215fddf554377e8ef0f", "withdrawn": "", "abstract": "The joint roles played by space and competition in determining the coexistence of competing species have long interested ecologists.  Classic observations have led to several ‘truths’ about this relationship, two of which were made by Joe Connell more than a half century ago.  The first is that in a habitat that has a gradient of suitability, species are found along the gradient from benign up to the limit of their tolerance, while the lower limit is set by competition.   A second observation he made was that in a habitat with discrete patches coexistence of species is determined by a competition-colonization tradeoff.  A more recent empirical observation made by Dallas and coauthors is that species are often most abundant at the edges, not the middle of their range though other data shows the opposite.  Using models based on ordinary differential equations, both implicit and spatially explicit, as well as integro-difference equations, I will show how to explain and reconcile these different observations.", "id": "Paper/70132", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70132"}, {"title": " Complexity of the spectral radius of nonnegative tensors via geometric programming ", "webprogram_exclude": "0", "session_ids": ["Session/16950"], "source_sha256": "5156707b2a8a57579db3fb3074a2712577333fbaba56f6a7086c783136a50e05", "withdrawn": "", "abstract": "We show that the spectral radius of a homogeneous polynomial map, or equivalently of a partially symmetric nonnegative tensor,\ncan be approximated in polynomial time.   We further show that the logarithm of the positive eigenvector is polynomial-time approximable if the polynomial map satisfies a strong irreducibility condition.\nWe also show that the maximum of a nonnegative homogeneous $d$-form over the $\\ell_d$ unit ball can be approximated in polynomial time.   In particular, the spectral radius of uniform weighted hypergraphs and some known upper bounds on the clique number of uniform hypergraphs are polynomial-time computable.  We establish these results by studying an unconstrained geometric programming problem which consists in\nminimizing a function given by the maximum of finitely many log-Laplace transforms of discrete nonnegative measures over a Euclidean space.  \n  Under a coerciveness assumption, we show that an $\\varepsilon$-minimizer\n  can be computed in a time that is polynomial in the input size and in $|\\log\\varepsilon|$. This is obtained by establishing bit-size estimates on approximate\n  minimizers in terms of a geometric condition number, and by applying the ellipsoid method. Then, we relate the tensor eigenproblem to the Poisson equation\n  arising in discrete potential theory, and bound this condition number in terms of mean hitting times.\nAs an application, we provide an example showing that the Phase-I approach needs exponentially many bits\nto solve the feasibility problem in geometric programming. This talk will also include an overview of the spectral problem for nonnegative tensors, covering its link with non-linear Perron-Frobenius theory and tropical geometry.", "id": "Paper/70133", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70133"}, {"title": " Approximate Syzygies, Tensor Methods and Smoothed Analysis ", "webprogram_exclude": "0", "session_ids": ["Session/16950"], "source_sha256": "24a345137fffc6073b451f4519aaa6c930b7a4378e6f0c0d712cb3f62eb76fb0", "withdrawn": "", "abstract": "We develop new techniques for proving smoothed analysis bounds for algorithmic problems related to tensor decompositions, and their applications. The main technical contribution is smoothed analysis for approximate syzygies of a given set of low-degree homogenous polynomials. Smoothed analysis is a powerful paradigm for proving robust, polynomial time guarantees of algorithms on worst-case computationally intractable problems. While polynomial time smoothed analysis guarantees are desirable, they have been challenging to obtain as they entail lower bounds on the least singular value of random matrices with limited randomness. The matrices we consider have entries that are given by polynomials of a few underlying base random variables. We use these ideas to obtain new smoothed analysis guarantees in previously open settings.", "id": "Paper/70134", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70134"}, {"title": " A Distributional Laguerre Transform ", "webprogram_exclude": "0", "session_ids": ["Session/19336"], "source_sha256": "cbc813c84fab5781d9c4bdfb9276d35708a356c75bcf6e91bad3c37f9bce13ec", "withdrawn": "", "abstract": "In this paper, a new class of test function spaces $S_{\\alpha}$, and $I$ are defined and it is shown that the Laguerre transform is an isomorphism from $S_{\\alpha}$ onto $I$. Exploiting the above results, the Laguerre transform in corresponding distribution spaces are defined and it is shown that the distributional Laguerre transform is an isomorphism from $S_{\\alpha}'$ onto $I'$.  Moreover, the continuity and boundedness of the the continuous Laguerre wavelet transform of distributions in the space $\\tilde{S_{\\alpha}}([0, \\infty)\\times (0, \\infty))$ are discussed.", "id": "Paper/70135", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70135"}, {"title": " \\title{A two-sex model of HPV vaccination, screening, and cervical cancer} ", "webprogram_exclude": "0", "session_ids": ["Session/19353"], "source_sha256": "7fb1f653d1969d3655e88eff63dd0f4c6783c2eb23ba5bdc97614c98cab523c9", "withdrawn": "", "abstract": "\\begin{abstract}\nVaccination against human papillomavirus (HPV) and cervical screening are important strategies for reducing cervical cancer, but incomplete uptake may delay population-level control. We develop a two-sex deterministic compartmental model linking heterosexual HPV transmission to cervical cancer progression. To account for recurrent high-risk HPV infection, individuals who clear infection are allowed to become susceptible again. We derive the basic reproduction number $R_0$ and control reproduction number $R_c$ and analyze the corresponding disease-free and endemic equilibria. The full model also exhibits backward bifurcation driven by imperfect vaccination. A subset of parameters in a reduced model was estimated using cancer incidence from the SEER9 registry and national cervical cancer mortality data for the United States. Structural and practical identifiability analyses were conducted, together with local and global sensitivity analyses. The results show that $R_c$ increases with transmission rates and decreases with vaccination coverage, while transmission and screening detection rates strongly influence cervical cancer incidence. These findings provide a quantitative framework for evaluating vaccination and screening strategies to reduce HPV transmission and cervical cancer burden.\n\\end{abstract}\n\n\n\n\\noindent\\textbf{Keywords:} HPV, cervical cancer, vaccination, screening, control reproduction number", "id": "Paper/70136", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70136"}, {"title": " Link between quantum measurement and the iε term in the QFT propagator ", "webprogram_exclude": "0", "session_ids": ["Session/18321"], "source_sha256": "13bf0e178c870671e76eb59aa35fd7401658402e722a51c7c7a4f940c4c9daf9", "withdrawn": "", "abstract": "In quantum field theory propagators, infinitesimal iε term is added to avoid poles. In this talk we present a model where iε is finite instead of infinitesimal. We show that it is equivalent to continuous measurement model where path integral is weighted by the Gaussian centered on classical trajectory where ε is the Gaussian parameter. We claim that this leads to the emergence of transition from quantum to classical on the scale proportional to inverse power of ε. Thus, the assumption that ε is infinitesimal is equivalent to the assumption that nature is quantum on all scales. Conventional quantum field theory formalism implicitly makes both of those assumptions without noticing the logical link between the two. In the model we present we abandon both of them at the same time and notice the logical connection between abandoning one and abandoning the other. This talk is based on the following paper: R Sverdlov and L Bombelli, \"Link between quantum measurement and the iε term in the QFT propagator,\" arXiv:1306.1948 (2013), and Phys. Rev. D 90: 125020 (2014).", "id": "Paper/70139", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70139"}, {"title": " Projection schemes, asymptotic centers and the fixed point property in Banach spaces ", "webprogram_exclude": "0", "session_ids": ["Session/17782"], "source_sha256": "50e2694a57561e0b05929f2e3482c3d0bf9859bbdcdb5bcfcfe0f5aae23d5392", "withdrawn": "", "abstract": "We introduce the notion of a projection scheme on a Banach space and develop an abstract framework for studying the fixed point property (FPP) for nonexpansive mappings. Within this framework, we obtain a general criterion ensuring the FPP for a broad class of nonreflexive Banach spaces. In particular, every uniformly convex Banach space admits an isometric embedding into a nonreflexive Banach space having the FPP. This criterion also unifies and extends several previously known fixed point results for Banach spaces with Schauder bases.\n\nAs an application of our general result, we characterize the FPP for variable Lebesgue spaces. More precisely, we prove that if  $(\\Omega,\\Sigma,\\mu)$ is a $\\sigma$-finite measure space and $p:\\Omega \\to [1,\\infty]$ is a measurable function,  then $L^{p(\\cdot)}(\\Omega)$ has the FPP if and only if it does not contain an isometric copy of $\\ell_1$. Consequently, as in the classical Lebesgue spaces, the presence of an isometric copy of $\\ell_1$ completely characterizes the failure of the FPP in variable Lebesgue spaces. This result yields a class\nof nonreflexive Banach  spaces with the fixed point property that contain isometric copies of infinitely many $L^p$-spaces, $1<p<\\infty$.  Although nonreflexive sequence spaces with the FPP are known, to the best of our knowledge, these variable Lebesgue spaces provide the first examples of nonreflexive Banach function spaces with the FPP.", "id": "Paper/70140", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70140"}, {"title": " Components of subregular <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.936ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 833.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\Delta</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-394\" d=\"M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-394\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Hessenberg varieties ", "webprogram_exclude": "0", "session_ids": ["Session/18308"], "source_sha256": "1c6b23f26ea4e31cfd2ac9d009bf074bcb359bc780698807e65f8777919d9b24", "withdrawn": "", "abstract": "A fundamental problem in the study of the flag variety is how the Poincar\\'{e} dual class of an interesting subscheme decomposes into the Schubert basis.  Nadeau and Tewari give a complete, combinatorial resolution of this problem for the class of the permutahedral variety, which is  'the' regular semisimple Hessenberg variety for the minimal indecomposable ideal $\\Delta$.  We now consider subregular Hessenberg varieties for $\\Delta$, which have the same overall class as the permutahedral variety, with the added twist of having multiple irreducible components.  In this talk, based on joint work with Woo and Zhuang, I will classify these components, present a formula for their classes, and describe how they give a combinatorial refinement of Nadeau and Tewari's result.", "id": "Paper/70141", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70141"}, {"title": " Constructing Symmetric Patterns on Cubes ", "webprogram_exclude": "0", "session_ids": ["Session/17986"], "source_sha256": "a3b1fea0e5b47e29907fd14c08d2223d83735d08093f6169be1d58df830b17c8", "withdrawn": "", "abstract": "The full point symmetry group of the cube has 48 elements and contains a rich structure with 33 subgroups. However, it can be hard to compare patterns arising from different subgroups by looking at polyhedral nets or projected two-dimensional images that hide 3 or more faces.  This work shows how the Jackson cube, a modular origami design, can be used to easily create a pattern with a given subgroup symmetry from a set of six patterned strips of paper. This technique can be used to help study symmetry patterns naturally associated with the cube.", "id": "Paper/70144", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70144"}, {"title": " Formulas for Koornwinder polynomials ", "webprogram_exclude": "0", "session_ids": ["Session/18375"], "source_sha256": "54ff8fb718942250cc05a2ac22a55987ba22cba968138b0e107c7811b69d8258", "withdrawn": "", "abstract": "Koornwinder polynomials are the `universal' Macdonald polynomials of classical type, specializing in various ways to the Macdonald polynomials from every classical root system.  They are also Macdonald polynomials in their own right for the non-reduced root system of type $(C^\\vee, C)$.  In this talk I will discuss my joint work with Laura Colmenarejo and Arun Ram on monomial coefficient formulas for Koornwinder polynomials, beginning with the operator theoretic creation operators before moving on to tableaux-based combinatorial formulas.  Our main result is a new `compression formula'  that has dramatically fewer terms than previous formulas for many cases.  We conclude by comparing our results with other formulas for Koornwinder and classical Macdonald polynomials.", "id": "Paper/70147", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70147"}, {"title": " Risk assessment in topologically connected dynamical systems with applications to neurodegenerative diseases ", "webprogram_exclude": "0", "session_ids": ["Session/19364"], "source_sha256": "d356316105edbfaeeeea3eab6c3e8e0c6e707e45b4295011fb9cb38a64a59e63", "withdrawn": "", "abstract": "Risk is an intrinsic part of our daily lives. It governs the choices we make, what possibilities we forgo, and what opportunities we may set forth to pursue. While visible risk can be managed and contended with, invisible risk, however, is particularly insidious in form and in function. As the brain ages, it undergoes changes; one example is the onset of low-grade chronic inflammation as our immune system becomes less effective.  Disruptions to brain equilibrium can shift the biological and neurological mechanisms that give rise to neurodegenerative diseases like Alzheimer's Disease (AD).  We understand that what brain areas are affected by AD, and in what order, can tell us something about the severity of AD and its associated health risks. \n\nIn this talk, I will discuss a novel framework to assess risk in network dynamical systems that makes use of a recent advance in topological data analysis.  I am working to apply my framework to the study of the shape of first passage times to AD pathology and to understanding the associated health factors, like inflammation, as risk indicators on the road to developing AD.", "id": "Paper/70149", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70149"}, {"title": " Taking shape: patterns in flowing, growing, and phase-changing materials ", "webprogram_exclude": "0", "session_ids": ["Session/17370"], "source_sha256": "d32cd7da0962befb65bf15558dccc3de3e5f24c4e3ec0cf89f59391ba4435b22", "withdrawn": "", "abstract": "Many fabrication processes are designed to suppress instabilities in order to reproduce a prescribed geometry. Here I ask the opposite question: when can local instabilities and geometric constraints be used to select global form? I will discuss soft-material systems in which patterns emerge through flow and growth as the material progressively arrests. In fused-filament 3D printing, under-extrusion destabilizes uniform deposition and produces a periodic sequence of adhered droplets and stretched threads. Experiments and a minimal model reveal how the pattern is selected by material supply, nozzle motion, and interaction with the previous layer, and how this local mechanism propagates through stacked layers and curved printing paths. I will then turn to expanding foams, where growth, bubble-scale rearrangements, confinement, and solidification shape both local structure and global morphology. Together, these systems frame a common local-to-global problem in which transient material dynamics become encoded into persistent spatial form. I will emphasize reduced models, geometric control parameters, and emerging questions in growth-driven pattern formation.", "id": "Paper/70150", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70150"}, {"title": " Multigraph Models of Chromosome Aberration Pathways in Cancer ", "webprogram_exclude": "0", "session_ids": ["Session/18358"], "source_sha256": "4f06cf18d1b28a4d2a5e2c5b83d4172fd28e85a6e675da2a7424462edf5fd8c9", "withdrawn": "", "abstract": "Exchange-type chromosome aberrations arise from chromosome breaks and rejoining events and play an important role in cancer genome evolution. Aberration multigraphs provide a mathematical framework for encoding these rearrangements and their possible formation pathways as cycles. Motivated by prostate cancer data of Baca et al., where complex chains of rearrangements known as chromoplexy were identified, we study how multigraph models can be used to characterize and compare possible aberration pathways.\n\nA central challenge is that experimental data may not determine the underlying cycle structure uniquely. We combine theoretical and computational methods to analyze these ambiguities and use chromosome fragment reversals to organize possible cycle structures into a graded partial order. This framework provides a way to study cancer chromosome rearrangement pathways in the presence of missing or incomplete data.", "id": "Paper/70152", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70152"}, {"title": " Enumeration of low elements in rank 3 Coxeter groups ", "webprogram_exclude": "0", "session_ids": ["Session/17943"], "source_sha256": "019c10e9612e8cbaff48e92af2b6e071eb3daf1c01c59f75b63fe1796658958d", "withdrawn": "", "abstract": "Coxeter groups admit geometric representations in which roots encode the behavior of reduced words. In particular, small roots encode the states of finite-state automata recognizing reduced words, leading naturally to enumeration problems for small roots and the associated low elements. We study small roots and low elements for rank 3 hyperbolic Coxeter groups with no $\\infty$-bonds. Using the projective geometric representation, we translate their classification into a geometric problem involving the position of normalized roots relative to the isotropic cone. This allows us to explicitly classify and enumerate the small roots and low elements in each family.", "id": "Paper/70155", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70155"}, {"title": " Supersolvability and antichain cutsets in real-ranked lattices ", "webprogram_exclude": "0", "session_ids": ["Session/18138"], "source_sha256": "bd7ebb3cc499577f4fc3a8289d18dbc727148d294bdf8c709e3f832a638cb7a6", "withdrawn": "", "abstract": "A limit construction of von Neumann and of Björner extends a family of semimodular lattices of finite rank to a $[0,1]$-ranked analogue.  For example, this limit construction on the family of finite Boolean lattices is cryptomorphic to the measure algebra and Lebesgue measure on $[0,1]$.  Rank modularity of elements in the finite lattices goes forward to these limit objects.  In particular, we recover a sensible notion of supersolvability.  Motivated by these and other examples, we examine supersolvable real-ranked lattices.\n\nWe consider in this setting an \\emph{antichain cutset}, an antichain that meets every maximal chain.  In a discrete supersolvable lattice, every antichain cutset is a level set, as is not too difficult to prove.  In the real-ranked setting, rank functions can vary as to their level sets; for example, different measures on $[0,1]$ yield different families of sets of fixed measure.  We show that every antichain cutset is a level set with respect to some rank function, as is not too easy to prove.  Our approach works through the topology induced on maximal chains by the rank function, and uses connectedness together with continuity properties of rank, join, and meet.", "id": "Paper/70156", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70156"}, {"title": " Stability of the Prékopa-Leindler inequality ", "webprogram_exclude": "0", "session_ids": ["Session/18442"], "source_sha256": "b9e8326961ef0b8a189defd6e5911a1e1c1035730ecee5cc7be1aacc94264a4d", "withdrawn": "", "abstract": "The Pr\\'ekopa-Leindler (PL) inequality serves as a functional analogue of the Brunn-Minkowski (BM) inequality on the size of sumsets in $\\mathbb{R}^n$. Since PL is obtained from BM in the limit as the dimension tends to infinity, it yields dimensionally independent results in geometry, analysis, and probability, motivating the considerable attention its stability has garnered in recent years. While substantial progress has been made in the geometric setting of BM, a sharp quantitative stability result for the PL has remained out of reach. In this talk, we will introduce these inequalities and present recent results that resolve this long-standing open question. Based on joint work with Alessio Figalli and Marius Tiba.", "id": "Paper/70157", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70157"}, {"title": " Uniformly Positive Scalar Curvature on Manifold Interiors ", "webprogram_exclude": "0", "session_ids": ["Session/17691"], "source_sha256": "fefa9f32e50302840b6717feb84829a7da67ffb16427d823dd4a30df3c4abedc", "withdrawn": "", "abstract": "Let \\(X\\) be a compact manifold of dimension \\(5\\), \\(6\\), or \\(7\\). We show that if \\(\\operatorname{Int}X\\) admits a complete metric of uniformly positive scalar curvature, then \\(X\\) admits a positive scalar curvature metric with minimal boundary. In dimensions \\(6\\) and \\(7\\), the metric may moreover be chosen to be a product near the boundary.", "id": "Paper/70163", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70163"}, {"title": " Continuous invariant-based asymmetry of periodic crystals ", "webprogram_exclude": "0", "session_ids": ["Session/18078"], "source_sha256": "82eaf077f8365bfbd15f835ff0c448c08212c65ca81c0062bd9f4a26ee6ede66", "withdrawn": "", "abstract": "Quantifying the deviation of a periodic crystal from higher symmetry is complicated by discontinuous measures of asymmetry, especially when ideal symmetry can be broken under arbitrarily small perturbations. For example, the relative multiplicity $Z'$, which measures the number of geometrically non-equivalent units in a periodic crystal, can scale up under arbitrarily small atomic displacements inside the crystal structure, which makes $Z'$ unreliable for a practical detection of symmetry. \nA continuous geometric measure can overcome this limitation.\nWe introduce a Continuous Invariant-based Asymmetry ($\\text{CIA}$) for periodic crystals, expressed in physically meaningful \\aa ngstr\\\"oms, which quantifies the deviation of a crystal structure from higher symmetry. \nWe represent the formula units in an asymmetric unit of a periodic crystal (such as full molecules, atoms or ions) as geometric blocks and derive invariant blocks from these representations. We then compare the invariant blocks using the Earth Mover's Distance ($\\text{EMD}$), with Root Mean Square ($\\text{RMS}$) and Chebyshev distances as ground metrics. The resulting $\\text{CIA}$ of a periodic crystal measures the minimum corresponding perturbation that makes all formula units of the crystal structure geometrically equivalent within the same structure. \nOur experiments on several crystal structure prediction (CSP) datasets suggest that approximately half of the simulated crystal structures have high $\\text{CIA}$ values, while the experimental structures in these datasets have $\\text{CIA} = 0$. Moreover, analysis of the Cambridge Structural Database (CSD) shows that many crystal structures with high values of $Z'$ in the CSD turned out to be close to higher symmetric forms due to having low $\\text{CIA}$ values. Thus, $\\text{CIA}$ can also help in understanding the relationship between theoretical predictions and experimental observations by identifying structures close to higher symmetry forms.", "id": "Paper/70175", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70175"}, {"title": " Analyzing UAV Image Stitching Algorithms for Onboard Computation in Realtime Scenarios ", "webprogram_exclude": "0", "session_ids": ["Session/18241"], "source_sha256": "7bb801335a02c44c25ae9c9a9e64ddba084e0be97a5bc8e8b03bfc2040c2938b", "withdrawn": "i", "abstract": "Unmanned Aerial Vehicles (UAVs) rely on image stitching for emergency response, precision agriculture, and search-and-rescue operations by combining individual camera frames into high-resolution panoramic maps. To provide immediate situational awareness and enable visual navigation, image stitching algorithms must execute in real time directly on resource-constrained, onboard hardware. However, standard feature-based image stitching pipelines relying on floating-point descriptors are computationally heavy, leaving it unclear which descriptors optimize the trade-off between spatial accuracy and real-time execution. To address this uncertainty, traditional floating-point descriptors (SIFT, SURF) are systematically benchmarked against lightweight binary descriptors (ORB, TEBLID) across diverse UAV datasets, comparing visual quality metrics (PSNR, SSIM, and LPIPS) with runtime performance (throughput, memory, and power draw). Finally, the comparative analysis aims to establish an optimal selection strategy for accurate and performant UAV image stitching algorithms.", "id": "Paper/70181", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70181"}, {"title": " Higher Categories as Directed Homotopy Types ", "webprogram_exclude": "0", "session_ids": ["Session/18209"], "source_sha256": "7e303576c113444340ca5b539487014d8b2d091d5a7dc3b2726da308dbf5a77d", "withdrawn": "", "abstract": "We demonstrate that the fundamental apparatus of homotopy theory—Postnikov towers, skeletal filtrations, obstruction theory, and Puppe sequences—arises intrinsically in higher category theory. Higher categories are built by iteratively attaching directed cells, in the spirit of CW complexes, while their Postnikov towers give rise to homotopy posets carrying obstruction classes. The associated graded consists of wedges of spheres and directed spheres, leading to stabilization phenomena and a categorical analogue of the Freudenthal suspension theorem.\nThis is joint work with David Gepner.", "id": "Paper/70184", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70184"}, {"title": " A Uniform Construction of Cohomology Theories of Varieties via Fundamental Groupoids ", "webprogram_exclude": "0", "session_ids": ["Session/19356"], "source_sha256": "d187b23c8ad41213279c6f22b92630ac99706ae8cfe54b4eec81c904277c5a07", "withdrawn": "", "abstract": "We prove that the cohomology of a variety is fully recovered from the diagram of fundamental groupoids of its Zariski open subsets in various cohomological settings. This follows from a new sheaf theory that replaces the target category of Zariski sheaves with a fibered category while retaining the Zariski site as the source. Our sheaves assign each Zariski open subset a module over its fundamental groupoid. Each choice of a fundamental groupoid functor and suitable abelian coefficient category yields a cohomology theory on varieties, providing a uniform construction of several cohomology theories. \n\nThe topological fundamental groupoid with abelian groups recovers singular cohomology. The \\'etale fundamental groupoid with discrete abelian groups recovers \\'etale cohomology. The pro-algebraic fundamental groupoid with vector spaces recovers algebraic de Rham cohomology. Most importantly, the pro-algebraic fundamental groupoid with commutative formal groups recovers both \\'etale and algebraic de Rham cohomology in a single sheaf category. In each case, we prove a comparison theorem with the corresponding classical theory or theories. We conjecture that the Nori fundamental groupoid with commutative formal groups recovers both \\'etale and p-adic cohomology.", "id": "Paper/70187", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70187"}, {"title": " Mathematical foundations of Geometric Data Science ", "webprogram_exclude": "0", "session_ids": ["Session/18078"], "source_sha256": "a816c5c3db86e9730ac67926cfb50a48caa9dafcf10a571baabcce6ed890c22c", "withdrawn": "", "abstract": "The first fundamental and often ignored question in Mathematical Data Science is “same or different?” While sounding deceptively simple, this question is notoriously hard for many objects with ambiguous inputs. When walking or driving, our brains (but not computers) easily recognize obstacles whose visual representations change in our moving coordinate system.\n\nIf a rigid object is given by ordered points such as corners, its rigid shape is uniquely determined by a quadratic-size distance matrix. However, for important objects such as protein structures whose main atoms are ordered, a complete and linear-size invariant only recently detected thousands of unexpected duplicates in the Protein Data Bank.\n\nIf given points are unordered, which is the most practical case, the naïve extension of matching such clouds (finite sets of points) or their distance/Gram matrices under Euclidean motion needs exponentially many permutations of points. \n\nIt was a big embarrassment that even 4 points in the plane had no better than a brute-force complete isometry invariant based on all 4!=24 permutations of 4 points until the problem was solved [1], for a fixed dimension, in polynomial time for any number of unordered points under rigid motion [2, Theorem 5.3].\n\nNoise in real data motivates the second fundamental question of Data Science: \"how much different?\" A rigorous answer needs a distance metric that satisfies all metric axioms and changes continuously under perturbations of given points, for example, in the Lipschitz sense.   \n\nThis geo-mapping problem can be stated for many data objects, such as periodic sets, embedded graphs, simplicial complexes, and measures, under other equivalences, including isometry composed with uniform scaling, affine or projective transformations [3, Problem 1.4.5].   \n\n[1] V.Kurlin. Complete invariants of atomic clouds under rigid motion with Lipschitz continuous metrics in polynomial time. MATCH Comm. Math. Comp. Chemistry, v.97(2), p.379-428 (2027).\n\n[2] D.Widdowson, V.Kurlin. Pointwise Distance Distributions for detecting near-duplicates in large materials databases. SIAM Journal on Applied Mathematics, v.86(3), p.898-918 (2026).\n\n[3] O.Anosova, V.Kurlin. Geometric Data Science (290+ pages), arxiv:2512:05040, the latest version at https://kurlin.org/Geometric-Data-Science-book.pdf.", "id": "Paper/70190", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70190"}, {"title": " How Many People can Fit in an Iglu (Igloo): Using Hyperbolic Trig, Solids of Revolution, and Historical Data for a Calc 2 Modeling Lesson ", "webprogram_exclude": "0", "session_ids": ["Session/18088"], "source_sha256": "bde6df630c0d95c0fb71166e2a16fd73789804cd6e1a3d96c7d8cf45458b2a36", "withdrawn": "", "abstract": "This presentation discusses the use of hyperbolic trigonometric functions and solids of revolution to represent an Inuit iglu (igloo), determining its volume, arc length, and surface area. It then discusses an associated Calculus 2 modeling lesson that involves determining the number of Inuit people (from various time periods) that could have fit in different size iglus, taking into consideration differences in gender and sexual orientation.", "id": "Paper/70192", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70192"}, {"title": " Orbit dimensions in generalized Takiff algebras ", "webprogram_exclude": "0", "session_ids": ["Session/17666"], "source_sha256": "75ef74c094a1f97d33a93b70b4e378d31e218b94851050ad64a307161008f3f7", "withdrawn": "", "abstract": "The index $\\chi(\\mathfrak{g})$ of a Lie algebra is the minimal codimension of a coadjoint orbit. Two computations of it stand behind this talk: Rais and Tauvel's formula $\\chi(\\mathfrak{g}_m)=(m+1)\\chi(\\mathfrak{g})$ for the generalized Takiff algebras\n$\\mathfrak{g}_m=\\mathfrak{g}\\otimes\\mathbb{C}[T]/(T^{m+1})$ and Elashvili's conjecture, proven by Yakimova, de Graaf, Charbonnel and Moreau, that a centralizer in a reductive Lie algebra has the same index as the algebra itself.\n\nFor $n\\geq m$ and an adjoint orbit $\\mathcal{O}\\subset\\mathfrak{g}_m$, let $\\Omega_{m,n}(\\mathcal{O})$ be the variety of elements of $\\mathfrak{g}_n$ whose truncation modulo $T^{m+1}$ lies in $\\mathcal{O}$.\n\nFor $\\mathfrak{g}$ reductive, the codimension of a generic orbit in $\\Omega_{m,n}(\\mathcal{O})$ specializes to both computations above: to the first at $\\mathcal{O}=\\{0\\}$ with $(m,n)$ arbitrary, to the second at $(m,n)=(0,1)$ with $\\mathcal{O}\\subset\\mathfrak{g}$ arbitrary. In both cases it equals $(n-m)\\chi(\\mathfrak{g})$. I will show that this value is always a lower bound, discuss proven equality cases holds and conjecture that it holds for every $\\mathcal{O}$ and every $n\\geq m$.", "id": "Paper/70193", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70193"}, {"title": " Lightning Method of Fundamental Solutions for Laplace Equations with Non-harmonic Boundary Data with Multiple-Precision Computing ", "webprogram_exclude": "0", "session_ids": ["Session/17823"], "source_sha256": "50b3b7dca933cea48e17ad7abb7a51e946623038be5b849e1c493ef67bdfb138", "withdrawn": "", "abstract": "The method of fundamental solutions (MFS) is a boundary-type meshless method that approximates the solution by fundamental solutions with source points placed outside the computational domain. Its boundary-only and integration-free formulation makes the MFS simple and highly accurate.\nHowever, the resulting system can become severely ill-conditioned, particularly when high accuracy is sought and the source points approach the physical boundary. In addition, conventional source distributions may be inefficient for problems with non-harmonic or discontinuous boundary data that induce localized corner singularities. \n\nThis study develops two complementary extensions of the conventional MFS for Laplace equations. First, a Multiple-Precision Method of Fundamental Solutions (MPMFS) is introduced to overcome the loss of numerical accuracy caused by ill-conditioning. By employing multiple-precision arithmetic,\nthe MPMFS permits very ill-conditioned systems to be solved while retaining sufficient significant digits, thereby extending the attainable accuracy beyond that of standard double-precision computation. Second, a Lightning Method of Fundamental Solutions (Lightning MFS) is developed to\nefficiently resolve localized corner singularities. Inspired by the Lightning Method, fundamental-solution sources are clustered root-exponentially toward singular boundary points, concentrating the\napproximation capability in regions where the solution varies rapidly. Multiple-precision computation can additionally be used with the Lightning MFS when strong source clustering produces severe ill-conditioning.\n\nThe MPMFS and Lightning MFS therefore address two different limitations of the conventional MFS: loss of numerical precision due to ill-conditioning and inefficient representation of localized singular behavior, respectively. Numerical examples for Laplace problems with non-harmonic boundary data are used to examine their accuracy and convergence and to demonstrate the advantages of combining multiple-precision computation with lightning-type source clustering when required.\n\n\\textbf{Keywords:}\nLaplace equation; non-harmonic boundary data; method of fundamental solutions; multiple-precision computing; lightning method; lightning method of fundamental solutions", "id": "Paper/70194", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70194"}, {"title": " Indiscernible Extraction Beyond Stability ", "webprogram_exclude": "0", "session_ids": ["Session/19340"], "source_sha256": "9366eb3d7029fbda2bcbf546000d086a8aff5163c796d4260c2ae16480d7c71a", "withdrawn": "", "abstract": "Bounded $k$-splitting is a higher-arity generalization of stability. Hanson established indiscernible extraction results for these theories under large-cardinal hypotheses, raising the question of whether such assumptions are necessary. Building on this work and Shelah’s classical arguments for stable theories, I will present type-counting and indiscernible extraction results in ZFC for these theories. As an application, I will show that theories with bounded $k$-splitting admit total bounded ultraimaginary Morley sequences without any large-cardinal assumption.", "id": "Paper/70195", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70195"}, {"title": " A geometric analysis of the Protein Data Bank and AlphaFold2 predictions ", "webprogram_exclude": "0", "session_ids": ["Session/18078"], "source_sha256": "2c1a4af959a7d44babcd712de20b569cc0ffefb1f87f6e96f68a0d8f37c438fe", "withdrawn": "", "abstract": "A 3-dimensional structure of a protein backbone is an equivalence class of all embedded backbone atoms under rigid motion. The moduli space of protein backbones is infinitely continuous and contains physically realizable backbones as a sparse subset.\n\nWe designed a linear-size Backbone Rigid Invariant (BRI) and proved its completeness for protein backbones (under rigid motion, also distinguishing mirror images) and its Lipschitz bi-continuity under atomic perturbations [1].\n\nWe computed the BRI  for all 707K+ chains with full geometric data in the Protein Data Bank (PDB) within a few hours on a modest desktop computer.\n\nAll-vs-all comparisons detected thousands of unexpected duplicates, where the majority of pairs turned out to have identical x,y,z coordinates, which is unlikely to happen in independent experiments.\n\nIn dozens of cases, identical backbones have different sequences of amino acids, which likely requires corrections in the PDB, confirmed by several authors [2].  \n\nMore recently, a geometric analysis of the PDB and AlphaFold2 (latest version 6) datasets detected numerous violations of the expected geometry in chemical bond lengths and angles, as well as clashes of atoms whose positions were predicted to be too close.\n\n[1] O.Anosova et al. A complete and bi-continuous invariant of protein backbones under rigid motion.\nMATCH Comm. Math. Comp. Chemistry, v.94(1), p.97-134 (2025).\n\n[2] A.Wlodawer et al. Duplicate entries in the Protein Data Bank: how to detect and handle them. Acta Crystallographica D, v.81(4), p.170-180 (2025).", "id": "Paper/70198", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70198"}, {"title": " Eigenvalues of characters, Adams operations, and Feit’s conjecture ", "webprogram_exclude": "0", "session_ids": ["Session/17832"], "source_sha256": "14bdc4fbc1feeaa9652c28fb4149adc0d249f19367abf921be4f8535f39b2668", "withdrawn": "", "abstract": "We introduce an integer $S(G,\\chi,n)$ associated to a finite group $G$, a character $\\chi$ of $G$ and a positive divisor $n$ of the exponent of $G$. It can be defined in two different ways: As the sum of certain coefficients of the canonical induction formula of $\\chi$, or as the multiplicity of the trivial character in an alternating sum of certain Adams operations of $\\chi$. It turns out that this integer is always non-negative and that it is positive if and only if there exists an eigenvalue of order $n$ for one of the matrices appearing in a representation affording $\\chi$. This is joint work with Gabriel Navarro and is motivated by the Feit Conjecture.", "id": "Paper/70199", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70199"}, {"title": " Homological shift ideals of weighted oriented graphs ", "webprogram_exclude": "0", "session_ids": ["Session/19342"], "source_sha256": "160b71dffb9a1e53d5ea14dc6bdd9e2c4523447c50fe107d06d72a6a217c3d4b", "withdrawn": "", "abstract": "In this paper, we study the homological shift ideals of edge ideals associated with weighted oriented graphs. For a weighted oriented graph $D$, let $HS_k(I(D))$ denote the $k^{th}$ homological shift ideal of its edge ideal $I(D)$. If $D$ is vertex-splittable, then we characterize that $HS_1(I(D))$ has linear quotients if and only if $D_6$, $D_7$, and $D_8$ are not induced subgraphs of $D$. Furthermore, we show that if $I(D)$ has linear quotients, then $\\sqrt{HS_k(I(D))} = HS_k(I(G))$, for all $k\\geq 1$, where $G$ is the underlying simple graph of $D$. We show that if $I(D)$ has homological linear quotients, then $I(G)$ also has homological linear quotients. If $D$ is a tree, then we establish the following characterization:     \n    \n    $HS_k(I(D))$ \\text{ has linear quotients for all } $k\\geq 0$ $\\iff$  $G$ is a star graph or a broom graph and  $D$ is $D_i$-free, for  $i=1,2,5,6,8$.", "id": "Paper/70200", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70200"}, {"title": " The Math Fantastic: Your Storytelling Toolkit for Models, Conjectures, and Experiments ", "webprogram_exclude": "0", "session_ids": ["Session/18211"], "source_sha256": "c0dd4aeb291f6b572e78abaadb5f5732be22524f12a2769b70efbb40bb2bcbd4", "withdrawn": "", "abstract": "Every child has a story to tell. That's an opportunity: through stories, we can help children make a good world possible with better mathematics. We can make imagined futures credible with math and science (Robinson, 2026). Mathematical fiction doesn't have a shelf to itself in most libraries, yet many experienced math circle leaders start every topic with a story. Planning to study the bridge between stories and mathematics from enactivist perspectives (Kieren, 2002), we have invited designers working at the intersection of math circles and mathematical fiction to share subject-specific ways stories enable children's mathematics. We found that \"the bridge\" is the wrong metaphor: story/math are inseparable aspects of helping children learn while exploring, experimenting, and playing with deep mathematics. Imagination as \"dwelling in worlds that merge and cross boundaries between real and fictional\" serves to unlock \"unexpected possibilities that pervade everyday life\" (Nemirovsky et al., 2012). Building imaginary worlds and dwelling on what follows from their fantastic inner logic is one way to describe to a five-year-old what mathematicians (and storytellers) do.\n\n\"How to Solve It\" (Polya, 1945) was the book of its times, giving practical heuristics for arriving at solutions. These strategies still apply, and in a contemporary math circle, we aspire for more. We want our students to notice mathematical structures and systems in the world, to wonder and conjecture about regularities, to model and to prove, to visualize and to make art, and to organize data into knowledge for tracing impacts. That is, math circles aim to raise makers of mathematics: young authors who tell their own math stories with and for their communities, and whom we can support with techniques rooted in imaginary worlds of fantasy and science fiction. This paper is a collection of such mathematical fiction techniques for broad-reach mathematical circles.", "id": "Paper/70206", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70206"}, {"title": " Most Juntas Saturate the Hardcore Lemma ", "webprogram_exclude": "0", "session_ids": ["Session/18311"], "source_sha256": "fb101a523ee6c26b4d8e627b4e134dc1185ff7dd1dda9876b7c2c56ba1141744", "withdrawn": "", "abstract": "Consider a function that is mildly hard for size-$s$ circuits. For sufficiently large $s$, Impagliazzo's hardcore lemma from 1995 guarantees a constant-density subset of inputs on which the same function is extremely hard for circuits of size $s' \\ll s$. A natural question arising from this lemma is whether the size degradation from $s$ to $s'$ is necessary. We present a simple proof that a random junta witnesses the tightness of the hardcore lemma with high probability.", "id": "Paper/70208", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70208"}, {"title": " Best practices in teaching introductory statistics in the modern classroom ", "webprogram_exclude": "0", "session_ids": ["Session/18064"], "source_sha256": "d9897bb216de6f97b48eb69e748b70332d6273f01fd5eeb8fd8c9bb7d701c097", "withdrawn": "", "abstract": "Statistical understanding is critical for an informed society in a world increasingly being shaped by data. However, numerous studies have shown that the public struggles to understand fundamental statistical concepts. Contributing to this issue are Introductory Statistics students who generally struggle to apply statistical concepts to real-world contexts, show poor post-course retention and end of course performance, and often have minimal engagement during the course. Adding to this complex and challenging milieu, are continually changing expectations of students and institutions about the topics and methodology for Introductory Statistics. As a result, many teachers are left uncertain where to begin. In this talk, we will begin by seeing how choices instructors make about what is in their course (content) and how to teach (pedagogy) are inextricably linked when one thinks about building an Introductory Statistics course. We will then talk about how one can transform traditional methods of teaching statistics by incorporating active learning strategies and a simulation-based approach, in the broader context of the statistical investigation process. Then, we will see how statistical thinking, statistical investigations, and multivariable thinking can be brought into an introductory course that makes heavy use of simulations in a way that directly aligns with the ASA's Guidelines for Assessment and Instruction in Statistics Education (GAISE) recommendations for teaching introductory statistics. We will also share results from the peer-reviewed research supporting the impact of this approach on student learning and engagement. Along the way, we will share freely available student-facing activities and applets, as well as a wide variety of faculty development resources available, to bring this approach into the classroom. Instructors will leave the talk motivated and empowered to make lasting changes to their Introductory Statistics courses.", "id": "Paper/70212", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70212"}, {"title": " Smooth approximation of discrete structures: Usecases of machine learning in Lie theory ", "webprogram_exclude": "0", "session_ids": ["Session/18130"], "source_sha256": "00a9c83d80515f33f0f9d7469aa65a0c9dcd3e437f64334c254b73e29d658fae", "withdrawn": "", "abstract": "Traditionally, artificial neural networks excel in domains with noisy data, even when input and output may have some margin of error and training data is imperfect. When working directly with discrete mathematical structures, however, the margin of error disappears: The training data can be complete and mathematically accurate, but mechanistic interpretability of the model's inner working requires near perfect prediction accuracy.\n\nIn my talk, I will review a past study on affine Deligne-Lusztig varieties (together with Bin Dong, Xuhua He, Pengfei Jin and Qingchao Yu) as well as preliminary ongoing work (together with Tasman Fell, Baran Hashemi, Paul Kerr, Bayley Whitbread, Victor Zhang and others). I will introduce mathematical problems from Lie theoretic combinatorics and explain which strategies were successful for transforming mathematical data into patterns and finally precise conjectures.", "id": "Paper/70214", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70214"}, {"title": " AI Supported Teaching and Learning ", "webprogram_exclude": "0", "session_ids": ["Session/19349"], "source_sha256": "65c82bb983bc9bb4294c0494c709f1e63e92dc81302c1d4816b0f0434af05a70", "withdrawn": "", "abstract": "This project integrates collaborative, AI-supported mini-projects into a Calculus I course. Throughout the semester, students work in pairs to complete these projects, designed to strengthen foundational algebra skills, improve exam preparation, and connect calculus concepts to their academic disciplines and real-world applications.\n\nStudents utilize AI tools to explore ideas, find relevant information, receive personalized support, and consider various approaches to solving mathematical problems. A key component of each project is critically evaluating AI-generated content: students must verify calculations, assess the accuracy and relevance of the responses, and justify their conclusions with appropriate mathematical reasoning.\n\nClass time is dedicated to discussing project ideas, sharing results, and reflecting on AI's effectiveness and limitations as a learning tool. Overall, these mini-projects aim to foster collaboration, critical thinking, information literacy, and student agency while creating a more personalized and inclusive learning environment. This presentation will introduce the project structure, provide activity examples, and discuss how AI-supported learning can enhance student engagement and success in Calculus I.", "id": "Paper/70216", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70216"}, {"title": " Persistent symmetric tensors and their Hessian ", "webprogram_exclude": "0", "session_ids": ["Session/18294"], "source_sha256": "b7901ef23127bc7c34552fe84c477bd2fdcc4290d94a96f6d37f0429848cf459", "withdrawn": "", "abstract": "Persistent tensors were introduced by Gharahi and Lysikov via a recursive construction inspired by quantum information theory. In a nutshell, they constitute a class of tensors that remain well-behaved under the substitution method and, consequently, admit nontrivial lower bounds on tensor rank. In a work joint with Gharahi, we investigate the symmetric case -- namely, symmetric persistent tensors, or equivalently, persistent polynomials. We establish that a symmetric tensor  is persistent if the determinant of its Hessian equals the power of a nonzero linear form. The converse is verified for cubic tensors and in small dimension, by leveraging classical results of B. Segre. \nWe discuss connections with invariants of some prehomogeneous spaces and homaloidal polynomials.", "id": "Paper/70218", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70218"}, {"title": " Monge-Ampère-type equation for forms of positive degree and Demailly’s transcendental Morse inequality ", "webprogram_exclude": "0", "session_ids": ["Session/18337"], "source_sha256": "2606c4281a00edfa3453747abc6bdd2cc0e26cafb26caafc208cfe4a6dbd8601", "withdrawn": "", "abstract": "The Monge-Amp\\`ere-type equation for forms of positive degree was introduced by Dinew and Popovici to prove the qualitative part of an analytic version of Demailly's transcendental Morse inequality for higher cohomology classes, conditional on the solvability of this nonlinear PDE. In this talk, we first show that Demailly's qualitative inequality can be proven unconditionally. We introduce a general gauge-fixing that leads to the $(a,b)$ Monge-Amp\\`ere-type equation. By deriving \\emph{a priori} estimates, we establish the solvability of this class of equations for different parametric values $(a,b)$. As a geometric application, this framework reduces to the classical complex Monge-Amp\\`ere equation, which yields the Demailly's qualitative inequality for higher-degree forms. Further, we prove that the uniqueness of these solutions can be significantly strengthened under the kernel condition $\\bar{\\partial}^*u=0$.", "id": "Paper/70222", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70222"}, {"title": " Monomial Cayley Graphs: An Algebraic Approach to the Hadwiger–Nelson Problem ", "webprogram_exclude": "0", "session_ids": ["Session/17882"], "source_sha256": "f4462d0688939918cfa616b1d9e2153934f7eab6bcb96df16f0de79ce3043292", "withdrawn": "", "abstract": "The Hadwiger–Nelson problem asks how many colors are needed to color the plane so that points at unit distance receive different colors.\nWhat role do algebraic relations among edge directions play in this problem?\nBeginning with examples such as the Moser spindle and de Grey’s five-chromatic graph, we introduce monomial Cayley graphs, whose connection sets consist of all signed monomials in finitely many unit complex parameters.\nThis framework places finite unit-distance constructions inside infinite graphs organized by their generating rotations.\n\nWe use these examples to develop coloring techniques based on polynomial relations, additive characters, and cyclotomic evaluations.\nFor graphs generated by a single rotation, the algebraic nature of the parameter yields broad two-, three-, and four-color results, including a complete classification for roots of unity and an explicit four-chromatic example.\nWe conclude with the conjecture that every one-parameter monomial Cayley graph is four-colorable and discuss how combining rotation parameters can guide searches for higher-chromatic unit-distance graphs.", "id": "Paper/70223", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70223"}, {"title": " Unit Rhombuses in Euclidean Ramsey Theory ", "webprogram_exclude": "0", "session_ids": ["Session/19321"], "source_sha256": "367fedcfb9adf3a55ee43de9f28175ae7065aaee9e485c74a98828d57407a2e2", "withdrawn": "", "abstract": "In this talk, we present a proof that any 2-coloring of the plane contains 4 points of the same color forming a rhombus with unit sides and non-unit diagonals. We discuss a general strategy for proving results of this form, and pose some open problems.", "id": "Paper/70224", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70224"}, {"title": " Quantum circuit diagrams and web graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18384"], "source_sha256": "073714de5d95d00b51a206c5a03527640eb7bdb7ddb6cbe9b4ebc46ec9962e44", "withdrawn": "", "abstract": "Quantum computing is based on a similar model to conventional computing: information travels into a system, is transformed by passing through a sequence of gates, and then exits the system. However, where data in conventional computing comes as bits that can be thought of as zero or one, quantum data comes as qubits that can be thought of as a pair of complex numbers, representing the probability that the qubit is either zero or one; and where conventional computing uses the standard logic gates NOT, AND, and OR, quantum computing uses gates that represent certain matrix operations. In this talk, we give a brief introduction to quantum circuit diagrams and then describe a process to measure the cumulative transformation encoded by the quantum circuit diagram, inspired by a related kind of planar graph called a web.", "id": "Paper/70226", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70226"}, {"title": " Recent Developments on Ill-Posedness of the Euler Equation ", "webprogram_exclude": "0", "session_ids": ["Session/17822"], "source_sha256": "4a21211c080d28f49e74a3cfdebe744fa93b4dfdbc4359803d76a052a61f3b19", "withdrawn": "", "abstract": "There were various recent developments on ill-posedness of the three-dimensional Euler equations. I will discuss some of our recent results on this topic. This is in collaboration with Alexey Cheskidov.", "id": "Paper/70227", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70227"}, {"title": " Different mediums, different math ", "webprogram_exclude": "0", "session_ids": ["Session/18074"], "source_sha256": "2582823aa3a67ed60732c9fb3169a56c1b185646449208c0ade399a7f2030f04", "withdrawn": "", "abstract": "They say “the medium is the message,” but how does this apply to math content? Online math comes in many formats: video, text, games, short-form and long-form, animated and live action. \n\nFor creators, choosing a medium means choosing not just how to present an idea, but which ideas can be presented effectively at all. For consumers, understanding the strengths and limitations of each format helps you find the content that you actually want.\n\nI’ll talk about my experiences creating and consuming content in these different forms, highlighting the trade-offs and opportunities.", "id": "Paper/70229", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70229"}, {"title": " Hydrodynamics and Pattern Formation in Active Fluids ", "webprogram_exclude": "0", "session_ids": ["Session/17370"], "source_sha256": "282e093cf48b145472a489976372760ee5eb2b167a9ce233dda0c2ee390a3287", "withdrawn": "", "abstract": "Active particles convert energy from their environment into motion and, through their interactions, spontaneously organize into dynamic structures across scales. I will discuss experiments with Quincke rollers—electrically driven colloids that provide a versatile model system for studying active matter and its coupling to fluid flow. Individual particles can be programmed to exhibit run-and-tumble–like dynamics, while dense populations self-organize into dynamic clusters, turbulence-like flows, and multi-vortex patterns reminiscent of bacterial suspensions. When confined within a deformable droplet, the collective motion generates large shape fluctuations and drives spontaneous droplet locomotion resembling amoeboid crawling. I will highlight how hydrodynamic interactions, confinement, and deformable boundaries couple particle-scale activity to large-scale pattern formation and emergent motion. I will discuss the mathematical modeling of this system, highlighting our progress on analytical solutions for single-particle dynamics near boundaries and the remaining challenge of simulating many-body hydrodynamic and electrostatic interactions in large, confined populations.", "id": "Paper/70237", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70237"}, {"title": " Extending TAaCGH: From Topological Signatures to Cancer Genomics ", "webprogram_exclude": "0", "session_ids": ["Session/18309"], "source_sha256": "f5899e76d9dc257194d85498d07e4fe54924f2c9edcfb9a8b346997fb13f6aba", "withdrawn": "", "abstract": "TAaCGH is a topological framework for detecting phenotype-associated copy-number aberrations in cancer genomic data developed by Arsuaga and collaborators. The method uses persistent-homology summaries to identify genomic regions whose structure differs between patient groups. We describe recent extensions of this framework that connect topologically detected regions with gene annotation, expression, mutation, and survival data. In breast cancer, this integrated pipeline is being used to investigate candidate regions associated with molecular subtypes and clinical outcomes. This work illustrates how topological data analysis can serve as the first stage of a broader pipeline for discovering and evaluating biologically meaningful structure in high-dimensional genomic data.", "id": "Paper/70238", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70238"}, {"title": " Obstructions to the existence of compact minimal submanifolds ", "webprogram_exclude": "0", "session_ids": ["Session/17871"], "source_sha256": "85f6746bb8e587dcbfd92c1e30b17d022647a70e4158c00bbc91588358e7f7de", "withdrawn": "", "abstract": "In this work we identify obstructions to the existence of compact minimal submanifolds in the noncompact ambient setting. We develop two complementary approaches using techniques from conformal geometry and PDE.", "id": "Paper/70241", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70241"}, {"title": " Discrete Lattices, Continuous Curves: Mathematical Trajectories in Spatial Sound ", "webprogram_exclude": "0", "session_ids": ["Session/18233"], "source_sha256": "9bd3ce417b5339b242ae6e27ddf77f8dd9d0798b9f7900186a3652e89d992765", "withdrawn": "", "abstract": "Composers and sound artists have long treated the placement of sound in space as an aesthetic decision, rather than a simple function of how the auditory system localizes a source. This talk takes the psychoacoustics of spatial hearing—specifically the head-related transfer function—as a starting point rather than a destination, asking instead how spatial placement becomes a formal, mathematically legible process.\nTwo historical episodes serve as points of departure: the siting of British Isles megalithic structures and the antiphonal practice of cori spezzati at St. Mark’s Cathedral in Venice. Both represent spatial sound decisions made prior to any explicit mathematical model. The twentieth century offers more reasoned approaches: Iannis Xenakis's collaboration with Le Corbusier on the Philips Pavilion, alongside his UPIC system, recast spatial and architectural form as a single geometric object, opening the way for complex curves to govern continuous sound trajectories in multichannel space.\nThe talk traces this lineage into the presenter's own practice, including the sound installation Murmuration, which uses Poisson-distributed robotic woodblocks attached to trees. It culminates in a hybrid method for object-based spatialization: a Hamiltonian path fixes an ordered set of waypoints through a discretized spatial lattice, while Bézier interpolation supplies the continuous motion between them—unifying combinatorial routing and continuous-curve design into a single trajectory. This synthesis offers a framework to better understand the mathematics of spatial-sound aesthetics, with implications for object-based formats such as Dolby Atmos.", "id": "Paper/70245", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70245"}, {"title": " Practical Existence Theorems for Deep Learning Approximation in High Dimensions ", "webprogram_exclude": "0", "session_ids": ["Session/18224"], "source_sha256": "ea55c9decbbaf6a6504ee5a4ddafbaa13b4d4662f3f44781177a225f830615ca", "withdrawn": "", "abstract": "Deep learning is arguably the main driving force behind the current AI revolution. While this paradigm continues to enable breakthroughs across a wide range of applications, its mathematical foundations remain far from being fully understood. Motivated by deep learning methods in scientific computing, I will illustrate the framework of practical existence theorems. These theorems aim to bridge the gap between theory and practice by combining constructive approximation results for deep neural networks with recovery guarantees from least-squares and compressed sensing theory. They provide sufficient conditions on network architecture, training strategy, and training set size to guarantee a prescribed level of accuracy for a target function class.\n\nI will highlight recent advances in this area and demonstrate applications of practical existence theorems to high-dimensional function approximation, reduced-order modeling, data-driven dynamical systems, and physics-informed machine learning.", "id": "Paper/70247", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70247"}, {"title": " Magic positivity of zonotopal classes of wonderful varieties and matroids ", "webprogram_exclude": "0", "session_ids": ["Session/18219"], "source_sha256": "16bb653ac7c0f7b85467a10d03f4a3604049de1c26d9297297beb036d844fe49", "withdrawn": "", "abstract": "For a smooth projective variety, Snapper showed that the Euler characteristic of the $x$th tensor power of a line bundle is a polynomial in $x$, called the \\emph{Snapper polynomial}. Snapper polynomials contain a host of intersection-theoretic information and positivity properties of $K$-classes on a variety. \n\nWe study Snapper polynomials on the $K$-rings of matroids through the lens of magic positivity and real-rootedness. These are two of the strongest positivity properties of polynomials, and imply many numerical positivity results about the coefficients of the polynomials in question. We introduce zonotopal classes in the $K$-ring of the toric variety associated to a matroid, which generalize line bundles given by lattice zonotopes. We prove that for every loopless matroid, the Euler characteristic of $x$th tensor power of a zonotopal class is magic positive, establishing the real-rootedness of their $h^{\\ast}$-polynomials. We also introduce analogues of zonotopal classes on the Deligne--Mumford--Knudsen moduli space $\\overline{\\mathcal{M}}_{0,n}$ of stable rational curves, and show that their Snapper polynomials are magic positive. We compare these results by studying the Snapper polynomials of cotangent bundles whose first Chern classes are the $\\psi$-classes. Despite the fact that these Snapper polynomials are not magic positive if and only if $n \\geqslant 8$, we prove directly that $h^{\\ast}$-polynomials of any two distinct cotangent bundles on $\\overline{\\mathcal{M}}_{0, n}$ are real-rooted for any $n$.", "id": "Paper/70250", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70250"}, {"title": " Revisiting Superlinear Convergence of Proximal Newton-Like Methods to Degenerate Solutions ", "webprogram_exclude": "0", "session_ids": ["Session/18069"], "source_sha256": "c9025aa9b743316dcfe02aeb407e1cdcf9b8e9d4ad5f7166b4d295802ca9cc47", "withdrawn": "", "abstract": "We describe inexact proximal Newton-like methods for solving\ndegenerate regularized optimization problems and for the broader problem of\n finding a zero of a generalized equation that is the sum of a\ncontinuous map and a maximal monotone operator.\nSuperlinear convergence for both the distance to the solution\nset and a certain measure of first-order optimality can be achieved\nunder a H\\\"olderian error\nbound condition, including for problems in which the continuous map is\nnonmonotone, with Jacobian singular at the solution and not Lipschitz.\nSuperlinear convergence is attainable even when\nthe Jacobian is merely uniformly continuous, relaxing the standard\nLipschitz assumption to its theoretical limit.\nFor convex regularized optimization problems,\nwe introduce a novel globalization strategy that ensures strict\n\tobjective decrease and avoids the Maratos effect, attaining local\n\t$Q$-superlinear convergence \n    without prior knowledge of problem parameters.\nUnit step size acceptance in our line search strategy does not rely on\ncontinuity or even existence of the Hessian of the smooth term in the objective,  making\nthe framework compatible with other potential candidates for\nsuperlinearly convergent updates.", "id": "Paper/70253", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70253"}, {"title": " Distinct Distances in <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.732ex\" height=\"2.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -1006.6 1176.4 1152.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbb {R}^3</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJAMS-52\" d=\"M17 665Q17 672 28 683H221Q415 681 439 677Q461 673 481 667T516 654T544 639T566 623T584 607T597 592T607 578T614 565T618 554L621 548Q626 530 626 497Q626 447 613 419Q578 348 473 326L455 321Q462 310 473 292T517 226T578 141T637 72T686 35Q705 30 705 16Q705 7 693 -1H510Q503 6 404 159L306 310H268V183Q270 67 271 59Q274 42 291 38Q295 37 319 35Q344 35 353 28Q362 17 353 3L346 -1H28Q16 5 16 16Q16 35 55 35Q96 38 101 52Q106 60 106 341T101 632Q95 645 55 648Q17 648 17 665ZM241 35Q238 42 237 45T235 78T233 163T233 337V621L237 635L244 648H133Q136 641 137 638T139 603T141 517T141 341Q141 131 140 89T134 37Q133 36 133 35H241ZM457 496Q457 540 449 570T425 615T400 634T377 643Q374 643 339 648Q300 648 281 635Q271 628 270 610T268 481V346H284Q327 346 375 352Q421 364 439 392T457 496ZM492 537T492 496T488 427T478 389T469 371T464 361Q464 360 465 360Q469 360 497 370Q593 400 593 495Q593 592 477 630L457 637L461 626Q474 611 488 561Q492 537 492 496ZM464 243Q411 317 410 317Q404 317 401 315Q384 315 370 312H346L526 35H619L606 50Q553 109 464 243Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJAMS-52\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-33\" x=\"1021\" y=\"581\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18139"], "source_sha256": "026ab8240e405996a034e0043923f71035f8cf4d1fa90776ba12c8f494670def", "withdrawn": "", "abstract": "The Erd\\H{o}s distinct distances problem asks to determine the minimum number of distinct distances spanned by $N$ points in $\\mathbb{R}^2$. This was resolved up to polylogarithmic factors by Guth and Katz in 2015. In their work, they developed tools now central to incidence geometry and proved a lower bound of $\\Omega(N/\\log N)$. However, the analogous problems in higher dimensions remained open for a long time.\n\nIn this talk, I will talk about joint work with Jonathan Tidor and Dmitrii Zakharov that resolved the distinct distances problem in $\\mathbb{R}^3$ up to subpolynomial factors. I will mention some difficulties in generalizing the earlier proof by Guth and Katz and some high-level ideas addressing those issues.", "id": "Paper/70255", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70255"}, {"title": " Topological Deep Learning for Viral Genomes, Proteins, and RNA Motifs ", "webprogram_exclude": "0", "session_ids": ["Session/18358"], "source_sha256": "a5485a409030c72d23389e20013e830cd21635872a4495147c93329fb4185e24", "withdrawn": "", "abstract": "Topological methods provide powerful tools for analyzing complex, high-dimensional data. In this talk, I will present recent advances in Topological Deep Learning (TDL) and their applications to key problems in bioscience. A central concept in TDL is Persistent Spectral Graphs (PSGs), a method in Topological Data Analysis (TDA) that is designed to capture intricate topological changes and homotopy shape evolution information for high-dimensional biological data. I will demonstrate how PSG-based representations of biomolecules can be incorporated into AI pipelines to yield TDL models with strong predictive power.\nApplications span multiple biological domains, including forecasting the emergence of new COVID-19 variants, inferring RNA secondary structure motifs, and improving model selection for peptide–protein complexes predicted by AlphaFold2 and AlphaFold3.", "id": "Paper/70256", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70256"}, {"title": " Who Owns the Question? Undergraduate Research After AI ", "webprogram_exclude": "0", "session_ids": ["Session/18262"], "source_sha256": "17f9259df6fc3b337e2351699cb74c76c2bc2f8aa430f871597ab25b0bdf7935", "withdrawn": "", "abstract": "In most undergraduate research, the advisor supplies the question. We do this for defensible reasons: students can execute once given a question, projects must finish in a semester, and a well-chosen question protects a student from a dead end. We argue the cost has been badly underestimated: choosing the question is not preparation for research; it is the research, and supplying it gives students the one part of the work they could have done without us while withholding the part they cannot learn any other way. We further argue that generative AI removes the main practical excuse. When literature triangulation, counterexample search, and computational exploration become cheap, a student can afford to pursue a question that might fail. We propose the Question Formulation Technique as the missing front-end procedure, argue for guardrails that keep AI out of the question itself, and ask what we should be grading instead of theorems.", "id": "Paper/70258", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70258"}, {"title": " Asymptotic Enumeration of Acyclic Orientations on Complete Multi-Partite Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/19346"], "source_sha256": "74b1eba0958fa645566a412edf890b6d516c865aff9401c62eeef58024977a69", "withdrawn": "", "abstract": "Motivated by questions of Donald E. Knuth and Peter J. Cameron, we consider acyclic orientations on a complete tripartite graph with equal part sizes.  We obtain a generating function which provides the distribution of the length of the longest path. \n    Letting the part size tend toward infinity, we obtain asymptotics for the average length of the longest path. Using Analytic Combinatorics in Several Variables, we obtain asymptotics for the average length of the longest path as the part size tends to infinity.\n   We will also discuss future directions, where these same methods are promising for investigating unequal part sizes, multipartite graphs with more than three parts, as well as the more refined problem of asymptotic distribution of longest path length.", "id": "Paper/70261", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70261"}, {"title": " Boolean Function Inequalities for Classical and Quantum Error-Correcting Codes ", "webprogram_exclude": "0", "session_ids": ["Session/18090"], "source_sha256": "661527a6da3ab02d8c26baf0a44a30d622d892355e48001ec6f5760c1eaf2205", "withdrawn": "", "abstract": "We discuss new Boolean function inequalities in the style of hypercontractivity / Samorodnitsky's inequality.  These allow us to prove decodability bounds for various classical and quantum channels, by comparison with the easier erasure channel.  Joint work with Olakunle Abawonse and Jan Hązła (AIMS Rwanda).", "id": "Paper/70262", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70262"}, {"title": " Intrinsic ergodicity for <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.054ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 884.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\frak B</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJFRAK-42\" d=\"M48 506Q48 568 120 629T268 691Q362 691 425 594L431 585L441 594Q478 628 528 657T629 686Q665 686 687 670Q703 658 718 584T753 506Q756 505 763 505Q778 505 804 512L815 516L820 496Q820 494 808 490T774 476T732 454Q720 445 708 437L675 415L640 394L625 383Q626 382 635 382Q652 382 670 379T712 364T754 336T784 289T797 220Q797 172 776 122Q769 106 766 102T745 84Q654 11 619 -8T538 -27Q483 -27 387 10T249 47Q218 47 186 34T133 8T112 -5T104 7T97 21L196 82Q259 120 284 140Q333 181 351 214Q368 251 368 353Q368 588 228 620Q222 621 205 621Q160 621 139 596Q117 569 117 548Q117 526 162 470T208 387Q208 352 179 320T104 264Q88 256 86 256Q83 256 70 266L82 274Q134 309 134 343Q134 352 130 359Q118 377 100 401T72 439T56 470T48 506ZM453 528Q457 496 457 419L458 357L488 367Q554 390 622 425Q673 449 673 453L671 454Q669 456 665 460T657 473T648 498T639 541Q629 597 616 613Q599 633 567 633Q534 633 493 599Q471 577 457 540L453 528ZM713 176Q713 252 661 295T528 339Q512 339 494 336T466 330T455 325Q454 325 452 311T444 270T425 217L420 207L304 118L319 116Q381 111 475 74T602 37Q655 37 684 79T713 176Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJFRAK-42\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-free integers in number fields ", "webprogram_exclude": "0", "session_ids": ["Session/19357"], "source_sha256": "560f99309bf5297ab96cc3ded1034992d411241241bf1edfde24f6e6690ea231", "withdrawn": "", "abstract": "Let $K$ be a number field with ring of integers $\\mathcal{O}_K$, and let $\\mathfrak B$ be an\nErd\\H{o}s family of ideals in $\\mathcal{O}_K$. We prove that the associated $\\frak{B}$-free\nsubshift $(X_{\\frak B},(S_a)_{a\\in\\mathcal{O}_K})$ is intrinsically ergodic: it carries a unique\nmeasure of maximal entropy, which we identify explicitly as a relatively\nindependent extension of the Haar rotation on $\\prod_{\\frak b\\in\\frak B}\\mathcal{O}_K/\\frak b$. This is\nthe first proof of intrinsic ergodicity for $\\frak B$-free systems beyond dimension\none, and relies on the work of Ara\\'ujo--Dymek--Ku\\l aga-Przymus. Via their reductions, we  also settle\nthe $k$-free and $\\frak B$-free lattice-point cases and the $k$-free number-field case.\nFor the purpose of illustration, we will mostly discuss the case of square-free integers in $\\mathbb{Z}[i]$.\nPreprint available at https://arxiv.org/abs/2607.11330", "id": "Paper/70263", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70263"}, {"title": " Continuous Time Trading with Multiple Insiders and Price Impact ", "webprogram_exclude": "0", "session_ids": ["Session/18328"], "source_sha256": "507c456cbbf4738a89f653d602a1bc48f403afb58e539450e6a9ab7c977eb4da", "withdrawn": "", "abstract": "We study imperfect competition among risk-averse insiders in a continuous time Kyle-Back market with price impact.  Novel to our work is that we allow informed traders to (i) obtain their private signal about the asset's terminal payoff at different times throughout the investment horizon, and (ii) trade as uninformed agents prior to obtaining their signal. We prove existence of a linear equilibrium where it is endogenously optimal for insiders not to trade prior to obtaining their signal. Our main application is when one insider observes her signal at time zero, while a second insider observes the payoff at a later time $t_1$. Compared to the benchmark when the second insider is absent, we show that anticipating future competition, the first insider trades more aggressively prior to the second's arrival and less aggressively after-words. Price informativeness is higher before entry while market depth is lower. After entry an interesting phenomenon occurs.   There is a unique entry time $t_1^*$ such that if $t_1 > t_1^*$ then after $t_1$ both price informativeness and market depth exceed the benchmark case. However, for $t_1 < t_1^*$ both informativeness and depth cross their respective benchmark counterparts at (separate, explicitly identifiable) times after $t_1$. Lastly, we show the first insider’s welfare, or indirect utility, is lower than the benchmark case, but increases with the entry time $t_1$.  By contrast the second insider's welfare decreases with $t_1$.  We conclude that insiders are motivated to obtain their signals as early as possible.", "id": "Paper/70271", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70271"}, {"title": " MU-Thom Spectra and Bökstedt periodicity ", "webprogram_exclude": "0", "session_ids": ["Session/18287"], "source_sha256": "9e6b998698f65de8f64537bcbb31e8544782ed2b1ccce2ec665920f5fcd707b1", "withdrawn": "", "abstract": "We will study how Eilenberg-Mac Lane spectra arise as $\\mathbb{E}_3$-$\\mathrm{MU}$-Thom spectra. Furthermore, we will use these $\\mathrm{MU}$-Thom spectra results to descibe $\\mathrm{Spec}(\\mathrm{THH}_{\\ast}(\\mathrm{BP}\\langle n \\rangle)$ in terms of Witt vectors.", "id": "Paper/70274", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70274"}, {"title": " Adaptive dynamics of discriminate and indiscriminate mating ", "webprogram_exclude": "0", "session_ids": ["Session/18248"], "source_sha256": "18bdb626ba702250fb6befd4bfeb2881d0e40aa98ba2e324e0f9b6b6370e1454", "withdrawn": "", "abstract": "Same-sex sexual behavior (SSB) is observed across many animal taxa. Some instances of SSB likely arise from animals' mating indiscriminately and/or with imperfect assessment of their partner's sex. Selection on indiscriminate mating strategies depends on the costs and benefits of mating and distinguishability of the sexes-—which in turn depend on evolvable signals of sex. Other factors like population density (which determines the rate of encountering potential mates) and investment roles (i.e., which sex invests more in reproduction) are likely relevant to the evolution of same-sex and different-sex mating, but there is no consensus as to the direction of these effects. We develop a new model of adaptive coevolution of sexual signaling and discrimination, explicitly incorporating encounter rate, mating costs, and investment roles. Coevolutionary dynamics typically lead to two distinct equilibria: one with no sexual signals and indiscriminate mating; the other with high-quality signaling and exclusively different-sex mating. Low-density conditions favor indiscriminate strategies, due to the steep opportunity costs of missing a possible mate. High density can favor either discriminate or indiscriminate strategies, depending on investment roles. By providing theoretical predictions for the effects of encounter rate and investment roles, our model bridges gaps between theoretical and empirical work on SSB.", "id": "Paper/70276", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70276"}, {"title": " Inference on the Reliabilty of a <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.211ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 521.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">k</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-6B\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-out-of-<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.395ex\" height=\"1.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -576.1 600.5 721.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">n</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-6E\" x=\"0\" y=\"0\"></use>\n</g>\n</svg> System: A Non-parametric Approach ", "webprogram_exclude": "0", "session_ids": ["Session/18343"], "source_sha256": "7df09d1be9455e6c72ea9fd63cc99285d08a5734869d2d6395acb4e5cb5a1f5b", "withdrawn": "", "abstract": "Efficient reliability assessment of a multi-component engineering system is important when evaluating system performance and failure behavior, but the underlying component lifetime distribution is unknown. We propose a nonparametric $U$-statistic-based estimator for the reliability function of a $k$-out-of-$n$ coherent system. The estimator is unbiased and possesses the uniformly minimum-variance unbiased estimator (UMVUE) property, with consistency and asymptotic normality established using Hoeffding's projection. An extensive simulation study is conducted for a $2$-out-of-$4$ system to evaluate the finite-sample performance of the proposed estimator in comparison with the conventional empirical plug-in estimator. The proposed estimator demonstrates improved efficiency, with smaller mean squared error and risk values under four loss functions, while achieving satisfactory $95\\%$ asymptotic confidence interval coverage. Finally, an application to microcircuit conductor failure data demonstrates the practical utility of the proposed method for efficient nonparametric reliability assessment of a complex engineering system.", "id": "Paper/70278", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70278"}, {"title": " Straight-line trajectories on the mucube ", "webprogram_exclude": "0", "session_ids": ["Session/18269"], "source_sha256": "d0ffc8d084db2c9df2f75edc7a0abae215cb308d81d1fc5d73799df40f252664", "withdrawn": "", "abstract": "The mucube is an infinite, $\\mathbb{Z}^3$-periodic, square-tiled, half-translation surface whose natural embedding in $\\mathbb{R}^3$ casts a checkerboard shadow on each of the three coordinate planes. It is highly symmetric. I will discuss joint work with Andre Oliveira, Chandrika Sadanand, and Sunrose Shrestha, where we classify the directions in which straight-line trajectories on the mucube are periodic.", "id": "Paper/70280", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70280"}, {"title": " Density of the multidimensional Lagrange spectrum ", "webprogram_exclude": "0", "session_ids": ["Session/18261"], "source_sha256": "536b468ba22b807c0e19d1b1cc899abaf646bc69dbc3d03c592c9b24018ec481", "withdrawn": "", "abstract": "The Lagrange spectrum is a classical object in number theory, defined as the set of values of $\\liminf_{q\\to\\infty} q \\dist(q\\alpha,\\mathbb{Z})$ where $\\alpha$ runs through irrational numbers. It has a complicated structure, with the discrete part, Hall's ray, and a transitional part in between. One can similarly define Lagrange spectrum in the multidimensional set-up, and until now not much has been understood about it. I prove that, unlike in the one-dimensional case, the closure of the multidimensional Lagrange spectrum is equal to the interval between 0 and its supremum. The proof relies on a correspondence between Diophantine approximation and dynamics on the space of unimodular lattices and proceeds by studying a dynamical counterpart of the Lagrange spectrum. The latter is shown to be equal to the interval between 0 and its maximum by means of an argument utilizing the higher rank nature of the set-up. A passage from full dynamical spectrum to the density of the Diophantine spectrum is achieved by applying equidistribution of expanding translates of horospheres in the space of lattices.", "id": "Paper/70281", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70281"}, {"title": " The Polynomial Shift Operator on Time Scales ", "webprogram_exclude": "0", "session_ids": ["Session/17446"], "source_sha256": "5b8361e4b0f729229b1d9a0cf2ae42d78dbcc9d545b1cdf33141ae8a5217bc2c", "withdrawn": "", "abstract": "We introduce the polynomial shift operator on time scales as a tool for extending power series solution methods for dynamic equations, allowing for the construction of time scale analogues of classical special functions. Explicit computation of this operator on arbitrary time scales presents significant challenges and currently only yields results for isolated time scales. We demonstrate applicability of the polynomial shift through examples, including time scale analogues of some special functions. Finally, we present explicit computations of the polynomial shift for select time scales.", "id": "Paper/70283", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70283"}, {"title": " Recent Advances in Learning Collective Behavior ", "webprogram_exclude": "0", "session_ids": ["Session/18282"], "source_sha256": "b3824ee0864c1f634adef4743c8f07e011ae867978a98791ea321f7d4089cb95", "withdrawn": "", "abstract": "We present three new directions in understanding collective behavior (clustering, flocking, milling, swarming, synchronization) from the machine learning point of view\n1) how to recover the interaction function from static patterns\n2) how to re-discover Newton's universal law of gravitation from JPL's solar data\n3) how to distinguish the physical concept of local neighborhood", "id": "Paper/70285", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70285"}, {"title": " Development of 1D Fluid Dynamics models for the Study of Vascular Disease ", "webprogram_exclude": "0", "session_ids": ["Session/18122"], "source_sha256": "3de95aab8b984d7ae827079ba5c1d1d2542ea651003b2dbf574f6b11fde0f63f", "withdrawn": "", "abstract": "Diagnosing the hemodynamic effects of such vascular changes can be challenging, and successful treatment requires early and accurate diagnosis of the disease subtype.  The incorporation of mathematical models in data analysis is crucial for understanding physiological processes and developing more effective diagnosis and treatment strategies. This talk demonstrates the use of fluid-dynamics models for patient-specific hemodynamic prediction, providing insight into the current disease state of a given patient and offering insights into the effects of manipulating the vascular domain, boundary conditions, or material parameters.  We employ a multiscale approach to examine pulmonary and hepatic vasculatures at both the network and vessel levels, constructing models that include large arteries and veins, arterioles and venules, as well as capillaries. We represent the large arteries and veins using a directed graph derived from computed tomography images. The network of arterioles and venules is modeled as structured trees, with parameters informed by data. The capillary network is depicted as a sheet connected to arterioles and venules in a ladder-like arrangement. In the large vessels, we solve the one-dimensional Navier-Stokes equations, while in the network of smaller vessels and capillaries, we solve linearized equations. These smaller-scale equations are connected to the larger ships through outflow boundary conditions. We emphasize the significance of sensitivity analysis and parameter inference in customizing models for individual patients and demonstrate how calibrated models can effectively predict treatment effects.", "id": "Paper/70287", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70287"}, {"title": " The Billiard Number of a Knot ", "webprogram_exclude": "0", "session_ids": ["Session/17808"], "source_sha256": "5984b856e6fc462a1b0fa4d6b8f784c4463d4aa96a507698301c0c99ff563281", "withdrawn": "", "abstract": "In rational polyhedra such as the cube, periodic billiard orbits unfold to closed geodesics on a flat torus and are classical; in irrational polyhedra, where no such unfolding exists, essentially the only known examples lived in the regular simplex. We exhibit thousands, many certified in exact arithmetic --- all-faces (Fagnano-type) orbits in every Platonic solid, new for three of them; exhaustive low-period censuses; and a $3$-adic rigidity theorem showing that every periodic orbit of the regular tetrahedron is isolated and rational.\n\nThese orbits are closed polygons, hence have knot types (when embedded), and the censuses reveal which knots occur and when: trefoils first, in every Platonic solid but the cube. We organize this in a new invariant, the \\emph{billiard number} $B_P(K)$ --- the least period realizing the knot $K$ in the table $P$ --- whose minimum over all tables equals the stick number for the thirty-five knots where we have computed it.\n\nThroughout, computation in collaboration with an AI assistant led the way: exhaustive searches, interactive 3D visualizations, and exact-arithmetic certificates that turn numerical discoveries into theorems, along with two cautionary tales in which confident large computations were wrong and exhaustive ones set them right.", "id": "Paper/70289", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70289"}, {"title": " Finding Small Solutions in Relative Thue Equations over Imaginary Quadratic Fields ", "webprogram_exclude": "0", "session_ids": ["Session/17913"], "source_sha256": "a456bd276165a37e2ce5ea940ad6fe1c8ec0742966331114ebe831e20deb838d", "withdrawn": "", "abstract": "There are several techniques that we use to bound large solutions of Thue equations. Different methods are then required to find small solutions.  However, oftentimes new techniques are needed for find those elusive medium solutions, especially over imaginary quadratic fields. We will look at one possible approach to finding such mid-range solutions.", "id": "Paper/70291", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70291"}, {"title": " Everywhere unbalanced configurations ", "webprogram_exclude": "0", "session_ids": ["Session/18139"], "source_sha256": "c6525e0f327b9db1096cabb23bfac3c19f35f4973861d1a33caec3e6952b4e25", "withdrawn": "", "abstract": "An old problem in discrete geometry, originating with Kupitz, asks whether there is a fixed natural number $k$ such that every finite set of points in the plane has a line through at least two of its points where the number of points on either side of this line differ by at most $k$. We give a negative answer to a natural variant of this problem, showing that for every natural number $k$ there exists a finite set of points in the plane together with a pseudoline arrangement such that each pseudoline contains at least two  points and there is a pseudoline through any pair of points where the number of points on either side of each pseudoline differ by at least $k$. Moreover, we may find such a configuration with at most $2^{2^{ck}}$ points, which, by a result of Pinchasi, is best possible up to the value of the constant $c$. Joint work with David Conlon.", "id": "Paper/70292", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70292"}, {"title": " How to Cheat at Arithmetic Statistics ", "webprogram_exclude": "0", "session_ids": ["Session/18335"], "source_sha256": "3402dfd4cbec7d6e4e3b746c5e84f265ef029074a23d7472e81edf1e5a5ac7a1", "withdrawn": "", "abstract": "Before Bhargava's groundbreaking work, Akihiko Yukie embarked on an ambitious program to understand the zeta functions of prehomogeneous vector spaces, and then prove arithmetic density results for counting number fields.\n\nIt turns out that a half-understood zeta function theory, together with the headline results from Bhargava's work, is enough to push this program further. I will explain how.", "id": "Paper/70294", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70294"}, {"title": " The natural flow and non-positively curved manifolds ", "webprogram_exclude": "0", "session_ids": ["Session/17960"], "source_sha256": "8c1bc3cb39f96d9452c516c1bb4c182fd9c840c0e201d61b020284b758999368", "withdrawn": "", "abstract": "In this talk, I will discuss a flow recently introduced by the authors for studying non-positively curved manifolds. I will focus on a few applications of the flow regarding the topology and of such manifolds and on some dynamical features of the flow.", "id": "Paper/70296", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70296"}, {"title": " The Evolution of Students’ Conceptualizations of Mathematical Proof in Introductory Proof Courses ", "webprogram_exclude": "0", "session_ids": ["Session/18068"], "source_sha256": "19985a0a9393ad9e0286494e37437126b0a45b546da4422d2424bf0587dd8e8e", "withdrawn": "", "abstract": "Many US universities designate an introduction to proof course to support students’ enculturation into proof-centered mathematics. My work builds on existing research about mathematical proof by examining how students’ conceptions of mathematical proof and relevant mathematics evolve during introductory proof courses. Eight undergraduates participated in a longitudinal study examining how their goals, engagement patterns, and beliefs (including conceptions of proof) evolved during a sequence of two proof courses. In this talk I report only on students’ beliefs related to their conceptions of proof and relevant mathematics. I organize my results into three phases of learning. In phase one, students engaged in proof tasks with familiar mathematical content (e.g. even and odd integers) enabling them to productively integrate their intuitive and scientific conceptions of the mathematical content and basic proof techniques. In phase two, students engaged in proof tasks involving mathematical content they had not hitherto covered, including rings, homomorphisms, and bijections, requiring them to develop novel intuitive concepts to support their nascent scientific reasoning about the content. This co-evolution of intuitive and formal conceptions provided fertile ground for students to continue to develop their logical knowledge needed for proof tasks. In phase three, students studied real analysis, including convergent sequences and limits of functions. While the mathematical content in this phase was familiar to students, they did not integrate the formal definitions with those pre-existing conceptions as easily as in the prior phases. Students tended to rely on proof outlines, which they adjusted to suit the particular function or sequence by leveraging both intuitive and formal conceptions of the mathematical object. These findings describe a potential trajectory of students’ development of proof competency that is supported by both scientific and intuitive concepts of relevant mathematics. Implications for instruction include supporting students’ development of mathematical intuition and its integration with formalization and proof.", "id": "Paper/70298", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70298"}, {"title": " The inhomogeneous Cauchy-Riemann equation with or without Dini continuity ", "webprogram_exclude": "0", "session_ids": ["Session/19336"], "source_sha256": "e9577a1315430d9b1c405ca0e258552a1a16bbe8f6337ba210a6ebdab2594303", "withdrawn": "", "abstract": "Regarding the interior regularity of the inhomogeneous Cauchy-Riemann  equation $\\partial u/\\partial\\bar z=f$, it has been known since the work of Chern, and Hartman and Wintner, that the property of Dini continuity of $f$ is sufficient for the continuity of all first derivatives of $u$.  We show by example that $f$ can be continuous and very close to Dini continuous, while $u$ is classically differentiable everywhere and vanishing to infinite order at a point, but $\\partial u/\\partial z$ is discontinuous.  The main application is to the regularity of $J$-holomorphic curves for rough almost complex structures $J$.", "id": "Paper/70299", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70299"}, {"title": " Fast Algorithms for Structured Matrices: Inversion and Randomized Black-Box Compression ", "webprogram_exclude": "0", "session_ids": ["Session/18345"], "source_sha256": "00784c8f05fec5623c745fe3826cb02eb857969f5cb11f1bb7cc11c45d73fe58", "withdrawn": "", "abstract": "Many matrices arising in scientific computing are dense, but nevertheless possess internal structure that makes them easier to store and manipulate than general dense matrices. The talk will begin with some simple examples, including banded and semiseparable matrices, and use these to motivate the broader idea of data sparsity.\n\nThe talk will then discuss rank-structured matrices, including hierarchical ($\\mathcal{H}$, or $\\mathcal{H}^{2}$) matrices, and describe how their structure can be exploited to construct fast algorithms for tasks such as matrix-vector multiplication, and matrix inversion.\n\nIn the final part of the talk, randomized techniques for black-box compression of structured matrices will be described. \n\nThe emphasis throughout will be on the basic algorithmic ideas, on the relationships between different notions of matrix structure, and on how exposing hidden low-rank structure can lead to substantial reductions in computational cost.", "id": "Paper/70300", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70300"}, {"title": " The Frobenius and finiteness of homological dimensions ", "webprogram_exclude": "0", "session_ids": ["Session/18347"], "source_sha256": "f82b75feadf15dd58243568f29adb679acf9295cc674af621de3eeaa6b1ede79", "withdrawn": "", "abstract": "Given a local ring $(R,\\mathfrak m, k)$, the residue field can often be used as a ``test module'' giving a bound for the worst possible behavior of a (finitely generated) $R$-module. For example, the maximum possible length of a projective resolution of any finitely generated $R$-module is achieved by taking our module to be $k$. \nAs another example, a finitely generated $R$-module $M$ has $\\operatorname{pd} M$ finite if and only if $\\operatorname{Tor}_i^R(k,M)$ vanishes for $i\\gg0$. A result of Avramov--Miller says that if $R$ is a positive characteristic complete intersection ring, then $k$ can be replaced by $F_*^eR$. In this talk, we will describe progress towards relaxing the complete intersection hypothesis. We will specifically focus on $R$-modules having finite unramified CI-dimension, a variant of CI-dimension we introduce to restrict potentially weird mixed characteristic behavior.", "id": "Paper/70301", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70301"}, {"title": " Radio Graceful Labelings of Generalized Petersen and Moore Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17963"], "source_sha256": "c517ac4682837c92ed2305a270bf1fd40b078225523fac531857dcab851dbb99", "withdrawn": "", "abstract": "First introduced by Hale in 1980, the frequency assignment problem (or channel assignment problem) addresses the challenge of assigning frequencies to transmitters such that interference is minimized. In 2001, Chartrand et al. formulated the radio labeling problem to model the frequency assignment for radio towers, with modern applications to cellular and satellite networks. For a simple, connected graph $G = (V(G), E(G))$, a radio labeling is a mapping $f: V(G) \\rightarrow \\mathbb{Z}^+$ satisfying $|f(u)-f(v)| + d(u,v) \\geq \\text{diam}(G)+1$ for any distinct vertices $u,v$, where $d(u,v)$ is the distance between $u$ and $v$ in $G$ and $\\text{diam}(G)$ is the diameter of $G$. A graph is radio graceful if there is a radio labeling such that $f(V(G)) = \\{1, \\dots, |V(G)|\\}$. In this talk, we investigate the radio gracefulness of several highly structured families of graphs, including generalized Petersen graphs and low-diameter graphs. We first discuss multi-layer generalized Petersen graphs, determining conditions under which these graphs are radio graceful. We then extend these ideas to low-diameter graphs arising from extremal degree-diameter problems, including Moore graphs, bipartite Moore graphs recognized as $(r,g)$-cages, and approximate Moore graphs such as Erdős–Rényi polarity graphs and McKay–Miller–Širáň graphs. We establish a necessary and sufficient condition for radio gracefulness in bipartite graphs of diameter 3, determine the radio number of $(r,g)$-cages arising from generalized $n$-gons, and find that Erdős–Rényi polarity graphs and McKay–Miller–Širáň graphs are radio graceful. This talk is joint work with Katherine Benson, Zhanar Berikkyzy, Karen Collins, Daniela Ferrero, Amanda Niedzialomski, and with An Cao, Julian Hutchins, and Orlando Luce.", "id": "Paper/70303", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70303"}, {"title": " Counting cylinders on the Mutetrahedron ", "webprogram_exclude": "0", "session_ids": ["Session/18269"], "source_sha256": "a6249b62be91594f3ec6e29123fe9023f46beb83d21c361f325c31b665b61db6", "withdrawn": "", "abstract": "The Mutetrahedron is a triply periodic polyhedral surface that is an infinite cover of a compact half-translation surface. Unlike compact translation surfaces—which exhibit quadratic cylinder growth—we show that the number of isotopy classes of cylinders of length at most $R$ grows subquadratically and at least linearly in $R.$ We establish this by applying a recent Veech group computation for the Mucube and introducing a homological characterization of cylinder curves for the Mutetrahedron, which also yields density of its cylinder directions.", "id": "Paper/70304", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70304"}, {"title": " Twisted Bad in the plane ", "webprogram_exclude": "0", "session_ids": ["Session/18261"], "source_sha256": "adca60d5b0fb0b54a10cb32af6cc17fddbd3ac6ec0b5b50fd2c25ef6a993fea3", "withdrawn": "", "abstract": "The \\emph{twisted badly approximable set} associated to a vector $\\boldsymbol{\\alpha} \\in \\mathbb{R}^m$ is the collection $\\mathrm{Bad}_{\\boldsymbol{\\alpha}}$ of all $\\boldsymbol{\\gamma} \\in \\mathbb{R}^m$ for which $\\boldsymbol{\\alpha}$ is ``badly approximable with inhomogeneous parameter $\\boldsymbol{\\gamma}$,'' meaning that\n\\[\n  \\liminf_{q\\to\\infty} q^{1/m}\\|q \\boldsymbol{\\alpha} - \\boldsymbol{\\gamma}\\| > 0,\n\\]\nwhere $\\|\\cdot\\|$ denotes distance to $\\mathbb{Z}^m$. It is known that if $\\boldsymbol{\\alpha}$ is \\emph{nonsingular}, then $\\mathrm{Bad}_{\\boldsymbol{\\alpha}}$ has zero measure, and if $\\boldsymbol{\\alpha}$ is \\emph{very singular}, then $\\mathrm{Bad}_{\\boldsymbol{\\alpha}}$ has full measure.  If $\\boldsymbol{\\alpha}$ is neither, then $\\mathrm{Bad}_{\\boldsymbol{\\alpha}}$ can be null or full. I will discuss ongoing joint work with Akshat Das, where we give finer conditions on $\\boldsymbol{\\alpha}$ that determine the measure of the twisted bad set. In particular, we characterize when it is null or full in dimension $m=2$.", "id": "Paper/70305", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70305"}, {"title": " Maximum Incidence Nullity: Toward a Fort-Packing Bound for Maximum Nullity ", "webprogram_exclude": "0", "session_ids": ["Session/17911"], "source_sha256": "97f34129128cd0f9775aa1c3b33796c239897686ae7b21fdaedd9a8552464207", "withdrawn": "", "abstract": "Given a graph $G$, the maximum nullity $M(G)$ is the largest\nnullity among the real symmetric matrices whose off-diagonal zero--nonzero\npattern is described by the edges of $G$.  A fort is a nonempty set of vertices\nsuch that no vertex outside the set has exactly one neighbor in the set, and the\nfort number $\\operatorname{ft}(G)$ is the maximum number of pairwise disjoint forts in $G$.\nEvidence suggests the conjecture $\\operatorname{ft}(G)\\leq M(G)$, but constructing a witness\nmatrix in general remains difficult.\n\nRecent work by Hicks et al. shows that the minimal supports of the nonzero\nvectors in the null space of a fixed matrix form a compatible collection of\nforts.  Compatibility is necessary in this setting, but it does not guarantee\nthat an arbitrary collection of forts can simultaneously support null vectors\nof a common matrix.  For disjoint forts, Furst et al. give an exact\ncharacterization: they can simultaneously support null vectors precisely when,\nfor every pair of forts, the bipartite graph consisting of the edges between\nthem is bridgeless.  Hence, a bridge in one of these bipartite graphs is the\nexact obstruction to simultaneously realizing the disjoint forts as null-vector\nsupports.\n\nIn this talk, we introduce a new graph parameter, the maximum incidence\nnullity $\\operatorname{MI}(G)$, defined as the largest number of linearly independent\nincidence vectors of forts that can occur in the null space of a common matrix\nin $\\mathcal{S}(G)$.  By replacing disjointness with linear independence, this parameter\nhas the potential to overcome bridge obstructions through overlapping forts.\nSince $\\operatorname{MI}(G)\\leq M(G)$, proving $\\operatorname{ft}(G)\\leq \\operatorname{MI}(G)$ would establish the\nconjectured bound.  We present repair techniques that replace an obstructed\ndisjoint fort packing with an overlapping collection whose incidence vectors\nremain linearly independent and can be realized by a common matrix.  We\nconclude with examples where these techniques establish $\\operatorname{ft}(G)\\leq M(G)$ and\ndiscuss the remaining obstacles to a general proof.", "id": "Paper/70306", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70306"}, {"title": " Sensitivity Analysis of a Sex-Trafficking Compartmental Model ", "webprogram_exclude": "0", "session_ids": ["Session/19359"], "source_sha256": "6e70521e50ae8c84c776892eb77fa640efb4c37b3e36a2f6b5ae841413e909ff", "withdrawn": "", "abstract": "We develop a deterministic compartmental model that couples victim and trafficker populations to study the dynamics of sex trafficking. Using the next-generation matrix method, we derive the trafficking reproduction number $$R_0=\\frac{\\beta_2(1-\\rho)}{\\xi+\\mu},$$ highlighting the roles of the potential trafficker activation rate $\\beta_2$, recruitment fraction $1-\\rho$, prosecution rate $\\xi$, and removal rate $\\mu$ in trafficking persistence. We use two-parameter contour analysis and time-dependent Partial Rank Correlation Coefficients (PRCC) to examine parameter sensitivity. The results show that $\\beta_2,\\, 1-\\rho$, and $\\xi$ are the dominant parameters over t = 10–200, while $\\beta_1$ (trafficker–susceptible contact rate), $\\Psi$ (rescue/rehabilitation rate), and $\\sigma$ (recidivism rate from prosecuted to potential trafficker) have primarily transient effects, and $\\mu$ (natural death rate), $\\gamma$ (relapse from rescue to susceptible), and $\\delta$ (death rate from trafficking) have little influence. Numerical simulations illustrate how changes in these parameters affect the long-term trafficking burden and the potential impact of intervention strategies.", "id": "Paper/70307", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70307"}, {"title": " Making the Cartesian Connection: Exploring Algebraic, Graphical, Linguistic, and Metacognitive Obstacles ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "96ec5cc6fcef9123bcf600f107dbc4b8417aea48e2f09802ab3e0e7fd87526b7", "withdrawn": "", "abstract": "Understanding the Cartesian Connection, which is defined as the relationship between an algebraic equation and the set of all points on its graph, is integral to success in Calculus, yet research has shown that many students struggle with making this connection. However, few studies have closely examined what obstacles students face in making the Cartesian Connection. We conducted exploratory teaching interviews with nine undergraduate students to investigate what obstacles students face in attempting to make the Cartesian Connection. In this poster presentation, we focus on interviews with two of the students: Ellie and Chloe. We found that students struggled with mathematical language, underlying graphical meanings, underlying algebraic meanings, and metacognitive issues. We discuss specific obstacles related to each category, as well as evidence associated with those obstacles. We include implications of our findings for teaching and future research.", "id": "Paper/70310", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70310"}, {"title": " Divergent CR maps, foliations, and approximation ", "webprogram_exclude": "0", "session_ids": ["Session/18295"], "source_sha256": "437b21d4eacec666ea293728dfaa3e322769f17c11f6c9ad17e049b6c34909f1", "withdrawn": "", "abstract": "The existence of ``bad'' CR maps between CR manifolds --- divergent formal maps in the real-analytic category, or maps of finite smoothness failing to be smooth in the smooth category --- turns out to be governed by the geometry of the target: roughly speaking, such maps can only appear when the target carries a foliation by (formal) complex varieties of a particularly trivial kind, into which the bad behaviour can be absorbed. In this talk, we discuss this relationship and its consequences. Chief among these is approximation: in the absence of such foliations, formal CR maps between real-analytic hypersurfaces in two and three complex dimensions can be approximated, in the Krull topology, by convergent maps.", "id": "Paper/70314", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70314"}, {"title": " Schrödinger bridge with transport relaxation ", "webprogram_exclude": "0", "session_ids": ["Session/18293"], "source_sha256": "186daf1ea43f0a02c2100013c57cedec3344048d3094ac6e446673b7faa438ff", "withdrawn": "", "abstract": "Motivated by modern machine learning applications where we only have access to empirical measures constructed from finite samples, we relax the marginal constraints of the classical Schrödinger bridge problem by penalizing the transport cost between the bridge's marginals and the prescribed marginals. We derive a duality formula for this transport-relaxed bridge and demonstrate that it reduces to a finite-dimensional concave optimization problem when the prescribed marginals are discrete and the reference distribution is absolutely continuous. We establish the existence and uniqueness of solutions for both the primal and dual problems. Moreover, as the penalty blows up, we characterize the limiting bridge as the solution to a discrete Schrödinger bridge problem and identify a leading-order logarithmic divergence. Finally, we propose gradient ascent and Sinkhorn-type algorithms to numerically solve the transport-relaxed Schrödinger bridge, establishing a linear convergence rate for both algorithms.", "id": "Paper/70315", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70315"}, {"title": " Unitary Stability of Primes After Right Appending an Arbitrary String of Nines or Zeros ", "webprogram_exclude": "0", "session_ids": ["Session/19367"], "source_sha256": "c4d8cc4391c4e5f5b2fe20ab74ea071774f033145921eb7ef3da447e847dcc8f", "withdrawn": "", "abstract": "It has been shown by M. Filaseta, J. Juillerat, and the presenter that for every positive integer $k$, there exist $k$ consecutive primes that are both widely digitally delicate and Brier numbers. R. Philpott and the presenter have shown that for any positive integer $k$, there exist $k$ consecutive primes that remain composite when appending a string of zeros to the right of the units digit and then changing the new units digit to any base ten digit. They also find an explicit example of a prime with this property and strengthen the result by adding the condition that the primes are Brier numbers. J. Juillerat and the presenter have refined this result further so that the primes are widely digitally delicate, Brier numbers, and remain composite when appending a string of zeros or nines to the right of the units digit and then changing the new units digit except potentially when appending a string of a multiple of 8704 nines.", "id": "Paper/70317", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70317"}, {"title": " The Euler–Kronecker constants distinguish <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.468ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 1062.7 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbb {Z}_\\ell</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJAMS-5A\" d=\"M39 -1Q29 9 29 12Q29 23 60 77T219 337L410 648H364Q261 648 210 628Q168 612 142 588T109 545T97 509T88 490Q85 489 80 489Q72 489 61 503L70 588Q72 607 75 628T79 662T81 675Q84 677 88 681Q90 683 341 683H592Q604 673 604 666Q604 662 412 348L221 37Q221 35 301 35Q406 35 446 48Q504 68 543 111T597 212Q602 239 617 239Q624 239 629 234T635 223Q635 215 621 113T604 8L597 1Q595 -1 317 -1H39ZM148 637L166 648H112V632Q111 629 110 622T108 612Q108 608 110 608T116 612T129 623T148 637ZM552 646Q552 648 504 648Q452 648 450 643Q448 639 266 343T77 37Q77 35 128 35H179L366 339L552 646ZM572 35Q581 89 581 97L561 77Q542 59 526 48L508 37L539 35H572Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2113\" d=\"M345 104T349 104T361 95T369 80T352 59Q268 -20 206 -20Q170 -20 146 3T113 53T99 104L94 129Q94 130 79 116T48 86T28 70Q22 70 15 79T7 94Q7 98 12 103T58 147L91 179V185Q91 186 91 191T92 200Q92 282 128 400T223 612T336 705Q397 705 397 636V627Q397 453 194 233Q185 223 180 218T174 211T171 208T165 201L163 186Q159 142 159 123Q159 17 208 17Q228 17 253 30T293 56T335 94Q345 104 349 104ZM360 634Q360 655 354 661T336 668Q328 668 322 666T302 645T272 592Q252 547 229 467T192 330L179 273Q179 272 186 280T204 300T221 322Q327 453 355 590Q360 612 360 634Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJAMS-5A\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-2113\" x=\"943\" y=\"-220\"></use>\n</g>\n</svg>-Extensions over CM Fields ", "webprogram_exclude": "0", "session_ids": ["Session/19367"], "source_sha256": "53214c5b61beb58b42807df2f1a7a3cf8f9ca8f9398486fd9a1f6644bc26865e", "withdrawn": "", "abstract": "For a global field, we define its Euler--Kronecker constant to be the constant term of the Laurent expansion of logarithmic derivative of its Dedekind zeta function at $s=1$.\nWe prove, conditionally on GRH, that over any fixed CM field $K$ and an odd prime $\\ell$ and for all sufficiently large $n$, the Euler--Kronecker constant of the $n$th layer of the cyclotomic $\\mathbb{Z}_\\ell$-extension of $K$ exceeds that of any anti-cyclotomic $\\mathbb{Z}_\\ell$-extension of $K$. \nOur dependence on GRH is rooted in Ihara's work, where he discovered that for global fields possessing many primes of small norm, the associated Euler--Kronecker constants tend to be negative and large in magnitude. Our argument critically depends on the existence of a prime which splits completely in every layer of anti-cyclotomic extensions.", "id": "Paper/70318", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70318"}, {"title": " Constructing web graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18386"], "source_sha256": "6e6626434f0223458cc3ae22d0d82af0d5671271d7eb65608933c13ac248d00e", "withdrawn": "", "abstract": "Web graphs are a family of planar, directed, trivalent graphs with boundary that arise naturally in representation theory and knot theory as a way to model the vectors invariant under the action of quantum $\\mathfrak{sl}_n$. The theory of classical web graphs is most robustly understood for $n=2$ and $n=3$, where small-rank phenomena guarantee a remarkable basis of quantum invariant vectors that is indexed by web graphs with beautiful properties. However, this breaks down when $n \\geq 4$. Recently, Gaetz et alia used plabic webs to build a basis of quantum invariant vectors for $\\mathfrak{sl}_4$ that have many of these useful properties, including rotation-invariance (up to certain relations). In this talk, we describe some constructions of web graphs. We focus on the case of $\\mathfrak{sl}_4$ but, time permitting, will describe some general results.", "id": "Paper/70319", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70319"}, {"title": " Arithmetical Structures on Coconut Trees ", "webprogram_exclude": "0", "session_ids": ["Session/17963"], "source_sha256": "14ff45f01e2896e46c6f38b58f78b199d56ae8075126d94a74f06199bbd65d4c", "withdrawn": "", "abstract": "An arithmetical structure on a graph is an assignment of positive integers (labels) to its vertices such that the label of any vertex v divides the sum of the labels of the neighbors of $v.$ We focus on a family of graphs called coconut trees which can be defined as a star glued to one end of a path. We then provide a careful treatment of arithmetical structures on these graphs. This is a joint work with Pamela E. Harris, Alexander Diaz-Lopez, Brian Ha, Jonathan Rogers, Theo Koss.", "id": "Paper/70320", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70320"}, {"title": " Unit lattices of totally complex, non-CM <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.979ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 1282.4 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">D_4</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-44\" d=\"M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-44\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-34\" x=\"1171\" y=\"-213\"></use>\n</g>\n</svg>-octic number fields ", "webprogram_exclude": "0", "session_ids": ["Session/19361"], "source_sha256": "6bfd36bffcb5656cd837627604e053a0df4542d312fccd67da239c80d83c5169", "withdrawn": "", "abstract": "The unit group of the ring of integers of a number field $K$ is a finitely generated abelian group which, modulo its torsion subgroup, can be endowed with the structure of a lattice. The rank of this lattice is determined by the number of real and complex embeddings of $K$, and its \\textit{shape} is determined by the lattice up to scaling, rotation, and reflection. We investigate the shapes of the rank 3 lattices arising from the unit groups of totally complex, non-CM $D_4$-octic number fields.", "id": "Paper/70322", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70322"}, {"title": " Redistricting from the Bottom Up: Sampling Communities of Interest with Differential Privacy ", "webprogram_exclude": "0", "session_ids": ["Session/19338"], "source_sha256": "0cb755812890233fee6b9fc3cde9ef1c9903431b25944ed75fb1b1f24201311c", "withdrawn": "", "abstract": "Independent Redistricting Commissions (IRCs) are a promising tool for bottom-up redistricting, but their public testimony processes are vulnerable to adversarial manipulation. We propose using differential privacy to draw redistricting plans that incorporate community of interest (COI) testimonies while remaining robust to adversarial input. Treating individual testimonies as data points, we use the marked edge walk (MEW) to sample from differentially private distributions of redistricting plans via the exponential mechanism. We introduce two score functions and demonstrate that both can be targeted by MEW across a range of privacy budgets. Applying this method to Missouri's mid-cycle redistricting using 808 COI testimonies, we show that COI-informed sampling outperforms an uninformed baseline and the enacted plan. An adversarial experiment demonstrates that the method can be robust to attacks under certain privacy budgets and may perform better in practice than formal group privacy guarantees imply. We also find that stronger COI preservation tends to spread minority and Democratic representation more evenly across districts.", "id": "Paper/70323", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70323"}, {"title": " Persistence and bifurcation of steady-states for dynamical systems on large networks using graphons ", "webprogram_exclude": "0", "session_ids": ["Session/18109"], "source_sha256": "833737d0129243d469736606c1b95ba63fcd7ff0764f1643b96fb1c0432815a8", "withdrawn": "", "abstract": "Large networks of interacting species are often modeled by differential equations on large random graphs.  Analysis of these networks often relies on the use of a continuum limit where the discrete adjacency matrix is replaced by a nonlocal operator known as a graphon.  Analysis in the graphon case is often more tractable.  The goal of the current work is to develop mathematical tools allowing one to assert the existence and bifurcations of steady state solutions in the finite dimensional problem based upon their existence in the continuum model.  Our primary motivations come from Kuramoto models of coupled oscillators and our main applications include the existence of twisted states in random networks and the bifurcation to synchrony in systems of non-identical oscillators.", "id": "Paper/70324", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70324"}, {"title": " Finite Element Methods for the Stokes Problem on Multiply Connected Domains ", "webprogram_exclude": "0", "session_ids": ["Session/17872"], "source_sha256": "c48f5b4948a1b881a0ba34349ad06384014696c034bb5cf0e74256c331747d41", "withdrawn": "", "abstract": "We investigate finite element methods for the Stokes/Navier-Stokes problem on multiply connected domains in $\\mathbb{R}^2$. We focus on boundary conditions for which the space of harmonic forms is non-trivial.", "id": "Paper/70325", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70325"}, {"title": " Higher-arity stability and indiscernible extraction ", "webprogram_exclude": "0", "session_ids": ["Session/18589"], "source_sha256": "2fa90332eefe028de84f956d229ded8fe9ee24bd5f927ab29e6af8c98028c8de", "withdrawn": "", "abstract": "Neostability theory is the branch of model theory that studies certain classes of combinatorially tame first-order theories and more generally local combinatorial tameness within arbitrary theories. These tameness notions are often intimately linked to the behavior of indiscernible sequences. We will discuss a new higher-arity stability notion that allows for improved indiscernible extraction.", "id": "Paper/70329", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70329"}, {"title": " Peel neighborhoods ", "webprogram_exclude": "0", "session_ids": ["Session/18105"], "source_sha256": "e987836c73646a15e0f4df8e046a4b7a23602c347f82db680a6bfdacd2112f3d", "withdrawn": "", "abstract": "We introduce the canonical, parameter-free, and efficiently computable notion of peel neighborhoods in a finite metric space of strict negative type. Using adaptive scheduling and/or soft threshold to upper bound their radius or cardinality allows peel neighborhoods to be computed at scale, enabling useful microscopic descriptions of geometry and topology. As an example of their utility, peel neighborhoods enable efficient and performant estimates of local dimension and detections of singularities in samples from stratified manifolds.", "id": "Paper/70332", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70332"}, {"title": " The Wild Number of an Edge-Colored Graph ", "webprogram_exclude": "0", "session_ids": ["Session/18205"], "source_sha256": "eb52949485b808633e44adeb85d913b610e603a0abd10da4064c47f914118370", "withdrawn": "", "abstract": "Imagine a city and its transportation networks. Is it possible to get from one location to another using only a given mode of transportation? Modeled as an edge-colored graph, is there a path from one vertex to another using only edges of a given color? We introduce the wild number of an edge-colored graph as a measure of how far away a graph is from having a spanning tree in every color and then discuss bounds and computational complexity. This work was inspired by a question posed during a REUF 2017 project on generalized graph splines.", "id": "Paper/70333", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70333"}, {"title": " AND and XOR Lifting: From Boolean Function Analysis to Communication Complexity ", "webprogram_exclude": "0", "session_ids": ["Session/18090"], "source_sha256": "2a2a50dbd6800c3e7586068e9f79920720efc6fc5334497e252f4c9891660442", "withdrawn": "", "abstract": "How does the algebraic structure of a Boolean function govern the communication needed to compute it on distributed inputs? Given a Boolean function, consider the two-party problems obtained by applying it to the coordinate-wise AND or XOR of the players’ inputs. These simple constructions connect fundamental questions in communication complexity to structural questions about Boolean functions. Matrix rank corresponds to sparsity in the monomial or Fourier basis, while decision trees using AND or parity queries give natural communication protocols.\n\nI will survey these connections through the lens of the log-rank conjecture, which asks whether low matrix rank guarantees efficient deterministic communication. I will discuss recent structural results for Boolean functions with sparse polynomial representations and their applications to AND functions, including connections between classical and quantum communication. I will also highlight the corresponding questions for XOR functions, where understanding Fourier sparsity and restrictions to affine subspaces remains a central challenge. The talk will emphasize the Boolean function analysis viewpoint and accessible open problems; no prior background in communication complexity will be assumed.", "id": "Paper/70334", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70334"}, {"title": " Bohr-Sommerfeld conditions for quantum Zeno Hamiltonians ", "webprogram_exclude": "0", "session_ids": ["Session/17999"], "source_sha256": "632e6026492db8db8ad8671a2cab53ce7802e83ee8141151a9e4836fbc5afd2a", "withdrawn": "", "abstract": "The quantum Zeno effect is a consequence of the collapse of the wave function axiom. It leads to the dynamics\nof Hamiltonians of the form $\\hat{H}_Z =\\Pi\\hat{H}\\Pi$, \nwhere $\\hat{H}$ is a quantum Hamiltonian driving a free dynamics and $\\Pi$ \nan orthogonal projection. In this talk, I will take $\\Pi$ to be a spectral projector of a quantum Hamiltonian  local local circle action with a K\\\"ahler phase space\n(for example, the span of the harmonic oscillator eigenstates with energy ≤ 1). (In the configuration space setting, $\\hat{H}_Z$ belongs to a semi-classical\nversion of the Melrose-Uhlmann class of singular pseudo-differential operators.)\nI will focus on the construction of quasi-modes, which concentrate not only on the level sets of $H$ \nintersected with the classically-allowed region corresponding to $\\Pi$ (the\nunit disk in the example), but also on its boundary.   In one degree of freedom, the first correction in the Bohr-Sommerfeld spectrum is given by the eigenvalues of the momentum operator on an associated metric graph.\nThe boundary concentration of the quasi-modes is related to the infinite-speed boundary propagation\nof singularities under \n$\\hat{H}_Z$. \nThis is joint work with L. Charles, Y. Guedes-Bonthonneau, and S. V\\~{u} Ng\\d{o}c.", "id": "Paper/70336", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70336"}, {"title": " Coding Theory: From Foundations to Frontiers ", "webprogram_exclude": "0", "session_ids": ["Session/18388"], "source_sha256": "35a6a6c571a553495449b03287d1c90af6b8c2fd1290b1b7b0cb4eeb9609c3df", "withdrawn": "", "abstract": "A transform approach is used for polycyclic codes over finite local rings. This allows us to study them in terms of linear algebra and invariant subspaces as well as understand the duality in terms of the transform domain. Some structural properties of repeated-root polycyclic codes over finite fields in terms of matrix product codes will also be discussed.", "id": "Paper/70340", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70340"}, {"title": " Priority Scheduling in the M/G/1 with Preemption Overhead ", "webprogram_exclude": "0", "session_ids": ["Session/17976"], "source_sha256": "17cdeaa8ced900305c3493e57c40d84fbbb38261d163e5eea8ded1fe63c1b8e2", "withdrawn": "", "abstract": "Preemptive scheduling policies, in which a job's service is paused to let higher-priority work through, are ubiquitous, from CPU scheduling to hospital triage. In practice, though, preempting a job is rarely free: pausing and resuming it costs overhead, whether from a context switch, a cache reload, or a handoff delay. Despite this, queueing-theoretic analyses of preemptive policies almost never account for overhead. This is largely because overhead is hard to analyze even in principle. It creates a two-way dependency between a job's service length and the arrivals that occur during that service: an arrival can trigger overhead that ``lengthens’’ the job, which in turn allows still more arrivals during service. This makes even the stability region difficult to characterize, let alone the response time distribution.\n\nWe give the first response time distribution analysis of the M/G/1 queue under class-based preemptive priority with preemption overhead, where overhead is incurred (stochastically) whenever a job is paused or resumed. Our key tool is the job joint transform, which captures a job's effective service time jointly with the arrivals it sees during that time, allowing us to disentangle the two-way dependency and derive a recursive formula for the Laplace transform of response time for jobs of any class, from which all response time moments follow. \n\nThis new analytical tool, the job joint transform, is useful well beyond analyzing this one policy: it applies to a broad family of systems with similar ``service-arrival’’ dependencies, including preempt-repeat scheduling and queues with state-dependent arrival rates, making it a first step toward a general framework for analyzing overhead in queues.", "id": "Paper/70341", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70341"}, {"title": " Supplementing Standards-Based Grading with Engagement Points ", "webprogram_exclude": "0", "session_ids": ["Session/18081"], "source_sha256": "39ea36ab2045c10e09c62e9479c8baccd66cda5d229c1c0dfe4c3b0d7a3f70f8", "withdrawn": "", "abstract": "In my first-semester calculus courses, I use a standards-based grading model with 8-10 ``Big Ideas'' that students must pass by the end of the course. Passing the Big Ideas is evidence that my students can apply the material to later courses, either in the calculus sequence or in their major. For this reason, I group all other assignments in my course into a single broad category, which I call ``Engagement Points''. These points are earned through a combination of problem sets, group work, projects, or any other assignment I create, and there are many more points available than I expect students to earn. Therefore, students can choose the assignments that help them learn best, and to earn a given grade, they need only pass enough Big Ideas and earn enough Engagement Points.\n\nIn this talk, I will speak to the additional flexibility of this system and its ability to help my students focus on the most important aspects of the course (passing the Big Ideas). Also, after earning enough Engagement Points, some of my students stopped submitting any assignments, so I will share data and analyze whether this drop-off may have impacted their performance on later Big Idea attempts.", "id": "Paper/70343", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70343"}, {"title": " The effect of predation on the dynamics of Chronic Wasting Disease in deer ", "webprogram_exclude": "0", "session_ids": ["Session/17988"], "source_sha256": "71f4ecb60370687edc4dc54ebc54063910c6cd9fa36213dee4df57c16cd646da", "withdrawn": "", "abstract": "Chronic Wasting Disease (CWD) is a neurological disease that impacts deer populations and is caused by a misfolded protein known as a prion. The disease has spread widely in deer populations in the American West. CWD is transmitted both directly by infected individuals and indirectly through environmental exposure. The prion that causes the disease can remain infectious for more than a decade, making the disease difficult to control. We use mathematical modeling to assess the feasibility of using predators, such as wolves, to control CWD outbreaks in models of varying complexity. We find that wolves, or other predators, may be able to help control the disease in deer populations. Beyond eliminating infected individuals from the population, predators and human hunters can also limit the susceptible population, which is beneficial for avoiding future outbreaks of CWD. Though our analysis is largely qualitative in nature, we note that estimating parameters from the existing data is a challenge for this system and describe how to handle structural identifiability issues that emerge in nonlinear epidemiological models when not all relevant state variables can be measured. Estimating unique parameters from the existing data may be important for managerial decision making, forecasting, and other quantitative modeling contexts.", "id": "Paper/70344", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70344"}, {"title": " Stability Analysis of a Nonlinear Multiscale PDE System for Tridispersive Double-Diffusive Porous Convection ", "webprogram_exclude": "0", "session_ids": ["Session/18444"], "source_sha256": "227303ce7974c3dd9dc429a2cd31e63b809abf32d8cdf82ab386c84444e4d89a", "withdrawn": "", "abstract": "We develop and analyze a novel nonlinear multiscale PDE system modeling buoyancy-driven double-diffusive convection in a tridispersive porous medium. Motivated by heat exchangers, heat pipes, and fractured reservoirs, where a single-porosity description is inadequate, the model couples three Darcy-type momentum equations (macro-, meso-, and micro-scale phases) with a parabolic energy equation and a solute transport equation, capturing interphase momentum exchange, multi-porosity/multi-permeability effects, and thermodiffusion. We study stability of the background conduction state through both linear and nonlinear theory. Linear instability is analyzed via the Fourier mode method, while nonlinear energy stability is established through two independent approaches- the standard integral inequality method and the differential constraint method. The resulting eigenvalue problems are solved numerically using a Chebyshev spectral collocation scheme. \nResults show that interphase momentum transfer and permeability ratios delay the onset of instability, and reveal a subcritical instability region undetectable by linear theory alone, underscoring the necessity of nonlinear analysis for multiscale porous-media PDE models.", "id": "Paper/70346", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70346"}, {"title": " LLMs and the single developer ", "webprogram_exclude": "0", "session_ids": ["Session/18208"], "source_sha256": "b7ae8c9502088d1fed232d1e21957135025ef537a576cc769fd867fecb862708", "withdrawn": "", "abstract": "A vibrant developer community is a marker of a successful open source software project, and indeed has been touted as an open source advantage: \"many eyes make all bugs shallow.\"  Some mathematical software projects achieve this marker, such as the main open source computer algebra systems.  On the other hand, there are a large number of useful and maintained mathematical software projects with small developer communities.  For example, many of the packages that come with computer algebra systems are maintained by a single person.\n\nGap.app is a macOS frontend for and distribution of the GAP computer algebra system. It was first released in 2007, and in recent years it averages around 50 downloads per month.  Active development on it requires fairly intimate knowledge of GAP, of macOS, and of Objective-C with manual memory management.  Partly because of these requirements, it has been a solo project of the speaker more or less throughout.\n\nThis talk will survey some of the ups and downs of this long-lived software project, with particular emphasis on the advantages and disadvantages of the artificial additional set of eyes that can now be provided by an LLM.  In the case of Gap.app, the model quickly identified some difficult bugs, both known and unknown.  It was also on occasion confidently wrong.  More subtly, the designs it proposed were sometimes a poor fit for existing architecture, and blind adherence to its suggestions would have accumulated technical debt.", "id": "Paper/70348", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70348"}, {"title": " Stochastic diffusion approximations for eco-evolutionary dynamics in fluctuating populations ", "webprogram_exclude": "0", "session_ids": ["Session/19370"], "source_sha256": "4046c79cc0a9ccc10a7477c0d138494a7d3bfb3ffdcbd6f93e470c720eba77ec", "withdrawn": "", "abstract": "We develop a rigorous diffusion framework for eco-evolutionary dynamics in a two-type population whose total size fluctuates. Demographic stochasticity is modeled by a continuous-time birth–death process for the two types with density-dependent rates, while selection acts through weak frequency-dependent mechanisms. Under a large-population diffusion approximation and time-scale separation, the dynamics reduce to a fast–slow stochastic system: population size evolves on the fast ecological scale, whereas type frequencies evolve on the slow evolutionary scale. The fast variable describes fluctuations in total abundance, while the slow variable tracks the relative abundance of the two types. We analyze the resulting singularly perturbed diffusion using inner and outer solutions and matching, obtaining uniformly valid approximations across the relevant time scales. This yields explicit approximations for fixation probabilities, mean times to absorption, and the quasi-stationary distribution of type frequencies conditional on non-absorption, including leading-order corrections due to population-size fluctuations and weak frequency-dependent selection. This reduction preserves both demographic and environmental noise and remains accurate on intermediate and longtime scales. In contrast to constant-size diffusion models, the framework retains the feedback from fast ecological variability to slow evolutionary change and clarifies how demographic stochasticity interacts with selection. As an application, we study a public goods model with frequency-dependent interactions and characterize transient coexistence and eventual fixation. The results show when demographic and ecological fluctuations amplify or counteract weak selection and provide a tractable foundation for linking ecological variability with evolutionary change.", "id": "Paper/70350", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70350"}, {"title": " Maximizing Total Biomass in a Dynamic Population Model with Allee Effect ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "6c7916c3ae6ec17862182fdf2a32c864f9dbacc825b8d6c9fa7fa94325fe9c45", "withdrawn": "", "abstract": "We study the impact of dispersal on total equilibrium biomass in a fragmented population model with Allee effects. The system consists of two habitat patches coupled by symmetric migration, where local dynamics follow an Allee-effect growth law with patch-specific carrying capacities and critical density thresholds. We show that dispersal can decrease, increase, or produce a nonmonotonic change in total equilibrium biomass, depending on the ratio of intrinsic growth rates relative to parameter-dependent thresholds. We derive explicit threshold conditions separating these regimes and determining when dispersal is beneficial or detrimental. Our analytical results are supported by bifurcation analysis and numerical simulations.", "id": "Paper/70353", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70353"}, {"title": " On the Lucky and Displacement Statistics of Stirling Permutations ", "webprogram_exclude": "0", "session_ids": ["Session/18367"], "source_sha256": "8045ccf236a1fa43cee8082d37ed980181add02d26314f3f9cdc7857ddd33c1a", "withdrawn": "", "abstract": "A \\textit{parking function} of length $n$ is a tuple $\\alpha=(a_1,a_2,\\ldots,a_n)\\in [n]^n$ whose rearrangement into weakly increasing order $\\beta=(b_1,b_2,\\ldots,b_n)$ satisfies $b_i\\leq i$ for all $i\\in[n]$. We investigate two statistics of parking functions when $\\alpha$ is a Stirling permutation: luck and displacement.  A \\textit{Stirling permutation} of order $n$ is a permutation of  the multiset $\\{1,1,2,2,3,3,\\ldots,n,n\\}$ where any value $j$ appearing between the two instances of $i$ satisfies $j>i$. A car $i$ is said to be \\textit{lucky} if it parks in its preferred spot, $a_i$. An extremely lucky Stirling permutation is a Stirling permutation where the maximum number of cars are lucky.\nAnother statistic for parking functions is known as its  \\textit{displacement}. The displacement of a car is defined as the difference between where it parks and its preference. \n\nAmongst our results we show that for any positive integer $n$, the number of extremely lucky Stirling permutations of order $n$ is the Catalan number $C_n$. We also describe a formula for the displacement of each car in an extremely lucky permutation. This is a joint work with Laura Colmenarejo, Aleyah Dawkins, Jennifer Elder, Pamela E. Harris, Kimberly J.~Harry, Selvi Kara, and Bridget Eileen Tenner.", "id": "Paper/70359", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70359"}, {"title": " The MCM as a senior capstone experience ", "webprogram_exclude": "0", "session_ids": ["Session/18066"], "source_sha256": "da5e9aca2306ce923907010fff6bf83bc748c23f46ba3665e1e429aa7cad1904", "withdrawn": "", "abstract": "At Carleton College, senior mathematics majors complete a two trimester senior capstone project advised by a faculty member.  For several years, I have used this senior capstone as a way to recruit and prepare students for the Mathematical Contest in Modeling.  Teams spend several months practicing in the lead-up to the MCM, then debrief and present their results publicly after the contest.  I’ll discuss my ideas for approaching team preparation, my teams’ experiences, and feedback I’ve received from students along the way.", "id": "Paper/70360", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70360"}, {"title": " Starscapes and special points on varieties ", "webprogram_exclude": "0", "session_ids": ["Session/18366"], "source_sha256": "ad706ca8ca474c65cf16c29f59fc89d21fd267d72c8b8a3bc5a117a5b0df2550", "withdrawn": "", "abstract": "While the study of rational points is well-established, much less is known about points on varieties defined over solvable extensions, or extensions with other sorts of bounded complexity. In joint work with Jesse Wolfson, we establish effective techniques for obtaining points on intersections of hypersurfaces via the classical theory of polar cones---often producing dense supplies of such points.\n\nAfter a brief introduction to our approach and its applications to the resolvent degree of finite groups, this talk focuses on attempts to illustrate the underlying geometry of our key lemmas. In particular, we generalize the established illustrative genre of algebraic starscapes into these new regimes. Along the way, we will explore what can go wrong, highlight remaining questions, and offer various invitations to explore the arithmetic of special points.", "id": "Paper/70365", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70365"}, {"title": " Open-Source Software for Computing Code Automorphisms ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "d5c9e5c7d4127ee9c7d7da1dccb0e94910e3b194afa31c97dafd6fab1319e41e", "withdrawn": "i", "abstract": "An error-correcting code is a mathematical structure that models the flow of information through a noisy communication channel and seeks to mitigate errors through redundancy. These codes have a wide range of uses spanning from satellite transmissions to cryptographically secure communication schemes. An automorphism of a code is a permutation of the coordinate positions that preserves the code, and these symmetries are useful in helping to answer questions of code equivalence, classification, and decoding. Our work focuses on implementing and testing algorithms for code automorphism computation using GAP and the GUAVA package. We present an efficient algorithm for generating all codewords of a desired Hamming weight based on existing solutions to the Information Set Decoding (ISD) problem. Our second contribution is the development of a bipartite implementation of Leon's algorithm that constructs a codeword incidence matrix and iteratively refines row and column partitions. This refinement progressively reduces the search space for coordinate permutations, enabling efficient identification of code automorphisms. Overall, our contributions address a gap in the available GAP/GUAVA workflow by extending Leon-style code automorphism computation beyond the binary setting and replacing exhaustive codeword enumeration with information-set decoding, yielding a more scalable and efficient framework for automorphism computations in code-based cryptography.", "id": "Paper/70371", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70371"}, {"title": " Optimal Sparsification of Gaussian Processes ", "webprogram_exclude": "0", "session_ids": ["Session/18442"], "source_sha256": "05bd8492451b3fbdd13a190b51327e5ba9e939153b766b6f9071230aaabb8f37", "withdrawn": "", "abstract": "Title: Optimal Sparsification of Gaussian Suprema\n\nAbstract: Suprema of Gaussian processes are fundamental objects in probability theory, with applications throughout mathematics, statistics, and theoretical computer science. This talk is about \\emph{sparsifying} Gaussian suprema: replacing a large Gaussian process with a much smaller one while approximately preserving its supremum. I will describe a recent optimal sparsification theorem that exponentially improves previous bounds, along with some of the ideas behind the result. The talk will be self-contained and will assume no prior background on Gaussian processes.", "id": "Paper/70377", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70377"}, {"title": " COMAP Mathematical Modeling Contest as a Pathway to Undergraduate Research ", "webprogram_exclude": "0", "session_ids": ["Session/19005"], "source_sha256": "ad0e88b2eeaa1c6ab0c87f52d2d5fd75c59f7f7e67f176229ee5263797cfcf87", "withdrawn": "", "abstract": "We have been organizing COMAP Math Modeling contest for a number of years. We have created a system of introductory workshop followed by a weekly schedule of workshops on specific topics, throughout the Fall semester. The workshops are given by fellow faculty experts. Typical examples of these workshop topics include differential equations, dynamical systems, data analysis, Monte Carlo methods, etc. We also hold mock competition-style problem solving sessions. In the Spring semester, we focus more on the logistical, time, and team management aspects of the competition. Typically, we have had around ten teams every year, with multiple notable mentions. \n\nWe view the COMAP competition not just as a standalone competition similar to hackathons, but as a preparatory step to Undergraduate Research, for the applied and computational math and data science. We have multiple programs for undergraduate research and we have found that COMAP math modeling competition serves as an excellent platform for undertaking subsequent summer research project. Through COMAP competition, students acquire and improve their skillset significantly and participation in both have been increasing every year.", "id": "Paper/70379", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70379"}, {"title": " A Multiscale Fourier Feature-based PINN for the Poisson-Boltzmann Model in the Electrostatic Analysis of Proteins ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "5c6976561f319cb313e8672e2bdeac9b73b99076bd39ec062efda59204bf3562", "withdrawn": "", "abstract": "The electrostatic potential of proteins is necessary for computing the solvation free energy used for biomolecular modeling and drug discovery. However, the widely used Poisson-Boltzmann Equation (PBE) for solving electrostatic potential presents significant numerical challenges such as singular atomic charges, nonlinear terms, and sharp dielectric interfaces. Applying Physics-Informed Neural Networks (PINN) to the PBE provides a promising alternative to traditional numerical solvers. Existing PINN approaches address the PBE's piecewise nature by using domain decomposition architectures; however, the resulting loss functions are complicated and can lead to training instability and poor computational efficiency. We utilized a PINN method that employs a Sobolev extension to represent a piecewise continuous function in $\\mathbb{R}^n$ as a continuous function in $\\mathbb{R}^{n+1}$, a setting more suited to neural network approximation. From here, we incorporate multiscale Fourier features to enable us to approximate the electrostatic free energy of the linear PBE, nonlinear PBE, and the size-modified PBE within the same architecture. We analyze and validate this approach against the Kirkwood sphere PBE benchmark, which has an analytical solution. We also employ Eulerian solvent excluded surface (ESES) software to generate interface and collocation points to validate this approach against a state-of-the-art PB numerical solver over a diverse set of proteins.", "id": "Paper/70382", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70382"}, {"title": " Resolving Inverse Singular Value Problems with SSVP Liberation Sets ", "webprogram_exclude": "0", "session_ids": ["Session/17911"], "source_sha256": "dacac602950bfa9a940f48408c3ad7ecda68ed7975b06411b4806b610cf296c6", "withdrawn": "", "abstract": "The Inverse Singular Value Problem for a Pattern asks: given an $m \\times n$ pattern $P$ with $m\\leq n$ and a non-increasing list $\\sigma_1\\geq \\sigma_2 \\geq \\cdots \\geq \\sigma_m\\geq 0$ of real numbers, does there \nexist a matrix $A$ with pattern $P$ and  singular values $\\sigma_1, \\ldots, \\sigma_m$? The Strong Singular Value Property (SSVP) is a strong matrix property whose implications provide a toolkit for resolving families of inverse singular value problems. One such tool is the Superpattern theorem. If $A$ has the SSVP, the Superpattern theorem asserts the existence of  matrices with the same singular values as $A$ but with different patterns. In this talk, we discuss an variant of the Superpattern theorem for matrices without the SSVP and describe how to apply it to certain direct sums of matrices.", "id": "Paper/70383", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70383"}, {"title": " Musings about efficient representations, sparsity and redundancy ", "webprogram_exclude": "0", "session_ids": ["Session/18224"], "source_sha256": "caff9c2de115d0b4ef54beafd3ecdcd82b08820b6ea02b90f5fd93c79bc04885", "withdrawn": "", "abstract": "The presentation will review some mathematical results that highlight the importance of efficient representations (of e.g. signals, data, functions, operators), redundancy and sparsity in \"old-fashioned\" mathematics (i.e. before neural networks). The speaker will argue that these may explain part of the success of some AI algorithms, and explain her belief that it is important to continue to study, and eventually understand, the underlying mechanisms that lead to the effectiveness of Neural Nets.", "id": "Paper/70386", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70386"}, {"title": " Structures of infinite tensors ", "webprogram_exclude": "0", "session_ids": ["Session/16950"], "source_sha256": "d4a3e0ed7023937d69ad81ba1c80e94be141f1e81b54304956fc8e1320a90c50", "withdrawn": "", "abstract": "A \\textit{tensor space} is a vector space $V$, typically of countably infinite dimension, equipped with a tuple $f$ of multilinear forms. Tensor spaces are partially ordered by \\textit{embeddability}: $(V, f) \\preceq (W,g)$ if there is an injective linear map $\\phi\\colon V \\to W$ with $f = \\phi^* g$, i.e.\\ $g \\circ \\phi^{\\otimes d} = f$ in each component. Two mutually embeddable tensor spaces are \\textit{isogenous}.\n\nWe introduce a new definition of rank of multilinear forms and we use this to classify isogeny classes of tensor spaces. As an example, we show that the isogeny classes of cubic spaces whose form has infinite strength are isomorphic, as ordered sets, to $\\mathbb{N}_{\\geq 0} \\cup \\{ \\infty\\}$.\n\nThis result is another instance of stabilization of infinite-dimensional tensors, in their incarnation as points on GL-varieties. We will touch upon this theory and its connection with theoretical computer science.\n\nJoint work with Andrew Snowden.", "id": "Paper/70389", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70389"}, {"title": " Modeling and Simulation of the Ion-Binding-Mediated Swelling Dynamics of Mucin-like Polyelectrolyte Gels ", "webprogram_exclude": "0", "session_ids": ["Session/17988"], "source_sha256": "302145d1b5fe683ea6f4160c4d03de9f3a4b644da80740e1607c6ddc9382d1a6", "withdrawn": "", "abstract": "Volume phase transitions in polyelectrolyte gels play important roles in many biophysical processes such as DNA packaging, nerve excitation, and cellular secretion. The swelling and deswelling of these charged polymer gels depend strongly on their ionic environment. In this talk, I’ll sketch our two-phase model of polyelectrolyte gel dynamics with an emphasis on gel swelling and deswelling.  The model treats the polyelectrolyte gel as a mixture of two materials, the network and the solvent. The dynamics of gel swelling is governed by the balance between the mechanical and chemical forces on each of these two materials. Simulations based on the model illustrate that the chemical forces are significantly influenced by the binding/unbinding reactions between the ions and the network, as well as the resulting distribution of charges within the gel. The dependence of the swelling rate on ionic bath concentrations is analyzed, and this analysis highlights the importance of the electromigration of ions and the induced electric field in regulating gel swelling.", "id": "Paper/70397", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70397"}, {"title": " Accelerated Interpolation Using Conformal Maps ", "webprogram_exclude": "0", "session_ids": ["Session/19344"], "source_sha256": "6b6aab8190e7cbb6ecb5477b2552e40885bb79d8c72ca1e6c91ee7b7d8c18fe2", "withdrawn": "", "abstract": "Convergent polynomial interpolation methods on a finite interval must necessarily use nodes that have strong clustering near the endpoints of the domain. For functions that are highly smooth at the endpoints of the domain, this may result in a method which uses $\\pi/2$ too many points to reach an accurate approximation. Following previous work on the acceleration of interpolatory quadrature rules using conformal maps, we apply a conformal mapping strategy for polynomial interpolation to mitigate this $\\pi/2$ effect. For the approximation of high-dimensional interpolants of analytic functions, we implement the transformed quadrature rules in the sparse grid setting, and we show that in certain settings the convergence improvement can be exponential with growing dimension. Numerical examples demonstrate the benefits and drawbacks of the approach, as predicted by the theory.", "id": "Paper/70403", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70403"}, {"title": " Growth-Based Grading in Calculus 1 - Implementation, Evaluation, and Considerations ", "webprogram_exclude": "0", "session_ids": ["Session/17812"], "source_sha256": "2ced47d9115499f8d4e1046b0609ca6c4cd6b2b201b8c5d1b97bf3ee9b286696", "withdrawn": "", "abstract": "The theory of growth mindset (Dweck, 2006) posits that students who believe in their ability to grow and develop skills tend to achieve better outcomes. Providing students with opportunities to learn from feedback and improve performance sends the message that math ability is not fixed and growth is possible.\n\nBeginning in 2022, we redesigned our STEM and non-STEM Calculus 1 courses by implementing mastery-based grading with reassessment opportunities and growth mindset message, i.e. growth-based grading. For two years, we randomly assigned students in Calculus 1 to either growth-based grading and traditional grading. In Calculus 1 for STEM majors, students with growth-based grading demonstrated statistically significantly higher proficiency and reduced equity gap on final exam questions than the students with traditional grading. Earlier results showed no statistically significant differences between the two groups in the non-STEM Calculus 1. In Fall 2024, a redesign of Calculus 1 for non-STEM majors and a different experimental design led to significant improvement for students in the growth-based grading group. We will report on the details of implementation, data analysis and impact on student outcomes from the past 4 years.\n\nMoreover, growth-based grading is designed to allow students’ outcomes to change as they demonstrate additional proficiency, and conventional point-based grade summaries may provide limited information about their current trajectory. To address the challenge of tracking student progress in the growth-based system, we developed a learning-target-based forecasting tool that uses demonstrated proficiency to provide an interpretable and responsive outlook while preserving the central principles of the growth-based philosophy. \n\nReference: Dweck, C. S. (2006). Mindset: The new psychology of success.", "id": "Paper/70404", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70404"}, {"title": " From Solitary Spark to Shared Practice: Contributing to PRIMUS ", "webprogram_exclude": "0", "session_ids": ["Session/18341"], "source_sha256": "fc1ab334a51d097e05b179c067e424c58daec18b9e76fcc0679e03e2cf826e35", "withdrawn": "", "abstract": "PRIMUS (Problems, Resources, and Issues in Mathematics Undergraduate Studies) is a great venue to bring your observations and ideas to a broad audience. Its scope includes both RUME and SoTL projects, but also a space in between these publishing paradigms. In the talk, we will provide background about the journal, explain the editorial process, and offer suggestions to consider as you prepare your manuscript.  Both speakers are PRIMUS subject editors.", "id": "Paper/70405", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70405"}, {"title": " Z-properties and flips in shortest-path posets ", "webprogram_exclude": "0", "session_ids": ["Session/18372"], "source_sha256": "7a0d1446989084bb81cdcc264a8d7f8b9d0127f15371cec754358bb37c7c6500", "withdrawn": "", "abstract": "Let $[u,v]$ be a Bruhat interval in a Coxeter group, and let $SP(u,v)$ be the poset formed by the vertices and edges lying on shortest directed paths from $u$ to $v$ in the Bruhat graph $B(u,v)$. Label the edges of $B(u,v)$ by reflections and fix a reflection order $<_T$. If $SP(u,v)$ has a unique rising maximal chain with respect to $<_T$, then $SP(u,v)$ is EL-shellable and Gorenstein$^*$. It is conjectured that these posets $SP(u,v)$ are a lattice and isomorphic to a Bruhat interval. In this talk, we will describe several structural results toward these conjectures. In particular, the unique-rising chain property is hereditary (intervals in unique-rising-chain $SP(u,v)$ are themselves shortest-path posets with a unique rising chain). Moreover, the reflection order also satisfies a weak $Z$-property. As a further application, the lattice conjecture holds for the broad class of hereditarily atom-separable shortest-path posets.\r\n\r\nWe will conclude by explaining how these results interact with du Cloux’s theory of abstract Bruhat intervals and Reading’s shaving–zipping recursion for Bruhat intervals and how the remaining non-separable cases reduce to a geodesic lifting problem controlled by root circuits and rank-three polygon moves.", "id": "Paper/70407", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70407"}, {"title": " Predicting Coupled Cluster Wavefunction Amplitude Tensors via an Equivariant Graph Neural Network ", "webprogram_exclude": "0", "session_ids": ["Session/18032"], "source_sha256": "9ac3f23ffc309e94516f9c26e110b1566c455deca64bd5a848352588c811d588", "withdrawn": "", "abstract": "For the past 100 years, it has been the goal of quantum chemists and mathematicians to practical computational develop methods to solve the time-independent Schr{\\\"o}dinger equation for large systems of electrons. Efforts have followed two major directions, finding point-wise solutions in real-space using grid-quadrature methods and developing tensor approximations to the exact $N$-dimensional wavefunction. Both of these directions have their issues. Interpolative grid-based solutions require the use of domain decomposition strategies, such as large and complicated multiresolution grids. Tensor-based solutions, while more efficient than grid solutions, are plagued by the curse of dimensionality. These solutions routinely require the construction of order-2, 4 and 6 tensors resulting in a polynomial increase in memory and time costs with number of electrons. These issues restrict accurate electronic methods to relatively small chemical system.\n\nWith the rise in popularity of in the use of machine learning (ML) for scientific computing, there have been many investigations into its effective use to predict values and properties of chemical systems. Direct application of ML methods to existing methods in quantum chemistry is made difficult by exactly the problems described above. For example, in real-space the low statistical correlation of the exact wavefunction makes neural network training very inefficient. In this work, we seek to improve the application of ML to accurate electronic structure methods. We do this by first developing a low-order preserving coupled cluster algorithm. Subsequently, we develop an equivariant graph neural network method to predict the low-order tensor quantities in this coupled cluster algorithm.", "id": "Paper/70409", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70409"}, {"title": " Research on student learning and instruction at the mathematics-physics interface ", "webprogram_exclude": "0", "session_ids": ["Session/18199"], "source_sha256": "511ac8a7b02e9fbc756e9028a6e145b3dcfa865d5ad66d0b593fdbce15ff6ddb", "withdrawn": "", "abstract": "Our team has been working at the mathematics-physics interface in undergraduate physics courses, studying student reasoning and developing instructional materials to support instruction. Much of the work has focused on courses for physics majors targeting the mathematical tools used in physics core theory courses like electricity and magnetism or quantum mechanics. More recently, we have investigated the mathematical practices in introductory calculus-based courses. This work has been supported by a series of NSF grants (PHYS-1406035, PHYS-1912660, DUE-2336910, DUE-2539369). \n\nIn this talk we will highlight these projects and some of their findings and outcomes, including discussions of studies of student reasoning and behavior for specific mathematical and physical contexts. This will include empirical studies of student reasoning but also more theoretically-oriented work. We will also briefly describe investigations of instructional practices and alignment between mathematics and physics and their implications for student learning. We believe this work sheds light on implicit assumptions about learning and transfer that influence instructional practice and gaps between practices in mathematics and physics.", "id": "Paper/70414", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70414"}, {"title": " Legendrian Non-simplicity of Whitehead Doubles of the Trefoil via Knot Floer Homology ", "webprogram_exclude": "0", "session_ids": ["Session/18218"], "source_sha256": "7babc2b1acaf9eb148ec7a549be91b9aa9cdcdc9c20fdba855e583ed4b923f73", "withdrawn": "", "abstract": "The classification problem for Legendrian knots asks to what extent classical invariants, namely the Thurston–Bennequin number ($tb$) and rotation number ($rot$), determine Legendrian isotopy classes. It has long been understood that these invariants are not sufficient in general, suggesting the need for finer tools arising from knot Floer homology. In this talk, we demonstrate the Legendrian non-simplicity of Whitehead doubles of the trefoil using the knot Floer homology framework. In particular, we utilize the LOSS invariant and the surgery triangle in Heegaard Floer homology to distinguish pairs of Legendrian Whitehead doubles that have identical classical invariants. This provides an explicit negative answer to the question of Legendrian simplicity for Whitehead doubles of the trefoil and demonstrates how knot Floer homology refines the classical classification problem.", "id": "Paper/70415", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70415"}, {"title": " Non-uniqueness of Leray solutions from smooth data in a Navier-Stokes model ", "webprogram_exclude": "0", "session_ids": ["Session/17822"], "source_sha256": "07b6c86eaa512e617db9da217df1bf4ea4f9cd02516618bec905283b10ae8977", "withdrawn": "", "abstract": "Recently, non-uniqueness of Leray-Hopf solutions from rough initial data was proved by Hou, Wang, and Yang following a program of Jia and Sverak. This is a step along the way to a more fundamental question: is there non-uniqueness of Leray solutions from smooth data? And can multiple solutions arise from Leray's original compactness construction? These problems are difficult because the solution must blow-up, then continue coherently past the blow-up time. We provide a positive answer to both in a natural dyadic model of the 3D Navier-Stokes equations.", "id": "Paper/70416", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70416"}, {"title": " Practical Indistinguishability in a Gene Regulatory Network Inference Problem ", "webprogram_exclude": "0", "session_ids": ["Session/18127"], "source_sha256": "224bcabd06036d7f0e27ef774a31452993369d84aaaee45ccff54b719726fb9d", "withdrawn": "", "abstract": "Current automated model discovery algorithms have been widely applied to biological data sets, but often require high-frequency temporal sampling of the system, relatively low noise, and the explicit measurement of most, if not all, relevant state variables. Biological data from experimental studies often deviate from at least one of these characteristics. To explore inference outside this data regime, we attempted an inference problem based on infrequently sampled, noisy gene expression data collected over the course of development in the nematode Pristionchus pacificus. This nematode can form one of two distinct mouthform phenotypes during development, depending on specific environmental conditions and its genetic background, but the structure of the regulatory network underlying this developmental decision is currently unknown. To learn more about the underlying mechanism, we study the structural identifiability and distinguishability of approximately 14,000 candidate gene regulatory network models, then fit this model ensemble to gene expression data across three experimental conditions. We then used machine learning approaches to find model sets, or collections of models with shared regulatory features that best fit the data, for each experimental condition. In the intersection of the three model sets, there exists a regulatory network model that explains the data across all three conditions, uncovering a new possible regulatory network that may control the developmental decision. This study acts as a generalized sensitivity analysis across model structures, illuminating what we can honestly infer about biological systems from limited experimental measurements.", "id": "Paper/70418", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70418"}, {"title": " Geodesic flows and slow downs of continued fraction maps ", "webprogram_exclude": "0", "session_ids": ["Session/17913"], "source_sha256": "9a4136f7310a0abc0eb5435c5423c627a5cc8fcabe3f51ac62932ad08a6eeaa4", "withdrawn": "", "abstract": "We will start by looking at the Farey tent-map as a slowdown of the Gauss map for the regular continued fractions.\nThe connection between cutting sequences of geodesics on the modular surface $PSL(2,\\mathbb{Z})\\backslash\\mathbb{H}$ and regular continued fractions was established by Series, and Heersink expanded the cross-section of the geodesic flow on the unit tangent bundle for the Farey map. I will look at explicitly connecting Heersink's cross-section with Series' cutting sequence description. \n \nI will then describe the slowdown of the even Gauss map using cutting sequences of geodesics on the modular surface $\\Theta\\backslash\\mathbb{H}$ and even continued fractions. This modular surface has two cusps, slightly complicating the geometric description of the cutting sequences.", "id": "Paper/70429", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70429"}, {"title": " Understanding rotation groups of the Platonic solids with origami and symmetric colorings ", "webprogram_exclude": "0", "session_ids": ["Session/18235"], "source_sha256": "1187d83c8036cd905950d76d4ba3a484993094783a2bc57b666bb87c7c395513", "withdrawn": "", "abstract": "The Platonic solids are highly symmetric objects whose rotation groups are well known, both as finite subgroups of the special orthogonal group and as subgroups of permutation groups. We create origami models of these objects with rotationally-invariant colorings in order to easily identify their rotation groups as subgroups of the appropriate permutation group.", "id": "Paper/70430", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70430"}, {"title": " A grid-free Hopf-formula solver for left-invariant optimal control and Hamilton-Jacobi equations on Lie groups ", "webprogram_exclude": "0", "session_ids": ["Session/17703"], "source_sha256": "f38b0f9c34c2113d0486e0ccef59d0a0e227d9808ec5cd61537af5e28833bf51", "withdrawn": "", "abstract": "We propose a grid-free pointwise solver for the value function of fully actuated left-invariant Bolza problems on connected finite-dimensional Lie groups, motivated by the Euclidean Hopf formula.  The value function is represented as the inf-convolution of the initial datum with a reduced action kernel.  Under the standing Tonelli assumptions, every fixed-endpoint minimizer is a normal Lie-Poisson characteristic, and the reduced endpoint map is globally defined and surjective. \nConsequently, the action kernel is the minimum characteristic action over the complete endpoint fiber, and the value function admits a global Hopf representation formula as a finite-dimensional minimum over all initial reduced covectors. This formula remains valid at cut points and in multiple-minimizer regimes. \nThe representation is the pointwise primitive of a grid-free solver, in which each objective evaluation is supplied by a reduced-flow oracle. \nWe show both asymptotic and quantitative  convergence for the discrete oracle.  Numerical experiments validate the implementation against independent closed-form references and test asymmetric, product, and coupled systems. The selected-chart nonabelian product benchmark reaches state dimension $768$ without any state-space mesh, with mean pointwise solve time $2.26$ seconds at the largest instance. We then study eight applications on state spaces from $(SO(3))^4$ to $T^{1{,}048{,}576}$.", "id": "Paper/70435", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70435"}, {"title": " Follow the Arrows: Exploring the World of Quiver Representations ", "webprogram_exclude": "0", "session_ids": ["Session/18380"], "source_sha256": "ea0d4f093d1b5b6d3bf7e791f7e7e6c195811f1e296867afb19193f50c3bfb94", "withdrawn": "", "abstract": "A representation of a quiver is a way of describing a collection of vector spaces and the linear maps between them in a single diagram. The quiver itself is a directed graph of the underlying shape of the representation. We will give a taste of some projects I have worked on related to quivers. These projects address the questions: When are two representations essentially the same? Is it possible to classify all representations of a given quiver? How do small changes in the quiver's shape affect its representations?", "id": "Paper/70436", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70436"}, {"title": " A Mélange of Grading Strategies in an Applied Multivariable Calculus I Course ", "webprogram_exclude": "0", "session_ids": ["Session/18476"], "source_sha256": "b7ccc83c3409633b05f7f61b53f40c925f9eff102e9c9299220aa2729ed8506e", "withdrawn": "", "abstract": "Alternative grading has been shown to positively impact outcomes related to student learning and confidence. The implementation of these strategies requires buy-in from students as well as assignments and assessments that reflect the grading philosophy of the course. Often, courses will make use of several alternative grading paradigms. This talk provides a case study in incorporating standards-based grading, mastery grading, specifications grading, and contracts-based grading in a non-traditional first course in college calculus. Discussions of instructor, teaching assistant, and student reflections on the grading system will also be included.", "id": "Paper/70437", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70437"}, {"title": " Portfolio Combination with Transaction Costs: A Reinforcement Learning Approach ", "webprogram_exclude": "0", "session_ids": ["Session/18245"], "source_sha256": "55658125e9b707dd23e9209444b17bf51f565805870f138f486003ff5468925b", "withdrawn": "w", "abstract": "We study the portfolio combination problem of a multiperiod investor facing transaction costs. The portfolio in each period is a combination of the current holdings and an estimated target portfolio chosen by investors. A reinforcement learning agent chooses the combination coefficient to maximize the investor's expected utility, based on a low-dimensional state built from exponentially weighted estimates of realized mean and variance. In our empirical study, we demonstrate that the proposed framework achieves superior out-of-sample performance relative to benchmark portfolios.", "id": "Paper/70438", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70438"}, {"title": " An Application of the Duffing Dynamical System to Music Composition ", "webprogram_exclude": "0", "session_ids": ["Session/18233"], "source_sha256": "741e3385f1c21e511309e8bdbbb4b3612c31a742419ac672133fea3aab046712", "withdrawn": "", "abstract": "The talk will discuss the use of a Duffing dynamical system  in music composition. The Duffing equation is a second order differential equation that exhibits chaotic behavior under certain conditions.  The code allows parameters and initial conditions that produce both chaotic variation and stable behavior over time to be explored in the composition of the piece and applied to melodic, harmonic, and timbral structures. Examples from the resulting professional performances/recordings for piano and violin and description of the code will be presented.", "id": "Paper/70439", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70439"}, {"title": " A Hierarchical Spatiotemporal Model for Underreported COVID-19 Cases Using Wastewater Surveillance Data ", "webprogram_exclude": "0", "session_ids": ["Session/19338"], "source_sha256": "986473d3a843bf7fa5d5ee9f5d9ad1a0ff57b346d9b75f60fc9c3f84d25927b3", "withdrawn": "", "abstract": "Wastewater surveillance provides a complementary, population-level measure of infectious disease activity and offers a useful alternative to clinical case reports, which are often affected by under-reporting. However, wastewater and clinical surveillance data often exhibit substantial temporal fluctuations and heterogeneous patterns across locations, making it challenging to estimate the true disease burden. In this study, we propose a hierarchical spatiotemporal model to estimate the true number of COVID-19 cases using reported cases and SARS-CoV-2 wastewater concentrations. The proposed framework incorporates the following key components: a location-specific reporting process to account for spatial heterogeneity in under-reporting, a negative binomial latent process to estimate the unobserved true number of infections while accommodating overdispersion, and an autoregressive structure with an ARCH component to capture temporal dependence and large, time-varying fluctuations in disease activity. Within this framework, wastewater viral concentrations and relevant covariates inform the latent infection process, while the reporting process is modeled separately to account for under-reporting. This framework enables simultaneous estimation of the true disease burden and location-specific reporting probabilities from can be extended to other infectious diseases with incomplete clinical reporting.", "id": "Paper/70440", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70440"}, {"title": " Quantum Cellular Automata and Invertible Phases of Matter ", "webprogram_exclude": "0", "session_ids": ["Session/17925"], "source_sha256": "65de5d77582924360aed347ddb4c1927cdd2bd0cf5d46d235e724eee079e179b", "withdrawn": "", "abstract": "In the algebraic approach to quantum many-body systems, observables localized in bounded regions form a net of von Neumann algebras, generating what is known as a quasi-local algebra. I will discuss the classification of invertible quasi-local algebras under a notion of equivalence that generalizes Brauer equivalence and captures only large-scale properties. I will explain that this problem coincides with the classification of invertible phases of lattice systems and quantum cellular automata in one dimension higher. This provides an explicit construction of non-trivial quantum cellular automata and invertible states in dimension two. Using K-theory of the symmetric monoidal category of invertible quasi-local algebras and bounded spread isomorphisms, I propose a definition of a spectrum of invertible phases as conjectured by A. Kitaev.", "id": "Paper/70441", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70441"}, {"title": " A mean-field description of bounded-confidence opinion dynamics on large networks ", "webprogram_exclude": "0", "session_ids": ["Session/18260"], "source_sha256": "ed41ec9430560450d249e4fe37ba1a68d8dbccb47c3b07b5e4a0c10a373a5c3d", "withdrawn": "", "abstract": "Mean-field (MF) theories of bounded-confidence opinion dynamics typically assume either that a population is fully mixed or that the individuals of a population interact with each other according to one of a few special network families. We derive an MF approximation of the Deffuant--Weisbuch (DW) model on large networks by incorporating network topology through graphons, which are limiting objects of dense graph sequences. The MF DW equation on graphons is a kinetic partial integro-differential equation for the opinion density that holds for any graphon and recovers the fully mixed DW equation when the graphon is constant. We identify a class of degree-homogeneous graphons, including the Erd\\H{o}s--R\\'enyi and Watts--Strogatz graphons, on which the DW dynamics is the same as in a fully mixed population. This accounts for the qualitatively similar behavior that has been reported for networks with various different topologies. We show that the DW dynamics on networks is governed by the normalized degree function of the graphon, so a dense graph and a sparse graph that one draws from the same graphon evolve identically. We observe that the DW dynamics converge faster and that the opinion-domain boundaries have higher opinion densities for heterogeneous graphons, such as stochastic-block-model graphons and power-law graphons, than for the constant graphon of a fully mixed population. This excess density consists of small-degree nodes that no longer update their opinions because the opinions of all of their neighbors differ from their own opinions by more than the confidence bound. We thus identify an ``opinion cluster'' as a connected component with at least two nodes in an effective-interaction network. Agent-based simulations on synthetic graphs and a real-world social network agree closely with the theory. Although the agent-based dynamics depend on the network size, they converge to the MF solution as the network becomes infinitely large.", "id": "Paper/70445", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70445"}, {"title": " Bad primes for invariants of CM Picard curves and effective CM method ", "webprogram_exclude": "0", "session_ids": ["Session/17903"], "source_sha256": "9addacf20a3da1beb3027ac4d12502db3a312a2aff96965b4aae2c3cd361b4c7", "withdrawn": "", "abstract": "We give an exact formula to completely determine the set of all primes dividing the denominators of several natural invariants for Picard curves with a given CM order. Bounds on these primes were known earlier for some invariants. We use a Gross--Zagier-type big CM value formula due to Bruinier--Kudla--Yang, and apply it to certain automorphic Green functions that arise as Borcherds lifts. This work makes the CM method completely effective for Picard curves.", "id": "Paper/70446", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70446"}, {"title": " Energetic Drivers of Proteostasis Collapse During Metabolic Stress ", "webprogram_exclude": "0", "session_ids": ["Session/19371"], "source_sha256": "21b883a4c7d0aa0ba8835580e7c6b784dcc5f51c6a3f140f51a53fcafde1207b", "withdrawn": "", "abstract": "Cell death under metabolic stress is linked to lost protein homeostasis, but whether failure stems from protein-folding network breakdowns or energy limitations remains unclear. Because protein synthesis, chaperone-assisted folding, and degradation require substantial ATP, these pathways are sensitive to energetic fluctuations. To evaluate how energetic constraints dictate proteostatic stability, we extend a kinetic model of native and unfolded protein populations by incorporating an energy component. The resulting nonlinear system captures spontaneous and chaperone-mediated folding, stress-induced autocatalytic feedback, and saturation-limited degradation pathways. Through nondimensionalization, we identify key kinetic ratios governing state transitions. Phase plane and bifurcation analyses characterize equilibrium structures, revealing regimes of stable homeostasis, bi-stability, and complete loss of steady states. By incorporating energy dynamics, the energetics-included model highlights potential thresholds where repair and clearance mechanisms may become unsustainable. Ultimately, this framework links metabolic stress to proteostatic collapse, providing a means to evaluate quantitative boundaries between adaptive responses and irreversible dysfunction.", "id": "Paper/70447", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70447"}, {"title": " Products of Terms in Arithmetic Progression Equal to a Cube ", "webprogram_exclude": "0", "session_ids": ["Session/19361"], "source_sha256": "51641288f724ad1d2e58e14c2d3975a242d19b8649038ee449f92b21a9425469", "withdrawn": "", "abstract": "The study of when perfect powers can be represented by a product of two or more consecutive positive integers dates back to Goldbach and Euler. This problem was solved by Erd\\H{o}s and Selfridge, who showed no perfect power can be represented in this form. The natural next question is: when can a perfect power be written as the product of an arithmetic progression of integers. This translates to the study of solutions to the Diophantine equation\n\\[\n     n(n+d)\\cdots(n+(k-1)d)=y^\\ell,\n\\]\nwhere $n,d, k, y, \\ell\\in\\mathbb{Z}$ with $k\\geq 3,~d\\geq 1$, $~\\ell\\geq 2$, and  $\\gcd(n,d)=1$. Modern progress on this problem for $\\ell=3$ includes work by Hajdu, Tengley, and Tijdeman, which we build upon. We improve their results and combine them with additional elliptic curve methods to increase the length, $k$, of the arithmetic progression for which all possible solutions are determined.", "id": "Paper/70449", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70449"}, {"title": " Determining modes and Kolmogorov-like dissipation scales for the Hall and electron magnetohydrodynamics ", "webprogram_exclude": "0", "session_ids": ["Session/17757"], "source_sha256": "1c813f2eecc703bcc2acb3cb33babb6e69c6b60e90d901cef26fcc340b8d3706", "withdrawn": "", "abstract": "Kolmogorov’s theory of turbulence suggests that, in three-dimensional fluid flows, most of the energy is concentrated in Fourier modes with wavenumbers below a certain threshold, known as the Kolmogorov dissipation wavenumber. At scales beyond this threshold, viscous effects become dominant. Similar dissipation scales have been identified through numerical studies and simulations involving Hall and electron magnetohydrodynamics (MHD), which are important models for understanding turbulence in astrophysical plasmas.\n\nIn this work, we use Littlewood–Paley decomposition methods to develop a rigorous mathematical counterpart to these physically observed scales. Specifically, we prove the existence of time-dependent determining wavenumbers for weak solutions of the Hall- and electron-MHD equations. This improves on earlier results, which were not optimal and did not establish a connection with phenomenological dissipation scales. We demonstrate that their time averages are bounded above by the Kolmogorov-type dissipation wavenumbers predicted by phenomenological models of plasma turbulence. Furthermore, we establish a uniform bound on the magnetic determining wavenumber from Besov regularity.", "id": "Paper/70450", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70450"}, {"title": " From Spatial Clustering to Dynamical Mechanisms of Endothelial Heterogeneity ", "webprogram_exclude": "0", "session_ids": ["Session/18357"], "source_sha256": "d842408bcffabd42b6353f0b8232285fd1c62f16da95ca4c2e675c539c725c70", "withdrawn": "", "abstract": "Endothelial cells exhibit phenotypic heterogeneity across organs and vessel types. Quantitative image analysis shows that such heterogeneity also persists within confluent endothelial monolayers under controlled in vitro conditions. Single-cell measurements of junction organization, proliferative state, and NOTCH pathway activity yield multimodal, non-Gaussian distributions. Spatial correlation and cluster-size analyses further show that similar signaling states form spatially organized clusters. These statistics quantify heterogeneity but cannot distinguish among stable subtypes, stochastic fluctuations, and dynamically maintained states.\n\nTo test whether local cell–cell signaling can generate this organization, we developed a multiscale model of an endothelial monolayer. Cell geometry and rearrangement are represented using a Cellular Potts model, while NOTCH dynamics within each cell are described by ordinary differential equations. The monolayer defines a contact network whose edge weights depend on cell–cell contact areas, allowing tissue geometry to modulate signaling. The model incorporates lateral inhibition, lateral induction, cis interactions, and feedback, with key timescales constrained by single-cell experiments.\n\nModel exploration produced stable states, synchronous oscillations, and spatially heterogeneous asynchronous oscillations of the NOTCH target HES1. Productive cis interactions generated contact-dependent dynamics that reproduced both the observed single-cell distributions and their spatial clustering. In contrast, HES1 autoregulation produced global synchronization inconsistent with the measured local organization. The model also predicted that reducing intercellular contact would suppress heterogeneity, consistent with experiments comparing sparse and confluent cultures.\n\nThis work shows how spatial statistics can be coupled to nonlinear dynamical models to discriminate among candidate mechanisms. Although we use correlation and cluster-size measures rather than topological data analysis, the study illustrates how mathematical descriptors of cellular patterns can constrain their possible generative dynamics.", "id": "Paper/70451", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70451"}, {"title": " Slope gap distributions of Veech surfaces and return times of the horocycle flow ", "webprogram_exclude": "0", "session_ids": ["Session/17902"], "source_sha256": "d23bad3d6e08d3862af3ada3461318d6e67ca73509eb241811541cb6aa22e047", "withdrawn": "", "abstract": "We will talk about an algorithm for finding the slope gap distribution of Veech surfaces that builds on work of Kumanduri, Sanchez, and Wang. We will illustrate it with the case of the double heptagon surface. This is joint work with Nada Ali, Uma Arengo, Taylor McAdam, Carson Newman, Noam Scully, and Sophia Zhou.", "id": "Paper/70454", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70454"}, {"title": " The Question of Whether: From Statistical Significance to Scientific Understanding in the Classroom ", "webprogram_exclude": "0", "session_ids": ["Session/18064"], "source_sha256": "ffb1a8bd885e51799bf24646089878d896a09f87469f9090a50fe67eebc27c29", "withdrawn": "", "abstract": "Introductory statistics courses often organize scientific inference around the question of whether an effect is statistically significant. But scientists rarely need a binary verdict about a null hypothesis. They need to understand the magnitude of an effect, the uncertainty surrounding its estimation, and the implications of that uncertainty for scientific conclusions and practical decisions.\n\nThis talk explores how a modeling-first statistics course might be rooted in the questions scientists actually ask of data. Drawing on the critique of statistical significance developed by Ziliak and McCloskey in The Cult of Statistical Significance and from my book Bernoulli’s Fallacy, I will argue for an approach that emphasizes effect-size estimation and the communication of uncertainty through posterior distributions. Rather than asking students simply to decide whether an effect exists, we must encourage them to investigate how large it might be, how probable scientifically meaningful outcomes are, and what conclusions the evidence supports.\n\nThrough concrete scientific examples, I will show how a shift in the questions posed to students can reshape their approach to statistical reasoning and the conclusions they communicate. The goal is to develop students’ capacity to use data not merely to classify hypotheses, but to reason quantitatively about an uncertain world.", "id": "Paper/70456", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70456"}, {"title": " Enumerating Parking Assortments with a Given Defect ", "webprogram_exclude": "0", "session_ids": ["Session/18085"], "source_sha256": "775a13ee9e765f015341b1f0a56c0cf75086360a164b4f5f3f74151cc51bbff6", "withdrawn": "", "abstract": "Parking assortments are a variation on parking functions with two differences.  First, in addition to having different preferences represented in a vector $\\textbf{x}=(x_1, x_2, ..., x_n)$, cars may be of a variety of different lengths represented in the vector $\\textbf{y}=(y_1,y_2, ..., y_n)$.  In a standard parking function, every entry of vector $\\textbf{y}$ would be 1.  Additionally, when parking, a car, $i$, checks to see if it can fit in its preferred parking spot, $x_i$.  To do so, parking spots $x_i$ to $x_i+y_i-1$ would need to be empty.  If spot $x_i$ is taken, it proceeds to the first block of empty spots after its preference.  If this block of of size $\\geq y_i$, the car parks in the first $y_i$ spots.  If car $i$ cannot park in the first block of open spots at or after its preference, it cannot park.  This project explores a representation of parking assortments on lattices as decorated Dyck paths, how defect is defined for parking assortments, and the enumeration of parking assortments with a given defect.  The presentation will include a recursive formula for for the total number of parking assortments on a street of length $m$ given $\\sum y_i$ with a defect of 0.", "id": "Paper/70461", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70461"}, {"title": " Sequences that do frame reconstruction ", "webprogram_exclude": "0", "session_ids": ["Session/17945"], "source_sha256": "6749074412386a1559c24b7d78bb4a91c948ed5adae9545262f8dad9a00b7744", "withdrawn": "", "abstract": "Frames allow every vector in a Hilbert space to be reconstructed stably from inner-product data. In this talk, we relax the frame reconstruction formula by allowing the operator in the decomposition to be noninvertible. We give a complete classification of sequences that admit this decomposition in terms of their associated frame operators. We also construct examples that admit this reconstruction but are not frames, illustrating several ways in which the frame conditions can fail. Finally, we determine when certain Schauder bases, including unconditional bases and exponential bases, satisfy the relaxed reconstruction formula.", "id": "Paper/70463", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70463"}, {"title": " Bicolored bosonic solvable lattice models ", "webprogram_exclude": "0", "session_ids": ["Session/18365"], "source_sha256": "d2f19d0e7e10af51e737b05870e1f412818e6e6d0e23b0acc25a5e646d649513", "withdrawn": "", "abstract": "The study of solvable lattice models originated in statistical mechanics, and has since formed rich connections with areas of mathematics including combinatorics, probability, and representation theory. Bosonic and colored variants of solvable lattice models have been studied in recent years by Aggarwal, Borodin, Brubaker, Buciumas, Bump, Gustafsson, Naprienko, Wheeler, and many others. We will showcase how a class of these models connects to symmetric functions and representation theory.", "id": "Paper/70464", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70464"}, {"title": " Portfolio Combination with Transaction Costs_A Reinforcement Learning Approach ", "webprogram_exclude": "0", "session_ids": ["Session/18328"], "source_sha256": "937df80b6ff4c0582c6e78bf247002cbd4b9b84f13fc0485323970131be1c886", "withdrawn": "", "abstract": "We study the portfolio combination problem of a multiperiod investor facing transaction costs. The portfolio in each period is a combination of the current holdings and an estimated target portfolio chosen by investors. A reinforcement learning agent chooses the combination coefficient to maximize the investor’s expected utility, based on a low-dimensional state built from exponentially weighted estimates of realized mean and variance. In our empirical study, we demonstrate that the proposed framework achieves superior out-of-sample performance relative to benchmark portfolios.", "id": "Paper/70465", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70465"}, {"title": " Archimedes Blown Out of Proportion: Symbolism and the Intelligibility of Mathematics ", "webprogram_exclude": "0", "session_ids": ["Session/17713"], "source_sha256": "c2d6dce8226d4a2d601fcdf672620cad2fd7e3f26de579b4a3441fb27178433f", "withdrawn": "", "abstract": "Isaac Barrow’s seventeenth-century edition of the Archimedean corpus reveals a longstanding problem in reading historical mathematics: how to reconstruct reasoning that the surviving text does not fully explain. Proposition 4 of \\textit{Sphere and Cylinder} II asks how to divide a sphere into segments whose volumes stand in a given ratio, a problem that reduces to a proportional relation we recognize as equivalent to a cubic equation. Barrow, a teacher of Isaac Newton and an important figure in the early development of calculus, regarded geometry as the foundation of mathematics and algebra as secondary. Yet as he worked through the geometric demonstration, he balked at the cumbersome proportional reasoning and proposed that Archimedes must have used a secret algebraic method.\n\nThis presentation compares Archimedes’ geometric analysis with Barrow’s algebraic reconstruction. Archimedes develops the solution through geometric constructions and compounded proportions; Barrow translates these relationships into symbolic equations, introducing variables and algebraic operations. The economy of symbolic calculation makes Archimedes’ argument appear unnecessarily cumbersome and gives Barrow the impression that he has uncovered the reasoning concealed by the surviving text. This episode shows how symbolic notation became a tool for reconstructing historical mathematical reasoning and, in the process, shaped what counted as an intelligible mathematical argument.", "id": "Paper/70466", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70466"}, {"title": " From Choi Matrices to Quantum Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18229"], "source_sha256": "5da751788b22e3fadc79006cf15bf1391a019b81c5b2b6ee116635b12f9efa7f", "withdrawn": "", "abstract": "Linear maps between matrix algebras admit several natural matrix representations, each of which reflects different structural properties of the map. In this talk, I will discuss the relationship between the Choi matrix and the standard matrix representation of a linear map between matrix algebras, and explore its implications for different notions of positivity. In particular, this relationship allows us to characterize, in the square matrix setting, when positivity of a map and positivity of its standard matrix representation coincide.\n\nI will then present applications of this framework to quantum information and quantum graph theory. We will discuss the Choi matrix, Kraus operators, and measurement systems associated with a quantum channel to its standard matrix representation, and use these connections to recover relationships between different formulations of quantum graphs.", "id": "Paper/70467", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70467"}, {"title": " Unbiased rough integrator and no arbitrage ", "webprogram_exclude": "0", "session_ids": ["Session/18124"], "source_sha256": "dffff8da20362c63e1131b5508aab18a464d8d6e6c661b6ba6f8cd942cf24a83", "withdrawn": "", "abstract": "Rough path theory extends classical stochastic calculus beyond the It\\^o setting, providing a pathwise framework for continuous non-semimartingale models. We investigate the capacity of this framework to support frictionless no-arbitrage markets, formalized through a No Controlled Free Lunch (NCFL) condition. We establish a rough Kreps–Yan theorem, demonstrating that NCFL is equivalent to the existence of an equivalent measure under which the price driver is an unbiased rough integrator. Our main contribution is a classification of these unbiased rough integrators across progressively richer classes of controlled portfolios, a result built upon a combinatorial description of one-dimensional rough paths. Specifically, for Markovian-type portfolios, the admissible drivers are time-changed Gaussian-Hermite rough paths. Introducing path-dependent signature-type portfolios further restricts this admissible class to Hermite rough path lifts of time-changed Chen-Hermite almost Brownian motion. Critically, under additional natural assumptions or by reintroducing simple strategies, the model recovers the It\\^o rough path lift of Brownian motion. This demonstrates that sufficiently rich frictionless rough-path market models are effectively constrained back toward the classical semimartingale paradigm. The framework applies broadly to one-dimensional $\\alpha$-H\\\"older rough paths (for arbitrarily small $\\alpha>0$) within the tensor algebra setting. Part of this research is a joint work with Qijin Shi.", "id": "Paper/70468", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70468"}, {"title": " A Frobenius version of the normalized volume and Tian’s criterion for K-semistability ", "webprogram_exclude": "0", "session_ids": ["Session/17929"], "source_sha256": "5ebd931ca9167629c4305245b932f6b8c823ed81282141307d19c45b329599cb", "withdrawn": "", "abstract": "The normalized volume of a Kawamata log terminal (klt) singularity was introduced by Chi Li, who used it to characterize K-semistability of a complex Fano variety in terms of the singularity of the cone over X. Moreover, for general (complex) klt singularities, a local stability theory has been established via the study of the normalized volume (and its minimization). In this talk, I will present joint work with Yuchen Liu, who introduced a positive characteristic analog of Li's normalized volume (called F-volume) by incorporating the Frobenius map. I will discuss a Frobenius version of Tian's criterion for K-semistability of Fano varieties by relating the F-volume to the Frobenius-alpha invariant. As applications, we compute the limit F-volumes of two-dimensional singularities via reduction modulo p and show that the limit matches Li's normalized volume. Time permitting, I will also mention the connection to the F-signature, which underlies the proof of our main results.", "id": "Paper/70470", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70470"}, {"title": " A Nonlocal Isometry Game for Quantum Metric Spaces ", "webprogram_exclude": "0", "session_ids": ["Session/17834"], "source_sha256": "c2c03889da3e0a5b6e7f38a0fc20dfa2afa4c6b8600aacb5ea09abe942d14531", "withdrawn": "", "abstract": "Nonlocal games have recently received significant attention in operator algebras and quantum information theory, leading to fruitful interactions between these areas. A nonlocal game involves\ntwo non-communicating players who cooperate to win against a referee, providing an operational framework for studying various mathematical structures arising in quantum information.\n\nIn this talk, I will introduce a nonlocal game designed to determine whether two quantum metric spaces are isometric. Unlike traditional nonlocal games, this game involves both quantum inputs\nand quantum outputs and provides a quantum analogue of metric isometry games. I will describe the associated game C^{*}-algebra and discuss its relationship with operator-algebraic formulations of quantum isometry groups.", "id": "Paper/70474", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70474"}, {"title": " Pressing sequences in nonbinary fields ", "webprogram_exclude": "0", "session_ids": ["Session/18227"], "source_sha256": "ce8c6f216b04bbfc4ffba4ac4158e043c2fc54e76c276853e6f590f7e6b7a28c", "withdrawn": "", "abstract": "Pressing sequences of simple undirected graphs totally colored by a field arise naturally in computational phylogenetics, where (over GF(2)) they correspond to sortings-by-reversal of signed permutations which model gene sequences in related organisms. They can be viewed through several surprising different lenses, including as a purely algebraic version of positive definiteness, as linear extensions of a collection of posets, and as pivot sequences of a restricted form of symmetric Gaussian elimination applied to (weighted) adjacency matrices.  We discuss the question of ``pressability'', i.e., when a graph has a successful pressing sequence, showing in particular a direct connection with the theory of sparse Cholesky factorization.", "id": "Paper/70477", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70477"}, {"title": " The F-signature on the big cone ", "webprogram_exclude": "0", "session_ids": ["Session/18219"], "source_sha256": "edeb2b211bcc6237abe7c6d2462d650ec09dceff6f7febebcf01ed3c315d6dcc", "withdrawn": "", "abstract": "The F-signature is a numerical invariant of singularities in positive characteristic that measures asymptotic properties of the Frobenius map. While initially studied as an algebraic invariant of local rings, there has been recent interest in the geometric and global aspects of this invariant. In previous work with Seungsu Lee, we studied the F-signature of a projective variety as a continuous function on the ample cone. In this talk, I will discuss continuation of our work where we extend the F-signature function to the big cone. The results include existence of the F-signature for big divisors, continuity and positivity of the F-signature on the big cone and transformation rules under birational contractions for big and semi-ample divisors. As a key tool, we also study similar properties for the Frobenius-alpha invariant. The geometric aspects of our techniques will be presented and emphasized.", "id": "Paper/70478", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70478"}, {"title": " The Geometry of Redistricting Space ", "webprogram_exclude": "0", "session_ids": ["Session/18310"], "source_sha256": "40c1167e8ffedb5d232d0a332c4a8e94331563504be5369164869663b959cab3", "withdrawn": "", "abstract": "When auditing a redistricting plan, one often places a probability measure on the space of all plans and samples from that measure. The choice of measure can significantly influence which plans are considered typical, as well as their political characteristics and consequences. In this talk, I will present two new clustering methodologies that can be used to understand these consequences and, if desired, account for them. One approach is a generalization of K-means and the other a novel approach to diffusion maps. These methods can be used to (i) develop and sample from new interpretable classes of measures, (ii) provide a more robust framework for asking where gerrymandering has occurred, and (iii) establish novel and more robust convergence metrics for related sampling algorithms.", "id": "Paper/70484", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70484"}, {"title": " Investigating Housing Price Changes Using Several Mixed-Effect Models ", "webprogram_exclude": "0", "session_ids": ["Session/18554"], "source_sha256": "951d37e5827204f899d4e953ce297ec8fd9a435e6e6971dc564e2cf6da7b6bd2", "withdrawn": "", "abstract": "We investigate how the real estate market changed following the COVID-19 pandemic. As major, long-term financial commitments, housing markets are highly sensitive to macroeconomic and socioeconomic fluctuations. The COVID-19 pandemic had a significant impact on housing prices, and many expected property prices to decline following the pandemic. However, we observed the opposite of what we expected. Utilizing a panel-data framework with mixed-effects models, this paper quantifies the specific impact of the pandemic shock on local housing dynamics. Our results indicate that shifts in buyers’ behavioral preferences, coupled with evolving socioeconomic conditions, such as the adoption of remote work and changes in interest rates, counteracted downward pressures and instead contributed to accelerated price appreciation.", "id": "Paper/70485", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70485"}, {"title": " Extreme paradoxes in instant-runoff voting and single transferable vote ", "webprogram_exclude": "0", "session_ids": ["Session/18097"], "source_sha256": "a4d9522e28e3ef1bff8635099abf73db1fb20a9e83fcb8f6814533710a88efe0", "withdrawn": "", "abstract": "Instant-runoff voting (IRV) and single transferable vote (STV) select winners through rounds of elimination and vote transfers. Both methods can exhibit voting paradoxes: raising a candidate on some ballots can make that candidate lose, and removing a losing candidate can change who is elected. In this talk, we investigate extreme versions of these known paradoxes: how many candidates these effects can involve in one election, and whether restrictions on voter preferences limit their extent.\n\nFor IRV, we construct an election with $k$ candidates and complete voter rankings that produces $k-1$ different winners (the largest possible number) as we vary the number of top choices retained on every ballot. Even when voters rank candidates by distance along a common line (1-Euclidean preferences), the number of different winners can grow linearly with the number of candidates. These results resolve open questions of Tomlinson, Ugander, and Kleinberg about ballot truncation.\n\nWe construct profiles with extreme upward monotonicity paradoxes: every original loser can become the winner after suitable changes that move the original winner higher on some ballots. A single IRV profile can also exhibit multiple extreme paradoxes, simultaneously attaining tight bounds for downward monotonicity, negative involvement, and candidate deletion. For reinforcement, we construct profiles where every original loser wins in both parts of a suitable division of the same electorate. We also show that, even with 1-Euclidean preferences, IRV can successively eliminate the Condorcet winner among the remaining candidates, ultimately electing a candidate who loses head-to-head majority votes to all but one rival.\n\nFor STV, several extreme committee changes persist with ballots that are prefixes of 1-Euclidean rankings. Removing one losing candidate, or deleting just two ballots that list only original losers, can replace the entire elected committee.", "id": "Paper/70486", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70486"}, {"title": " Multigraded regularity of matrix Schubert varieties ", "webprogram_exclude": "0", "session_ids": ["Session/18253"], "source_sha256": "53793483455d68974b239f8a5769a4ea404e491494c5b45dc12a1f219cf45202", "withdrawn": "", "abstract": "I will discuss some recent results on the multigraded regularity of matrix Schubert varieties.  This work is motivated by two areas of study that have generated significant interest in recent years.  The first is focused on computing Castelnuovo-Mumford regularity for families of combinatorial algebraic varieties, while the second is focused on understanding homological properties and invariants in the setting of multigraded commutative algebra.", "id": "Paper/70487", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70487"}, {"title": " Image and Kernel Persistence on Temporal Knowledge Networks ", "webprogram_exclude": "0", "session_ids": ["Session/18114"], "source_sha256": "55187ff241be1660940165d69d6d3c467e95603ec7362dab42a08b4d01911a09", "withdrawn": "", "abstract": "We present a computational framework using image and kernel persistence to compare temporal knowledge networks constructed from two sources of scientific knowledge: research grants and publications. In these networks, nodes represent scientific concepts, edges are assigned the time at which two concepts first co-occur, and cycles in the resulting filtered clique complexes indicate potential gaps in the organization of scientific knowledge. We compare the networks through maps into a common filtered comparison space. Image persistence tracks topological features from a source network that remain visible in the comparison space, while kernel persistence tracks features that are mapped to zero. This framework provides a way to study the relationship between funding and subsequent scientific activity, including whether, where, and how quickly gaps appearing in grant portfolios are filled by publication-derived structure. We construct and validate publication and grant networks across 154 scientific fields. We use this dataset to compare multiple constructions of the common filtration and examine how these modeling choices affect the resulting topological summaries and representative cycles.", "id": "Paper/70492", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70492"}, {"title": " Deep, but not Difficult: Neurovarieties of Polynomial Residual Networks ", "webprogram_exclude": "0", "session_ids": ["Session/17835"], "source_sha256": "29ada4a907f8980a1e113ad095ba7b505a358cf92fa23621a1673172f31d7674", "withdrawn": "", "abstract": "Problem: find a toy model of a neural network that is analytically tractable, yet flexible enough to yield insights about neural networks used in practise. One solution attempt: replace all activation functions with polynomials. For neural networks with polynomial activation functions, understanding the network comes down to algebraic geometry: questions about expressivity and training bias translate naturally into questions about fibers and singularities. I will tell you more about this correspondence and exemplify it with results for residual networks concerning fibres of the parametrisation map and singularities on the neurovariety. Interestingly, the results support some of the informal explanations for the desirable training properties of residual networks.", "id": "Paper/70493", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70493"}, {"title": " Four dimensional Murasugi sum ", "webprogram_exclude": "0", "session_ids": ["Session/18344"], "source_sha256": "529718ffa9907f25cdbf1abc11b9e27d39b3b1de57e74fc0bba5cbac26b90ca5", "withdrawn": "", "abstract": "In this talk, I will describe different constructions of spanning solids for knotted surfaces in the 4-sphere, several of which will use a 4-dimensional analogue of Murasugi sum. In particular, I will describe notions of arborescent surface-links and state solids for broken surface diagrams.", "id": "Paper/70495", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70495"}, {"title": " Performance Decoupling and Multi-Criterion Evaluation of Non-Reversible Langevin Dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/19370"], "source_sha256": "7103b4509ff5f98c9249e123aeb3d7448d08e4591b21c96f1b10a32afd802317", "withdrawn": "", "abstract": "Non-reversible perturbations of Langevin dynamics provide a general mechanism for modifying stochastic sampling behavior while preserving a prescribed invariant distribution. However, improvements in one measure of performance need not translate into improvements in another. We investigate this \\emph{performance decoupling} for overdamped Langevin diffusions on $\\mathbb{R}^d$ of the form\n\\[\ndX_t=\\left[-\\nabla U(X_t)+C(X_t)\\right]dt+\\sqrt{2}\\,dW_t,\n\\]\nwhere $C:\\mathbb{R}^d\\to\\mathbb{R}^d$ is chosen so that the Gibbs measure\n$\\mu(dx)\\propto e^{-U(x)}\\,dx$ remains invariant. We develop a multi-criterion framework for evaluating the resulting dynamics, combining stochastic stability and geometric ergodicity, $L^2(\\mu)$ spectral relaxation, asymptotic variance of ergodic averages, and first-passage behavior. Using a Foster-Lyapunov approach, we establish conditions ensuring stochastic stability and geometric ergodicity.", "id": "Paper/70497", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70497"}, {"title": " Functional models for generalized resolvents associated with quantum graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17804"], "source_sha256": "3e254d949e395ae975329bfc8ba51abffbe3aa540888602ac2b3bca529e170a8", "withdrawn": "", "abstract": "Asymptotic analysis of second-order partial differential operators defined on thin networks converging to metric graphs  in the most interesting \"resonant\" case naturally reduces to a generalized resolvent associated with an ordinary differential expression on the limiting graph. In the leading order, the corresponding impedance matching conditions at the graph vertices are linear in the spectral parameter; taking account of further terms in the asymptotic expansion leads to the vertices acquiring non-trivial internal structures, which means that the corresponding impedance conditions are defined by Herglotz functions with measures having a finite number of unit masses. A further spectral analysis of such models, up to and including the scattering theory, is facilitated by an explicit construction of the functional model representation, which I will address in this talk. I remark in particular that this construction reduces to the Clark-Alexandrov-Poltoratskii theory in the special case where the underlying graph is an infinite chain. In the general setup, it leads to a more general vector-valued model space.", "id": "Paper/70499", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70499"}, {"title": " Analysis of fairness measures on optimized districting plans ", "webprogram_exclude": "0", "session_ids": ["Session/18310"], "source_sha256": "52af3462514148e98c2127e2372167796837bc28c1785143b452748c2dd38631", "withdrawn": "", "abstract": "Political redistricting can be modeled by representing a districting plan with a partition of an underlying graph that represents the geography of a given state. We are often interested in evaluating the `fairness' of a particular enacted map using this model, appealing to a large literature describing metrics that capture different aspects of representation and applying mathematical sampling tools to provide state-specific context using empirical election data. This talk will demonstrate how recent advances in sampling methods and optimization techniques allow us to explore the relationships between these metrics and discover unintuitive results or paradoxes when they are used to define what counts as a fair plan. This analysis is particularly relevant post-Callais and is also informed by the context of legislation like Utah's SB1011 from 2025. I will also discuss a connection to multimember districts with proportional election systems as a potential partial remediation.", "id": "Paper/70501", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70501"}, {"title": " Fibers in the Curve Complex Fibration ", "webprogram_exclude": "0", "session_ids": ["Session/18082"], "source_sha256": "72f8348b7ec28593064d2c0680abf0816a2b86f730d745c93dc24c27ca619b55", "withdrawn": "", "abstract": "The curve complex of a surface gives a way to relate information about curves on the surface to a simplicial complex structure. Motivated by connections to the Birman exact sequence, one can look at the map between the curve complexes (or appropriate subcomplex) induced by forgetting punctures on the surface. For surfaces with complexity $\\xi(S) = 3g-3+n\\geq2$ with genus $g$ and $n$ punctures, Kent-Leininger-Schleimer showed that the fibers of the forgetful map forgetting one puncture are $\\pi_1(S,z)$-equivariently homeomorphic to the Bass-Serre tree. This leads to questions about what happens for lower complexity surfaces and the case where you forget multiple punctures. In this talk I will discuss further progress on these questions, including if the fibers are $\\text{CAT}(0)$ when forgetting two punctures.", "id": "Paper/70503", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70503"}, {"title": " The Circular Security Introduced by Automorphism Keys ", "webprogram_exclude": "0", "session_ids": ["Session/18307"], "source_sha256": "5ad6eb4cf97261cf8bd7c965a873b5eaee3d5614aee43bc81ea28d683c3c4eed", "withdrawn": "", "abstract": "Every known FHE scheme from LWE relies on an unproven circular security assumption, and these assumptions have historically been stated scheme by scheme, making them impossible to compare or cryptanalyze. Micciancio and Vaikuntanathan (PKC 2024) addressed this by defining “circLWE”, a single assumption at the level of the LWE problem implying the circular security of a broad family of schemes. They explicitly leave the ring setting as an open problem. We give a formulation of circular security over Module-LWE, stated in full generality over R_q^d and derived from the key material that module-BGV/BFV schemes publish. Because M-LWE specializes to Ring-LWE at rank one and to LWE at ring degree one, the definition covers all three settings. We prove linear \"circ-M-LWE\" from decisional M-LWE above an explicit rank threshold, and show that automorphism (Galois) keys require no assumption beyond the linear one.", "id": "Paper/70504", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70504"}, {"title": " CANCELLED-No talk \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/19339"], "source_sha256": "8fc8af594c64a3555ccb485e94102329d0a83764e912b97ae01ac3b50dcc5999", "withdrawn": "", "abstract": "We study forward and inverse problems for a semilinear radiative transport model where the absorption coefficient depends on the angular average of the transport solution. Our first result is the well-posedness theory for the transport model with general boundary data, which significantly improves previous theories for small boundary data. For the inverse problem of reconstructing the nonlinear absorption coefficient from internal data, we develop stability results for the reconstructions and unify an $L^1$ stability theory for both the diffusion and transport regimes by introducing a weighted norm that penalizes the contribution from the boundary region. The problems studied here are motivated by applications such as photoacoustic imaging of multi-photon absorption of heterogeneous media.", "id": "Paper/70505", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70505"}, {"title": " The secondary fan and multigraded algebra ", "webprogram_exclude": "0", "session_ids": ["Session/18318"], "source_sha256": "aa434cd04ea90326de9ff2c6ce09d305f226638ec90b4fb5e165166398457beb", "withdrawn": "", "abstract": "The secondary fan of a multigraded ring parametrizes toric varieties which can be constructed from the ring: by GIT quotient, via the combinatorics of simplicial fans, or by choosing an irrelevant ideal.  It elegantly connects these perspectives on toric varieties and has appeared in much of my recent work about multigraded resolutions.  I will give a brief introduction to the secondary fan and explain its relevance to commutative algebra and to my own research, following notes I have written on the subject.", "id": "Paper/70507", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70507"}, {"title": " Forward and inverse problems of a semilinear transport equation ", "webprogram_exclude": "0", "session_ids": ["Session/18298"], "source_sha256": "b354b28b842a5d735e60790830613054e181c1d4f42da5561c53f04976b984ae", "withdrawn": "", "abstract": "We study forward and inverse problems for a semilinear radiative transport model where the absorption coefficient depends on the angular average of the transport solution. Our first result is the well-posedness theory for the transport model with general boundary data, which significantly improves previous theories for small boundary data. For the inverse problem of reconstructing the nonlinear absorption coefficient from internal data, we develop stability results for the reconstructions and unify an $L^1$ stability theory for both the diffusion and transport regimes by introducing a weighted norm that penalizes the contribution from the boundary region. The problems studied here are motivated by applications such as photoacoustic imaging of multi-photon absorption of heterogeneous media.", "id": "Paper/70508", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70508"}, {"title": " Localization via IR-RGB Pixel Correspondence ", "webprogram_exclude": "0", "session_ids": ["Session/18241"], "source_sha256": "3c60253859d7a241001bdac6d8bae9e596b898faf86cf724f36bf4b4a4419633", "withdrawn": "", "abstract": "We developed a cross-modal visual localization pipeline for matching infrared (IR) query images with RGB reference images in indoor nighttime environments. The project aimed to retrieve relevant RGB reference frames for each IR query and identify reliable IR–RGB pixel correspondences despite substantial appearance differences between the two modalities. The pipeline combined global image retrieval, local pixel-level matching, and geometric verification. We paired image descriptor extractors with descriptor aggregators to retrieve the 12 most similar RGB reference images for each IR query. We then used cross-modal pixel matchers and geometric verification to identify the three most promising references. We evaluated different combinations of these methods to determine which produced the most reliable matches across sensor modalities. Finally, we used the verified IR–RGB correspondences to connect IR image pixels to 3D map points reconstructed from RGB reference videos, enabling camera-pose estimation within the 3D map.", "id": "Paper/70513", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70513"}, {"title": " Dynamics of the Diffusive Holling Type II Predator–Prey System with Double Free Boundaries ", "webprogram_exclude": "0", "session_ids": ["Session/18289"], "source_sha256": "b28060340153982f3252af3cd768c51248e0e41fd8fa80aa52eefdc5ac9d96af", "withdrawn": "", "abstract": "We study a one-dimensional diffusive Holling type-II predator–prey system with double free boundaries. The model describes the spread of interacting predator and prey populations into a previously unoccupied habitat. The invasion fronts evolve according to Stefan-type conditions driven by the combined diffusive fluxes of both species. We establish global existence and uniqueness of solutions, develop comparison principles, and analyze the long-time dynamics. We prove a spreading–vanishing dichotomy and derive sufficient criteria involving the initial habitat size and boundary mobility. When spreading occurs, we obtain upper and lower bounds for the asymptotic propagation of both free boundaries.", "id": "Paper/70514", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70514"}, {"title": " A Formally Verified Apéry-Set Algorithm and a Lean-based Audit of Numerical Semigroups Literature ", "webprogram_exclude": "0", "session_ids": ["Session/18241"], "source_sha256": "8d7994b5975f68e96d02b446174b157f3260743d115c1f69b8044278300bbbba", "withdrawn": "", "abstract": "Can a computer catch mathematical errors that humans miss? We take up this question for the Frobenius problem in numerical semigroups, providing a Lean 4 algorithm for computing the Apéry set, providing Frobenius numbers and related invariants, and use it alongside GAP to check results from the mathematical literature. Our investigation verifies numerous published computations while also uncovering several discrepancies, illustrating how formal verification and computer-assisted mathematics can complement traditional mathematical reasoning and peer review. Each discrepancy is traced to a minimal counterexample and a specific point where the paper-based derivation fails.", "id": "Paper/70515", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70515"}, {"title": " Complete Hierarchies for the Geometric Measure of Entanglement ", "webprogram_exclude": "0", "session_ids": ["Session/18294"], "source_sha256": "90cd1d76ac21f25a92a7ed4ae8648460632d028e3f137b2beb548fe4764f3c83", "withdrawn": "", "abstract": "In quantum physics, multiparticle systems are described by quantum states acting on tensor products of Hilbert spaces. This product structure leads to the distinction between product states and entangled states; moreover, one can quantify entanglement by considering the distance of a quantum state to the set of product states. The underlying optimization problem occurs frequently in physics and beyond, for instance in the computation of the injective tensor norm in multilinear algebra. Here, we introduce a method to determine the maximal overlap of a pure multiparticle quantum state with product states based on considering several copies of the pure state. This leads to three types of hierarchical approximations to the problem, all of which we prove to converge to the actual value. Besides allowing for the computation of the geometric measure of entanglement, our results can be used to tackle optimizations over stochastic local transformations, to find entanglement witnesses for weakly entangled bipartite states, and to design strong separability tests for mixed multiparticle states. Finally, our approach sheds light on the complexity of separability tests.", "id": "Paper/70517", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70517"}, {"title": " Erdos distance problems ", "webprogram_exclude": "0", "session_ids": ["Session/18139"], "source_sha256": "8f6f04e4aa8653808dad7d38d9db522823454b17fa41f7202f31186683eedd68", "withdrawn": "", "abstract": "We will survey the recent developments around several old geometric problems of Erdős, in particular the Erdős unit distance problem.", "id": "Paper/70519", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70519"}, {"title": " Counting ℓ-interval Fubini Rankings Through Their Parking Outcomes ", "webprogram_exclude": "0", "session_ids": ["Session/18085"], "source_sha256": "ce9199916e49660dcb776869779499c2470125af1f14555cc3bae85ff3e8a4fa", "withdrawn": "", "abstract": "Fubini rankings with $n$ competitors are $n$-tuples with entries in $[n] = {1, 2, 3, \\ldots, n}$ that encode the conclusion of a race that allows ties. Since Fubini rankings are parking functions, we can study their parking outcomes, which are permutations encoding the final parking order of the cars using the Fubini ranking as a preference list. We establish that the number of Fubini rankings with $n$ competitors having a fixed parking outcome $\\pi \\in \\mathfrak{S}_n$ is given by $2^{n−k}$, where $k$ denotes the number of runs in $\\pi$. We then define several subsets of Fubini rankings: $\\ell$-interval Fubini rankings (where at most $\\ell$ + 1 competitors tie at any rank), and specifically the $1$-interval Fubini rankings, known as unit Fubini rankings. We give formulas for enumerating these subsets, and conclude with some directions for further study.", "id": "Paper/70521", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70521"}, {"title": " On the <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.07ex\" height=\"2.009ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -576.1 460.5 865.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">q</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-71\" d=\"M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 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y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-31\" x=\"1230\" y=\"0\"></use>\n</g>\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"2047\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJAMS-43\" x=\"2437\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"3159\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18085"], "source_sha256": "268fbb39eccd884a400bdfb27526003ed0153d76934c50e0eaa256d320a2a997", "withdrawn": "", "abstract": "In combinatorial representation theory, Kostant's weight multiplicity formula $m(\\lambda,\\mu)$ is a tool that provides a means of determining the multiplicity of a weight $\\mu$ in the adjoint representation of a simple Lie algebra $\\mathfrak{g}$, and in this work we consider the case of $\\mathfrak{g}=\\mathfrak{sl}_{r+1}(\\mathbb{C})$. \n    In practice, performing calculations of Kostant's weight multiplicity formula is computationally intense, as the number of terms in this alternating sum grows factorially as the rank $r$ increases, of which most terms provide zero contribution to the overall sum. \n    In this work, we determine the Weyl alternation set, that is the terms in the alternating sum with nonzero contribution, for integral weights $\\lambda$ the highest root of $\\mathfrak{sl}_{r+1}(\\mathbb{C})$, and $\\mu$ any nonempty collection of distinct simple roots. We show that the alternation set is enumerated by a product of Fibonacci numbers, with the product being dependent on the choice of distinct simple roots. Then we compute the weight $q$-multiplicity for any nonempty collection of distinct simple roots.", "id": "Paper/70524", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70524"}, {"title": " Transforming Split Graphs: Inverses, Degree Sequences, and Ferrers Diagrams ", "webprogram_exclude": "0", "session_ids": ["Session/18317"], "source_sha256": "82006e19d2753a5d9a1fce284dd52b6a748f9fb2c05939a13ef667c1c4cf0d52", "withdrawn": "", "abstract": "A graph is a \\emph{split graph} if its vertex set can be partitioned into a clique and a stable set. Given such a partition, its \\emph{inverse} is obtained by removing all edges within the clique and adding all edges between vertices in the stable set, while preserving the edges between the two parts.\n\nIn this talk, we discuss how degree sequences and Ferrers diagrams can be used to understand operations on split graphs. We consider the \\emph{block representation} of a degree sequence, which encodes information from its Ferrers diagram, and describe how the block representation of a partitioned split graph transforms under taking inverses and complements.", "id": "Paper/70525", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70525"}, {"title": " Involutions on <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"6.562ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 2825.2 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">(\\infty ,n)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-221E\" x=\"389\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2C\" x=\"1390\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-6E\" x=\"1835\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"2435\" y=\"0\"></use>\n</g>\n</svg>-categories of  Bordisms and Reflectopm TQFTs ", "webprogram_exclude": "0", "session_ids": ["Session/18210"], "source_sha256": "c4c8f449046a06e60bf0b9852dd2d32cd2fd726bb9dce18bfa72c87a6f0985d1", "withdrawn": "", "abstract": "Formally, a topological quantum field theory (TQFT) is a symmetric monoidal functor from a category of bordisms into an appropriate target category. Depending on the choice of bordism category, the theory may carry extra structure compatible with the monoidal structure — namely, an involution. By involution, we mean a $\\mathbb{Z}/2$ action on the bordism category which is compatible with the monoidal structure. In this talk, I will outline how to get these actions on the $(\\infty,n)$-categories of bordisms defined by Calaque and Scheimbauer, and I will define reflection TQFTs, in the sense of Freed and Hopkins, in this setting. Furthermore, I will exemplify what kind of obstructions a reflection structure imposes on the point values of a theory.\nLemm", "id": "Paper/70528", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70528"}, {"title": " Spectral Networks and the homology of the Spectral Curve ", "webprogram_exclude": "0", "session_ids": ["Session/17283"], "source_sha256": "c371032335950d39c02ad762847e49d9376f8f2de69787904cd3cccdcb2313a0", "withdrawn": "", "abstract": "In the paper by Gaiotto, Moore and Neitzke on Spectral Networks, they introduce the Fock-Goncharov’s Spectral Networks associated with an ideal triangulation of a surface with punctures. These Spectral Networks give rise to a non-abelianization construction that gives coordinates on the character varieties of representations of the surface fundamental group into the Lie group $SL(k,\\mathbb{R})$, where $k$ is the rank of the Spectral Network. The coordinates depend on the choice of a basis of the homology of the Spectral Curve of rank $k$ on the given surface. \n\nIn this work, we give an explicit description of the Spectral Curve of rank $k$ from the ideal triangulation, understanding its building blocks and glueing them together. We explicitly construct a basis for the homology of the Spectral Curve and this basis gives coordinates for the character variety, as explained above. The case $k = 3$ was done by Rogozinnikov in his Master Thesis, here we generalize his construction to higher rank. An explicit basis of the homology of the Spectral Curve can also be useful to solve other problems such as computing Spectral data.", "id": "Paper/70529", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70529"}, {"title": " An Area-Charge Inequality for Charged Initial Data Sets ", "webprogram_exclude": "0", "session_ids": ["Session/18266"], "source_sha256": "0968d8bb3f146b38f0c652a9d4cda8fb4241e1940374bd140efdcb25a53fb28d", "withdrawn": "", "abstract": "Consider a complete, asymptotically flat, charged initial data set $(M,g,E,B,k)$ for the vacuum Einstein equations satisfying the dominant energy condition $\\mu \\geq |J|$. Suppose that $k=0$, $\\text{div}_g(E)=0$, and the cosmological constant $\\Lambda \\geq 0$. We define $Q = \\frac{1}{4\\pi}\\lim_{\\rho \\to \\infty} \\int_{S_\\rho} g ( E, \\nu ) dA_g$ to be the charge of $M$. Suppose that $M$ has $\\ell > 0$ asymptotically cylindrical ends. By examining inequalities involving a charged harmonic function $u$ on $M$ and applying the dominant energy condition, I will show that $\\lim_{t \\to \\infty} \\text{Area}_g u^{-1}(t) \\geq \\frac{4\\pi Q^2}{\\ell}$. The limit of the area of $u^{-1}(t)$ can be interpreted as representing the sum of the areas of the spherical cross-sections of the asymptotically cylindrical ends.", "id": "Paper/70530", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70530"}, {"title": " Rough Feature Estimation in Bayesian Inversion ", "webprogram_exclude": "0", "session_ids": ["Session/18446"], "source_sha256": "877840304db06d31773bf1f2075fb4810a60f48a3654075f8988a9b65f39c4c0", "withdrawn": "", "abstract": "We consider the construction of non-Gaussian prior distributions for the stabilisation of inverse problems. The target is to build priors capable of modelling inhomogeneous structures, discontinuities, and high-frequency components. We consider two possible avenues: 1) building up hierarchical priors based on non-stationary Matérn-type priors with stochastic partial differential equation representations, and, 2) directly constructing non-Gaussian priors, with heavy-tailed noise driving the random fields. We first consider the mathematical and statistical properties of these random fields, and then show how to utilise them for practical inverse problems. We explicitly consider the inherent computational cost related to constructing these models, as we end up working with high-dimensional, heavy-tailed, and multimodal posteriors. Hence, obtaining the estimators and quantifying uncertainty are non-trivial tasks, and need to be considered when choosing optimisation and MCMC strategies.", "id": "Paper/70533", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70533"}, {"title": " Toward a Fusion of Large Language Models and Small Interpretable Models for Mathematical Discovery ", "webprogram_exclude": "0", "session_ids": ["Session/18130"], "source_sha256": "1c54d2a053d4c5f6d2676fc06ce33eac010dea6f28a171701bfa8e09003ba25a", "withdrawn": "", "abstract": "More efforts in AI for math have focused on two approaches, the use of large language models (LLMs) to resolve well-specified conjectures and the use of small, narrow models for more open-ended, human in the loop exploration. The former leverage broad text-based mathematical knowledge gained from internet-scale training while the latter are example driven, detecting relevant signals from within a vast number of examples. Both approaches have complementary strengths with the former able to build on past results and describe solutions in human understandable, while the latter can detect patterns that may not be easily inferred from existing theory. In this work we present progress toward a fusion of these two paradigms. Our system, which we call SIEVE, uses an LLM to train and interpret small models trained on a mathematical dataset of interest. Based on the result of the interpretability, the model refines a running conjecture, refines the training and test set, and retrains the model to narrow the conjecture until the LLM can prove it. We demonstrate the efficiency of this system on a problem related to a combinatorial interpretation of the structure constants of symmetric functions.", "id": "Paper/70534", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70534"}, {"title": " Higher-rank Graph L^{p}-operator algebras ", "webprogram_exclude": "0", "session_ids": ["Session/18381"], "source_sha256": "14b25baa7d91e7c276b1a479b0a098f4886cd1a7f9a483d7d3552e70486534c7", "withdrawn": "", "abstract": "We generalized the notion of k-graph $C^*$-algebras to $L^p$ algebras. We define higher rank Levitt path algebras, see some examples, and prove some results in the $L^p$ k-graph case.", "id": "Paper/70536", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70536"}, {"title": " Redesigning a Large Multi-Section Coordinated Course: A Constrained Optimization Problem ", "webprogram_exclude": "0", "session_ids": ["Session/17971"], "source_sha256": "ae7ada33f0aa1d067c8fbb2b5955777895e3b4f3f2880d1db8a155d59aa92796", "withdrawn": "", "abstract": "", "id": "Paper/70537", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70537"}, {"title": " On the Halfspace Representation of Nonbinary Linear Codes ", "webprogram_exclude": "0", "session_ids": ["Session/18020"], "source_sha256": "23f8e9ae3cc9b79d760612260392519c00cbadbc6fee8609a2b405159b282f27", "withdrawn": "", "abstract": "Low-density parity-check (LDPC) codes are defined as the null space of a sparse parity-check matrix over a finite field. For many efficient decoders, the specific matrix representation is crucial, as different representations lead to varying decoding failures. In linear programming (LP) and graph-cover decoding, pseudocodewords appear as undesirable, but detectable, outputs. Although much analysis is channel-dependent, pseudocodewords can also be studied in relation to parity-check matrix representation. By determining a complete halfspace representation of the codeword polytope for codes defined over a single parity check, we discuss a framework that offers insights into decoding failures and advances our understanding of how code representation impacts decoding performance. Nonbinary LDPC codes have been studied as a powerful alternative to binary LDPC codes. However, in many cases their decoding is less well understood. In this talk, we discuss recent progress toward determining a halfspace representation for single parity-check codes over nonbinary fields.", "id": "Paper/70539", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70539"}, {"title": " Simulating Single Transferrable Voting for Colorado’s State House ", "webprogram_exclude": "0", "session_ids": ["Session/18097"], "source_sha256": "bcf229570bcc8439a60be826a700768a48534d5dffc0f6686a8f41474f82e537", "withdrawn": "", "abstract": "Social choice theory research demonstrates that multi-member districts with single transferable voting (STV) results in more proportional representation than single-member districts with plurality elections. We investigated how using multi-member districts and ranked ballots with STV would affect the representation of political parties in the Colorado House of Representatives. We produced 10,000 multi-member districting plans of Colorado, generated ranked ballots for each of these plans using returns from the 2022 Colorado attorney general race, and simulated full-scale STV elections with these ballots. Our work found that STV elections for the Colorado House of Representatives gave more proportional partisan representation than the current system, and our modeling choices offer a sense of the variability of potential outcomes.", "id": "Paper/70541", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70541"}, {"title": " Resampling-based statistics to address the crisis of irreproducible results ", "webprogram_exclude": "0", "session_ids": ["Session/18064"], "source_sha256": "0e087619da605f42f3f22cfe0fedc73da5434c728be3e90805a8494cd9337ef8", "withdrawn": "", "abstract": "The biological and social sciences are facing a crisis of irreproducible ‘findings’. Many studies that announce “statistically significant” results, or that find “no difference” in outcomes, are based on flawed statistical methodologies, undermining both professional and public confidence in the results and in the methods that produced those results.\nCourses that teach statistics to biology and social science students fail to prepare them to deal with this crisis, and in fact perpetuate the misunderstandings that are at the root of the crisis. \nThe development of statistics in the 19th and early 20th centuries was, of necessity, dominated by a focus on formulas. The purpose of the formulas was to calculate ‘statistical significance’ and, when confirmed, declare a result to be publishable. These famous formulas include the t-test, the chi-squared test, ANOVA, etc. \nIn order to derive the formulas, very heavy assumptions had to be made. All distributions in sight had to be Gaussian, and the measures used had to be limited to mean values. Since these assumptions are often untrue in reality, traditional statistics became an exercise in misapplication, with disastrous consequences. \nThe typical statistics course taught to undergrads today still clings to the formula-based approach, resulting in a pedagogical horror: students are taught to plug-and-chug, plugging numbers into the famous formulas, which are meaningless to them. This ‘shut up and calculate’ is Bad Pedagogy, here in the service of Bad Science. \nBut if we ask: why the famous formulas? \nSo the watershed that divides traditional statistics from the more modern approach was brought about by the introduction of the computer. Computer-simulation methods such as resampling provide deep insights into the actual thought processes that underly statistical reasoning, as well as being applicable to a much wider class of data distributions and to measures used to describe them. \nIn this 21st century approach, the student, instead of asking ’which formula should I be plugging numbers into?’ learns to ask questions like: if the two groups in this experiment were just 2 random draws from the same set, how big a difference would I be likely to see? How does this compare to the actual difference that I observed?", "id": "Paper/70543", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70543"}, {"title": " Maximum Intersecting Families of Spanning Trees ", "webprogram_exclude": "0", "session_ids": ["Session/18227"], "source_sha256": "eebc7f6eabcf794a95fd472e7ce10bac7517aece1eba9ba508ad4fbf5d47cffe", "withdrawn": "", "abstract": "The classical Erdős-Ko-Rado theorem characterizes the maximum intersecting families of $k$-sets in $[n]$. Several analogs of these results arise from varying the ambient family and notion of intersection. Examples of such variations include characterizing the largest intersecting families of: permutations of a set, subspaces of a vector space, and triangulations of a convex $n$-gon. \n\nIn a recent paper, Frankl et al. characterize maximum $t$-intersecting families of spanning trees of $K_n$, for $n$ sufficiently large. To this end, they make use of a probabilistic tool in conjunction with an extramal set theoretic one, namely, the Lopsided Lovász Local Lemma (LLLL) and the recently developed spread approximation technique.\n\nIn this talk we present results on maximum $t$-intersecting families of $K_{n,n}$ where we replace the application of their probabilistic tools (LLLL) with spectral graph theoretic ones based on Laplacian eigenvalues of graphs.    \n\nThis is based on joint work with Gordian Bruns, Alexander Gavrilyuk, Josias Gomez and Nathan Lindzey.", "id": "Paper/70544", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70544"}, {"title": " 4-Neighbor Bootstrap Percolation in King’s Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18299"], "source_sha256": "245450b5899209540df5001d693a75ced27a7f2b3973955ab13ccb965d64a912", "withdrawn": "", "abstract": "$k$-bootstrap percolation is a cellular automaton. Some nodes in a graph begin \"infected\", then other nodes are infected if they have at least $k$ infected neighbors. Nodes do not recover. The $k$-percolation number of a graph is the minimum number of initially infected nodes required to infect the entire graph under the $k$-bootstrap percolation process. Brešar and Hedžet (2024) bound k-percolation numbers for certain $k$ in various strong products of graphs. King’s graphs are two-dimensional strong products; they can also be thought of as graphs modeling the available moves of a chess king. This talk will show strategies for obtaining 4-percolation numbers for various King’s graphs.", "id": "Paper/70549", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70549"}, {"title": " Whose Authority, Which Rationality? AI Issues as Springboards for Nature of Mathematics Discussions ", "webprogram_exclude": "0", "session_ids": ["Session/18262"], "source_sha256": "36f403b4811cf90223a9bbd50074c7c6eab8d1a1000fc2344caac296a7a23b34", "withdrawn": "", "abstract": "With the recent use of GenAI in the proof of a Millennial Problem, questions have emerged concerning authorship and authority within the discipline of mathematics. These questions create space for mathematics educators to hold classroom conversations with students about the role of a mathematician and the epistemological and cultural weight mathematics carries in our society.\n\nIn this presentation, we share examples of conversations we have held with students to evaluate aspects of the Nature of Mathematics that students explore in the age of GenAI. We will incorporate the concerns expressed in the open letter from Fields Medalists on AI Companies' misaligned goals compared to the goals of the mathematics community (https://mathandai.org/). AI Companies' traditions value successful marketing, demonstrations of computational prowess, and rapid improvement. The mathematical community's traditions value human collaboration, proper crediting of ideas, new human understanding, and creative works that enlighten culture and promote human thriving. \n\nFollowing Alysdaire MacIntyre's approach in \\textit{Whose justice? Which rationality?} this talk will explore attempts to settle the conflict between these two traditions, whose positions look irrational from the other's standpoint.", "id": "Paper/70551", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70551"}, {"title": " Modular Atoms: Investigations in Elemental Reasoning ", "webprogram_exclude": "0", "session_ids": ["Session/18062"], "source_sha256": "671a21018e15b96d47fd39f21d8d7bc7789e931aba60f772ebc72f59ba89fdbc", "withdrawn": "", "abstract": "Modular Atoms is a collection of puzzles and explorations in modular arithmetic driven by logical reasoning, a scientific spirit of discovery and awe, and themes inspired by magical folk legends and ancient books.\n\nStudents will travel to the mysterious Planet H, where molecules such as water, ammonia, and methane retain their familiar structures, but each atom's mass is always an integer. Under this constraint, students play detective-scientists to investigate which molecular masses are possible, identify emerging patterns, and build mathematical explanations. They also roleplay as ancient lore-keepers who craft books of mystical conjectures... will their  mathematical prophecies be fulfilled?\n\nIn this talk, participants will engage with selected puzzles and experience firsthand how playful experimentation and reasoning can lead to compelling mathematical patterns and generalizations. These low-floor, high-ceiling activities use playful experimentation to guide students naturally from conjectures to proofs, establishing connections to basic divisibility, greatest common divisors, the Chinese Remainder Theorem, and Diophantine equations.", "id": "Paper/70555", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70555"}, {"title": " Developing Almost Shallow Permutation Classification Through Pattern Counts ", "webprogram_exclude": "0", "session_ids": ["Session/18386"], "source_sha256": "f67a13e4f2f0c6c4e338d57602f95cb8309454dee480fe7930da3b5f4c4645ae", "withdrawn": "", "abstract": "Shallow permutations are a class of minorly scrambled permutations that were introduced in a seminal paper by Diaconis and Graham in 1977. Recently Berman and Tenner characterized shallow permutations using pattern avoidance, in particular introducing a new kind of pattern they call arrow patterns. We investigate the next simplest class of permutations, which we have named “almost shallow permutations.” We aim to extend Berman and Tenner’s work with arrow patterns to similarly classify a set of patterns that are avoided by almost shallow permutations.", "id": "Paper/70557", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70557"}, {"title": " The Alexander polynomial of satellite knots via the quantum enveloping superalgebra ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "2cf80fc290aa621ed84f59ec91a3b9271dbb6987a9f64395ae8864d0de38cb13", "withdrawn": "", "abstract": "Let $K$ be a knot in $\\mathbb S^3$, and let $P$ be a knot inside the solid torus. The satellite knot $P(K)$ is obtained by glueing $P$ into a tubular neighborhood of $K$. Seifert computed the Alexander polynomial of $P(K)$ in terms of the Alexander polynomials of $P$ and $K$ as $\\Delta_{P(K)}(q^2)=\\Delta_P(q^{2})\\cdot \\Delta_K(q^{2e})$ for some integer $e$. Many traditional proofs of Seifert's formula are topological. We give a novel representation-theoretic proof of this formula using the quantum enveloping superalgebra when the winding number of $P$ is nonzero. We use the cabling homomorphism to construct an oriented framed tangle whose closure is $P(K)$ and analyze its action on $U_q(\\mathfrak{gl}(1|1))$-modules. The Alexander polynomial is the modified trace of this action. An isotypic decomposition of the relevant tensor products separates the representation-theoretic contributions of the pattern and companion, yielding the factorization in Seifert’s formula.", "id": "Paper/70559", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70559"}, {"title": " G-Mapper: Learning a Cover in the Mapper Construction ", "webprogram_exclude": "0", "session_ids": ["Session/18105"], "source_sha256": "8c6d47cbe134bd17b4f0544d7d3de8f1be715b34179695ccbf3e4e47d9ad27d1", "withdrawn": "", "abstract": "The Mapper algorithm is a visualization technique in topological data analysis (TDA) that outputs a graph reflecting the structure of a given dataset. However, the Mapper algorithm requires tuning several parameters in order to generate a \"nice\" Mapper graph. This work focuses on selecting the cover parameter. We present an algorithm that optimizes the cover of a Mapper graph by splitting a cover repeatedly according to a statistical test for normality. Our algorithm is based on G-means clustering which searches for the optimal number of clusters in $k$-means by iteratively applying the Anderson-Darling test. Our splitting procedure employs a Gaussian mixture model to carefully choose the cover according to the distribution of the given data. Experiments for synthetic and real-world datasets demonstrate that our algorithm generates covers so that the Mapper graphs retain the essence of the datasets, while also running significantly faster than a previous iterative method.", "id": "Paper/70560", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70560"}, {"title": " Osculating <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.395ex\" height=\"1.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -576.1 600.5 721.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">n</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-6E\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Spheres and <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.395ex\" height=\"1.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -576.1 600.5 721.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">n</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-6E\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Spherical Curves ", "webprogram_exclude": "0", "session_ids": ["Session/19352"], "source_sha256": "f2540dcb945ae712f2470846d8a546e9b852e428533ca8d633ecef5df622e42f", "withdrawn": "", "abstract": "We extend to $n$-spheres\nboth Barr\\'e de Saint Venant's classical curvature characterizations of \nthe locus of centers, radial vectors, and radii\nfor osculating 2-spheres along a curve\nand also Ces\\`aro's classical particular and general ``natural equations'' characterizing\nany curve lying in a 2-sphere (all recently extended to 3-spheres).\nSurprisingly, both sets of results are inductively related.\n\nWe establish these results for $n$-spheres by an elegant inductive proof sequence,\nsublimating higher-order contact calculations into higher-dimensional Frenet frame calculations,\nthereby minimizing explicit contact calculations.\nIn the process, we identify the recursive polar ``ballcap invariant'' sequence $\\beta_n$ for osculating spheres.\nWe use these results to obtain versions of Lancret's Theorem \ncharacterizing certain spherical helices.", "id": "Paper/70561", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70561"}, {"title": " A Lower Bound for the First Non-zero Basic Eigenvalue on a Singular Riemannian Foliation ", "webprogram_exclude": "0", "session_ids": ["Session/18266"], "source_sha256": "20315ff4756da95e3b4ab40d7741603c96bba3d478e08084eba7d726c77ffc58", "withdrawn": "", "abstract": "In the talk, we provide a lower bound of the first non-zero basic eigenvalue on a closed singular Riemannian manifold $(M^n,\\mathcal{F})$ having basic mean curvature that depends on the given lower bound of the Ricci curvature $Ric(M)\\geq (n-1)K$ and the diameter of the leaf space $d_{M/\\mathcal{F}}$. For foliations given by points, the results cover estimates of the first non-zero eigenvalues lower bounds, which are Zhong-Yang estimate, Yang estimate and Shi-Yang estimate when $K=0,K<0$ and $K>0$, respectively. \n\nWe also show a rigidity result that corresponds to the case of $Ric(M)\\geq 0$. This is  a generalization of Hang-Wang rigidity, which is the equality case of Zhong-Yang estimate.", "id": "Paper/70563", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70563"}, {"title": " Singular perturbations of operators with empty spectrum: a first-order example ", "webprogram_exclude": "0", "session_ids": ["Session/19368"], "source_sha256": "64d644ebc4dd84ec4f9455ecbdfd95f67e15dc809a62cad5ff7a543a84c32668", "withdrawn": "", "abstract": "We consider a non-selfadjoint operator that is obtained as the singular perturbation of an operator with empty spectrum in the form of a non-local point interaction. We discuss necessary and sufficient conditions for when the root functions of the operator and its adjoint are complete. Also, we describe the distribution and location of the eigenvalues on the complex plane. This is joint work with Christoph Fischbacher.", "id": "Paper/70564", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70564"}, {"title": " Efficient Locally Recoverable Codes for Sustainable Cloud Storage ", "webprogram_exclude": "0", "session_ids": ["Session/17808"], "source_sha256": "3ec35889bc52d219ee1f39e5f7b9e4982fb875471324dce3f2126fcb0a2de5f9", "withdrawn": "", "abstract": "Error-correcting codes (ECCs) are mathematical algorithms and objects that cleverly encode redundancy into digital data before it is transmitted or stored so that any errors (which occur constantly!) can be detected and corrected. As cloud storage and computing become ubiquitous, it is necessary to develop extremely good codes that are suited to these applications; in particular, we need efficient codes to minimize the resource impact of storage.  A very desirable property for cloud storage codes is local recoverability, meaning that if any codeword symbol is erased, it can be recovered from a small number of other symbols. In evaluation codes (where codewords derive from evaluating functions on some algebraic variety), often local recovery and related properties are often possible to obtain by exploiting structures of the underlying algebraic variety.  The process of creating these codes is both motivated and informed by computation.  This talk will explain the motivation and basics of locally recoverable codes from algebraic geometry and briefly describe some recent promising constructions.", "id": "Paper/70565", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70565"}, {"title": " The <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.259ex\" height=\"2.009ex\" style=\"vertical-align: -0.671ex; margin-left: -0.089ex;\" viewBox=\"-38.5 -576.1 542 865.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">p</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-70\" d=\"M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-70\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-adic valuations of some polynomial functions associated with a quartic integral ", "webprogram_exclude": "0", "session_ids": ["Session/18867"], "source_sha256": "0acab8dd1fb59e56982fe3ac301e410f66f6844d77414108cc47974e19a3302f", "withdrawn": "", "abstract": "Through various methods, one can find\n$$N_{0,4}(a;m)=\\int_{0}^{\\infty}\\frac{dx}{(x^{4}+2ax^{2}+1)^{m+1}}=2^{-m-\\frac{3}{2}}\\pi(1+a)^{-m-\\frac{1}{2}}P_{m}(a),$$\nwhere $P_{m}(a)=\\sum_{\\ell=0}^{m}d_{\\ell}(m)a^{\\ell}$ is some polynomial; many proofs exist in the literature. We use complex integration techniques to arrive at an alternative form for the coefficients of $P_{m}(a)$ and, eventually, seek a favorable form for calculating the sequence of $p$-adic valuations $\\nu_{p}(d_{\\ell}(m))$, where $\\nu_{p}(n)$ represents the largest exponent in which $p^{\\nu_{p}(n)}$ divides $n$. This talk will explore the beginnings of a new project that is the result of collaborative efforts that first began at a REUF workshop in 2019 and was recently supported by an AIM REUF continuation award. It will be presented by Justin Trulen and Jane Long.", "id": "Paper/70566", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70566"}, {"title": " Implicit Cumulant Independent Component Analysis ", "webprogram_exclude": "0", "session_ids": ["Session/17849"], "source_sha256": "b69cad940022f747f60c42dce5f97c6fac9e4be11a4138adfc179df9bc03b0d5", "withdrawn": "", "abstract": "An issue that often arises with tensor decomposition is the curse of dimensionality: tensors are often too large and decomposing these efficiently often requires increased computation time and storage. This talk explores implicit tensor decomposition, which addresses this issue by decomposing tensors without explicitly forming these. We propose an algorithm that calculates the tensor CP decomposition of an higher-order cumulant directly from samples and without explicitly forming the cumulant tensor. We successfully apply this algorithm in Independent Component Analysis.", "id": "Paper/70567", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70567"}, {"title": " <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.162ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 500.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">2</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-32\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-adic Valuations and Iterative Sequences ", "webprogram_exclude": "0", "session_ids": ["Session/18867"], "source_sha256": "80dd20d8385863d8700781f6431ccb9396516d3a61353cf68c7b3e08b4c775ec", "withdrawn": "", "abstract": "The $p$-adic valuation of an integer is the largest power of a prime $p$ that\ndivides the given integer. In this talk, we will look into the behaviors of $2$-adic valuation sequences \ngenerated by the iterations of linear functions $f(x)=ax+b\\in \\mathbb{Z}[x]$. \nThe properties of interest include whether such sequences\nare constant, periodic, eventually constant, eventually periodic, or unbounded, depending\non $a,b$, and the initial value $c\\in \\mathbb{Z}$. We will include ways to visualize these sequences.\n\nThis question was studied by REU students at Ursinus College in Summer 2023, but the project stems from an ongoing REUF 2019 collaboration. We will discuss differences between 2-adic valuations generated by this process and polynomial sequences.", "id": "Paper/70569", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70569"}, {"title": " Alternates, Assemble! Selecting Optimal Alternates for Citizens’ Assemblies ", "webprogram_exclude": "0", "session_ids": ["Session/18310"], "source_sha256": "f7a37cb80d0d5bf06af995b3d8b864621a9ef4756e4dcf2beb1b257f425beb86", "withdrawn": "", "abstract": "\\emph{Citizens' assemblies} are an increasingly influential form of deliberative democracy, where randomly selected people discuss policy questions. The legitimacy of these assemblies hinges on their representation of the broader population, but participant dropout often leads to an unbalanced composition. In practice, dropouts are replaced by preselected \\emph{alternates}, but existing methods do not address how to choose these alternates. To address this gap, we introduce an optimization framework for alternate selection. Our algorithmic approach, which leverages learning-theoretic machinery, estimates dropout probabilities using historical data and selects alternates to minimize expected misrepresentation. Our theoretical bounds provide guarantees on sample complexity (with implications for computational efficiency) and on loss due to dropout probability mis-estimation. Empirical evaluation using real-world data demonstrates that, compared to the status quo, our method significantly improves representation while requiring fewer alternates.", "id": "Paper/70570", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70570"}, {"title": " Obtaining the Chamanara Surface from the van der Corput sequence ", "webprogram_exclude": "0", "session_ids": ["Session/18100"], "source_sha256": "ed4b9afff86663cb0afaea26d6fc228cd68b10cd67fa38b122e35d261440ba2c", "withdrawn": "", "abstract": "We investigate a family of $4$-regular graphs constructed to test for the presence of combinatorial structure in a sequence of distinct real numbers. We show that the graphs constructed from the Kronecker sequence can be embedded into the torus, while the graphs constructed from the binary van der Corput sequence can be embedded into the Chamanara surface, in both cases with the possible removal of one edge. These results generalize to embeddings of sequence graphs coming from interval exchange transformations into associated translation surfaces.", "id": "Paper/70572", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70572"}, {"title": " Mathematical Modeling of Luteinizing Hormone and Serum Testosterone in Men: Precursory to and Concurrent with Hormone Replacement Therapy ", "webprogram_exclude": "0", "session_ids": ["Session/18248"], "source_sha256": "e742e49a8c43f5717b5fd51c73daa05d6a5d8f46914093d86092df71dcf9409f", "withdrawn": "", "abstract": "Hormone replacement therapy (HRT) comprises various delivery methods to control and balance one's endocrine levels within a safe, effective range. In particular, HRT is a necessary, life-saving treatment against gender dysphoria, hypogonadism, and more. In this work, we utilized a compartmental, semi-mechanistic approach to model testosterone and luteinizing hormone (LH) in transgender and cisgender men prior to and throughout HRT. As our source model, we studied the non-autonomous, nonlinear system of ODEs developed by Fattinger et al. (Am. J. Physiol. 271:E775–E787, 1996) to predict the response of endogenous testosterone and LH to Antide – a gonadotropin-releasing hormone antagonist. We introduced key modifications that produced more qualitatively reasonable solution behavior and allowed for an analytic solution to approximate serum testosterone over long timescales. Further, we verified that our modified model mimics the same predicted levels of average testosterone in healthy cisgender men as reported in Fattinger et al. Possible variations in model outcomes were examined through two distinct lenses: biological intuition of the application field and a local sensitivity analysis of the linearized system. We leveraged these analyses to refit a subset of the model parameters to data representing transgender and hypogonadal men before HRT due to scarcity of clinical data for transgender individuals. With our modified model effectively serving as a blueprint for endogenous hormone behavior, we incorporated testosterone injection pharmacokinetics with dilute diffusion to present a cohesive, biologically-motivated system describing HRT in transgender and hypogonadal men.", "id": "Paper/70573", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70573"}, {"title": " Bridge-burning Cops and Robbers ", "webprogram_exclude": "0", "session_ids": ["Session/18106"], "source_sha256": "e559f58832283e7aad99b84e4a12b162d1b0808f022d78c2df43cf4b8d01da6e", "withdrawn": "", "abstract": "Cops and robbers is a widely studied game that models the search for information throughout a graph or network. The cop team usually consists of $k \\geq 1$ cops and the robber team usually consists of a single robber. Play begins with the initial placement of each player (starting with the cop team and ending with the robber) onto a vertex of the graph. The two teams then take turns moving from vertex to vertex by traversing the edges of the graph. The cop number is the minimum number of cops that are required to guarantee capture of the robber on the given graph. A recent variant of this game, introduced by Kinnersley and Peterson, mandates that each edge of the graph is deleted upon traversal by the robber. This gives rise to the bridge burning cop number which is interestingly incomparable to the standard cop number. This talk will present some nuances of the bridge burning cop number and introduce a new generalization that grants each edge multiple traversals by the robber before being deleted.", "id": "Paper/70574", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70574"}, {"title": " When Does a Model’s Decision Disagree With Its Own Probability Estimate? A Case Study in Rank-Consistent Ordinal Regression ", "webprogram_exclude": "0", "session_ids": ["Session/19364"], "source_sha256": "d4cce866d1c78c86af8fd33e886b49bec63a9a4f3cc17bb528b01880984ac88a", "withdrawn": "", "abstract": "Rank-consistent ordinal regression models such as CORAL predict an ordinal class using thresholded, monotonically ordered binary outputs rather than by taking the arg-max of a categorical probability vector. A class-probability distribution can nevertheless be derived from these cumulative threshold outputs, which raises a natural question: when does the class selected by the rank-consistency decision rule differ from the class having maximum derived probability?\n\nWe study this question in a five-class ordinal medical image classification task. The two decision rules disagree on 57% of test predictions. The source of the discrepancy is structural: the derived probability assigned to an interior class is determined by the difference between its two bounding cumulative threshold probabilities, whereas the ordinal decision rule depends only on whether successive thresholds lie above or below \\(1/2\\).\n\nConsequently, a class may be selected by the ordinal decision rule even when the probability assigned to that class by the derived distribution is small. In particular, when two adjacent threshold probabilities lie close to \\(1/2\\), their difference can be small even though their positions relative to \\(1/2\\) determine the predicted ordinal class.\n\nWe formulate and prove a boundary condition characterizing when disagreement between the ordinal decision rule and the arg-max of the derived class-probability distribution must occur, and compare this condition with the empirical disagreement pattern observed in the test predictions. The result clarifies an important distinction between threshold-based ordinal decisions and probability-based class selection in rank-consistent ordinal regression.", "id": "Paper/70576", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70576"}, {"title": " Near Maturity Asymptotics of Option Prices in Lévy models ", "webprogram_exclude": "0", "session_ids": ["Session/18058"], "source_sha256": "5c7d74974154015439814778a359b9295bb7d1bf96230fcb732a5994219c3726", "withdrawn": "", "abstract": "This paper reviews classical results on near-maturity option pricing in the presence of jumps and introduces new findings for American options. Specifically, we provide asymptotic expansions for the optimal early-exercise boundary of an American put option under an exponential L\\'evy model featuring a nonzero Brownian component and negative jumps of unbounded variation. These results offer practical guidelines for near-maturity model calibration for American options, which represent the most prominent and widely traded option style for individual stocks and exchange-traded funds (ETFs) in U.S. markets.", "id": "Paper/70577", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70577"}, {"title": " A multitype branching process approach to modeling diffusion on networks with communities ", "webprogram_exclude": "0", "session_ids": ["Session/19370"], "source_sha256": "5ac6eba9c3504e9cff8b95e6ac2a812c7aea473966e01c0bd02369835d1f7b45", "withdrawn": "", "abstract": "The dynamics of diffusion on complex networks are widely studied to understand how entities such as information, diseases, and behaviors spread through interconnected populations. Complex networks often exhibit community structure, and tools to analyze diffusion processes on networks with communities are needed. We show how a multitype branching process model can shed light on the interplay between community structure and the spread of information or disease. We model diffusion using the independent cascade model (ICM), in which activations occur in discrete time steps (generations). Each node is in one of three states: inactive, active, or removed. Each active node makes a single attempt to activate each of its inactive neighbors and is then removed in the next time step. The process continues until no active nodes remain. We show that, using only limited information about the network (the degree distributions within and between communities), we can track the number of active nodes in each generation in a two-community network with the probability-generating function (PGF) $G_{\\mathbf{N}(t)}(s_1,s_2) = \\sum_{n=0}^\\infty \\sum_{m=0}^\\infty P[N_1(t)=n,N_2(t)=m]\\, s_1^n s_2^m$, where $N_1(t)$ and $N_2(t)$ are the numbers of active nodes in communities 1 and 2 at generation $t$. This framework is particularly useful for deriving expressions for the extinction probability and the distribution of the total outbreak size. We also derive new quantities that are specific to spreading processes on networks with communities and would otherwise be difficult to calculate analytically, such as the probability that a contagion (e.g., a disease or a piece of information) is (re)introduced into a community where it has either never spread or has previously stopped spreading. The framework extends to any number of communities and offers a tractable alternative to large-scale simulations of spreading processes.", "id": "Paper/70578", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70578"}, {"title": " Top Heavy Shellings ", "webprogram_exclude": "0", "session_ids": ["Session/18138"], "source_sha256": "0917fe1a4e18467c315e377759104253739ece07d1a39c69ad057d0c23e76728", "withdrawn": "", "abstract": "A sequence $a_0,a_1,\\dots,a_n$ is called \\textit{top-heavy} if $a_i\\leq a_{n-i}$ for all $0\\leq i\\leq\\lfloor n/2\\rfloor$. We investigate how shellings can be used to establish top-heaviness of combinatorially defined sequences. As an example, we construct shellings that yield a direct proof that the Whitney numbers of the second kind of the graphic matroids of threshold graphs are top-heavy. The ordering of facets for these shellings arise using linear extensions of a poset associated to the graphs. These shellings provided a different proof of the Top-Heavy Theorem for matroids of Braden, Huh, Matherne, Proudfoot, and Wang in the very special case of threshold graphs. Time permitting, we will discuss connections between these shellings and Whitney duals.", "id": "Paper/70582", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70582"}, {"title": " A Mysterious Connection Between Tolerant Junta Testing and Agnostically Learning Conjunctions ", "webprogram_exclude": "0", "session_ids": ["Session/18311"], "source_sha256": "7fe97755916df7d5222307718a170b3aa86fec41a3d3e8c9e20c060106ec083b", "withdrawn": "", "abstract": "The main conceptual contribution of this paper is identifying a previously unnoticed connection between \ntwo central problems in computational learning theory and property testing: \n\\emph{agnostically learning conjunctions} and \\emph{tolerantly testing juntas}.  Inspired by this connection, the main technical contribution is a pair of improved algorithms for these two problems.\n\nIn more detail, \n\n(1) We give a distribution-free algorithm for agnostically PAC learning conjunctions over $\\{\\pm 1\\}^n$ that runs in time $2^{\\tilde{O}(n^{1/3})}$, for constant excess error $\\varepsilon$.  This improves on the fastest previously published algorithm by Kalai et al., which runs in time $2^{\\tilde{O}(n^{1/2})}$. \n\n(2) Building on the ideas in our agnostic conjunction learner and using significant additional technical ingredients from Boolean Fourier analysis, we give an adaptive tolerant testing algorithm for $k$-juntas that makes $2^{\\tilde{O}(k^{1/3})}$ queries, for constant ``gap parameter'' $\\varepsilon$ between the ``near''  and ``far''  cases.  \nThis improves on the best previous results, due to Iyer et al. and Nadmipalli and Patel, which make $2^{\\tilde{O}(\\sqrt{k})}$ queries.", "id": "Paper/70583", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70583"}, {"title": " The Ugly Sweater Theorem ", "webprogram_exclude": "0", "session_ids": ["Session/18100"], "source_sha256": "45f88876fda0e05cde4c0b1520ddcdf998421c83e5456d8060f15ff3528e97b8", "withdrawn": "", "abstract": "We describe a new tool that provides a simple visual test for whether an imaginary quadratic ring is a PID. We call this test (or, rather, the fact that it works) the Ugly Sweater Theorem. It generalizes Motzkin's classical theorem that imaginary quadratic rings are Euclidean if and only if unit discs centered on integers cover the complex plane. Due to ongoing, highly contentious debate between the co-authors, the new tool remains unnamed for now.", "id": "Paper/70584", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70584"}, {"title": " On KV Cache Quantization – a Mathematical View via Transform Coding and its Implications for Safety ", "webprogram_exclude": "0", "session_ids": ["Session/18190"], "source_sha256": "0bb3d0628aecfbad91ecbbc00f61417ee710feef4542f5c8e73a16b4ba966e5c", "withdrawn": "", "abstract": "Large language models (LLMs) have become a major tool in machine learning, and they increasingly operate over long contexts: documents, transcripts, and multi-turn histories spanning more than a million tokens.\n  At inference time, an LLM decomposes its input into tokens and then generates new tokens by sampling from next token predictions. In transformer models, each token yields a sequence of key-value (KV) pairs at each layer of the model. These values are cached to accelerate inference when generating new tokens.    As a consequence, the KV cache grows linearly with context length, and at long contexts it becomes the dominant memory cost of inference and reducing the memory footprint during inference has become a major challenge.\nIn that context, efficient quantization, that is, representing the cached information with as few bits as possible, plays a key role.\n\nExisting quantization methods address this bottleneck by representing the KV cache uniformly with lower-precision data types and designing quantization schemes to minimize reconstruction error in the cache itself, without accounting for how that error propagates through attention mechanisms. Our result establishes that, under a white-noise quantization model, the expected attention-aware distortion decomposes into additive key and value contributions that factor across tokens and channels. Building on transform coding and reverse water-filling, which are classical tools from signal processing and rate-distortion theory, we introduce Attention-Aware Transform Coding (AATC), which allocates bits over a calibration set to minimize attention-aware distortion. \n\nFor this method as well as other quantization approaches, we find that the focus on preserving accuracy can sometimes lead to compromised safety, so safety needs to receive special attention when making the representations more efficient.", "id": "Paper/70589", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70589"}, {"title": " Automated Structural Causal Maps by Information-Theoretic Measures ", "webprogram_exclude": "0", "session_ids": ["Session/19364"], "source_sha256": "624106057ac6563fcdc7c35c455958d03cf7dcc6228c5de28522118b77cb4045", "withdrawn": "", "abstract": "An automated method of constructing structural causal maps is presented from tabular data which optimizes a bias-corrected estimate of the mutual information between multiple variates such that confounding does not lead to suboptimality. The algorithm builds from lower to higher dimensionality up to an information-theoretic threshold so that overfitting is balanced against sufficiency. Granger causality determines directions of the acyclic graph network. Hence, the method is suitable to total automation. An example is given using measured servo data in the detection of the root cause of a catastrophic fault to illustrate the methodology within a predictive maintenance use case.", "id": "Paper/70590", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70590"}, {"title": " A Multi-Stage Framework for Emerging Attack Discovery in Domain Name System Distributed Denial-of-Service Traffic ", "webprogram_exclude": "0", "session_ids": ["Session/19345"], "source_sha256": "625924f9de57f0bc21db27426c9d117495819fe3cf8e65e80ca29ee6d48f3d45", "withdrawn": "", "abstract": "Distributed denial-of-service attacks can exhibit changing traffic structures that are difficult to identify from previously observed attack patterns. This study presents a multi-stage framework for emerging attack discovery in Domain Name System traffic using the DrDoS\\_DNS subset of CICDDoS2019. The framework combines cross-fitted Random Forest intensity scoring, Rectified Flow modeling, Transformer-based representation learning, novelty assessment, and clustering. A controlled future-like subset comprising 10\\% of the attack samples was withheld based on attack-intensity scores to evaluate discovery of behavior that differs from the known-attack baseline. The resulting 10,142 future-like samples had a mean intensity score 7.45 times higher than the known-attack subset. Rectified Flow generated synthetic known-like samples, with 4.40\\% flagged as novel compared with 90.82\\% of future-like samples. Transformer embeddings and PAM-style clustering identified 30 candidate emerging clusters under the selected minimum cluster-size threshold, capturing 9,366 of the 10,142 future-like samples. Cluster profiling revealed recurring differences in packet size, throughput, timing, directional asymmetry, header-related behavior, and burst-related activity. The results demonstrate how generative modeling, representation learning, novelty assessment, and clustering can be integrated to organize unusual attack behavior into coherent candidate groups and identify traffic characteristics for further investigation.", "id": "Paper/70594", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70594"}, {"title": " Statistics of special sequences of prime numbers ", "webprogram_exclude": "0", "session_ids": ["Session/18241"], "source_sha256": "c052d64d976aa51e6c52f6b9b909c0260d1b1456e67120048028975b5a3d9ef1", "withdrawn": "", "abstract": "Consider the question of how often a prime number is equal to the average of its nearest neighbors. We report on numerical investigations exploring connections between generalizations of this question and the Hardy-Littlewood k-tuples conjecture, as refined by work of Lemke-Oliver and Soundararajan.", "id": "Paper/70595", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70595"}, {"title": " Maximum sustainable yield under state-dependent stochasticity ", "webprogram_exclude": "0", "session_ids": ["Session/18023"], "source_sha256": "5eb381503d507b0f3f84e0c1b0ac5350190ebcfd28880f0e9393d5bee90b51ec", "withdrawn": "", "abstract": "\\begin{abstract}\nEnvironmental variability in exploited populations is rarely uniform across abundance. Aggregating species such as Pacific salmon are buffered at high abundance by the diversity of their subpopulations, while territorial species can become more variable as crowding increases. We ask how such abundance-dependent variability changes the harvest a population can sustain.\n\nFor a population harvested at a fixed per-capita rate, we obtain explicit formulas for the optimal rate and the yield it delivers. Two findings stand out. The correction to the classical deterministic target is set by the variability at the harvested equilibrium rather than at carrying capacity, so the level at which a stock is managed decides which part of the noise structure matters. The risk of losing the population is set by the variability near extinction, a separate quantity, so viability and productivity can be traded against each other. Variability can even raise expected yield under light harvest, when recruitment is convex at the managed equilibrium. \n\\end{abstract}", "id": "Paper/70599", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70599"}, {"title": " Oscillon Stability in the Presence of Kinetic Coupling after E-model <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.488ex\" height=\"1.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -576.1 640.5 721.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\alpha</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-3B1\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-attractor Inflation ", "webprogram_exclude": "0", "session_ids": ["Session/18300"], "source_sha256": "efe55fb032444cb90f30a8393b75688a414a387433c3b98dc6b76d8a3e32a2d9", "withdrawn": "", "abstract": "Oscillons are long-lived, spatially localized, soliton-like field configurations that can form through nonlinear dynamics during reheating after inflation. In this talk, I will present our study of post-inflationary oscillon dynamics in an E-model $\\alpha$-attractor scenario in which the inflaton is kinetically coupled to an ultralight axion. The kinetic coupling is described by a field-dependent function  $W(\\phi)=e^{2\\phi/\\mu_W}$ that arises in multifield dilaton--axion  $\\alpha$-attractor models, where the two fields span a hyperbolic field-space manifold. We perform nonlinear three-dimensional lattice simulations using \\texttt{GABE} to investigate how this interaction affects both the formation of oscillons and their subsequent evolution. We find that oscillons can still form in the presence of kinetic coupling for $\\mu_V \\lesssim 0.08\\,M_{\\mathrm{Pl}}$. However, in the parameter regime we can reliably evolve, fully formed oscillons are destabilized at later times for $\\mu_W \\gtrsim 0.06\\,M_{\\mathrm{Pl}}$ by backreaction from the populated $\\chi$ sector. Although our results do not provide direct evidence for oscillon decay into the $\\chi$ sector, they show that kinetic coupling can destabilize otherwise long-lived oscillons and thereby modify the post-inflationary dynamics of the E-model $\\alpha$-attractor. This points to a novel mechanism in which backreaction governs oscillon lifetimes.", "id": "Paper/70600", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70600"}, {"title": " Worst-case hardness of ideal lattice problems ", "webprogram_exclude": "0", "session_ids": ["Session/18307"], "source_sha256": "d17ac4fc88598c6a7a67f0bc21edd0c201ee872e852f17c8478bb1232eb7352c", "withdrawn": "", "abstract": "We describe a polynomial-time reduction that solves computational lattice problems (like the Shortest and Closest Vector Problems) in generic lattices given access to an oracle that solves them in ideal lattices. The reduction targets invertible ideals in monogenic orders of totally real number fields. This establishes the NP-hardness of approximating ideal-SVP (in the aforementioned setting) within constant factors and ideal-CVP within a factor of $n^{1/2-\\epsilon}$. The former underlies the security of order-LWE and ring-LWE based cryptosystems.", "id": "Paper/70601", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70601"}, {"title": " Random Matrix Properties and Asymptotic Freeness in IID Haar Quantum Processes ", "webprogram_exclude": "0", "session_ids": ["Session/17804"], "source_sha256": "a57d0d5eff69b34f22188e3b9ff078149357be2c14cdfbe4c242368f49f144ba", "withdrawn": "", "abstract": "This talk will address new results about the moment characterization and the joint limiting distribution of particular random density matrices emerging in the context of Ergodic Quantum Processes when the channels are given by Kraus Operators of lID Haar isometries. Ergodic Quantum Processes were introduced by Ramis Movassagh and Jeffrey Schenker in 2021 and are defined by the presence of decoherence in the channels describing the process. Among the random ergodic scenarios, the case of IID Haar Quantum Channels arises in a very natural way and it allows to perform explicit computations of the moments via Weingarten Calculus. In this work in progress with Jeffrey Schenker, we extend the statistical properties of the ergodic sequence of random density matrices to results about their joint distribution. In one of the\ncases, the suitable framework for this is provided by Free Probability.", "id": "Paper/70602", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70602"}, {"title": " The stochastic geometry of decision tree learning ", "webprogram_exclude": "0", "session_ids": ["Session/18343"], "source_sha256": "ebfaceff83ae3743a5e597e2cb813ba8999e62b765fc71cab952c1900c9937aa", "withdrawn": "", "abstract": "Random forests are a widely used class of prediction algorithms made of ensembles of randomized decision trees. The algorithms most commonly use only one covariate of the input data to partition the data in a given node of a tree. Oblique random forests are variants where splits are allowed to depend on linear combinations of the covariates. In this talk, we will discuss a class of efficiently generated random tree and forest estimators called oblique Mondrian trees and forests, as the trees are generated by first selecting a set of features from linear combinations of the covariates and then running a stochastic Mondrian process that hierarchically partitions the data along these features. Our theoretical analysis demonstrates that these estimators can adapt to dimension reduction models for which the output depends on a general low-dimensional relevant feature subspace and we quantify how robust the risk is with respect to error in the estimation of these relevant features. We will then discuss an approach for identifying the relevant feature subspace that uses a Mondrian forest to estimate the expected gradient outer product (EGOP). In addition, we introduce an iterative algorithm called Transformed Iterative Mondrian (TrIM) forest to improve the Mondrian forest estimator by using the EGOP estimate to update the set of features and weights used by the Mondrian partitioning mechanism.", "id": "Paper/70603", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70603"}, {"title": " Singularities of tensor varieties ", "webprogram_exclude": "0", "session_ids": ["Session/18355"], "source_sha256": "b147bd038056c78c7afbd00e31f4170761a326d76d094767a5ca85e37bad719a", "withdrawn": "", "abstract": "We discuss singularities of varieties arising naturally in the geometry of tensors. In particular, we give examples illustrating when tensor varieties with additional constraints have or do not have properties such as rational singularities, Cohen--Macaulayness, and the Gorenstein property. These varieties come from applications like machine learning and algebraic statistics.", "id": "Paper/70604", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70604"}, {"title": " A Combinatorial Perspective to Perturbation & Graph Eigenvectors ", "webprogram_exclude": "0", "session_ids": ["Session/19360"], "source_sha256": "293dc5935ba44afe1fff097d4960bc4b3e6494e74a8e660f3dd8feb00391a166", "withdrawn": "", "abstract": "Recently, Samanta \\emph{et al.} introduced a unifying perspective to common graph-associated matrices through the matrix $B_{\\alpha}(G)=\\alpha A(G)+(1-\\alpha)L(G)$ where $\\alpha\\in [0,1]$. We explore when eigenvectors of $B_{\\alpha}$ are shared between graphs differing by an edge or vertex perturbation. As a consequence, we provide existence and enumeration results on these graphs and the eigenvectors of their associated matrices.", "id": "Paper/70607", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70607"}, {"title": " Tabletop mathematics: Using complex board games to teach mathematical reasoning ", "webprogram_exclude": "0", "session_ids": ["Session/18235"], "source_sha256": "c8f1a725f220ef4b01dd488e91c2e330cd9550855d412daf88a6528110a9ec9f", "withdrawn": "", "abstract": "The revolution that has taken place in tabletop games over the last twenty years, led by complex board games from Europe such as Settlers of Catan, has created a valuable opportunity to teach mathematical reasoning and processes to undergraduates, particularly non-math undergraduates who see themselves as struggling to learn or like mathematics.  For over 10 years, I have been teaching an undergraduate general-education math course that uses board games instead of a textbook to teach different mathematical concepts including concepts in probability, optimization, graph theory and modeling.  The games used in the course are ideal for teaching general mathematical reasoning because each game is comprised of a mathematical system with its own set of structures and rules.  When tasked to analyze a game and develop optimal strategies, students naturally begin creating new concepts and crafting and testing different mathematical hypotheses about the dynamics in the game.  In particular, they are empowered to become creators of mathematics.  Further, the system dynamics students encounter in the games also occur in the real world.  When they observe how mathematical reasoning can lead to improved strategies and outcomes in game play, they also learn how it can be used to make better decisions in real-world settings.\n In this talk I will discuss the underlying philosophy of the course and provide examples of different games and the associated concepts students learn from each game.  I will also delineate the connection between board games and real-world contexts.  Finally, I will give evidence of the efficacy of the course as a way of getting the math phobic to love doing math.", "id": "Paper/70608", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70608"}, {"title": " Targeted County-Level Interventions Achieve Epidemic Control Without Statewide Lockdowns ", "webprogram_exclude": "0", "session_ids": ["Session/18260"], "source_sha256": "060c2066f6d8a8d5d314d9db9038bd18fff634047db8ba598a0a89a33a96f1d8", "withdrawn": "", "abstract": "When a new pathogen emerges, public health authorities must act rapidly to mitigate its spread while minimizing societal disruption. Despite extensive debate on localized epidemic control, no model-based study has systematically evaluated county-level interventions for statewide epidemic suppression in the United States. We present a metapopulation model that integrates county-level mobility data to assess targeted intervention strategies for pandemic preparedness. We identify epidemic hotspots as counties that generate disproportionately large statewide epidemics when serving as outbreak origins. These hotspots align with population-dense and highly connected locations but provide sharper spatial contrast than traditional centrality metrics. Targeted interventions reducing the basic reproduction number ($R_0$) only at hotspots achieve substantial epidemic control—reducing statewide epidemics by 60--90\\% in four representative states (Oklahoma, New York, Florida, and California)—without requiring broad lockdown measures. Hybrid strategies combining moderate reductions in $R_0$ (10--30\\%) with partial mobility restrictions (30--80\\%) from hotspot counties, while preserving activity elsewhere, achieve control equivalent to full suppression at hotspots. This framework demonstrates that strategic, location-specific interventions can replace blanket pandemic responses. It provides state and county decision-makers with a quantitative tool for prospective pandemic planning, enabling rapid hotspot identification and intervention design grounded in empirical mobility networks.", "id": "Paper/70609", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70609"}, {"title": " Stage-Structured Predator–Prey Dynamics under Continuous and Seasonal Prey Reproduction ", "webprogram_exclude": "0", "session_ids": ["Session/19353"], "source_sha256": "53954990701c3601a05f9533ec4538cdfc2c3616a94494dc57ab7eaa62210582", "withdrawn": "", "abstract": "Stage-structured models, based on population size or developmental stage, are widely used in discrete-time population modeling. We formulate a predator–prey model with juvenile and adult stages for both populations and Beverton–Holt prey growth. Only adult predators consume newborn prey, while fractions of surviving juveniles mature into adults at each time step. We show that the system is persistent and permanent when both the prey’s inherent net reproductive number and the predator’s invasion net reproductive number exceed one. We then extend the model by introducing a 2-periodic prey reproduction function representing breeding and non-breeding seasons and analyze a simplifying special case. Our study for this seasonal model shows that seasonality can benefit the prey when predator is not present, producing a higher mean prey density over a full period within a certain parameter region than the corresponding continuous-growth model. We also find that the seasonal model requires a lower fecundity threshold for the existence of a positive predator-free seasonal 2-cycle than the threshold required for the emergence of positive predator-free equilibrium in the continuous model.", "id": "Paper/70611", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70611"}, {"title": " Arc diagrams beyond Type A ", "webprogram_exclude": "0", "session_ids": ["Session/18138"], "source_sha256": "f792737f9a114a584ec5f6ac799869a07bdbf7a02be31f37e4b5d6629b77e87a", "withdrawn": "", "abstract": "Noncrossing arc diagrams are a visual representation of permutations. They naturally encode canonical join representations and contain complete information on lattice congruences and lattice quotients on the weak order of type A. This talk will provide an overview of the existing results on noncrossing arc diagrams for permutations and present analogous results (joint with Barnard and Reading) on arc diagrams for signed permutations (type B) and even signed permutations (type D). These results elucidate sublattice relationships between shard intersection orders on different finite Coxeter groups.", "id": "Paper/70613", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70613"}, {"title": " Egorov’s theorem on hyperbolic surfaces ", "webprogram_exclude": "0", "session_ids": ["Session/17999"], "source_sha256": "f3f74a99a620041b37e3fb6298125a12c3ee24554371c736de5a19e20988d8ee", "withdrawn": "", "abstract": "Motivated by the analysis of scattering resonances on infinite-area hyperbolic surfaces, we establish a quantum-classical correspondence up to time $\\log \\frac{1}{h}$. The main tool is a global quantization procedure inspired by the Zelditch quantization and the anisotropic calculus of Dyatlov--Zahl. In particular, the Egorov's theorem allows us to propagate deep into the cusp regions where the injectivity radius degenerates. Such an Egorov's theorem allows us to rule out the escape of mass into the cusps of the manifold. This talk is based on joint work with Alex Cohen and Zhongkai Tao.", "id": "Paper/70622", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70622"}, {"title": " Nutrient Reduction for Genome-Scale Metabolic Models ", "webprogram_exclude": "0", "session_ids": ["Session/19365"], "source_sha256": "926a8f2fc2ad1c0c04908e857d3daa962eb74a42f2e7aacc1ffdefd58c57b790", "withdrawn": "", "abstract": "Genome-scale metabolic predictions depend on network structure and environmental exchange constraints. We seek minimum-cardinality sets of permitted nutrient imports that satisfy prescribed growth requirements across multiple conditions.\n\nWe formulate this problem as a mixed-integer linear program with shared binary exchange-inclusion variables and condition-specific flux variables. A common set of permitted imports therefore supports a potentially different feasible flux state in each condition. Perturbations of qualitatively specified reference media identify candidate exchanges and alternative starting media, while sensitivity to uptake capacities provides complementary evidence.\n\nWithin the specified candidate sets, uptake bounds, and growth constraints, mixed-integer optimization certifies minimum support sizes of 16 and 21 exchanges for the Staphylococcus problems based on M9 and chemically defined medium (CDM), respectively, and 9 and 11 for the corresponding Bacillus subtilis problems. Additional searches identify alternative supports, subject to recorded enumeration limits. These results highlight nutrient substitution and joint sufficiency as properties that individual sensitivity rankings alone do not characterize.\n\nPlanned work will expand the support catalog, compare supports through common capability profiles, and use conditional flux variability analysis and omitted-exchange checks to assess changes in optimal or near-optimal flux ranges that growth preservation alone may miss. The aim is an interpretable, scenario-dependent reduction of environmental inputs, with separate assessments of growth capability and flux-range preservation.", "id": "Paper/70623", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70623"}, {"title": " Prompting Creativity: Assigning and Assessing Open-Ended Mathematical Art Projects ", "webprogram_exclude": "0", "session_ids": ["Session/17986"], "source_sha256": "ffcec98765c47d96319839084fe0c3add02c5124f27d36ebe58138e6498ef021", "withdrawn": "", "abstract": "In any class, assigning an open-ended creative project can come with a myriad of difficulties, from students’ indecision about how to choose a topic to grading potentially unfocused work. So why do it? For this talk, the author discusses, with examples, some of the most interesting student work that has come out of a general education Math in Art class, and how to ensure that students without art backgrounds can still have a reasonable chance at producing successful work.", "id": "Paper/70624", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70624"}, {"title": " On the Thermodynamic Formalism of the Standard Map ", "webprogram_exclude": "0", "session_ids": ["Session/18348"], "source_sha256": "162a4b0fd7e5786199ca71374a099aa60b3acf427cccf054c41d3fadfa8d37b3", "withdrawn": "", "abstract": "The Taylor-Chirikov standard family of maps is a canonical example of the coexistence of regular and chaotic behavior. For large parameters, the phase space carries horseshoes of large entropy while simultaneously being densely covered by elliptic isles of regular behavior. It remains an open question on whether the standard family has positive Lyapunov exponent for even a single parameter value. We study the construction of equilibrium states for the standard family using the framework of Climenhaga and Thompson. To do this, we seek a rigorous theoretical description of transport and stickiness around the elliptic islands in the standard family.  This is a Joint work with Bhullar, Call, and Hemenway.", "id": "Paper/70625", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70625"}, {"title": " Diophantine properties of subgroups of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"7.496ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 3227.4 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">SL_2(\\mathbb {Z})</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-53\" d=\"M308 24Q367 24 416 76T466 197Q466 260 414 284Q308 311 278 321T236 341Q176 383 176 462Q176 523 208 573T273 648Q302 673 343 688T407 704H418H425Q521 704 564 640Q565 640 577 653T603 682T623 704Q624 704 627 704T632 705Q645 705 645 698T617 577T585 459T569 456Q549 456 549 465Q549 471 550 475Q550 478 551 494T553 520Q553 554 544 579T526 616T501 641Q465 662 419 662Q362 662 313 616T263 510Q263 480 278 458T319 427Q323 425 389 408T456 390Q490 379 522 342T554 242Q554 216 546 186Q541 164 528 137T492 78T426 18T332 -20Q320 -22 298 -22Q199 -22 144 33L134 44L106 13Q83 -14 78 -18T65 -22Q52 -22 52 -14Q52 -11 110 221Q112 227 130 227H143Q149 221 149 216Q149 214 148 207T144 186T142 153Q144 114 160 87T203 47T255 29T308 24Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4C\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJAMS-5A\" d=\"M39 -1Q29 9 29 12Q29 23 60 77T219 337L410 648H364Q261 648 210 628Q168 612 142 588T109 545T97 509T88 490Q85 489 80 489Q72 489 61 503L70 588Q72 607 75 628T79 662T81 675Q84 677 88 681Q90 683 341 683H592Q604 673 604 666Q604 662 412 348L221 37Q221 35 301 35Q406 35 446 48Q504 68 543 111T597 212Q602 239 617 239Q624 239 629 234T635 223Q635 215 621 113T604 8L597 1Q595 -1 317 -1H39ZM148 637L166 648H112V632Q111 629 110 622T108 612Q108 608 110 608T116 612T129 623T148 637ZM552 646Q552 648 504 648Q452 648 450 643Q448 639 266 343T77 37Q77 35 128 35H179L366 339L552 646ZM572 35Q581 89 581 97L561 77Q542 59 526 48L508 37L539 35H572Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-53\" x=\"0\" y=\"0\"></use>\n<g transform=\"translate(645,0)\">\n <use xlink:href=\"#E1-MJMATHI-4C\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-32\" x=\"963\" y=\"-213\"></use>\n</g>\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"1780\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJAMS-5A\" x=\"2170\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"2837\" y=\"0\"></use>\n</g>\n</svg> on branched covers of the torus ", "webprogram_exclude": "0", "session_ids": ["Session/17902"], "source_sha256": "9243bbcc02c29dca114fe6aae2199c057c90a99913c8e0c16192161a2213796a", "withdrawn": "", "abstract": "In this talk, we will discuss methods of proving Diophantine estimates for the action of the group of affine homeomorphisms on a translation surface. We will begin with the classical case of $SL_2(\\mathbb{Z})$ acting on the torus and explain how the result can be lifted to certain square-tiled surfaces endowed with an action of a group of affine homeomorphisms. By different methods, we will prove Diophantine estimates for the action of affine homeomorphisms on any lattice surface. These two methods highlight a curious tension between the results that we will spell out. This work is joint with Chris Judge.", "id": "Paper/70628", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70628"}, {"title": " What are the odds that a conic bundle over a finite field is rational? ", "webprogram_exclude": "0", "session_ids": ["Session/18368"], "source_sha256": "70f722c81fc5f4c77777805afb1c82183d053abfad750674e08c1e1c3b55059c", "withdrawn": "", "abstract": "We study rationality of good conic bundles over finite fields. In particular, we ask for a given number $n$ of degenerate fibers, what is the proportion of good conic bundles that are rational. The Galois action on the Picard group factors through a cyclic subgroup of the Weyl group $W(D_n)$. A theorem of Colliot-Thélène shows that X is rational over $F_q$ if and only if the corresponding cyclic subgroup satisfies an explicit cohomological vanishing condition. We use this along with a equidistribution result of Chebotarev to study the asymptotic behavior of the proportion of rational good conic bundles.", "id": "Paper/70630", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70630"}, {"title": " Heat Field Signatures: From Point Clouds to Smooth Geometry ", "webprogram_exclude": "0", "session_ids": ["Session/18304"], "source_sha256": "c3045ba00ff451996f3092bac8413b4e0117be409aad4597212b10c284cbfe87", "withdrawn": "", "abstract": "We introduce \\emph{Heat Field Signatures} (HFS), a multiscale geometric representation of point clouds obtained by lifting discrete data to a family of smooth ambient heat fields. This provides a direct interface from finite point clouds to geometric analysis, without requiring meshes, graph Laplacians, normal estimation, or spectral decomposition. From the heat field, we derive closed-form global and local signatures capturing concentration, intrinsic dimension, anisotropy, and geometric transitions across scale, together with the \\emph{Heat Dimension Spectrum}, which summarizes multiscale dimensional composition. HFS yields interpretable and rotation-invariant representations that can be used directly or incorporated into learning models. Across synthetic and real-world geometric classification problems, including neuronal, tree, and protein structures, HFS substantially improves over standard point-cloud and multiparameter-persistence baselines while remaining computationally efficient. More broadly, the framework offers a way to bring tools from geometric analysis directly to irregular point-cloud data. Further details: \\url{https://arxiv.org/abs/2609.07975v1}.", "id": "Paper/70632", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70632"}, {"title": " Following van der Pauw: electrostatics experiments in complex variables ", "webprogram_exclude": "0", "session_ids": ["Session/19368"], "source_sha256": "6ae5f144337616d469062c2320a7e9c049ba8fc9aa75d6e4fc4994de4b5cb0c8", "withdrawn": "", "abstract": "The van der Pauw method is a remarkably effective way to compute the sheet resistance for a 2-dimensional semiconducting material.  With basic equipment from a physics laboratory (DC power source and multimeter), one can demonstrate concepts like Green's function, cross ratio, and Riemann map for a typical course in complex variables.  Here we review the setup and result for the smooth, simply connected case.  We then update on recent progress for the general situation, including measurement of the modulus for a doubly connected domain that has rotational symmetry via conformal mapping to an annulus.  The latter result was recently published in PRIMUS.", "id": "Paper/70635", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70635"}, {"title": " The triple linking measure of open curves in 3-space ", "webprogram_exclude": "0", "session_ids": ["Session/19358"], "source_sha256": "30ba1eed4a5057fe768d98eb082899ca2c414bc00708e9351e2fa22f81be3bfb", "withdrawn": "", "abstract": "Physical systems of filamentous material appear across nature and exhibit complex material properties and function that result, in part, from the entanglement present therein.  The Milnor triple linking number captures entanglement of three chains that can not be detected by linking number alone. It can be used as an alternative to knot polynomials that is also easier to compute in practice. In this talk, we will introduce a diagrammatic based formula for Milnor invariant of linkoids and virtual links derived from (virtual) group based Milnor invariant of links and study its properties. We will also define the Milnor measure of three open curves in 3-space and show that it is a continuous function of the curve coordinates that converges to the Milnor invariant of closed links as the open curves tend to close. We use the Milnor measure to study triple linking of random walks as a function of their length and we also apply it to polymer systems. Our results show that non-trivial triple linking occurs increasingly in random systems with increasing length and that (some) higher order linking, which cannot be detected by pairwise linking numbers, can be detected by the Milnor triple linking number.", "id": "Paper/70637", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70637"}, {"title": " The topological landscape of folded proteins ", "webprogram_exclude": "0", "session_ids": ["Session/19364"], "source_sha256": "4dea72e256569c95d521665250a905304e9f987b357850c8165d8e07438cd081", "withdrawn": "", "abstract": "We introduce three mathematical topology metrics as protein struc-\nture descriptors that quantify the entanglement complexity of a ter-\ntiary protein structure and employ those to all proteins in the Protein\nData Bank (PDB). We show that the distances within this continuous\nthree-dimensional space correlate with functional similarity. We also\nfind that the mathematical entanglement based landscape of protein\nstructural space diversifies across species and this topological diver-\nsity agrees with the evolutionary expansion of protein function across\nspecies. By analyzing mesophilic and thermophilic proteins we find\nthat experimentally observed melting temperatures reflect a change\nin their topological landscape. These results suggest that these topo-\nlogical metrics of protein structures effectively capture the structural\nfeatures associated with protein function and dynamics.", "id": "Paper/70641", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70641"}, {"title": " From the statistics of colliding particles to fluid motion ", "webprogram_exclude": "0", "session_ids": ["Session/18433"], "source_sha256": "566afe9fbd03d9929c36f7eb161c8ef42418d8727dc13fe30618a7214ba35f79", "withdrawn": "", "abstract": "This will be an expository account of the recent works of Deng-Hani-Ma who have proved, for long-time, that the statistics of colliding Newtonian particles yield the equations of fluid motion.", "id": "Paper/70643", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70643"}, {"title": " The Soccer Similarity Score: A Method for Identifying Similar Styles of Play in English Soccer ", "webprogram_exclude": "0", "session_ids": ["Session/18241"], "source_sha256": "44a411196d8221e249e2739e3420c486c9c604b3f6e82bb7127f830fe1524a13", "withdrawn": "", "abstract": "In this talk we introduce the Soccer Similarity Score. This is a metric to identify which teams in the English Premier League played most similarly to each other across 25 years. Using data collected from FootballReference.com, we measure the similarity between two teams by treating a team's season as an element of a 14-dimensional vector space, and performing a change of coordinates to remove correlation between variables. This process is more commonly referred to as finding the Mahanalobis Distance between two vectors. During the talk, we will discuss interesting results we found and why we believe the Similarity Score truly represents similarity between styles of play.", "id": "Paper/70644", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70644"}, {"title": " An orthogonal perspective on Gauss composition ", "webprogram_exclude": "0", "session_ids": ["Session/19361"], "source_sha256": "9596bf7fb9d32bfe85d4172b6be2d2b9c47d3b88eba0dc9f09793d1de3db4056", "withdrawn": "", "abstract": "We revisit Gauss composition over number rings from the perspective of orthogonal groups. Building on work of Kneser and Wood, we show that the Clifford and norm maps relate binary quadratic forms to modules over quadratic algebras. A concrete coprimitivity condition determines when two forms can be composed, and we give explicit formulas for their composition, recovering classical Dirichlet composition. We also clarify how narrow class groups emerge naturally from this orthogonal viewpoint. This is joint work with John Voight.", "id": "Paper/70646", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70646"}, {"title": " Distance Spectral Analysis of Proper Power Graphs of Finite Cyclic and Some Non-Cyclic Groups ", "webprogram_exclude": "0", "session_ids": ["Session/19354"], "source_sha256": "28ba16d90f7d1ded00d6b7f5535c45aa018888b432ca95de560202637b24924c", "withdrawn": "", "abstract": "The distance matrix of a graph $G$, denoted by $D(G)$, is an $n$x$n$ matrix with its rows and columns indexed by a set of vertices, $V(G)$. For $i\\neq j$, the $(i,j)$-entry, $d_{ij}$ of $D(G)$ is set equal to $d(i,j)$. Also, $d_{ii}= 0$, $i=1,...,n$. Here, $d(i,j)$ denotes the distance between the vertices $i$ and $j$, which is the length of a shortest $i-j$ path. The distance spectrum of a graph is the set of eigenvalues of its distance matrix, with counting multiplicity. The proper power graph of a group $G$, denoted by $\\mathscr{P}^*(G)$, is a graph with vertex set $G-{e}$, and two distinct vertices $u,v$ are adjacent if $u=v^m$ or $v=u^m$, for some positive integer $m$.The paper presents the structure of the proper power graph of the finite cyclic group, and the generalized quaternion group. Based on these structures, the distance spectrum of the proper power graph of a finite cyclic group is obtained. Finally, the characteristic polynomial and distance eigenvalues of the proper power graph of the generalized quaternion group are obtained, and a relation among the remaining eigenvalues is established.", "id": "Paper/70647", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70647"}, {"title": " Epidemic Thresholds and Disease Dynamics in Deterministic and Stochastic Metapopulations: Network Structure and Human Mobility ", "webprogram_exclude": "0", "session_ids": ["Session/17811"], "source_sha256": "85a10339ef55d04fc035255e923754fda03443a287bb76778da67a4a4af27f53", "withdrawn": "", "abstract": "We calculate epidemic thresholds and investigate disease dynamics in deterministic and stochastic networked metapopulation models, with particular emphasis on the roles of network structure and human mobility. Using an SIR-network framework, we first analyze epidemic thresholds across a range of network structures and mobility levels. For star-shaped networks, we obtain the same epidemic threshold formulas previously found for fully connected networks when all nodes have the same infection rate except one. This motivates the introduction of the Standard Threshold Property, which characterizes network structures sharing this threshold behavior. We then analyze cycle-shaped and more general networks, identifying classes of networks with the Standard Threshold Property and presenting conjectures for broader network structures. We next extend the framework to a stochastic model to examine how random fluctuations influence epidemic thresholds and disease dynamics. Numerical simulations compare the deterministic and stochastic dynamics across different network structures and mobility levels, illustrating the combined effects of network topology, human mobility, and stochasticity on epidemic outcomes.", "id": "Paper/70648", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70648"}, {"title": " Precalculus is useful! A project for health science and other majors ", "webprogram_exclude": "0", "session_ids": ["Session/19341"], "source_sha256": "375dc944fde23775958d029263aa6794d90ff0941332b2834cb2e52c1289a442", "withdrawn": "", "abstract": "Our precalculus classes are filled with many different students, but especially students who are interested in health careers.  In our course, students learn about both exponential and trigonometric functions, but students have difficulty seeing why these topics are useful for them.  In this semester-long project, students create a model for how their chosen drug with a repeated regular dose can be modeled using half-life, piece-wise functions, and visual approximations of trigonometric graphs.  They consider ways in which their model is a good or poor fit for reality and situations in which it may be helpful to use such a model.", "id": "Paper/70651", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70651"}, {"title": " COMAP for Dummies: How an inexperienced team of high school girls learned to math model ", "webprogram_exclude": "0", "session_ids": ["Session/19005"], "source_sha256": "2a622f64d4ee2fbd3a706ad6cea92d7226499976cd2e4567a551b1ba4518a739", "withdrawn": "", "abstract": "Learn how a group of students, having never math modeled before, took on COMAP’s HiMCM. Throughout the course of the competition, we faced many challenges: time management, effective communication, finding data, learning Latex, getting tangible results, and the dilemma of the usage of artificial intelligence. This talk will discuss how we overcame these obstacles to write a paper we’re proud of, and how we approached a complex issue without any prior knowledge or skills. We’ll walk you through our journey from inexperienced high school students to (semi) competent math modelers, sharing a few details about our solution along the way. We’ll also touch on the response from our community as an all-girls group recognized for math.", "id": "Paper/70652", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70652"}, {"title": " Shadow Diagrams, an <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.604ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 690.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathcal {L}</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJCAL-4C\" d=\"M62 -22T47 -22T32 -11Q32 -1 56 24T83 55Q113 96 138 172T180 320T234 473T323 609Q364 649 419 677T531 705Q559 705 578 696T604 671T615 645T618 623V611Q618 582 615 571T598 548Q581 531 558 520T518 509Q503 509 503 520Q503 523 505 536T507 560Q507 590 494 610T452 630Q423 630 410 617Q367 578 333 492T271 301T233 170Q211 123 204 112L198 103L224 102Q281 102 369 79T509 52H523Q535 64 544 87T579 128Q616 152 641 152Q656 152 656 142Q656 101 588 40T433 -22Q381 -22 289 1T156 28L141 29L131 20Q111 0 87 -11Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJCAL-4C\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-type Invariant, and Unknotting Number for Surfaces in <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.576ex\" height=\"2.509ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -934.9 1109.1 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">S^4</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-53\" d=\"M308 24Q367 24 416 76T466 197Q466 260 414 284Q308 311 278 321T236 341Q176 383 176 462Q176 523 208 573T273 648Q302 673 343 688T407 704H418H425Q521 704 564 640Q565 640 577 653T603 682T623 704Q624 704 627 704T632 705Q645 705 645 698T617 577T585 459T569 456Q549 456 549 465Q549 471 550 475Q550 478 551 494T553 520Q553 554 544 579T526 616T501 641Q465 662 419 662Q362 662 313 616T263 510Q263 480 278 458T319 427Q323 425 389 408T456 390Q490 379 522 342T554 242Q554 216 546 186Q541 164 528 137T492 78T426 18T332 -20Q320 -22 298 -22Q199 -22 144 33L134 44L106 13Q83 -14 78 -18T65 -22Q52 -22 52 -14Q52 -11 110 221Q112 227 130 227H143Q149 221 149 216Q149 214 148 207T144 186T142 153Q144 114 160 87T203 47T255 29T308 24Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-53\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-34\" x=\"926\" y=\"513\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18087"], "source_sha256": "5613600cdf72a71206493c54a01dcaafd0f33836fc6aa58a5e876cea5a8a4f72", "withdrawn": "", "abstract": "In 2017, Meier and Zupan defined bridge trisections, in which a knotted surface is represented by a tuple of tangles or, equivalently, shadow diagrams.  In ongoing joint work with Rom\\'an Aranda, Nobutaka Asano, Hironobu Naoe, and Marion Campisi, we define a new CW--complex for shadow diagrams and relate loops in this complex to bridge trisections.  We then define an invariant similar to Kirby and Thompson's $\\mathcal{L}$-invariant and show that this provides an upper bound for the unknotting number of a surface.", "id": "Paper/70654", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70654"}, {"title": " Singular loci of resectioning varieties ", "webprogram_exclude": "0", "session_ids": ["Session/18214"], "source_sha256": "986f810309865983e65ad165266457e8e94b8be5f4110ad5f7b38aa892c0c9ce", "withdrawn": "", "abstract": "A flatlander camera is a projective linear surjection\n$ A: \\mathbf{P}^2 \\dashrightarrow \\mathbf{P}^1.$ \nFor a fixed configuration of ordered points\n$X = (X_1, \\dots, X_n) \\in (\\mathbf{P}^2)^n$, \nconsider the rational map $\\psi_X$ from the space of flatlander cameras\nto $(\\mathbf{P}^1)^n$\ndefined by $ \\psi_X (A) = (AX_1, \\dots, AX_n)$.\nThe Zariski closure of the image of $ \\psi_X$ is defined as the \\emph{resectioning variety} $\\mathcal{R}_X^{2,1}.$ \nKnowing the geometry of the resectioning variety\nallows one to reconstruct camera data from a given set of images.\nThis is analogous to the \\emph{multiview variety}, which enables reconstruction of scene point data from fixed cameras. \nHowever, a significant difference between the multiview and \nresectioning varieties is the presence of singular points in \n$\\mathcal{R}_X^{2,1}.$\nWe study the geometry of these resectioning varieties and \nshow that, for generic $X$,\nthe singular locus of $\\mathcal{R}_X^{2,1}$\ndecomposes as the union of \n$n$ irreducible components, each isomorphic to $\\mathbf{P}^1 \\times \\mathbf{P}^1.$", "id": "Paper/70656", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70656"}, {"title": " Systematic Symmetries: Exploring Periodic Design Spaces ", "webprogram_exclude": "0", "session_ids": ["Session/18234"], "source_sha256": "7bf2f899120e8f77f51b8e4f276ebb4530e6a086c2144d565063c48092ce62e6", "withdrawn": "", "abstract": "As I was knitting \\textit{The Fundamentals of Lace}, a beaded wall hanging in which a single lace motif generates each of the nine symmetry groups compatible with knitted lace, I reflected on my design process.  For some of the groups, I had to make an aesthetic choice between multiple designs, and I became curious about the full range of pattern choices I had.  The investigations that followed led me to several new artworks, to a new craft form, and to this talk.", "id": "Paper/70657", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70657"}, {"title": " AI as Author, Students as Critics: Validating Mathematical Narratives for Conceptual Mastery ", "webprogram_exclude": "0", "session_ids": ["Session/18262"], "source_sha256": "f1cc5e0b80942be75eb91f731122fd940d2bf34267da65be0b30e279d80f5c60", "withdrawn": "", "abstract": "Generative AI can now produce engaging mathematical stories that embed problems in narrative contexts, and recent research has explored students creating such stories themselves to deepen engagement and conceptual understanding. Reliability problems persist in AI-generated narratives with subtle mathematical errors, making the preservation of reliable content a key challenge when integrating math into educational narratives. Research involving students' use of AI tools indicates that learners frequently struggle to identify errors in mathematical outputs. As a result, mistakes may go unnoticed in areas where learning is intended to take place.\nThis talk presents a classroom activity designed for an applied linear algebra classroom that transforms this reliability problem into a learning opportunity for students. Rather than treating AI-generated mathematical stories as finished instructional products, students are tasked with validating them. Students hunt for embedded errors, checking computational claims, and critiquing whether the narrative faithfully represents the underlying mathematical concepts. This validation activity serves as the pedagogical bridge between two strands of emerging research: the generation of AI-assisted mathematical stories and the documented need for learners to develop critical evaluation skills toward AI output. \nPreliminary observations suggest that error-finding in AI narratives promotes deeper engagement with definitions, assumptions, and edge cases than passive story consumption does, while cultivating the evaluative habits students will need as future practitioners of mathematics using AI tools.", "id": "Paper/70658", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70658"}, {"title": " Forgotten Characters in Sym and NSym ", "webprogram_exclude": "0", "session_ids": ["Session/18375"], "source_sha256": "c2bf7be1480f5bd8c359b3a7f50816fd9beb6eb7677ad0e57e2f15c5ea0ceb79", "withdrawn": "", "abstract": "The forgotten symmetric function is so-called because of its lack of apparent applications. In this talk, we show that this basis arises naturally when evaluating symmetric group characters on elements that extend a given \"partial permutation\". A partial permutation of a set X is a bijection between two subsets of X. In other words, this is permutation which might be \"forgetting \"some of its values, so the basis' name is actually quite apt! The connection is done through work of Hamaker and Rhoades on the path-power sum symmetric function. We then extend this perspective to QSym and NSym. In particular, we introduce a new basis for NSym arising from character evaluations on the 0-Hecke algebra and recover an analogue of the forgotten symmetric functions in QSym, mirroring the appearance of the forgotten symmetric functions from the Hamaker-Rhoades construction.", "id": "Paper/70659", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70659"}, {"title": " Analytic combinatorics of RNA folding: making ends meet or just meeting at the ends? ", "webprogram_exclude": "0", "session_ids": ["Session/18105"], "source_sha256": "7539dd64c1c3290f9b12a1e9ad4dbaa4743bba2e8f6e0d18909ae9367c3b0086", "withdrawn": "", "abstract": "It is well-established in biology that the two ends of an RNA sequence are consistently found in close proximity in the folded 3D molecule. Moreover, biologists view this property of end-proximity as “rather remarkable” when compared with the expected end-to-end distance for a random linear polymer. However, when viewed from a combinatorial perspective, we prove that the ends of a branched structure (which RNA folding generates) are almost certainly close. Using analytic combinatorics, our analysis considers branching models of increasing complexity: plane trees, Motzkin paths, and stochastic context-free grammars. In contrast to prior work, our multivariate results fully characterize all relevant end-proximity characteristics, permitting direct comparison with experimental data.", "id": "Paper/70660", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70660"}, {"title": " Stability and Sturm theory for dynamics on networks ", "webprogram_exclude": "0", "session_ids": ["Session/18109"], "source_sha256": "f0030ad4cc3022fd4c9ca19cec8d4806f640f30d7726b55b45d5828cd919c42b", "withdrawn": "", "abstract": "", "id": "Paper/70661", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70661"}, {"title": " The asymptotic structure of perturbed plane waves on Euclidean space ", "webprogram_exclude": "0", "session_ids": ["Session/18326"], "source_sha256": "a8352bbf8bcbb55ec8df428efe49d258fcc05a6d861939f85fcf2363dce38744", "withdrawn": "", "abstract": "A perturbed plane wave is a solution of the Schr\\\"odinger-Helmholtz equation $(\\Delta + Q - k^2)u = 0$ (where $Q$ is a perturbative term, e.g. multiplication by a potential) agreeing with the plane wave $e^{ikx}$ up to a correction. When $Q$ decays rapidly, the correction is an outgoing spherical wave $e^{ikr}f(\\omega)/r^{(d-1)/2}$, with $f$ smooth on the sphere. When $Q$ decays only at a short-range rate, $f$ becomes singular in the forward direction, and the wave acquires a \\emph{parabolic wake}, i.e. a correction term spreading along parabolas centered on the forward axis rather along rays; this can be seen numerically in simple examples like an inverse square potential. We discuss ideas behind our recent work, giving a complete physical-space description of this structure as a combination of plane and spherical waves, where the coefficients are polyhomogeneous not on the sphere at infinity, but on a parabolic blowup resolving the forward direction, refining the microlocal picture presented in earlier works of Melrose and Zworski. Joint work with N. Lohr, I. Oltman, and E. Sussman.", "id": "Paper/70663", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70663"}, {"title": " Median eignevalues of graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18085"], "source_sha256": "4324eec5a4920a15275a8c3f46b2894aaf38091dd42d7873f847b7e3097ea506", "withdrawn": "", "abstract": "The median eigenvalues of a graph are the eigenvalues of its adjacency matrix sitting at the centre of the spectrum. In mathematical chemistry, they correspond to the HOMO and LUMO orbitals, which play an important role in determining molecular reactivity. In this talk, we explore how the maximum degree of a graph controls its median eigenvalues. In particular, we confirm, for all but finitely many values of $d$, a conjecture of Mohar asserting that the median eigenvalues of a graph of maximum degree $d$ are bounded in absolute value by $\\sqrt{d-1}$. We will discuss some of the ideas behind the proof.", "id": "Paper/70664", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70664"}, {"title": " Topological Perspectives on Hypergraphs ", "webprogram_exclude": "0", "session_ids": ["Session/18324"], "source_sha256": "02f030001447adee087fd81b84f99cd6231352d5f67404c40421a61403a05541", "withdrawn": "", "abstract": "Hypergraphs offer a natural mathematical framework for representing higher-order interactions that traditional graph-based models often oversimplify. This talk investigates the development of topological invariants and categorical representations for such objects, emphasizing their utility in characterizing multi-way connectivity.\n\nIn this talk I will discuss my recent research involving homological and sheaf-theoretic frameworks as they apply to the structural analysis of relational data. These perspectives provide formal methods for evaluating the consistency and integrity of networked systems, with potential applications ranging from network analysis to the verification of knowledge representations. The discussion will focus on the interplay between these topological structures and the broader requirements for maintaining faithful representations of complex data.", "id": "Paper/70665", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70665"}, {"title": " An overview of aspects of metric fixed point theory. ", "webprogram_exclude": "0", "session_ids": ["Session/18364"], "source_sha256": "2afd5b3cb010fd6ff86432750ed91b11ba726d07fbd8d82a2847580cd0bebff0", "withdrawn": "", "abstract": "We will survey a number of interesting aspects of metric fixed\n                 point theory, due to various authors.", "id": "Paper/70670", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70670"}, {"title": " Middle Haar weights and almost unimodular quantum groups ", "webprogram_exclude": "0", "session_ids": ["Session/17834"], "source_sha256": "42d2ac369e7fbb41444f65595a1d56af1191745b1995d3bedd3a58f938687563", "withdrawn": "", "abstract": "The theory of locally compact groups is often partitioned into the unimodular and non-unimodular cases. Another natural division is provided by the class of almost unimodular groups, which is an enrichment of the unimodular groups that permits the generalization of many results from the unimodular setting. Crucially, both dichotomies have equivalent characterizations in terms of either the group itself or the group von Neumann algebra (i.e. the \"dual\" of the group). In joint work with Aldo Garcia Guinto and Lucas Hall, we show that this situation can be generalized to the von Neumann algebraic setting of locally compact quantum groups, where one has a von Neumann algebra equipped with a coproduct and left and right Haar weights along with a canonical dual. Our approach relies on a new object that we refer to as the middle Haar weight, which directly encodes (almost) unimodularity in a way analogous to the classical case. Consequently, one can define the class of almost unimodular quantum groups, which provides a unified (and tame) framework for studying both unimodular and compact quantum groups.", "id": "Paper/70672", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70672"}, {"title": " Geometric representations of q-Brauer algebra ", "webprogram_exclude": "0", "session_ids": ["Session/19352"], "source_sha256": "961ce1509ace39e57cb25f9fd35b0f828f430bdc15e880a5ef8f77433f475722", "withdrawn": "", "abstract": "Brauer introduced an algebra named ”Brauer algebra” on 1937 which was later generalized into ”q-Brauer algebra” by Wenzl on 2012. This algebra has a Hecke algebra structure and a Kazhdan-Lusztig type basis. I will give a geometric representation of a part of q-Brauer algebra. This is an ongoing work with Prof. P Achar.", "id": "Paper/70674", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70674"}, {"title": " Some positive Schur coefficients of claw-free graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18085"], "source_sha256": "ae8ea746f2dbb6d52cafacaa23370c47f81e632226cde421b0992c21023f754b", "withdrawn": "", "abstract": "The chromatic symmetric function was conjectured by Stanley in 1995 to have a positive Schur expansion for any claw-free graph.  At the GRWC workshop in 2024, I proposed making some partial progress on this by computing a few coefficients. After much work, we showed that for any claw-free graph, the coefficient for the Schur function of any partition shape of the form (a,b,1,...,1) is positive. However, in 2026, Stanley's conjecture was proven false independently and simultaneously by Matherne--Morales and Prajapati, just as we were writing up our paper. Nevertheless, our work is still applicable for slightly weaker conjecture of Foley--Hoang--MerkelIn that claw- and net-free graphs are e-positive. this talk, I will discuss the long and winding road of this GRWC project and the lessons I learned along the way.", "id": "Paper/70675", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70675"}, {"title": " State solids and Murasugi sums in four dimensions ", "webprogram_exclude": "0", "session_ids": ["Session/18344"], "source_sha256": "c8a559918118643d382f4468ed4471286c4ebad8026565243220a53eefb28c9e", "withdrawn": "", "abstract": "Given any diagram $D\\subset S^2$ of a knot or link $K\\subset S^3$, one can construct many spanning surfaces for $K$ by smoothing the crossings of $D$ in any manner, capping the resulting circles with disks, and connecting these disks with half-twist bands at the crossings.  I will describe a similar construction, which uses a broken surface diagram $D\\subset S^3$ of a knotted surface $K\\subset S^4$ to (attempt to) construct spanning solids for $K$.  As I will explain, however, not all choices of smoothings actually yield spanning solids, and fundamental questions here remain unanswered. Nevertheless, this construction naturally motivates an adaptation of classical Murasugi sum to dimension four, as well as a generalization of this adapted operation. We will see that Murasugi sum in 4D is a natural geometric operation.", "id": "Paper/70678", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70678"}, {"title": " Communicating Mathematics and Mathematics Research at the Human Scale ", "webprogram_exclude": "0", "session_ids": ["Session/18329"], "source_sha256": "522c96dcfa2b3f89411bd867c9caf2ff22fee4f39edb530430232278a4f52c61", "withdrawn": "", "abstract": "In contrast with the broad theme of this session, this talk is about the fundamental importance of doing and communicating mathematics face to face and at a small scale.  \nAt the same time, it is important that different communities of mathematicians are able to share resources towards, discuss good practices for, and have a way to celebrate and recognize effective modes of small-scale human communication. \n\nI and my collaborators will talk about a few large-scale initiatives that foster exactly this kind of exchange. \nOne is the new online journal \"Mathematical Discourse\", publishing videos of excellent seminar and colloquia talks.  \nAnother initiative, in a different vein, is the Directed Reading Program Network, which provides resources and a community for organizers of undergraduate-graduate reading/mentorship programs.  \nWe hope that, through these examples, you may find inspiration or models to create or support your own local initiatives to make, share, and communicate mathematics.", "id": "Paper/70692", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70692"}, {"title": " From de la Vallée Poussin Means to Zeros of Analytic Polynomials ", "webprogram_exclude": "0", "session_ids": ["Session/18256"], "source_sha256": "1b95c1fb3eddac3aa4e9726392d9b7855b576f69b9c76fff1b598a72c6c5f700", "withdrawn": "", "abstract": "In 2003, Ruscheweyh and Suffridge settled a 1958 conjecture of P\\'olya and Schoenberg on shape-preserving and subordination properties of the de la Vall\\'ee Poussin means of univalent analytic functions. Foundational to their work was a continuous extension of these means defined by way of solutions to a one-parameter family of differential equations.  We will briefly discuss how this work has branched into several directions in my research.  These include generalizations of the differential equation itself, as well as shape-preserving and subordination properties of convolutions of planar harmonic mappings on the unit disk. In particular, we will discuss how this work led to the introduction of a generalized harmonic half-plane mapping and the role the mapping has played in my more recent focus on the distribution of zeros of analytic polynomials. Some key results and current directions of this pursuit will be presented.", "id": "Paper/70693", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70693"}, {"title": " Do College Students Conceptualize Expressions and Equations as Distinct Objects? ", "webprogram_exclude": "0", "session_ids": ["Session/18068"], "source_sha256": "a47603f1948c7c36f205bb3c62ea96cc61becd17388735f19ca05400de03d406", "withdrawn": "", "abstract": "There is preliminary evidence that some students may blur boundaries between expressions and equations. This blurring may reflect transitional instability in students’ thinking that can occur when students assimilate new mathematical concepts, or it may reflect a need for more direct engagement in instruction about distinctions between expressions and equations as mathematical objects. In existing curricula, students are often asked to transform expressions and equations to produce equivalent symbolic representations, but it is less common to engage them with discussions about fundamental criteria that distinguish these objects from one another.\n\nThis report draws on 198 responses to open-ended questions designed to elicit information about how students assess the equivalence of algebraic expressions and/or equations. This data was collected from community college students across 18 different mathematics courses. We used variation theory as an analysis tool to describe which objects and equivalence criteria appeared to be pulled into students’ focal awareness as they were asked about assessing the equivalence of expressions and equations. \n\nResults from this study illustrate that college students may experience blurred boundaries between expressions and equations as objects, and that they may also conceptualize these objects as distinct but nonetheless experience blurred boundaries around their respective equivalence criteria. For example, students may attempt to apply equivalence criteria for algebraic expressions to algebraic equations by considering two equations as equivalent not just when they have the same solution set, but also when they are equal to the same number on the right side. Taken together, these patterns suggest substantial boundary blurring and crossing within the collective conception space represented by this sample. \n\nThis points to a critical need to examine instruction and curricula to assess the opportunities we are providing students to develop robust and distinct conceptions about algebraic expressions and equations as mathematical objects, including which criteria determine whether these objects are equivalent (and therefore which representations can result from mathematically valid transformation during mathematics tasks).", "id": "Paper/70698", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70698"}, {"title": " Imaging conductivity within its conformal class in a two dimensional hybrid inverse problem ", "webprogram_exclude": "0", "session_ids": ["Session/17859"], "source_sha256": "938f0921e522c337a351ec10e896808e49dc926a338e09382f7e7ff0ffd34d32", "withdrawn": "", "abstract": "I will present a method of reconstruction of a two-dimensional anisotropic conductivity from knowledge of one internal current density field generated by a specific voltage potential and the anisotropy class. The internal data is obtained by the coupling of Diffusion Tensor tomography with Current Density Imaging. Augmenting the existing uniqueness result of Moradifam et al., this reconstruction method is based on a different approach: Specific to two dimensional domains, the method use the internal data to determine first specific isothermal coordinates, thus reducing the problem to the isotropic case. A pullback of an existing method in the isotropic case solves the anisotropic problem. Numerical results are presented to illustrate the accuracy and resolution in this quantitative imaging method. This is joint work with A. Dimitriadis and A. Timonov.", "id": "Paper/70699", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70699"}, {"title": " Anderson duality for even-periodic derived stacks ", "webprogram_exclude": "0", "session_ids": ["Session/18287"], "source_sha256": "7323917619cf145cd1e604595746dbf02888857aace4cf671acf49f554000054", "withdrawn": "", "abstract": "In her thesis, Vesna Stojanoska gave an integral interpretation of the self-duality of $\\mathrm{Tmf}$, showing that its Anderson self-duality reflects Grothendieck--Serre duality for the compactified moduli stack of elliptic curves. Although her result does not rely on a full six functor formalism, it provides strong evidence that such a framework could be accessible in derived settings.\n\nThanks to recent advances in solid condensed mathematics and abstract six functor formalisms—particularly the work of Clausen--Scholze and Mann—there is growing potential for developing a six functor formalism for solid quasi-coherent sheaves on derived Deligne--Mumford stacks.\n\nIn this talk, I will present work in progress toward such a formalism, with the aim of interpreting Anderson duality as a homotopical incarnation of Grothendieck--Serre duality. This perspective is further supported by Proposition 3.15 in Devalapurkar’s paper \\emph{The Lubin--Tate Stack and Gross--Hopkins Duality}, which establishes a version of Anderson duality for even-periodic derived schemes.\n\nMy goal is to extend this result to the setting of derived Deligne--Mumford stacks. Specifically, if $f \\colon X \\to \\mathrm{Spec}(S)$ is an even-periodic smooth derived DM stack and $I_{\\mathbb{Z}}$ denotes the Anderson dualizing spectrum, then we expect $f^!(I_{\\mathbb{Z}}) \\in \\mathrm{Pic}(X)$, interpreted within the solid condensed setting.", "id": "Paper/70703", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70703"}, {"title": " Epidemic Forecasting Across Time Horizons: Integrating Mechanistic, Data-Driven, and Machine Learning Models ", "webprogram_exclude": "0", "session_ids": ["Session/19365"], "source_sha256": "44245ee19a30a34d2cee03bd66efa69cdeec4d09ddedfee3733945ff072c0527", "withdrawn": "", "abstract": "Accurate epidemic forecasting is challenging because the information most useful for prediction depends strongly on the forecasting horizon and the stage of an outbreak. We investigate this challenge using mechanistic, data-driven, hybrid, and machine-learning approaches for short- and long-term epidemic forecasting. For long-term forecasting, we develop data-driven approaches that capture broad epidemic trends and changing transmission dynamics across epidemic stages. For short-term forecasting, we investigate whether incorporating high-resolution data provides additional predictive information and improves forecasts over conventional epidemiological data alone. We compare model performance across different forecasting horizons and epidemic stages to examine how data resolution, model structure, and additional information affect predictive accuracy. Together, these results demonstrate that forecasting performance depends not only on model complexity but also on matching the model and available data to the forecasting horizon, highlighting complementary roles for mechanistic modeling, mobility-informed approaches, and machine learning in epidemic prediction.", "id": "Paper/70707", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70707"}, {"title": " Embedded surface invariants via the Broda-Petit construction ", "webprogram_exclude": "0", "session_ids": ["Session/19358"], "source_sha256": "4c2bf8840392952b6d3b2ebe01d26ef24651965d56d84c4a41b62d771ed46389", "withdrawn": "", "abstract": "We extend the Broda-Petit construction of dichromatic invariants of 4-manifolds to 4-dimensional (0,1,2)-handlebodies equipped with embedded surfaces. Using the banded-unlink description of embedded surfaces developed by Hughes, Kim, and Miller, we introduce additional coloring data consisting of a symmetric Frobenius algebra object and a module over it in an appropriate pair of ribbon fusion categories. We show that, under suitable categorical conditions, the resulting normalized evaluation is invariant under the moves relating banded-unlink presentations and hence gives an invariant of the embedded surface-handlebody pair. We also describe a related construction for boundary links and discuss examples arising from group-theoretic fusion categories.", "id": "Paper/70714", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70714"}, {"title": " Gordon-Litherland matrices (not) from 1-circle Kauffman states ", "webprogram_exclude": "0", "session_ids": ["Session/18384"], "source_sha256": "c80542497ba4d3de6e9064da7fcf67af8769c334c922355d099415262157a490", "withdrawn": "", "abstract": "Every connected diagram $D$ of a knot or link $K\\subset S^3$ has a 1-circle Kauffman state $x$, and the associated state surface $F_x$ has a nice Gordon-Litherland matrix $G$. When $D$ is alternating, $G$ can be taken to be of the form ${\\small \\begin{bmatrix} I_m&A\\\\ A^T&-I_n \\end{bmatrix}}$ for some $m$ and $n$ and some matrix $A$ of 1's and 0's.  We ask which matrices $A$ arise in this way (some do, some do not).  It is possible, and convenient, to reformulate our question in terms of spanning trees for planar graphs.  We will describe our approaches to these equivalent problems and the progress we have made.", "id": "Paper/70722", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70722"}, {"title": " Investigating Shifts in Socio‑Economic Factors Influencing Tourism to EU Destinations: Pre‑ and Post‑Pandemic Perspectives ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "2248b302ad8d6fbf07f68af79278a816b2d695b37c75ee4997c3b17f03a125b5", "withdrawn": "", "abstract": "The World Economic Forum publishes data known as the Travel and Tourism Development Index which measures tourism attractions based on different socio economic characteristics. This project focuses on the countries in the European Union and investigates different influential characteristics of tourism attractions. The Travel and Tourism Development data from two different time periods, representing pre and post pandemic eras, are investigated to evaluate any changes in the influential characteristics in the region. A mixture model based cluster analysis technique based on Gaussian distributions is applied to different rankings of a series of characteristics across different attractions, and compared with clustering results from hierarchical, prototype based, and density based clustering techniques. A series of non parametric tests are applied to evaluate uniformity of clusters. This poster discusses statistical modeling and its results to compare tourism attractions, as well as changes from the pre- to post-pandemic period within the European Union.", "id": "Paper/70726", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70726"}, {"title": " The Planar Ulam Floating Body Problem ", "webprogram_exclude": "0", "session_ids": ["Session/18266"], "source_sha256": "9428665913c62d8d44957a1a278212200e1b82839cc9c02927d9e11d29967147", "withdrawn": "", "abstract": "In my talk, I will discuss the Ulam Floating Body Problem: “Is a solid of uniform density which will float in water in every position a sphere?”, the Scottish Book. I will focus exclusively on the planar case, which can be formulated by considering the cross-section of a long cylindrical body of uniform relative density $\\rho<1$ placed in water.\n\nThe planar problem leads to a rich interplay between geometry, differential equations, and the analysis of floating conditions. In particular, I will discuss how the requirement that the body float in equilibrium in every orientation imposes strong geometric constraints on its boundary. These constraints can be expressed in terms of a perimetral density, $\\sigma$, which measures the portion of the boundary lying below the waterline in equilibrium.\n\nI will present recent results obtained jointly with Maksim Kosmakov and Pavel Zatitskii for the perimetral densities $\\sigma=\\frac16,\\,\\frac18,\\,\\frac38$.\nThese results establish new rigidity phenomena for the corresponding planar floating body problem and extend the range of densities for which one can prove that the floating conditions force strong geometric restrictions on the body. I will also briefly discuss the ideas behind the proofs, including the reduction of the geometric problem to a system of differential equations and the role of symmetry and dynamical-systems methods.", "id": "Paper/70727", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70727"}, {"title": " Image-Based Multiscale Modeling of Pulmonary Hemodynamics from Arteries Through Tissue to Veins ", "webprogram_exclude": "0", "session_ids": ["Session/18309"], "source_sha256": "4e721cd329bc9098a78abfc5ae54cb546c0a361381bff86a0f45ac2a77518bab", "withdrawn": "", "abstract": "Multiscale computational models built on anatomically accurate geometries let researchers study blood flow through the lungs and characterize the hemodynamics of the pulmonary circulation. Existing studies often treat arterial flow, tissue perfusion, and venous return separately, which leaves a gap in frameworks that connect them within a single model. This study develops a coupled model that links a one-dimensional (1D) pulmonary vascular network and a three-dimensional (3D) tissue perfusion model. In the vascular network containing the larger arteries and veins, flow and pressure are computed using a 1D fluid dynamics model derived from the Navier-Stokes equations for incompressible flow. The lung tissue is modeled as a porous medium, with flow driven by pressure differences between sources at the ends of the terminal arterial vessels and sinks where blood drains into the venous network. A 3D Darcy-type equation governs this pressure-driven transport and is solved over the full lung volume using the finite element method. Blood collected at the venous sinks then enters the 1D venous network, and the solver propagates this flow backward through the converging venous tree until it reaches a single outlet at the main pulmonary vein. This closes the circulation from the arteries through the tissue to the veins and allows mass conservation to be maintained across the whole system. The lung volume, terminal vessel locations, and vascular geometry are obtained by segmenting a CT image from a healthy adult. The model predicts pressure fields and regional blood flow throughout the lung and gives an integrated view of arterial flow, tissue perfusion, and venous return. It provides a basis for future studies of pulmonary vascular conditions such as pulmonary hypertension.", "id": "Paper/70730", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70730"}, {"title": " Quantification of residual finiteness in groups and their computability aspects ", "webprogram_exclude": "0", "session_ids": ["Session/17922"], "source_sha256": "458443e629f7e2646c0b6ff4a0f1387c3238fa722f9549c9fda53ae1a3cd74a0", "withdrawn": "", "abstract": "For a finitely generated residually finite group $G$, let $\\rho(w)$ be the least size of a finite quotient of $G$ in which a word $w$ survives ($\\rho(w)=1$ if $w=_G 1$); the residual finiteness growth $\\mathrm{RF}_G(n)$ is the maximum of $\\rho$ over words of length at most $n$. Using a robust family of two-generated groups of derived length $3$, we show that every non-decreasing large enough $f$, up to standard equivalence, can be realized as the residual finiteness growth of such a group. We then give a more specialized description of such growth functions for groups with solvable word problem. As an application, we will also discuss a conjugacy separable group with decidable word problem and undecidable conjugacy problem (answering a question of Minasyan) and, as a joint work with E. Rauzy, a residually finite group with co-c.e. word problem that is not realizable as a group of computable permutations of $\\mathbb{N}$ (answering a question of Nies).", "id": "Paper/70731", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70731"}, {"title": " Volumes of Complex Solids: Ancient Ideas, Modern Algebra, and Spatial Reasoning ", "webprogram_exclude": "0", "session_ids": ["Session/18554"], "source_sha256": "ed9f711cc71697cd1a48687ccf8b4c59153af1090da3843e715025a6f516d593", "withdrawn": "", "abstract": "This presentation examines historical and modern methods for estimating the volumes of complex geometric solids, drawing directly on the pedagogical concepts developed in the book \"Methods of Solving Solid Geometry Problems.\" We compare the mechanical, infinitesimal methods of antiquity with modern computer algebra tools to demonstrate how spatial intuition can be systematically developed in the mathematics classroom.\nFirst, we analyze Archimedes' equilibrium method for equilibrating concentric sections of a sphere, cone, and cylinder, demonstrating how ancient Greek ideas laid the foundation for integral calculus. We then compare these classical geometric proofs with modern algebraic and computational methods. Specifically, we explore the step-by-step decomposition of semiregular polyhedra, such as the cuboctahedron. Combining ancient mechanical heuristics with modern methods, this study offers concrete strategies to help students develop spatial imagination and learn how to solve stereometric problems.", "id": "Paper/70732", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70732"}, {"title": " Surjectivity of Galois representations of products of elliptic curves over function fields ", "webprogram_exclude": "0", "session_ids": ["Session/17450"], "source_sha256": "4e9c29fc367b8c097525e4c755a135a7608d804642704360834bccdd561e8181", "withdrawn": "", "abstract": "We discuss the surjectivity of Galois representations associated to products of non-isotrivial, non-isogenous elliptic curves over certain function fields of characteristic zero. Our main result generalizes a version of Igusa's theorem due to Cojocaru $\\&$ Hall and is related to work of Bakker $\\&$ Tsimerman, Griffon $\\&$ Pazuki, Masser $\\&$ W\\\"{u}stholz, and Serre.", "id": "Paper/70733", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70733"}, {"title": " Wave decay for variable speed wave equations ", "webprogram_exclude": "0", "session_ids": ["Session/17999"], "source_sha256": "c3bfa400572c71c2f820a557b4206432a8f8c57c58bf88e5716eacca26048ac7", "withdrawn": "", "abstract": "We will discuss recent work establishing logarithmic local energy decay for wave equations with variable wavespeed. Our approach relies on a study of the weighted resolvent of the associated semiclassical Schr\\\"odinger operator with a potential which is assumed to have minimal regularity and decay. We establish a Carleman estimate in order to obtain bounds on the weighted resolvent.", "id": "Paper/70734", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70734"}, {"title": " From Curriculum Reform to Open Digital Mathematics Textbooks: A Teacher-Driven Approach in Kenya and Beyond ", "webprogram_exclude": "0", "session_ids": ["Session/19341"], "source_sha256": "199d9908a75dbfad0a236c75c041e7f577d87ffa0ba7dfe2446b49a5132f6c11", "withdrawn": "", "abstract": "From 2017, Kenya's Ministry of Education implemented the Competency Based Curriculum (CBC) which was to overhaul the education system across all levels from pre-primary through to tertiary education. The new curriculum introduced a new three year school level, Junior School, and restructured the four year high school to a three year senior school. The main challenge to implementation of the curriculum was lack of trained teachers for the junior schools, inadequate retraining of teachers to deliver the CBC, lack of proper infrastructure development and teaching and learning resources. Mathematics was the most affected subject, especially in Junior school where some schools did not have math teachers, and teachers of other subjects had to cover for this shortcoming. To help mitigate these challenges, we started a project on authoring open digital math textbooks in line with CBC curriculum, with interactive content to help learners conceptualize the concepts and with digital exercises that have automated feedback. The project has since expanded to senior schools and through constant engagement by teachers, we created a teacher version with template lesson plans and delivery guides. \n\nA key feature of the project is the active involvement of mathematics teachers as co-developers. Teachers contribute their classroom experience to identifying learner needs, reviewing materials, and testing resources with their students. Feedback from teachers and learners is used iteratively to improve the textbooks and ensure that they are relevant to diverse classroom contexts, including differences in technology access and digital literacy.\n\nIn this presentation, we will share lessons from the development and classroom use of these resources, including the opportunities and challenges of teacher participation, digital content development, and open educational practices. Building on the Kenyan experience, the project is now extending to open digital undergraduate mathematics textbooks designed for reuse and adaptation across African universities. The broader vision is to support collaborative, sustainable, and locally responsive mathematics education through openly developed resources.", "id": "Paper/70739", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70739"}, {"title": " Selection of pushed pattern-forming fronts ", "webprogram_exclude": "0", "session_ids": ["Session/18109"], "source_sha256": "e142bfc364332eb243cfe359a98c75fe907a98be8a95e1340657ccc074856e43", "withdrawn": "", "abstract": "Complex coherent structures in physical systems often form after a homogeneous background state becomes unstable. When the transition out of the unstable state is seeded by a spatially localized perturbation, this perturbation grows and forms an invasion front, which propagates into the unstable state and selects a new state in its wake. The marginal stability conjecture asserts that the propagation speed is the unique speed for which the associated invasion front solution is marginally spectrally stable. In many cases, propagation at a fixed speed combines with oscillatory dynamics in either the leading edge or the wake of the invasion process to generate a spatially periodic pattern. Universal wavenumber selection laws predict the wavelength of this pattern through an appropriate combination of the selected speed and the frequency of the temporal oscillations. We explore this phenomenon in the FitzHugh-Nagumo system, a prototypical model for large amplitude pattern formation. In this setting, we give the first rigorous proof of the marginal stability conjecture and associated wavenumber selection laws for any pattern-forming invasion process.", "id": "Paper/70741", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70741"}, {"title": " A Singularity Theorem on Noncommutative Optimal Polynomial Approximants ", "webprogram_exclude": "0", "session_ids": ["Session/17756"], "source_sha256": "824005193fe3f7b001b66cc6eeab8ed3f7e96c31b06da4217abd9a5125b0c78b", "withdrawn": "", "abstract": "In signal processing, undoing a filter $f$ means applying its inverse $1/f$, which is often impractical, so one instead seeks a polynomial $p$ that makes $pf$ as close to 1 as possible. For a function $f$ in the Hardy space $H^2$ (the space of analytic functions on the unit disk whose Taylor coefficients at $0$ are square-summable), the optimal polynomial approximant (OPA) of degree $n$ is the polynomial $p$ minimizing $\\lVert pf - 1 \\rVert$ among all polynomials of degree at most $n$. A classical result shows that they have no zeros in the closed unit disk. \n\nIn this talk, we consider the noncommutative analogue. We replace complex numbers with tuples of matrices, polynomials with free polynomials in noncommuting variables, and $H^2$, with the full Fock space. In this setting, a \"zero\" of $p$ is a matrix tuple $X$ at which $p(X)$ is singular (non-invertible as a matrix). By leveraging an inner-outer factorization, we readily show that NC-OPAs are nonsingular on the row ball (the set of all tuples of matrices that act contractively as a row). Moreover, the full Fock space enjoys a robust theory of orthogonal polynomials, and we leverage this to show that NC OPAs are in fact nonsingular on the boundary of the row ball as well. In many ways, our setting is the \"correct\" multivariable generalization of classical Hardy space and the strength of our results is a demonstration of this fact.", "id": "Paper/70744", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70744"}, {"title": " A Modeling-First Introduction to Differential Equations for First-Year Calculus Students ", "webprogram_exclude": "0", "session_ids": ["Session/18271"], "source_sha256": "9bd4cbee34f85119975838d23d0e9eae98b670c370a5cc2b082332cac9766c2d", "withdrawn": "", "abstract": "This presentation describes a modeling-first approach to teaching differential equations in a first-semester calculus course. Students with a high-school mathematics background can develop a meaningful understanding of differential equations, including systems of differential equations, when they begin with dynamic systems, rates of change, and model structure rather than symbolic solution techniques.\n\nStudents use Insight Maker (\\url{insightmaker.com}), an online system-dynamics modeling environment, to construct stock-and-flow diagrams for problems involving interacting quantities, feedback loops, and changing rates. They identify stocks, flows, units, and assumptions that justify relationships among variables. Students then translate these diagrams into differential equations or systems of differential equations with initial conditions and move repeatedly among graphical models, equations, numerical simulations, and interpretations in context.\n\nNumerical simulation provides an accessible introduction to the ideas underlying scientific computing. Rather than treating parameters as fixed constants to insert into a solved formula, students vary parameters and initial conditions, compare simulated behavior, and explain how changed assumptions affect short- and long-term outcomes. Feedback-loop diagrams help students recognize how reinforcing and balancing processes produce exponential growth, constrained growth, equilibrium behavior, and other qualitative phenomena.\n\nI will share activity structures and instructional scaffolds that help first-semester calculus students build, revise, and analyze differential-equation models. I will also discuss student deliverables and assessments that ask students to justify model structure, connect a flow diagram to its associated differential equations, interpret numerical output, and communicate the consequences and limitations of their assumptions. This approach innovates undergraduate differential-equations teaching by integrating systems thinking, online modeling software, and numerical methods before symbolic techniques become the primary lens for understanding dynamic systems.", "id": "Paper/70745", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70745"}, {"title": " On Quad-256 - Classifying Quad-Cap Structures in AG(8, 2) ", "webprogram_exclude": "0", "session_ids": ["Session/18370"], "source_sha256": "3255d13f2728f9bd09f5cd71c5091a8bbd12515f619f283a380a0ec939cddb4b", "withdrawn": "", "abstract": "The card game \\textit{Quads} forms a model for the finite affine geometries AG(n,2). A quad corresponds to a plane in this geometry, and a cap is a quad-free set of points. We examine the application of coding theory in classifying, up to affine equivalence, all k-caps in AG(8, 2) of size $k \\geq 10$, up to k = 18, the maximum size for k-caps in dimension 8. By iterating through every possible combination of cards that produces a k-cap, we assign each cap a code. We find equivalence classes for k-caps for k = 10, 11, 12, 13, 14, 17, and 18, by comparing k-caps with equivalent codes and attempting to construct an explicit mapping between them.", "id": "Paper/70746", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70746"}, {"title": " Shifting Invasion Dynamics: Temperature Effects on Spongy Moth Population Establishment ", "webprogram_exclude": "0", "session_ids": ["Session/19353"], "source_sha256": "aac6805fad91610fcb186ba35f86652194ed5369da88ed7003560315a8b33d68", "withdrawn": "", "abstract": "The spongy moth \\textit{Lymantria dispar} is an invasive forest pest that has produced significant ecological damage across the United States. Temperature plays an integral role in shaping its invasion front in both the northern and southern regions. Climate change may simultaneously increase establishment along the northern boundary while imposing thermal constraints on populations along the southern boundary. We develop a discrete population model incorporating temperature-dependent fecundity, stage-specific survival rates, and the Allee threshold. In this talk, I compare the resulting population dynamics across northern and southern regions under historical and projected temperature scenarios. Model simulations reveal bistable dynamics in which establishment or collapse may occur depending on initial population density, with warming shifting these dynamics differently across the invasion front.", "id": "Paper/70747", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70747"}, {"title": " Wolff’s Ideal Theorem in the Multiplier Algebra of the Weighted Dirichlet Space Setting ", "webprogram_exclude": "0", "session_ids": ["Session/18305"], "source_sha256": "32e2ba24ec77f4150a29ef79ffa2ee57325e6302b71ec6ffa1d7a48763871869", "withdrawn": "", "abstract": "We consider T. Wolff's ideal theorem in the multiplier algebra of the weighted Dirichlet space setting. This generalizes the previous result of D.P. Banjade, H. Kwon, T. Neal, and A. Wittig on the unweighted case. That talk is based on joint work with D.P. Banjade and H. Kwon.", "id": "Paper/70751", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70751"}, {"title": " Mathematics to Save Honeybees: Modeling Colony Dynamics and Survival ", "webprogram_exclude": "0", "session_ids": ["Session/18325"], "source_sha256": "21bc62edbf19cd5696e8c638b4589a5600fbeb38bedd7aefeca3d5496f1e531b", "withdrawn": "", "abstract": "Honeybees (Apis mellifera) are essential to biodiversity and agriculture, pollinating nearly 85\\% of flowering plants and contributing an estimated \\$15–20 billion annually to U.S. crop production. Yet, recent widespread colony declines pose serious threats to both ecosystems and food security. In this talk, I will demonstrate how mathematical modeling offers powerful tools to uncover the mechanisms shaping honeybee colony growth, persistence, and collapse. Building on tractable frameworks-including nonlinear, nonautonomous, and delay differential equations-we integrate empirical data with theory to analyze the impacts of parasites, environmental variability, and pesticide exposure. These models reveal key drivers of colony collapse and provide actionable insights for mitigating Varroa infestations in changing environments and improving colony management. If time permits, I will discuss how mathematics powered with AI extend beyond honeybees to broader questions in complex adaptive systems, including information flow in social insect colonies and parallels in human collective decision-making.", "id": "Paper/70753", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70753"}, {"title": " Numerical methods for optimal control of convection-dominated equations ", "webprogram_exclude": "0", "session_ids": ["Session/17872"], "source_sha256": "f573440906c961caa4abe7ef7f1cc17a2bf68144bbe24f85eeb313b90e71f51c", "withdrawn": "", "abstract": "We introduce several stabilized methods, including continuous and discontinuous Galerkin methods, for solving optimal control problems constrained by second-order convection-dominated equations using a saddle-point reformulation. We then discuss different strategies for analyzing these methods. Numerical results are provided to support our theoretical findings.", "id": "Paper/70755", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70755"}, {"title": " Theory of Orthogonal Polynomials on the Sierpinski Gasket ", "webprogram_exclude": "0", "session_ids": ["Session/18305"], "source_sha256": "84913825707beb103016cce8020f3da384e1537ea94513486b054a8e7ecd2391", "withdrawn": "", "abstract": "We develop a complete theory of orthogonal polynomials on the Sierpi\\'nski Gasket. This work is based on spectral analysis of the fractal Laplacian developed by Kigami. For the family of symmetric orthogonal polynomials, we prove a fractal analog of the classical three-term recurrence with $2 \\times 2$ block matrix coefficients. We further develop spectral analysis of the corresponding block Jacobi operator and derive coefficient bounds. We extend existing spectral theory for the family of antisymmetric polynomials by proving unitary correspondence between the Green's operator and multiplication in an associated real polynomial space.", "id": "Paper/70756", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70756"}, {"title": " Modeling Cancer Dynamics and Empowering Students with Analytical and Computational Methods ", "webprogram_exclude": "0", "session_ids": ["Session/17765"], "source_sha256": "2455b6fa3d3144acc691f1a6c8060a0c138cb175ec5f4d3d4a1ffe44d8adcadc", "withdrawn": "", "abstract": "Ordinary differential equations (ODEs) provide a powerful mathematical tool for deciphering complex biological phenomena, particularly the intricate evolutionary dynamics of cancer. This presentation demonstrates how nonlinear Lotka-Volterra-type ODE systems can model competitive interactions between heterogeneous cell populations, such as drug-sensitive and drug-resistant cancer cells, in the context of cancer therapy. Using analytical methods including linear stability analysis, phase portraits, and bifurcation theory, we can identify critical thresholds and tipping points for the system. These insights are crucial for developing optimal, adaptive treatment regimens that prevent competitive escape and minimize chemoresistance, ultimately improving patient outcomes.\nBeyond clinical applications, this framework addresses an important pedagogical need: motivating students to master rigorous mathematical theory. We discuss how applying the abstract theory of ordinary differential equations to complex biological applications, combined with practical computational tools, transforms student learning. By simultaneously training students in precise analytical inferences and digital simulations, they receive immediate visual and numerical feedback. This two-pronged pedagogical approach bridges the gap between pure theory and applied data science, significantly increasing student engagement and preparing the next generation of interdisciplinary researchers.", "id": "Paper/70759", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70759"}, {"title": " The Forest Analytics for Carbon Tracking (FACT) Tool ", "webprogram_exclude": "0", "session_ids": ["Session/18327"], "source_sha256": "451cabf723c549a4db84dee77154f58ab8969efe6fe9815fc1c0b7248b42605f", "withdrawn": "", "abstract": "This talk provides an introduction to the new FACT platform (beta release) for forest analytics and forecasting, along with a detailed look at the mathematical modeling behind the harvested wood product tool.  FACT is a science-based platform that brings standardized forest and harvested wood product data into a single, transparent place at no cost to users.  It includes a Landscape tool, a Custom Forest Inventory tool, a Default Forest tool, a Harvested Wood Products tool, a Displacement Factor tool, and an Embodied Carbon tool.  These tools provide users the ability to evaluate forest carbon inventories, dynamics, and harvesting activities in user-defined areas of the US, providing a comprehensive “cradle to grave” outlook of forest carbon.", "id": "Paper/70765", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70765"}, {"title": " Exploring Boomerang Fractions ", "webprogram_exclude": "0", "session_ids": ["Session/18211"], "source_sha256": "c8ef76c9909bc68d8a514a6a397314f0003339da9b2489fb0efbfb8857678743", "withdrawn": "", "abstract": "Boomerang Fractions are sequences of fractions that start and (hopefully) end at 1\nwhile following several rules. First, a specific fraction $m/n$ is selected for the\nentire sequence. The sequence always starts at 1, and the second element of the\nsequence is always $1+m/n$. To obtain subsequent elements of the sequence, we may\neither add $m/n$ to the current value OR take the reciprocal. The goal is to find a\nsequence that returns to 1 as quickly as possible.\n\nStudents as young as 4th graders can easily conjecture and prove many different\nstatements about Boomerang Fractions, yet the general question remains open. Math\nCircle students are likely to be able to make publishable progress on aspects of this\nproblem. We present some new approaches to Boomerang Fractions that exemplify the\nkinds of results students may be able to find.", "id": "Paper/70766", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70766"}, {"title": " Immune Memory and Antibody Dynamics in Multi-Strain Infectious Disease Models ", "webprogram_exclude": "0", "session_ids": ["Session/19359"], "source_sha256": "9654d715897e8f7a5fdeb53250e10480f3f5ce351427cc0e77b9c7045aaf5504", "withdrawn": "", "abstract": "Immunity acquired through infection or vaccination against many infectious diseases wanes over time and can be boosted by re-exposure to the pathogen or antigen. For multi-strain pathogens with immune-mediated interactions, such as cross-protective immunity and antibody-dependent enhancement (ADE), modeling waning immunity is complicated by the need to account for infection history. Here, we extend a differential equations modeling framework that explicitly tracks population-level antibody dynamics, a measurable component of the immune response, to multi-strain pathogens and cross-reactive antibodies. Specifically, we model primary and secondary infections, with infection risks modulated by an antibody-dependent susceptibility probability function that distinguishes among naive, partially cross-protected, and ADE-prone immune states. We systematically investigate how the duration and strength of cross-immunity and ADE affect the amplitude and periodicity of epidemic behavior. Applied to dengue virus transmission, our model generates multi-annual cycles consistent with empirical observations under conditions similar to those considered in prior work, although the influence of short-lived cross-immunity is substantially greater than that of ADE. We further extend the model to allow homologous immunity to wane, permitting reinfection with a previously encountered serotype over longer time scales. This extension provides a framework for examining how short-lived heterologous cross-immunity and slower serotype-specific waning immunity interact to shape long-term dengue dynamics. Overall, our model provides a flexible framework that bridges individual-level immunity and population-level transmission for investigating immune-mediated interactions in dengue and other multi-variant diseases.", "id": "Paper/70767", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70767"}, {"title": " An Evolving Mathematical Model of a Mid-Power Rocket ", "webprogram_exclude": "0", "session_ids": ["Session/18271"], "source_sha256": "8ea0701bf14d851e4b298e2d2f92a08b29a34d980d81834938954de294b44ae3", "withdrawn": "", "abstract": "We have been working on a mathematical model of a rocket vehicle with a thrust forcing function, using a first order nonlinear ODE with a piece-wise thrust function corresponding to an actual mid-power (160 Ns impulse) rocket motor. Analysis of the flight velocity datasets for the powered portion of the flight show an approximate error of 16\\% between the experimental data and the model under an assumed coefficient of drag.  We have extended the model to include the coasting phase prior to parachute release and we are testing different nose cones with known drag coefficients to try to experimentally differentiate normal drag on the nose cone from viscous drag on the entire rocket. The mass of the propellant accounts for approximately 10\\% of the mass of the entire rocket. We are also investigating the measurements of the propellant burn rate to include a variable mass in the model, which currently assumes a constant mass. This is a progress report.", "id": "Paper/70770", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70770"}, {"title": " CM elliptic curves, QM abelian varieties, and vertically entangled 2-adic groups ", "webprogram_exclude": "0", "session_ids": ["Session/19367"], "source_sha256": "ce9985ba3ba788e9cb2718a007d0d864feee66489d4279fe7923d911403341c3", "withdrawn": "", "abstract": "Consider the elliptic curve $E$ given by the Weierstrass equation $y^2 = x^3 - 11x - 14$, which has complex multiplication by the order of conductor $2$ inside $\\mbz[i]$.  It was recently observed in a paper of Daniels and Lozano-Robledo that, for each $n \\geq 2$, $\\mbq(\\mu_{2^{n+1}}) \\subseteq \\mbq(E[2^n])$.  We prove that this (a priori surprising) ``tower of vertical entanglements'' is actually more a feature than a bug:  it holds for any elliptic curve $E$ over $\\mbq$ with complex multiplication by any order of even discriminant.  Furthermore, we prove that the same phenomenon holds for any abelian surface with potential quaternionic multiplication by an order in a quaternion algebra with even discriminant.", "id": "Paper/70771", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70771"}, {"title": " A spectral analysis of tree based Markov chains for redistricting problems ", "webprogram_exclude": "0", "session_ids": ["Session/18310"], "source_sha256": "bee4cdc71a40467f69a41970eaeb29e2c1b8fc4ac1317bb75a619eff76119568", "withdrawn": "", "abstract": "We analyze existing Markov chain models that employ spanning trees/forests used in redistricting from a spectral graph theory/Markov Chain Monte Carlo dynamics perspective. We do this by considering completely enumerable models for redistricting plans and constructing explicit transition probabilities. Working in both real-world data sets consisting of a subset of the counties in the state of North Carolina as well as in synthetic data sets, we observe and analyze various remarkable properties related to diffusion and sampling on the state space.  Our findings give some insight into the strengths and weaknesses of existing methods for considering congressional gerrymanders, as well as suggesting possible tools for tackling computational challenges in larger data sets on the scale of state-wide elections.  In such settings, it is not computationally feasible to enumerate all possible probability transitions between states in the state space of districting plans as in all the examples considered here.  This is joint work with Greg Herschlag, Jonathan Mattingly and Andrew Sun.", "id": "Paper/70772", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70772"}, {"title": " A Sharp Flexibility/Rigidity Threshold for the Isotropic Landau Equation ", "webprogram_exclude": "0", "session_ids": ["Session/18306"], "source_sha256": "8e1334226dd627a56b6ea8c276e552a5d5816972fdaaa83b7ac084b30d0ebeda", "withdrawn": "", "abstract": "In this talk I will discuss a sharp rigidity/flexibility threshold for stationary solutions of the Krieger--Strain equation, an isotropic model of the Landau--Coulomb equation. More precisely, there are nontrivial wild solutions lying in $L^{p}(\\mathbb{R}^3)$, $p < 6/5$, while solutions lying in $L^{6/5}(\\mathbb{R}^3)$ must be identically zero. These results are the first of their kind in kinetic theory. This talk is based on joint work with Will Golding and Matt Novack.", "id": "Paper/70775", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70775"}, {"title": " The Euler Characteristic Transform in Deep Learning: Expressivity and Representation ", "webprogram_exclude": "0", "session_ids": ["Session/18353"], "source_sha256": "d861d154eed0ed84a3ee099cfaf7af56c205d29de78073cea3706f72c366b044", "withdrawn": "", "abstract": "The Euler Characteristic Transform (ECT) records the Euler characteristic of directional sublevel sets, providing a complete invariant for geometric simplicial complexes when all directions are considered. This talk explores its role in understanding and designing geometry-aware neural networks.\n\nFirst, we introduce the Geometric Simplicial Weisfeiler–Lehman (GSWL) test, which incorporates vertex coordinates into simplicial color refinement to distinguish complexes with identical connectivity but different embeddings. GSWL bounds the expressivity of geometry-aware simplicial message passing, with matching discriminating power attainable on fixed finite families. Combined with the ECT, this yields a geometric expressivity characterization and an approximation framework.\n\nSecond, we examine how ECT encoding and aggregation shape representation learning. We introduce a continuous encoding based on vertex-level Euler-characteristic changes and compare six architectures for aggregating information across directions. Across six classification benchmarks, continuous encoding consistently improves accuracy, with controls attributing the gains to tokenization rather than additional model capacity. Encoding matters more than aggregation architecture in these experiments, while also shaping which architectural biases are beneficial. Together, these works connect theoretical expressivity with practical representation design.", "id": "Paper/70779", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70779"}, {"title": " A Comprehensive Study of Completion of Cofinite Algebraic Structures ", "webprogram_exclude": "0", "session_ids": ["Session/18241"], "source_sha256": "ad384c4611dd4848dd3375b340e1ee11f1682a8a28eaa9fc2558fcc6e01a01d8", "withdrawn": "", "abstract": "In this study, we consider cofinite topological structures, such as groups, rings, and modules.  We establish the necessary and sufficient conditions to establish the existence and uniqueness of their profinite completions.", "id": "Paper/70782", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70782"}, {"title": " Supporting Students Outside the Math Major via Standards-Based Grading and Inquiry Learning Techniques ", "webprogram_exclude": "0", "session_ids": ["Session/18476"], "source_sha256": "c6c5abd56e0ab90229064a5750076deba9cd420c7c5bb2e99395680b7d863719", "withdrawn": "", "abstract": "As interest increases in data science and artificial intelligence, the population of undergraduate students who rely on mathematical reasoning in their fields is rapidly increasing. However, students who take math courses to fulfill an external requirement rather than as their chosen field of study often enter these courses with a history of math-related anxiety or low confidence in the field. At UNC-Chapel Hill, a discrete math course was recently redesigned to meet the needs of students pursuing disciplines outside mathematics and statistics.  The redesign incorporated two major changes to improve student outcomes while supporting the development of mathematical confidence: an inquiry-based learning approach to the classroom, and a standards-based grading framework and assessment structure. This talk will report on the pilot offering of this redesign, focusing on how standards-based assessment practices and inquiry-based instruction can work together to support learners who do not typically view themselves as part of the mathematical community.\nThe pilot offering of the course brought in students with diverse backgrounds and areas of study, requiring no prerequisite coursework beyond elementary algebra. Beginning with logic and proofs and progressing to modeling and algorithms focused on discrete structures, the course sought to develop mathematical reasoning while emphasizing student-driven exploration and reflection, with particular attention given to improving students' confidence and sense of belonging alongside their proficiency.  Standards-based grading aimed to construct a system to reward consistent effort and growth throughout the course, making these priorities concrete and communicating them to students; inquiry-based learning complemented this approach by offering students ample opportunities to discuss material with each other and build a supportive class community.  Surveys administered at the beginning and end of the semester measured changes in students' attitudes toward mathematics, while recurring metacognitive reflections encouraged students to examine their own growth and learning processes.  These measures provide a lens through which to examine the effects of the course redesign on student confidence, belonging, and success in mathematics.", "id": "Paper/70785", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70785"}, {"title": " How can geometric combinatorics improve RNA folding predictions? ", "webprogram_exclude": "0", "session_ids": ["Session/18358"], "source_sha256": "b5d2613a7e82a259c50fe7edd3adabd788a3988f4321517ed5a532b644abd112", "withdrawn": "", "abstract": "Branching is a critical characteristic of RNA folding, yet challenging\nto predict correctly under the standard discrete optimization approaches.\nUsing methods from geometric combinatorics (convex polytopes and their\nnormal fans), we give a complete parametric analysis of the optimal\nbranching configurations under the current nearest neighbor thermodynamic\nmodel.  By `learning' better branching parameters, we can significantly\nimprove RNA folding prediction accuracy on well-defined families while\nalso illuminating why the general problems is so difficult.  \nBy reformulating our goal in view of this new insight, we demonstrate how further improvements may be possible.", "id": "Paper/70791", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70791"}, {"title": " Infinite tensors meet model theory ", "webprogram_exclude": "0", "session_ids": ["Session/17929"], "source_sha256": "b43e311671c787e5597661227dd6abea5adcc77dcb9e12ad14dc071763875e76", "withdrawn": "", "abstract": "We study the structures of tensors as the underlying dimension tends to infinity. Remarkably, once a suitable symmetry is taken into account (typically the infinite general linear group $\\operatorname{GL}$), these structures can be described in finite terms. A prime example is the space of infinite-by-infinite matrices of rank at most r: their defining equations are the $(r+1)\\times (r+1)$-minors, and all these are generated by one single minor up to the action of $\\operatorname{GL}$.\n\nIn this talk we introduce tensor spaces, a natural object that encodes an infinite tensor together with an intrinsic group of symmetries. After extending the notions of oligomorphic and omega-categorical to the linear setting, tensor spaces can be viewed as the linear analogue to the model theory of permutation groups. The theorem of Ryll-Nardzewski states that a countable structure is oligomorphic if and only if its theory is $\\omega$-categorical. We will present the linear analogue of the theorem of Ryll-Nardzewski for the case of tensor spaces equipped with two quadratic forms. The results are joint work with Andrew Snowden.", "id": "Paper/70798", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70798"}, {"title": " A 3D-1D Coupled Model for Contrast Agent Transport in the Brain ", "webprogram_exclude": "0", "session_ids": ["Session/18309"], "source_sha256": "843df484688a3f711436f968050dea6f5506ac16ea0230e739e6f49687c37601", "withdrawn": "", "abstract": "Contrast-enhanced imaging plays a central role in tumor diagnosis and grading, yet current clinical analysis relies on empirical signal processing with no knowledge of the underlying vascular geometry or transport physics. Our approach replaces this with a mechanistic forward model that predicts the spatial distribution of contrast from first principles. To do so, we construct a coupled 3D-1D advection-diffusion model implementing a discontinuous Galerkin scheme. The 3D tissue domain and 1D vascular network are extracted from BraTS MRI patient data. Transport in the vasculature is governed by a 1D advection-diffusion equation with a pressure-driven velocity field, coupled to a 3D diffusion-reaction equation in the surrounding tissue. The coupled system is discretized using a symmetric interior penalty discontinuous Galerkin method. We compare model predictions against T1-weighted contrast-enhanced MRI, which serves as the clinical gold standard for tumor characterization. A Morris screening sensitivity analysis is performed to identify which physiological parameters (including vascular permeability, diffusivity, and injection profile) most significantly drive the predicted contrast distribution. Preliminary results demonstrate that the physics-based model captures the spatial enhancement pattern observed in imaging and provides a quantitative framework for extracting tissue-level biomarkers from contrast data.", "id": "Paper/70799", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70799"}, {"title": " Exploring A Novel Derivation Method of Enzyme-Catalyzed Chemical Rate Equations ", "webprogram_exclude": "0", "session_ids": ["Session/19371"], "source_sha256": "d808c1fccf45adf098857426159a977b324153432f1ca6f46fe68e9a761906d9", "withdrawn": "", "abstract": "Deriving chemical rate equations is a core tenet in the study of enzyme kinetics in chemistry. Within the past century, multiple derivation methods have been introduced. The steady-state assumption method (Segel, 1975) is one of the more straightforward techniques, though it can become difficult to use with more complex enzyme-catalyzed reactions due to nonlinearities within its associated equations. A second method more suited to these complex reactions is called the King-Altman method (Segel, 1975), which utilizes techniques from matrix algebra to determine the associated rate equations. However, this second method can be time-consuming to apply to larger chemical reactions. A recent publication by Park in 2024 introduced a new rate equation derivation technique based on mean reaction time, i.e., the average amount of time it takes to complete a chemical reaction. Park provides an accessible formula to derive mean reaction time, and as proof of concept, applies the formula to the Michaelis-Menten equation. To the best of our knowledge, Park’s formula has not been applied to derive more complex types of enzyme-catalyzed reactions containing two substrates and/or two products. We extend Park’s work to show its efficacy in deriving these complex reactions. To verify our work, we compare our results to those obtained using the King-Altman method and also via comparison to published rate equations.", "id": "Paper/70801", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70801"}, {"title": " Cellular Homology of Watertight Models Part I ", "webprogram_exclude": "0", "session_ids": ["Session/18323"], "source_sha256": "bad9466aef7dd87d5cd411ac31f1c0e1f12e5fc7bc400053930a10bd6f90bcaf", "withdrawn": "", "abstract": "Computer-aided design (CAD) models are ubiquitous across engineering, architecture, manufacturing, and entertainment. Many of these models must possess specific geometric and topological properties tailored for downstream applications. One such property, commonly referred to as being “watertight,” intuitively means a model encloses a volume. Most definitions of a watertight model are equivalent to a two-dimensional manifold embedded in three-dimensional Euclidean space. This definition imposes both topological and geometric restrictions (an embedding is not self-intersecting) and can only be applied to models without interior geometry. To address these limitations, we introduce a novel, purely topological definition of a watertight CAD model. This talk begins with a brief background on CAD models and how they can be represented with regular CW complexes. We then formulate our new definition of a watertight CAD model using cellular homology and introduce “sheet decompositions,” a novel method for decomposing regular CW complexes. In part II of this talk, we utilize this framework to develop a fast algorithmic\nmethod to verify a CAD model is watertight.", "id": "Paper/70803", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70803"}, {"title": " Conductor-Discriminant Inequality for Tamely Ramified Cyclic Covers ", "webprogram_exclude": "0", "session_ids": ["Session/19367"], "source_sha256": "df1744683ad13af1935e46d7ce8a7400612748664c62bd099ffcfcfc6428d79b", "withdrawn": "", "abstract": "We consider $\\mathbb{Z}/n$-covers $X\\to\\mathbb{P}^1$ defined over discretely valued fields $K$ with excellent valuation ring $\\mathcal{O}_K$ and perfect residue field of characteristic not dividing $n$. Two standard measures of bad reduction for such curves $X$ are the Artin conductor of the minimal regular model of $X$ over\n$\\mathcal{O}_K$ and the valuation of the discriminant of an integral Weierstrass equation for $X$. We prove an inequality relating these two measures. Specifically, if $X$ is given by an affine equation $y^n = f(x)$ with $f \\in \\mathcal{O}_K[x]$ and $n\\mid\\deg(f)$, and if $\\mathcal{X}$ is its minimal regular model over $\\mathcal{O}_K$, then the negative of the Artin conductor of $\\mathcal{X}$ is bounded above by $(n-1)v_K(\\text{disc}(\\text{rad}(f))$. This extends previous work of Ogg, Saito, Liu, Srinivasan, and Obus--Srinivasan on elliptic and hyperelliptic curves.", "id": "Paper/70805", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70805"}, {"title": " Gravity beyond general relativity: a (quasi-)mathematical perspective ", "webprogram_exclude": "0", "session_ids": ["Session/18148"], "source_sha256": "211573c517309a00f21dbb644d555dadcfa0914ada1a1ce48babf8c8c3cbf513", "withdrawn": "", "abstract": "More than a century after its formulation, General Relativity stands firm as our best description of gravitational phenomena. However, theoretical and observational motivations invite us to explore classical theories of gravity beyond General Relativity. In this talk, I will give an overview of recent work in this field from a mathematical perspective. I will discuss the solution space of black holes (and their linear stability) in a broad class of theories of gravity, and give a bird's-eye view of recent work by the community on the well-posedness of the Cauchy problem in these theories.", "id": "Paper/70806", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70806"}, {"title": " A noncommutative Hardy space approach to linear independence of time-frequency shifts ", "webprogram_exclude": "0", "session_ids": ["Session/19339"], "source_sha256": "a5f25acf5749e58a1d278a1c63e0f8a3652fa54caabb2da113aeb4e744ce5d53", "withdrawn": "", "abstract": "In 1999, Linnell proved that if $\\Lambda \\subseteq \\mathbb{R}^2$ is a finite subset of a discrete subgroup, then $\\{e^{2\\pi i b x} g(x-a) : (a,b) \\in \\Lambda\\}$ is linearly independent for every nonzero $g \\in L^2(\\mathbb{R})$; the general Heil–Ramanathan–Topiwala conjecture is now known to be false. We use noncommutative Hardy space theory to give a new proof of Linnell's theorem and extend it to infinite combinations of time-frequency shift operators with $\\ell^1$ coefficients satisfying suitable support conditions.", "id": "Paper/70807", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70807"}, {"title": " Modeling and Forecasting Sea Surface Temperature Using Stochastic Differential Equations ", "webprogram_exclude": "0", "session_ids": ["Session/19322"], "source_sha256": "b2af6de5f1ecfbb61b19c3a4716e2a17822d20e4d477bd2686539c554714fb18", "withdrawn": "", "abstract": "Sea surface temperature (SST) exhibits a predictable seasonal cycle together with variability driven by unresolved atmospheric and oceanic processes. We present an observation-informed stochastic differential equation model that combines nonlinear relaxation toward a daily climatology with seasonally varying stochastic forcing. The model is numerically integrated using a stochastic Runge–Kutta method and evaluated across contrasting ocean regions using satellite-derived SST observations. The simulations reproduce the dominant seasonal warming and cooling patterns across datasets and regions, while seasonal modulation of the stochastic forcing helps capture annual variability. The framework provides a transparent and computationally inexpensive approach for SST simulation and forecasting.", "id": "Paper/70809", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70809"}, {"title": " On <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"4.803ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 2068 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">U(\\mathfrak h)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-55\" d=\"M107 637Q73 637 71 641Q70 643 70 649Q70 673 81 682Q83 683 98 683Q139 681 234 681Q268 681 297 681T342 682T362 682Q378 682 378 672Q378 670 376 658Q371 641 366 638H364Q362 638 359 638T352 638T343 637T334 637Q295 636 284 634T266 623Q265 621 238 518T184 302T154 169Q152 155 152 140Q152 86 183 55T269 24Q336 24 403 69T501 205L552 406Q599 598 599 606Q599 633 535 637Q511 637 511 648Q511 650 513 660Q517 676 519 679T529 683Q532 683 561 682T645 680Q696 680 723 681T752 682Q767 682 767 672Q767 650 759 642Q756 637 737 637Q666 633 648 597Q646 592 598 404Q557 235 548 205Q515 105 433 42T263 -22Q171 -22 116 34T60 167V183Q60 201 115 421Q164 622 164 628Q164 635 107 637Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJFRAK-68\" d=\"M88 427Q88 486 87 545T84 634T81 667Q81 673 82 673T89 676H94L117 600L200 661Q208 667 218 674T233 684L238 688L254 678Q222 646 216 637Q164 572 164 483V442V371Q187 390 244 431T312 478Q344 446 411 423L428 417L429 396Q434 297 434 218Q430 8 406 -34Q346 -111 262 -195L251 -205L249 -203Q248 -203 244 -199T236 -193Q226 -183 227 -182Q228 -182 244 -169T278 -140T301 -121Q330 -89 340 -22Q355 60 355 171Q355 200 353 244T348 321T344 354Q333 363 307 376T260 390Q241 390 179 350L164 341V121Q180 96 201 66L213 50Q210 46 172 11T131 -24Q130 -24 123 -11T102 25T77 65V78Q80 104 84 227T88 427Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-55\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"767\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJFRAK-68\" x=\"1157\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"1678\" y=\"0\"></use>\n</g>\n</svg>-Free <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"4.694ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex; margin-left: -0.041ex;\" viewBox=\"-17.5 -863.1 2021 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathfrak {sl}(2)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJFRAK-73\" d=\"M272 33Q284 33 290 70T296 138Q296 181 290 198T262 230Q257 232 246 232Q231 232 218 227T156 194L108 167L101 176Q90 192 75 219L69 230V284Q69 346 70 357V377L146 427Q181 450 202 464T223 477L225 476Q227 475 229 474Q231 472 242 466T270 450T296 431Q309 418 326 418Q342 418 361 429T392 450T403 459Q406 445 406 442Q406 440 384 421T338 382L316 363Q315 362 310 362Q292 362 251 371T173 396Q156 403 155 403Q143 386 143 342Q143 305 150 278T168 244Q171 242 181 242L190 243L315 300Q330 295 357 274Q358 273 362 270T366 266T369 261T372 253T373 239T374 217T374 185Q374 157 372 133T368 98T363 71T358 50L336 40Q288 20 255 2T211 -22T198 -29L190 -22Q181 -14 168 -3T138 19T104 38T70 46Q50 46 32 37T3 20T-9 11L-18 23L-1 41Q46 89 62 99T112 110Q141 110 157 103T225 62Q268 33 272 33Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJFRAK-6C\" d=\"M221 76L267 99Q268 98 269 96T271 88T270 82L262 76Q255 69 241 57T214 34L148 -20L98 56L99 89Q107 247 107 373Q107 494 101 621Q101 653 99 659V665L106 668L113 672L118 655Q122 642 131 617L138 597Q140 597 157 611L240 670L264 685Q265 685 270 680T276 674T269 667T247 647T219 617Q197 587 186 551T173 493T171 438Q171 376 175 282T179 147V117Q184 109 201 93T221 76Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJFRAK-73\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJFRAK-6C\" x=\"443\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"724\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-32\" x=\"1113\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"1614\" y=\"0\"></use>\n</g>\n</svg>-Modules of Finite Rank ", "webprogram_exclude": "0", "session_ids": ["Session/17666"], "source_sha256": "336aad49ac2327d39f21e1d51c742286a79527fa57a2548bb353e7a827be9106", "withdrawn": "", "abstract": "In this talk, we discuss non-weight $\\mathfrak{sl}(2)$-modules that are free of finite rank over $U(\\mathfrak h)$, where $\\mathfrak h$ denotes the Cartan subalgebra of $\\mathfrak{sl}(2)$. In particular, I will present a classification of simple scalar-type $U(\\mathfrak h)$-free modules of rank $2$ and introduce several families of simple finite-rank $U(\\mathfrak h)$-free modules. This talk is based on joint work with D. Grantcharov and K. Zhao.", "id": "Paper/70812", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70812"}, {"title": " Shape Derivatives for PDE-Constrained Shape Optimization of Obstacle Problems ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "4bfdc5fcd734093a9c9fdc95b4219d81556df9f5874cb34d32a6f9f39ddaebe0", "withdrawn": "", "abstract": "In this project, we implement an alternative method to solve PDE-constrained shape optimization problems with contact. Traditionally, the approach to these problems has employed two particular techniques that we aim to improve: 1) updating the mesh for each iteration of the algorithm and fitting it to the shape boundaries, and 2) discretizing the PDE system before setting up the optimization problem. Updating the mesh and fitting it to the boundaries is computationally expensive and can lead to ill-conditioned elements, while discretizing before optimizing can lead to error in the final solution. To address the first issue, we adapt the Cut Finite Element approach (CutFEM) to fix a background mesh and avoid unnecessary mesh regeneration. For the second, we incorporate the optimization problem into the continuous setting prior to discretizing. We do so by finding an expression for a \"shape derivative\" of the objective functional that is translated into the finite element formulation prior to running a simple gradient-descent algorithm. Our numerical experiments consider several obstacle functions, loads, and target regions, and the solutions show convergence of the same order as the existing methods. Furthermore, the constant mesh used throughout the computations has a lower condition number than under regeneration with an unfixed mesh. We will also compare the optimize-then-discretize approach used here with a standard discretize-then-optimize approach, where the fully discrete objective is differentiated directly. This comparison will help determine whether the CutFEM stabilization and the changing cut geometry cause the two computed gradients to differ.", "id": "Paper/70813", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70813"}, {"title": " Methods for the Realizability Problem for Saturated Transfer Systems of Cyclic Groups ", "webprogram_exclude": "0", "session_ids": ["Session/18384"], "source_sha256": "1b417cc595b07dc45ed0a8d6c0c8009b1350fcfa04002414e75120bb92313915", "withdrawn": "", "abstract": "The linear isometries operad is famously a poorly-behaved beast. For a cyclic group $G$, it transforms collections of $G$-representations into a certain kind of relation on the subgroup lattice of $G$ called a saturated transfer system. This transformation is not necessarily monotone: More representations does not always create a coarser relation. We take new steps towards answering the following question: \"Which saturated transfer systems can be realized by a linear isometries operad?\" By closely inspecting algebraic data, we are able to construct a thread of order weaving through this chaos. In particular, we study when cosets of certain subgroups of $G$ are in the image of our collection of $G$-representations under an isomorphism between $G$ and its Pontryagin dual. We discuss such strategies, and what obstructions to their generalization reveal about the question itself.", "id": "Paper/70820", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70820"}, {"title": " Relatives of Waring’s Problem with Non-Integer Degree ", "webprogram_exclude": "0", "session_ids": ["Session/17913"], "source_sha256": "3998b8dfaf2ac4ffd1bf24670a26d35cd345f2206c6b4a7ec6409fec413af4e8", "withdrawn": "", "abstract": "In this talk we will consider relatives of Waring's problem with non-integer exponents and describe the similarities and differences between these and the classical version of Waring's problem. The prototypical problem of this type is to count, for fixed $\\tau > 0$ and non-integer $\\theta > 2$, the number of positive integer solutions $(x_1,\\ldots,x_s)$ to the inequality \n\\[ |x_1^{\\theta}+\\cdots+x_s^{\\theta}-\\Lambda| < \\tau \\] \nas the real variable $\\Lambda > 0$ tends to infinity. Of particular interest is to reduce the value of $s$ for which one may prove an asymptotic formula for this quantity. We will discuss the techniques developed to tackle such questions and possible connections to other problems.", "id": "Paper/70824", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70824"}, {"title": " Building an African Open digital Assessment Ecosystem with STACK: Transforming Undergraduate Mathematics Teaching and Assessment ", "webprogram_exclude": "0", "session_ids": ["Session/17812"], "source_sha256": "69d3b7afeaa3a62773fb512ee27ab5fa2a38e5b77f22f3895b1b1160b9bed3b7", "withdrawn": "", "abstract": "African public universities face persistent challenges in undergraduate mathematics such as  high student to lecturer ratios with no teaching assistants, inadequate learning resources, and limited opportunities for meaningful student engagement with content and timely feedback to formative assessment. These constraints make individualised formative assessment difficult, while conventional assessment often provides feedback too late to influence learning.\n\nFrom 2019, we piloted STACK (System for Teaching and Assessment using a Computer Algebra Kernel) as a scalable, open-source approach to mathematics teaching and assessment. STACK enables automatically generated mathematical questions, computer algebra based assessment, and immediate personalised feedback, providing students with opportunities for repeated practice while extending lecturers' capacity to support large cohorts.\n\nFrom initial piloting experiences in Kenya, STACK has now been successfully integrated across six African countries, and in some cases, universities have institutionalized the technology as a primary tool for formative assessment for undergraduate mathematics. To accelerate integration, we developed  open STACK question banks, reusable assessment resources, and shared digital courses, enabling institutions to collaborate and reduce duplication in content development.\n\nThe project further explores generative AI agents to support STACK question authoring, lowering technical barriers by assisting educators in creating, adapting, validating, and generating feedback for mathematical questions while retaining human pedagogical oversight.\nSustainability is supported by the establishment of an African STACK community, which has developed local expertise, strengthened institutional collaboration, and successfully organised African STACK conferences for four consecutive years. We will present the gains made through the integration of STACK to support the formative assessment of undergraduate mathematics across Africa and discuss future developments such as integrating STACK with other technologies for proof assessment.", "id": "Paper/70825", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70825"}, {"title": " Finding shape in data with trivial persistence ", "webprogram_exclude": "0", "session_ids": ["Session/18304"], "source_sha256": "6d298d5db2bf5fab68e1d7202767bf7c51f8923a80b7345c32864174b3dd1447", "withdrawn": "", "abstract": "For standard filtrations of simplicial complexes (Vietoris-Rips, Cech, Delaunay) on point clouds, persistent homology is invariant under isometry, which is any distance-preserving transformation. This invariant detects high-dimensional cycles in complexes but may not distinguish between generic clouds of unordered points in the plane [1].\n\nMotivated by these limitations, for any fixed Euclidean dimension, we developed a complete invariant that suffices to reconstruct any unordered cloud uniquely under rigid motion (a composition of translations and rotations), also with a Lipschitz continuous metric, all computable in polynomial time in the number of given points [2] .\n\nThe more recent invariants satisfy two extra practically important conditions. First, the inverse Lipschitz continuity requires that any small perturbation of an invariant value gives us two reconstructed point clouds that can be almost matched pointwise under rigid motion up to a fixed Lipschitz constant. Second, the realizability requires that we can sample an invariant value from a Euclidean subset described only by inequalities (without any equations), hence reconstructing a cloud from the invariant with 100\\% guarantee.\n \nThe latest result is the extension of the side-side-side theorem from school geometry to a simple isometry classification of 4 unordered points by a 4x3 matrix, which reveals new families of quadrilaterals in the plane in addition to parallelograms and rhombi [3, Theorem 5.3]. \n\nThe most general geo-mapping problem aims to geometrically describe the shape of any real data under practical equivalences [4, Problem 1.4.5]. \n\n[1] P.Smith, V.Kurlin. Generic families of finite metric spaces with identical or trivial 1-dimensional persistence. J Applied Comp. Topology, v.8, p.839–855 (2024).\n\n[2] V.Kurlin. Complete invariants of atomic clouds under rigid motion with Lipschitz continuous metrics in polynomial time. MATCH Comm. Math. Comp. Chemistry, v.97(2), p.379-428 (2027). \n\n[3] D.Widdowson, V.Kurlin. Pointwise Distance Distributions for detecting near-duplicates in large materials databases. SIAM Journal Applied Mathematics, v.86 (3), p.898-918 (2026).\n\n[4] O.Anosova, V.Kurlin. Geometric Data Science (290+ pages), arxiv:2512:05040, the latest version at https://kurlin.org/Geometric-Data-Science-book.pdf.", "id": "Paper/70826", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70826"}, {"title": " The impact of optional quiz retakes on college students’ performance and attitudes towards mathematics in an introductory calculus course ", "webprogram_exclude": "0", "session_ids": ["Session/19349"], "source_sha256": "4bd86e7843ef0dc442232bfe88703cdc9e3d08fb4d88d6f4d1aa8e6ad2a0493e", "withdrawn": "", "abstract": "Educators play an important role in developing students’ positive attitudes toward mathematics, modeling a disposition to do math, and demonstrating the value of math as a way of thinking (Professional Standards for Teaching Mathematics, 1991; Royster et al., 1999). Assessment practices can contribute to this development. In contrast to high-stakes traditional exams, which can induce stress and anxiety, alternative grading practices are promising assessment strategies for improving student success and well-being. However, these systems are not always easy to implement in large courses, and they also do not always receive buy-in from departments and faculty. Incorporating components of alternative grading can help mitigate some of these negative effects in courses where instructors continue to rely on high-stakes assessments. The implementation of frequent, low-stakes quizzes with optional retakes represents one such strategy.\n\nAs part of their Calculus redesign efforts to support students and instructors, the Foundational Course Transformation Academy (FCTA) mathematics team at Notre Dame chose to administer optional quiz retakes in their Calculus I course in the fall. Under this model, students are provided with class time to retake a previous quiz. \n\nOur study examines the quiz-retake model in more detail, focusing particularly on the connection between quiz retakes and students’ performance and attitudes toward mathematics. We use a mixed-methods research design to answer a more complete range of research questions. We use students’ course data (quiz grades, exam grades, and quiz retake participation) to investigate the relationships among initial quiz performance, participation in retakes, and subsequent quiz and exam performance. In addition, we use student interviews to examine how quiz retakes relate to students’ attitudes toward mathematics, conceptualized through Di Martino and Zan’s dimensions of emotional disposition, view of mathematics, and perceived competence. We also study how these attitudes may relate to students’ decisions to participate in retakes. \n\nIn this session, we describe the quiz-retake model and share preliminary findings on quiz retakes, performance, and attitudes toward mathematics.", "id": "Paper/70834", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70834"}, {"title": " Empowering Faculty Journeys in Teaching Gateway Mathematics Courses ", "webprogram_exclude": "0", "session_ids": ["Session/18236"], "source_sha256": "d1b737a6fe403170accc6affe1ea3536ef968dfc85453bce06d0c0d41bf41eb8", "withdrawn": "", "abstract": "Across the country, faculty are continuously reimagining gateway mathematics instruction.  Over the past two years, our Gates Foundation–supported project at Education Equity Solutions studied faculty who achieved high success rates in high expectation, high support gateway math classes. We interviewed dozens of instructors and observed 30 classrooms across varied contexts. Despite differences in setting, we found striking commonalities: faculty built learning communities that emphasized belonging, prioritized active learning for conceptual understanding, used growth oriented assessment, and fostered students’ identities as capable math learners. Importantly, most did not begin their careers teaching this way. In this talk, we will highlight how professional development and technical assistance helped them transform their practice, what messaging created urgency for change, and what supports enabled them to start and sustain continuous improvement.", "id": "Paper/70837", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70837"}, {"title": " recent results on linear and non-linear dispersal models in math biology ", "webprogram_exclude": "0", "session_ids": ["Session/18289"], "source_sha256": "18efc852265d4e250fc4846d0f3b8b6f1e715e6215c321baf698b66ff54369b8", "withdrawn": "", "abstract": "Species dispersal is ubiquitous in ecological systems. In this talk we present recent results on linear and non-linear dispersal models, formulated via patch systems. We also investigate extensions of these to the spatially explicit or PDE case. We discuss applications of our results to control efforts for invasive pests in the advent of habitat fragmentation and climate change, as well to certain novel applications in cardiac health.", "id": "Paper/70839", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70839"}, {"title": " Generalized Cipolla and Tonelli-Shanks Algorithms for Solving Artin-Schreier Equations in Finite Fields ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "ee2f5533b1538518da80bc9068cf9b584630dad09e8a8b7855a205ed6d71d7f5", "withdrawn": "", "abstract": "This paper presents two algorithms to solve an Artin-Schreier equation $x^p-x=a$ in a finite field $F$ of characteristic $p$ when a solution in $F$ exists. These algorithms are adaptations of Cipolla's algorithm and the Tonelli-Shanks algorithm for solving $x^2=a$ in $\\mathbb{F}_p^{\\times}$ for odd primes $p$ when $\\left(\\frac{a}{p}\\right)=1$. Our analog of Cipolla's algorithm directly constructs a solution of $x^p-x=a$ in $F$ by working in the field $F[u]/(u^p-u-b)$ for any $b$ in $F$ with $\\text{Tr}_{F/\\mathbb{F}_p}(b)\\ne 0$. Our analog of the Tonelli-Shanks algorithm works in $F$ and iteratively reduces an ``error term'' into progressively smaller subfields of $F$ with $p$-power degree over $\\mathbb{F}_{p}$.", "id": "Paper/70842", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70842"}, {"title": " Diving Deeper into Rational Tangles ", "webprogram_exclude": "0", "session_ids": ["Session/17961"], "source_sha256": "c5d1307982b0773ecfd9ba56cd279f652a0f8285478938fab4d797d27b268019", "withdrawn": "", "abstract": "Rational Tangles is a topic involving two ropes and four dancers. As the dancers\nDo-Si-Do and Turn 'Em Round, the ropes create a tangle that can be named using\nrational numbers. During our summer Math Circle for middle and high school students,\nwe dove deeper into questions such as why this works, and how rational tangles relate\nto the modular group, continued fractions, the braid group on 3 strings, taffy\npulling machines, the Calkin-Wilf fraction tree, link invariants such as bracket\npolynomials and the Fox coloring, and the Euclidean Algorithm. We give a few tips for\nways to explore some of these delightful connections with groups of students.", "id": "Paper/70844", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70844"}, {"title": " On the Fourier Dimension of Sets of Multi-Dimensional Continued Fractions ", "webprogram_exclude": "0", "session_ids": ["Session/18256"], "source_sha256": "910c464b2a548538e0771c6a1614d755146638ec9e602c4a66d3ebd6c25c005d", "withdrawn": "", "abstract": "I will present some new results on the Fourier dimension of certain fractal sets of multi-dimensional continued fractions. This work is the result of a joint research collaboration with multiple SJSU students and is supported by the National Science Foundation under Award No. 2400329.", "id": "Paper/70849", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70849"}, {"title": " Cavity Mediated Interactions in Spin Systems ", "webprogram_exclude": "0", "session_ids": ["Session/19338"], "source_sha256": "99877659486827c0255a4540a68bf5d521ebfe1d20a15800bc00c8cd00fb5f89", "withdrawn": "", "abstract": "This research investigates the fundamental nature of cavity-mediated interactions in \nmany-particle spin systems, utilizing the Tavis-Cummings model. Despite their significance in \nquantum electrodynamics, the exact characteristics and emergent collective behaviors of these \ninteractions remain largely unresolved. A dual approach is employed: analytically deriving an \neffective Hamiltonian via the Schrieffer-Wolff transformation and validating these results through \nexact numerical quantum simulations on high-performance computing clusters. By \nbenchmarking effective theories against full system dynamics, this thesis aims to establish \ncomputationally efficient models that capture essential physics. The findings will bridge \nfundamental cavity QED with practical applications in quantum information processing and \npolaritonic chemistry.", "id": "Paper/70854", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70854"}, {"title": " What Did Reinforcement Learning Do to My Bijections? ", "webprogram_exclude": "0", "session_ids": ["Session/18130"], "source_sha256": "557a557904f186c6ff68db552c0566329b126f5e418d3d09568660d658aae0ea", "withdrawn": "", "abstract": "We study how reinforcement learning changes small, user-controlled Transformer models in a controlled combinatorial setting. Starting from models pretrained to imitate explicit mathematical constructions, we ask whether and how reinforcement learning can help discover a bijection, and how the resulting behavior generalizes beyond the training distribution. We evaluate both in-distribution performance and out-of-distribution generalization, and use behavioral experiments and interpretability tools to examine what reinforcement learning adds beyond imitation.", "id": "Paper/70855", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70855"}, {"title": " Project-Based Learning and Authentic Assessment in Applied Statistics ", "webprogram_exclude": "0", "session_ids": ["Session/18476"], "source_sha256": "daffac0a8876f4949cdd1cb73f9d7f1ec181f9784eb4d9cf48cb0432a8419b8b", "withdrawn": "", "abstract": "This presentation will highlight the use of project-based learning in Applied Statistics with Programming, where students apply statistical concepts and Python programming to real-world problems. The course uses multiple assessment approaches, including peer reviews, student presentations, voice recordings of project plans, written summaries, and final project assessments. These activities provide students with opportunities to receive feedback, reflect on their ideas, and progressively improve their projects. The presentation will discuss how combining formative and summative assessments can promote statistical reasoning, collaboration, communication, and individual accountability. Examples from the course will illustrate practical ways to design project-based assessments that engage students in meaningful, data-driven learning.", "id": "Paper/70858", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70858"}, {"title": " Some recent results on invasive species control ", "webprogram_exclude": "0", "session_ids": ["Session/18327"], "source_sha256": "8d1f16db0d3edd734aaffa6ef84fe819fdc08c4095b6e69bc4b4e4d99bb44797", "withdrawn": "", "abstract": "Invasive species continue to be a significant global problem. In this talk we resent recent results on linear and non-linear dispersal models, formulated via patch systems, aimed at the biological control of invasive pests, primarily the soybean aphid. In particular, we discuss applications of our results to control efforts in the advent of habitat fragmentation and climate change.", "id": "Paper/70863", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70863"}, {"title": " Errors Without Attractors: Ghost States Past the Fold of a Noisy Decision ", "webprogram_exclude": "0", "session_ids": ["Session/19365"], "source_sha256": "f64641b6e9e3ce148698347326332b2c390a824a522b370e1cabd3e73f4b50e2", "withdrawn": "", "abstract": "Bistable models of two-alternative decision making reduce near their instability to the imperfect pitchfork, whose noisy form is $dx = (h + rx - x^3)\\,dt + \\sigma\\,dW$ (Roxin and Ledberg, 2008). Here $r$ measures attention or urgency, and the input bias $h > 0$ (evidence) favors the correct option, making the incorrect choice the shallower of two wells. Classically, choice probabilities are well occupancies at the moment a choice is required, and reversals are Kramers escapes over the barrier. This picture has a hard edge. At the fold $r_c = 3(h/2)^{2/3}$, the shallow well and the barrier merge and vanish. Under strong evidence ($r < r_c$) the incorrect choice has no basin, so a description by well occupancies admits no errors; yet errors persist empirically and are conventionally absorbed into a lapse rate.\n\nWe give a description valid uniformly across the fold. We solve the full stationary moment hierarchy exactly, without closure: the moment generating function satisfies a third-order linear ODE whose solution space is spanned by integrals over Lefschetz thimbles of the quartic potential. This thimble decomposition assigns each choice conditional moments, whose mean is a noise-continued fixed point, and a normalized weight equal to its basin occupancy whenever the basin exists. Continuing the incorrect branch analytically below $r_c$ defines a ghost of the vanished choice, whose weight, defined without a basin or a real deterministic fixed point, gives a residual error rate past the fold. Near the fold at small noise, the problem reduces to Airy's equation: the ghost persists a distance of order $\\sigma^{4/3}$ below $r_c$, with prefactor set by the first zero of $\\mathrm{Bi}$. We also derive a closed-form lifetime of the incorrect choice, the time to reversal, which remains accurate as that choice loses stability, where Kramers estimates break down.", "id": "Paper/70865", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70865"}, {"title": " Data Dilemmas: An Analysis of Ethics Interventions in a Computational Mathematics Course ", "webprogram_exclude": "0", "session_ids": ["Session/18088"], "source_sha256": "01f9c73e3368ced10216e76cee7e07ad130431f15fbb0828fb89afa27460d018", "withdrawn": "", "abstract": "Our lives are increasingly influenced by the presence of algorithms, from the content we consume online to hiring decisions.  It is thus vital that undergraduate students have the space to engage with the ethical dimensions of generative artificial intelligence, data driven algorithms, and even science, technology, engineering, and mathematics (STEM) at large. Such preparation is important not just for students who may contribute to these technologies, but also for those who will use them, make decisions informed by them, or experience their consequences. In this talk, I first present a collection of  ethical interventions that have been integrated into our introductory data analysis and computational modeling course. This includes classroom activities, as well as an optional cross-institutional honors option in partnership with Ferris State University and the Zekelman Holocaust Center, which focuses on the Holocaust as a case study for STEM ethics and modern professional ethics guidelines. I then showcase our mixed-methods approach to evaluating the effectiveness of these interventions. Drawing on pre-, mid-, and post-semester surveys, field notes, and student artifacts, we investigate the development of students’ perceptions of ethics and their self-efficacy of applying ethical reasoning to their own work. Survey analysis showcases success through moderate positive effect sizes students on both constructs in multi-year course data. I advocate for reflective teaching practices in increasing content in mathematics and computing classes on ethics and bias. Finally, I conclude with reflections on considerations, challenges, and opportunities for implementing ethics within classrooms.", "id": "Paper/70868", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70868"}, {"title": " Can You Hear the Shape of an Integer? ", "webprogram_exclude": "0", "session_ids": ["Session/19361"], "source_sha256": "eae4ecc6eb87bfbf538f545a83927fc3167cdb0fe6e6e05708a6f26946434279", "withdrawn": "", "abstract": "Signal analysis is a powerful toolkit. Here we apply its methods to integers and integer sequences. We open with a motivating puzzle: if \\(C_n\\) denotes the \\(n\\)th Catalan number, how fast does \\(\\gcd(C_n^2,C_{2n})\\) grow? Stirling's formula shows that both \\(C_n^2\\) and \\(C_{2n}\\) have exponential growth base \\(16\\). Their gcd is far more mysterious and has a surprising growth rate:\n  \\[\n  \\gcd(C_n^2,C_{2n}) = \\left(\\frac{8}{e^{\\pi/2}}\\right)^{n+o(n)}\n  \\]\nTo understand the gcd's growth, write \\(a_n=\\gcd(C_n^2,C_{2n})\\). For each prime \\(p\\), we plot \\(v_p(a_n)\\), the exponent of \\(p\\) in \\(a_n\\), against \\(n/p\\). The resulting function \\(f(x)\\) is our signal. It satisfies\n  \\[\n  v_p(a_n) =_{a.e.} f\\left(\\frac{n}{p}\\right),\n  \\]\nand allows us to calculate the growth rate in closed form. \nThe same visual language reaches well beyond the opening puzzle. In the second half of the talk, we explore generalizations and applications. Prime signals offer arithmetic insight and suggest closed forms for Hankel transforms of sequences (Figure~\\ref{fig:hankel}). Krammer's \\(G\\)-function has different valuation staircases depending on \\(p\\bmod 15\\), echoing the discriminant \\(15\\) of the quaternion algebra underlying its arithmetic monodromy group~\\cite{Krammer1996} (Figure~\\ref{fig:krammer}). Extending the method to multivariate sequences lets us use optimization methods in irrationality proofs, and generate candidates for Rhin-Viola-like bounds on their denominators~\\cite{RhinViola2001} (Figure~\\ref{fig:cmf}).\n\nFinally, we show one algebraic implication: they can help decide whether a hypergeometric function is algebraic~\\cite{Beukers2010} (Figure~\\ref{fig:g3}).", "id": "Paper/70870", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70870"}, {"title": " Moving Beyond Implementation Studies: Three Ideas for Conducting Rigorous Research in Alternative Grading ", "webprogram_exclude": "0", "session_ids": ["Session/18440"], "source_sha256": "a5b01a2ef3294592170c7c270cecd4072c21e084348fac495e496daeac3a90e1", "withdrawn": "", "abstract": "Alternative grading (AG) implementations in post-secondary mathematics have surged in both number and popularity in recent years. However, as attendance at AG sessions at various conferences increases, many presentations largely focus on descriptive case studies of individual class implementations. While these studies are useful to instructors curious about AG, we must also advance the field by conducting rigorous mathematics education research to justify the efficacy of AG methods. In this presentation, I provide three specific ideas for how instructors might enact such research in their AG classes. These examples include content- or behavior-specific studies to identify concepts and practices crucial to success in a course, and longitudinal studies investigating relationships between students’ performance in AG and subsequent courses. I also discuss methods for collecting data for each study type and provide preliminary results from my work at Idaho State University to demonstrate the viability of these approaches.", "id": "Paper/70871", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70871"}, {"title": " Privacy and Efficiency in Group Testing for Prevalence Estimation ", "webprogram_exclude": "0", "session_ids": ["Session/18389"], "source_sha256": "fd784ddc8a88ad79beaa2d9154d0ec884974b8ff6b3d0fbafae7150936c59beb", "withdrawn": "", "abstract": "Understanding disease prevalence within a population is essential for guiding effective public health interventions. Originally introduced for case identification, group testing also provides a cost-effective approach for prevalence estimation in large-scale surveillance studies. In this talk, we show that group testing provides inherent privacy benefits, and use these properties to develop an optimal design strategy that balances privacy, statistical efficiency, and resource constraints. We then move beyond the standard setting of disjoint pools, and consider designs in which individuals may appear in multiple pools. We introduce estimation methods for such designs, and present results clarifying how overlap affects information and efficiency.", "id": "Paper/70873", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70873"}, {"title": " The Extremal Truncated Complex Moment Problem and Gröbner Bases ", "webprogram_exclude": "0", "session_ids": ["Session/18305"], "source_sha256": "93398bf471d924232ec752f3c35d74a0750687c23ae218935b68f0e2f66037ef", "withdrawn": "", "abstract": "Moments appear naturally in many areas of mathematics and have applications in areas such as probability theory, semidefinite programming and polynomial optimization.  \nIn this talk, we discuss new methods used to study the Truncated Complex Moment Problem (TCMP). In particular, we will present a generalization of a result from a 2014 paper by Curto and Yoo which can be used to find a numerical condition on a finite set of moments which is equivalent to the existence of a representing measure. \nThe primary new method used in obtaining this result is the application of Gr\\\"obner bases to the study of the TCMP. \nLet $M(k)$ be the moment matrix associated with a truncated sequence $\\gamma^{(2k)}$, and let $\\mathscr{V}$ be the algebraic variety associated with $M(k)$. \nIn the case where the problem is extremal, meaning that the rank of $M(k)$ is equal to the cardinality of $\\mathscr{V}$, we show that the (minimal) Gr\\\"obner basis for the ideal $I$ associated with $\\mathscr{V}$ contains exactly the polynomials corresponding to the column relations of $M(k)$. Additionally, this result can be used to find numerical conditions on the level of moments which are equivalent to the existence of a representing measure.", "id": "Paper/70874", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70874"}, {"title": " Tipping points are typical in ecosystems with higher-order interactions ", "webprogram_exclude": "0", "session_ids": ["Session/18042"], "source_sha256": "c0d16204c4393673536559cf72ef47d03986cfd371c029ef134df73ced7d5795", "withdrawn": "", "abstract": "Whether species-rich communities gradually erode or collapse abruptly under environmental change is a central question in ecology. Classical pairwise theory predicts that coexistence is always lost gradually, through smooth declines to extinction. Yet real ecological interactions are often strongly state-dependent, shaped by nonlinearities that fixed pairwise coefficients cannot capture. Here we show that higher-order (nonlinear) interactions make abrupt, irreversible loss of coexistence a typical route to community collapse: across diverse random communities, the equilibrium supporting coexistence disappears suddenly at a fold bifurcation. Using polynomial homotopy continuation to track equilibria as environmental conditions change, we find that folds progressively dominate the boundary of the coexistence domain as nonlinearity strengthens, replacing the gradual extinctions of pairwise theory. The sign structure of higher-order interactions controls both the onset of tipping points and whether biodiversity buffers or amplifies collapse. Because higher-order and nonlinear interactions are intimately linked, tipping points also arise generically in pairwise models with strong nonlinearity. Applying our continuation framework to a canonical model of plant–pollinator collapse, we formally resolve its bifurcation structure as fold-mediated, and show that fold bifurcations are typical across published multispecies models spanning mutualistic, competitive, and consumer–resource interactions. These results challenge the expectation that monitoring abundances suffices to anticipate collapse, and unify structural-stability theory, which delineates the safe operating space for coexistence, with critical-transition theory, which characterizes the nature of its boundaries.", "id": "Paper/70875", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70875"}, {"title": " Parameterized families of ideal classes arising from rational points on elliptic curves ", "webprogram_exclude": "0", "session_ids": ["Session/17808"], "source_sha256": "f061db6b11cd399008d764ad5f48eeb953939bd55f89c5a1e9424b8ae85088ba", "withdrawn": "", "abstract": "Elliptic curves and ideal class groups are two highly studied areas of algebraic number theory. We will begin by showing how integer and rational points on elliptic curves can give rise to families of ideals (parameterized by integers) in distinct orders of number fields. These orders are not necessarily the rings of integers, and so invertibility of the ideals must be verified. Past work has worked with quadratic orders to leverage the bijection with quadratic forms to accomplish this. Furthermore, in certain (common) cases, it has been known that this gives a homomorphism from a finite index subset of the rational points on the elliptic curve into the ideal class group of the order. Our aim has been to generalize these results to higher degree orders and all elliptic curves. Throughout this talk, we will discuss how our computations in SageMATH (and using information from the LMFDB) influenced the research, and was used to verify results and create conjectures for further work. This is based on work currently in progress.", "id": "Paper/70876", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70876"}, {"title": " Differential Equation Model for Column Adsorption Filters ", "webprogram_exclude": "0", "session_ids": ["Session/17953"], "source_sha256": "e82907b5b36ee1e57b6d2f90ef837f348b2b65fd385ca18a1960793fdd222088", "withdrawn": "", "abstract": "A mathematical model is derived to predict the response of adsorption based column filters. Adsorption based filters have a variety of applications including the processing of DNA and the purifying of  heavy metal contaminated waste water.", "id": "Paper/70879", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70879"}, {"title": " Inverse Learning for Mixed Mean Field Games ", "webprogram_exclude": "0", "session_ids": ["Session/18274"], "source_sha256": "0b6d6565e68007b66547cef7df9e990f6b52db0e76555237fb7193e48e031250", "withdrawn": "", "abstract": "Motivated by the sustainable management of common pool resources, mixed mean field games model populations in which agents combine cooperative and non-cooperative behavior. We introduce this class of models, analyze the associated equilibria, and discuss motivating examples. Because the degree of cooperation affects equilibrium outcomes but is typically unobservable, we then study how agents’ altruism levels can be inferred from observed state and control trajectories. We establish identifiability results and present numerical experiments illustrating the proposed inverse learning approach.", "id": "Paper/70880", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70880"}, {"title": " A Mathematical Guide to Operator Learning ", "webprogram_exclude": "0", "session_ids": ["Session/18472"], "source_sha256": "9272107abf342c56afe028ffcfe2932b6b33a5a06e86fca4628f1d01552e257c", "withdrawn": "", "abstract": "A fundamental challenge in modern scientific computing is learning an operator from finite data. In this talk, I offer a mathematical guide to operator learning, drawing a distinction between different types of observables and revealing the crucial role this choice plays in sample efficiency. We explore how the nature of the underlying partial differential equation governs the difficulty of learning the associated solution operator, and I present recent learning theory that quantifies the number of queries needed for accurate recovery. Diffusive systems, as we shall see, are forgiving; wave-like systems are not. Along the way, we reflect on what it means to learn in infinite dimensions and how mathematical structure can be exploited to tame the curse of dimensionality. I will conclude with examples involving evolving physical systems, including crack propagation, where the goal is no longer simply to learn an input-output operator but to build a model capable of predicting how a complex system evolves.", "id": "Paper/70881", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70881"}, {"title": " Mathematical models of complex data ", "webprogram_exclude": "0", "session_ids": ["Session/19358"], "source_sha256": "ab25686da005bfb58c2e3c44c2fc7a43aabe6b53287137c6e7c3c96be6594dcc", "withdrawn": "", "abstract": "Many real data objects are represented by point clouds, which are finite sets of unordered points, often with only inter-point distances without a Euclidean embedding.  \n\nFor standard filtrations of simplicial complexes (Vietoris-Rips, Cech, Delaunay) on point clouds, persistent homology is invariant under isometry  (any distance-preserving transformation ). This invariant detects high-dimensional cycles in complexes but may not distinguish between generic clouds of unordered points even in the plane [1].\n\nIn dimension 0,  the persistence of a point cloud C is essentially equivalent to a Minimum Spanning Tree with the vertex set C and a minimum total length of edges. Though this tree can  be locally unstable under perturbations of equidistant neighbors, the overall geometric shape remains almost the same.\n\nWe have extended   this observation to higher dimensions by extending a Minimum Spanning Acycle on C to a Homologically Persistent Skeleton HoPeS(C) whose extra critical  s implices represent all pairs (birth, death) in a persistence diagram [2].\n\nThis skeleton has optimal (reduced) subcomplexes having a minimum total length of simplices among all complexes that have the same homology as a given complex on C at the same scale.\n\nIn dimension 1, derived subgraphs of HoPeS(C) guarantee correct reconstructions of an embedded graph G given by a noisy sample C under explicit conditions on G and C [3].\n \nThe more recent developments towards stronger invariants beyond persistence include the geo-mapping problem that aims to geometrically describe the shape of any real data under practical equivalences [4, Problem 1.4.5].\n\n[1] P.Smith, V.Kurlin. Generic families of finite metric spaces with identical or trivial 1-dimensional persistence. Journal on Applied and Computational Topology, v.8, p.839–855 (2024).\n\n[2] S.Kalisnik, V.Kurlin, D.Lesnik. A higher-dimensional Homologically Persistent Skeleton. Advances in Applied Mathematics, v.102, p.113-142 (2019).\n\n[3] P.Smith, V.Kurlin. Skeletonisation algorithms with theoretical guarantees for unorganised point clouds with high levels of noise. Pattern Recognition, v.115, 107902 (2021).\n\n[4] O.Anosova, V.Kurlin. Geometric Data Science (290+ pages), arxiv:2512:05040, the latest version at https://kurlin.org/Geometric-Data-Science-book.pdf.", "id": "Paper/70882", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70882"}, {"title": " Continuous Time Reinforcement Learning in the Rough Setting. ", "webprogram_exclude": "0", "session_ids": ["Session/17976"], "source_sha256": "c7e68b1f041e7efc0462df89d68d3ad6a9db60b71d488d732936b6fdc02c0dc6", "withdrawn": "", "abstract": "Reinforcement learning (RL) is one of the three main paradigms of machine learning. Traditionally, it has been studied in discrete time and space via Markov decision processes. In 2020, Wang, Zariphopoulou and Zhou [WZZ] formulated a continuous version of RL under the machinery of stochastic control theory and proved results under this formulation. Non-Markovian dynamics in mind, Chakraborty Honnappa and Tindel [CHT] recasted this formulation and introduced rough paths as the \"random\" driver, instead of Brownian motion. In this talk we will review the [WZZ] construction and interpretation of continuous time RL. Moreover, we will mention the results by [CHT] and present our new results, such as the Pontryagin maximum principle, construction of a \"little\" q-function and its application in policy improvement. This is based on a joint work with Prakash Chakraborty, Harsha Honnappa and Samy Tindel.", "id": "Paper/70883", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70883"}, {"title": " Leveraging Experience, Honoring Fresh Voices: Mathematics Course Coordination Best Practices with Mixed Teams ", "webprogram_exclude": "0", "session_ids": ["Session/17971"], "source_sha256": "831470c0b50cb3bae50e1b0167d59ca98a30ee40b5ec2019fc7c02fab493ff06", "withdrawn": "", "abstract": "The question of who teaches introductory mathematics courses is as varied as the institutions from which the question is asked. When the answer, however, is a mix of full professors, term lecturers, and graduate students all serving as instructors of record in the same coordinated course, the strategies to honor contributions from all parties becomes even more nuanced. Course coordinators from a large research university in the Mid-Atlantic will share the best practices they have found to work in helping instructors feel a sense of fairness and autonomy while maintaining cohesive standards in Calculus I and Calculus II courses taught in a flipped classroom, active learning environment. We will discuss how we structure regular meetings to support pedagogical development, build administrative cohesion among the cohort of course coordinators, and incorporate methods for providing meaningful student feedback on assessments from a multitude of voices. Multi-tiered observation strategies will also be discussed with example documents and tools shared with participants as well as examples of guided teaching notes for instructors.", "id": "Paper/70887", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70887"}, {"title": " Homology of the Groups <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"3.951ex\" height=\"2.843ex\" style=\"vertical-align: -1.005ex;\" viewBox=\"0 -791.3 1701 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\Gamma _{2,n}</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-393\" d=\"M128 619Q121 626 117 628T101 631T58 634H25V680H554V676Q556 670 568 560T582 444V440H542V444Q542 445 538 478T523 545T492 598Q454 634 349 634H334Q264 634 249 633T233 621Q232 618 232 339L233 61Q240 54 245 52T270 48T333 46H360V0H348Q324 3 182 3Q51 3 36 0H25V46H58Q100 47 109 49T128 61V619Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-393\" x=\"0\" y=\"0\"></use>\n<g transform=\"translate(625,-150)\">\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-32\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-2C\" x=\"500\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-6E\" x=\"779\" y=\"0\"></use>\n</g>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/19358"], "source_sha256": "d6064dcc8fe3509812e0403cf04f52615e74f72e8a7feb43a0797c7f2f2a8dad", "withdrawn": "", "abstract": "The notion of graph complexes allows us to turn topological and algebraic questions into combinatorial questions. In this presentation, we take this approach to compute the homology of the groups $\\Gamma_{2,n}$, the group of homotopy classes of self-homotopy equivalences of a rank 2 graph which fix $n$ valence-one vertices, by considering graphs of genus 2. Our strategy is to filter these graphs into pieces whose Euler characteristics can be compute via combinatorial methods, which the final piece of the filtration corresponding to a single graph whose rank is equal to $\\Beta_{n+1}(\\Gamma_{2,n})$. Because $\\Gamma_{2,0}\\cong GL_2(\\mathbb{Z})$, one immediate application is a cohomological computation for $GL_2(\\mathbb{Z})$.", "id": "Paper/70888", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70888"}, {"title": " Some recent results for PDE models of angiogenesis with applications to cardiac health ", "webprogram_exclude": "0", "session_ids": ["Session/18275"], "source_sha256": "65cf1553a906b82502b529c46af05a49a1aed2e4051b5a3ed1a94c0f638e19b7", "withdrawn": "", "abstract": "Ischemic heart diseases represent the leading cause of mortality worldwide. Revascularization, the process to restore blood flow in blockages, and angiogenesis, the process by which new blood vessels form from existing ones, are highly complex but crucial in cardiac health. The large literature on angiogenesis has focused on linear diffusion in the cells – not non-linear diffusion. We investigate certain reaction diffusion models for angiogenesis, with p-Laplacian diffusion in the cells. This is more realistic, given the finite propagation speed of signals in endothelial cells. Preliminary numerical evidence suggests novel dynamics, such as increased cellular proliferation, not seen with linear diffusion. We discuss applications of our results to cardiac health.", "id": "Paper/70890", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70890"}, {"title": " Filtered RKDG Methods: Fourier Analysis for the Second-Order Case ", "webprogram_exclude": "0", "session_ids": ["Session/19344"], "source_sha256": "3a839e8b0503c2e5c92daf2c20963aa7bd384fde503079c8d762e01c4c29ae78", "withdrawn": "", "abstract": "In this work, we apply a Fourier approach to study the stability and accuracy effects of filtering on Runge–Kutta (RK) discontinuous Galerkin (DG) methods for scalar hyperbolic conservation laws. Both the standard RKDG method and its variant, the RKDG method with compact stencils (cRKDG), will be considered. We focus on the second-order schemes and apply the modal filters immediately after the DG operators at each RK stage. Using a Fourier-type analysis, we quantitatively assess the time step constraints for stability and accuracy of multiple filtered schemes. We show that the application of filters can significantly improve the Courant–Friedrichs–Lewy numbers while maintaining the optimal convergence rate. However, for problems containing sonic points, the convergence order of some filtered schemes may degrade. To address this issue, we apply filters only away from the sonic points and adopt a local time-stepping strategy for the cRKDG method to take advantage of the larger time steps enabled by the filters in these regions.", "id": "Paper/70892", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70892"}, {"title": " Arithmetic aspects of differential equations ", "webprogram_exclude": "0", "session_ids": ["Session/18263"], "source_sha256": "a6935ac81688017ee67103fd3a1f256a39a5c98b163feb28d4d51b45c9476790", "withdrawn": "", "abstract": "Grothendieck and Katz gave a conjectural arithmetic characterization of linear ODEs all of whose solutions are algebraic; this was generalized to non-linear ODEs by Ekedahl, Shepherd-Barron, and Taylor. These \"p-curvature conjectures\" are broadly open, though beautiful work has been done on them by Katz, Chudnovsky-Chudnovsky, André, Bost, and others. I'll explain new work in progress with Josh Lam proving these conjectures for a class of nonlinear ODE coming from algebraic geometry, and, time permitting, say what this has to do with the original conjecture of Grothendieck and Katz.", "id": "Paper/70893", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70893"}, {"title": " Sharp arithmetic localization beyond monotonicity and transversality ", "webprogram_exclude": "0", "session_ids": ["Session/18292"], "source_sha256": "d90002a54f05a859c43425be964939161bb8a928448e97daca14116b2f218b1d", "withdrawn": "", "abstract": "We prove sharp arithmetic localization for one-dimensional quasiperiodic potentials with jump discontinuities, beyond monotonicity and uniform transversality.  Our results include every non-constant $C^1$ monotone sampling function, even with arbitrarily large flat regions, and also certain  non-monotone potentials. A key new mechanism is a symbolic unique-continuation principle: first-return words to the region where $f'>0$ have no common Dirichlet resonance, forcing eigenfunction mass to transfer away from flat or negatively sloped regions and yielding the required anti-Lipschitz behavior of finite-volume eigenvalue branches.", "id": "Paper/70894", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70894"}, {"title": " Embeddings and models of n-dimensional octahedra ", "webprogram_exclude": "0", "session_ids": ["Session/18234"], "source_sha256": "7304d67a69b67adb10b92c2d0f0aa5df2554a2ee9852285e44b8d38ddd291de3", "withdrawn": "", "abstract": "In 1978, Jungerman and Ringel proved that the genus of the\n$n$-dimensional octahedron graph $O_n$ (that is, 1-skeleton of the dual of the $n$-dimensional hypercube) is\n$(n-1)(n-3)/3$,\nprovided that $n$ is congruent to 0 or 1 modulo 3. \nThey apply the machinery of current graphs to structures called\ncascades to prove the existence of rotational embedding schemes that yield\ntriangular embeddings.\nHowever, the various embedding schemes are never explicitly stated.\n\nWe take a much more elementary approach\nthat avoids current graphs and provides clear topological descriptions of the various\nembeddings. We use select faces of the \n$n$-dimensional cross-polytope that fit together edge-to-edge to form an orientable surface in $\\mathbb{R}^n$, in which\nthe 2-skeleton $O_n$ is automatically  embedded.\n\nAs a dividend, because these surfaces can be immersed in $\\mathbb{R}^3$,\nour method yields interesting 3-dimensional models of $n$-dimensional octahedra, practicable for relatively small values of $n$. Examples are shown.", "id": "Paper/70896", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70896"}, {"title": " Hiding Mathematics in Plain Sight ", "webprogram_exclude": "0", "session_ids": ["Session/18074"], "source_sha256": "f3d43f9473cacb76e7dc982c013d8570f3942a377a902b7df1c004e9b044a9ee", "withdrawn": "", "abstract": "Mathematical puzzles that translate well to social media must work on various levels. The goal of the puzzle must be instantly clear. The viewer is invested once they have a proposed hypothesis or solution methodology, even if it later turns out to be incorrect. And the discussions which develop in the comments that can involve hundreds or thousands of people can be intense. We look at the process of creating such social media posts and the online response.", "id": "Paper/70906", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70906"}, {"title": " Existence of Minimal Homotopies of Immersed Planar Curves ", "webprogram_exclude": "0", "session_ids": ["Session/18304"], "source_sha256": "3d8b9d140735d4a75177dd88fec6943fba520511128571edc2bced7dc7bd915a", "withdrawn": "", "abstract": "We study the existence of area-minimizing homotopies between homotopic curves in the plane.While the classical Plateau problem establishes the existence of least-area surfaces spanning a single Jordan curve, the corresponding existence theory for homotopies between curves is more subtle and is not covered by Plateau’s framework.Existing results in the plane are based on combinatorial and algebraic methods, such as decomposing a normal curve into a sequence of self-overlapping subcurves, each admitting an area-minimizing contraction.\n\nIn this paper, we develop a variational existence theory for minimum-area homotopies of immersed planar curves.Our approach adapts classical minimal surface methods by lifting an immersed planar curve with self-intersections into higher co-dimension, where it becomes embedded.For each lifted curve, we apply Douglas’s solution of the Plateau problem to obtain an area-minimizing disk.We establish uniform geometric bounds and compactness for the resulting family of Douglas minimizers and prove convergence, as the lifting parameter tends to zero, to a limiting map of $D^2$, mapping $\\partial D^2$ to the original planar curve. We thus obtain a homotopy whose swept area is minimal among all null-homotopies associated with the given pair of homotopic curves.\n\nA preprint is available at https://arxiv.org/abs/2605.29474v1.", "id": "Paper/70907", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70907"}, {"title": " Existence and Stability for Magnetic Solitons ", "webprogram_exclude": "0", "session_ids": ["Session/19363"], "source_sha256": "da3c66aa6efe9e202080298d5f14b06dc8a271e67e8805c36067f172eb9ed4bb", "withdrawn": "", "abstract": "Vortex solitons are ubiquitous patterns arising in physical systems ranging from geometric optics, superconductors, and superfluids to  \n Bose-Einstein condensates (BECs). For instance, optical vortices emerge as structured light beams carrying non-zero orbital angular momentum. In this presentation, we consider vortex solutions to a nonlinear Schr\\\"odinger equation (NLSE) with an angular momentum term. We first construct cylindrically symmetric vortex solutions via a variational method. Subsequently, we establish their orbital stability by conducting a detailed spectral analysis of the associated magnetic Hamiltonian.", "id": "Paper/70910", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70910"}, {"title": " Analyzing the Dunfield-Gong Sphere ", "webprogram_exclude": "0", "session_ids": ["Session/18087"], "source_sha256": "32281709e834f339a6a5ae4141a84a03c6b880a9d2929538ee333b881d6bd3ca", "withdrawn": "", "abstract": "In recent work of Dunfield and Gong, a homotopy 4-sphere and an associated knot were constructed using a strategy of Manolescu and Piccirillo. If the associated knot is not slice in the 4-ball, then the homotopy 4-sphere is an exotic $S^4$. Using methods from Sage and Snappy, Dunfield and Gong were unable to find a slice disk for this knot. Thus, the constructed homotopuy 4-sphere makes for a promising potential counterexample to the 4-dimensional Poincar\\'e Conjecture. If the Dunfield–Gong sphere is standard, a nice corollary is that there is a low-crossing potential counterexample to the Slice-Ribbon Conjecture. In this talk, we draw a handlebody diagram of the Dunfield–Gong Sphere and draw conclusions about its smooth structure.", "id": "Paper/70911", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70911"}, {"title": " Global liftings of infinite families of elliptic curves over finite fields ", "webprogram_exclude": "0", "session_ids": ["Session/19367"], "source_sha256": "b0ffe3e227aaa260d9505b23abfccf0edaa2d825eb012260ea3c4db1b3088834", "withdrawn": "", "abstract": "Fix a number field $K$. Given an infinite family of elliptic curves $E_\\mathfrak{p} /\\mathbb{F}_\\mathfrak{p}$  for a cofinite set $S$ of primes $\\mathfrak{p}$ of $K$, we discuss conditions for the infinite family to be liftable to a single elliptic curve $E/K$. We use the methods of S. Gun and V.K. Murty to extend the results from $\\mathbb{Q}$ to number fields.", "id": "Paper/70914", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70914"}, {"title": " Coordinated By Design: Developing a New Coordinated Course Sequence ", "webprogram_exclude": "0", "session_ids": ["Session/17971"], "source_sha256": "7e29f5064188e6de88164d3eb1b219b063dedb2de3e88939c0f40fbaf25fef4d", "withdrawn": "", "abstract": "In 2020, the mathematics faculty at Missouri University of Science and Technology embarked on a comprehensive review and redesign of our calculus offerings, resulting in a new two-semester Calculus I sequence which includes extensive algebra and trigonometry content.  This provided us with the opportunity to build a course from the ground up with coordination in mind rather than addressing the typical problems that come with adding the structure of coordination onto an existing course.  This talk will discuss both things we did well and things we should have paid more attention to with regards to coordination as we designed and implemented this new sequence.", "id": "Paper/70915", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70915"}, {"title": " Spectral Correspondences for  Maass Waveforms on Quaternion Groups \n\n  Towards the Resolution of a Conjecture at Level <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"4.716ex\" height=\"2.843ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -934.9 2030.4 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">4pu^2</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-70\" d=\"M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-75\" d=\"M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-34\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-70\" x=\"500\" y=\"0\"></use>\n<g transform=\"translate(1004,0)\">\n <use xlink:href=\"#E1-MJMATHI-75\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-32\" x=\"809\" y=\"513\"></use>\n</g>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18336"], "source_sha256": "39e85fd6cb5daa6a95d460a6e09f94dacdb35c842964831ad373948a67494c14", "withdrawn": "", "abstract": "\\begin{abstract}\nWe revisit the exceptional family $N=4pu^2$ in the spectral correspondence between Maass waveforms on quaternionic arithmetic surfaces and classical congruence quotients. For the coprime subfamily $(p,u)=1$, the relevant index-two non-Eichler order has an index-three norm-one subgroup, with deck group $C_3$. Its mean-zero spectrum therefore decomposes into an invariant sector and two nontrivial character sectors. Building on the holomorphic work of Tu--Yang, this talk presents a conditional Maass analogue: subject to verification of the stated standard local--global inputs, the invariant sector corresponds to the $2p$-new spectrum at level $2pu^2$, while each nontrivial sector corresponds to the $4p$-new spectrum at level $4pu^2$. The resulting relative-new space has multiplicity two, explaining the refined obstruction to a one-level correspondence within a specified special-order class. The statement includes complementary series and good-prime Hecke operators.\n\\end{abstract}", "id": "Paper/70921", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70921"}, {"title": " The Proof is in the Parsing: Computational Techniques for Error Detection in Late Medieval Astronomical Observations ", "webprogram_exclude": "0", "session_ids": ["Session/17713"], "source_sha256": "cf900cbf421d38078c137705f75a8477e5d00faee3624983ee24e5bac1aac678", "withdrawn": "", "abstract": "This paper will analyze a particular method of error detection in late medieval Latin astronomy, known as the \"probatio\". The \"probatio\" was a device intended to alleviate doubt, especially when the result of a computation did not satisfy the expectations of observation. Using the 14th-century astronomer John of Murs (fl. 1319 – 1347) as a case study, the paper re-examines his calculations for a solar eclipse, which he observed in Évreux on May 14, 1333, in light of the specific structure of the \"probatio\" method. The eclipse computation can be found on ff. 92v-93v of the manuscript Escorial, Real Biblioteca del Monasterio de San Lorenzo, MS O.II.10.", "id": "Paper/70925", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70925"}, {"title": " Mathematical and Computational Modeling of Pennycress Growth for Biofuel and Critical Mineral Applications ", "webprogram_exclude": "0", "session_ids": ["Session/19371"], "source_sha256": "c850076b4af3f7a4ab8c1ef6012aa2892eaae67cce8bfa03ccdf7ba98b2ce949", "withdrawn": "", "abstract": "Pennycress (\\textit{Thlaspi arvense}) has recently emerged as a promising crop for sustainable biofuel production. Its seeds contain high concentrations of oil that can be extracted and refined into fuels such as biodiesel and sustainable aviation fuel. As a fast-growing winter annual, pennycress can be cultivated between traditional summer growing seasons, providing an additional crop without directly competing with summer production. Pennycress can also accumulate critical minerals, such as nickel, from the soil, creating a low-cost alternative to traditional heavy mining.\n\nIn this talk, we investigate mathematical and computational approaches for modeling pennycress growth under varying genetic and environmental conditions. We explore traditional mathematical growth models, machine learning techniques, and physics-informed neural networks (PINNs) to capture differences in plant growth due to variations in genotype and soil nickel concentration. A central challenge is developing a model that is flexible enough to represent biological variability while remaining robust across experimental conditions. By improving our ability to characterize and predict pennycress growth, these methods may help identify high-performing genotypes and growing conditions for applications in biofuel production and critical mineral recovery.", "id": "Paper/70927", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70927"}, {"title": " A Climate-Forced Time-Delayed Model for Honey Bee Colony Dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/19353"], "source_sha256": "d1f1e8d6dd163dde0c6332271b43af90efb66c9e893681a7b5e51d3446144cb2", "withdrawn": "", "abstract": "Honey bees (\\textit{Apis mellifera} L.) are important pollinators whose populations are increasingly threatened by interacting environmental stressors, including pesticide exposure and climate variability. Time-delayed mathematical models have been used to characterize the demographic effects of pesticides on honey bee colonies, but models with constant environmental conditions cannot capture the effects of climate-driven variability on colony dynamics. In this work, we develop and analyze a delay differential equation model that integrates pesticide exposure with mechanistic climate forcing using observed climate data from Maricopa County, Arizona. The model incorporates temperature-dependent egg laying, rainfall-mediated pollen availability, temperature-dependent pollen degradation, cumulative heatwave stress, and climate-dependent adult mortality. We establish conditions for the existence of equilibria and colony extinction and show that positive colony equilibria arise through a saddle-node bifurcation. Numerical simulations under observed climatic conditions demonstrate pronounced seasonal variation in brood and adult worker populations and increased colony vulnerability during periods of elevated temperature and reduced floral resources. Simulations under future warming scenarios indicate further reductions in reproductive output, increased adult mortality, and greater potential for colony decline. Moreover, pesticide effects are amplified under adverse climatic conditions, illustrating the importance of incorporating environmental variability into models of pollinator population dynamics. The results provide a mechanistic framework for studying the combined effects of pesticides and climate change on honey bee colonies and highlight mathematical mechanisms underlying colony persistence and decline.", "id": "Paper/70933", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70933"}, {"title": " A Difference-Equation Framework for Modeling Organ Transplantation Dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/19369"], "source_sha256": "e9f494acc21c92dc8f63d0f479ce7c61af5f13d834d858a59d925808aefcaaac", "withdrawn": "", "abstract": "Organ transplantation is a life-saving process in which patients with failing or damaged vital organs receive donor grafts to improve their condition. However, in the United States, the demand for organs consistently exceeds the available supply, leading to long waiting times and limited access to transplantation. To better understand these dynamics, this project develops a difference equation model to examine the waitlist and donor populations, median waiting time, and 3-year survival rates. Data from the Organ Procurement and Transplantation Network (OPTN) on living donors, total donors, and transplant procedures was used to estimate key model parameters, while additional parameters were determined through biologically and clinically motivated assumptions. Parameter estimation yielded a living donor transplant efficiency of βlive = 0.00632 (R² = 0.324) and a strong relationship between total donors and transplants with βall = 2.022236 (R² = 0.986). The results demonstrate how differences between donor availability and transplant demand influence waitlist growth, while changes in median waiting time and survival rates illustrate additional factors affecting transplant system dynamics.Stability analysis examined how changes in model parameters affect system stability, while equilibrium analysis derived conditions under which the system reaches a steady state. Donor-scarcity analysis characterized waitlist behavior when donor supply acts as the primary limiting constraint. Overall, this model provides a mathematical framework for understanding the intricacies of the transplantation system, aligning with the UN Sustainable Development Goal 3: Good Health and Well-Being.", "id": "Paper/70937", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70937"}, {"title": " Nearly all <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.211ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 521.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">k</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-6B\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-SAT functions are unate ", "webprogram_exclude": "0", "session_ids": ["Session/18311"], "source_sha256": "150496e362878069b35dbad5ce3d899bda7f01fd5a6d3d0577cb3a153161f368", "withdrawn": "", "abstract": "We prove that a $1−o(1)$ fraction of all $k$-SAT functions on $n$ Boolean variables are unate (i.e., monotone after first negating some variables), for any fixed positive integer $k$ and as $n \\to \\infty$. This resolves a conjecture by Bollobás, Brightwell, and Leader from 2003.\n\nBased on joint works with József Balogh, Dingding Dong, Bernard Lidický, and Yufei Zhao", "id": "Paper/70940", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70940"}, {"title": " An Introduction to Cryptography and Post-Quantum Cryptography ", "webprogram_exclude": "0", "session_ids": ["Session/18073"], "source_sha256": "3cb9a9ae8c05bbf69ceb96e8f315c4150a1a02eb775a4418d09d61855e15df16", "withdrawn": "", "abstract": "Cryptography enables secure communication over insecure channels by relying on mathematical problems that are easy to verify but believed to be difficult to solve. This talk will introduce private- and public-key cryptography, encryption, and digital signatures, using RSA as a familiar example.\n\nWe will then discuss how quantum algorithms threaten many current public-key systems and motivate post-quantum cryptography: schemes designed to resist quantum attacks while running on classical computers. I will briefly survey code-based, lattice-based, isogeny-based, and multivariate approaches, including a small multivariate signing example. The talk will conclude with connections to computational complexity, coding theory, quantum information, secure multiparty computation, implementation, and cryptanalysis. No prior background in cryptography is assumed.", "id": "Paper/70941", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70941"}, {"title": " On the relation between S-Spectrum and Right Spectrum ", "webprogram_exclude": "0", "session_ids": ["Session/17954"], "source_sha256": "e63aa62d9da1ddd1a9584ec18c623e35653c611ebeebfc8a6bdafa16fdf6de07", "withdrawn": "", "abstract": "We use the $\\mathbb{R}$-linearity of $I\\lambda-T$ to define $\\sigma(T)$, the right spectrum of a right $\\mathbb{H}$-linear operator $T$ on a right quaternionic Hilbert space. We prove that $\\sigma(T)$ coincides with the $S$-spectrum $\\sigma_S(T)$. More precisely, the point, continuous, and residual components of the two spectra coincide. This provides a direct interpretation of the $S$-spectrum in terms of the invertibility properties of $I\\lambda-T$, analogous to the classical complex setting.", "id": "Paper/70943", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70943"}, {"title": " On the sharpness of general L2 Fourier restriction theorems ", "webprogram_exclude": "0", "session_ids": ["Session/19336"], "source_sha256": "57821e8894df38783617b345cc41a78c190f0911a6564e36241fbf0021d4cd8d", "withdrawn": "", "abstract": "I will present some new results on the sharpness of certain general L2 Fourier restriction theorems applicable to fractals. This work is the result of a joint research collaboration with Robert Fraser and Donggeu Ryou and is supported by the National Science Foundation under Award No.  2400329 and Award No. 2453364.", "id": "Paper/70944", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70944"}, {"title": " Professional Panel: Mathematics and the Department of Defense ", "webprogram_exclude": "0", "session_ids": ["Session/18323"], "source_sha256": "2efa1c0ec6cf49b390881127ced4e7a44f60efc3d4bc1d79e8600f8b785ea411", "withdrawn": "", "abstract": "This panel features mathematical scientists from across the Department of Defense (DoD) and collaborators who will discuss their career trajectories, professional development, and diverse pathways to collaboration within the government. Attendees will gain practical insights into civilian service, academic funding, and the intersection of mathematical research and government.", "id": "Paper/70945", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70945"}, {"title": " Group-Action Syndrome Decoding: A Framework for Cryptographic Search Problems ", "webprogram_exclude": "0", "session_ids": ["Session/18307"], "source_sha256": "f361c99a6c569a6808d4c29065e06c66a013f48cbe106a9d6c3292a3733b9962", "withdrawn": "", "abstract": "Several problems used in post-quantum cryptography share a common form: find a structured vector satisfying a system of linear equations over a finite field. We identify a common framework that captures many variations of this problem which we call group-action syndrome decoding (GASD), where the structured vector lies in an orbit of an efficiently computable linear group action. We show how this framework can recover many well-known problems, from ordinary syndrome decoding to the permuted kernel problem. Perhaps most surprisingly, the framework also captures the multivariate quadratic (MQ) problem, connecting coding-theoretic and algebraic search problems in the same formulation. We then consider cryptanalysis of GASD and generic constructions of signature schemes from suitable GASD assumptions. We conclude by examining promising concrete instantiations and their potential for secure and efficient signatures.", "id": "Paper/70947", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70947"}, {"title": " Epidemic Spread Modeling with Social-Distancing and Vaccination via Mean Field Games ", "webprogram_exclude": "0", "session_ids": ["Session/18260"], "source_sha256": "80c0ad41a0b92c2d156f19ccb6d138fea9b3f1ddb81a87cb1970f3de87578d9b", "withdrawn": "", "abstract": "The COVID-19 pandemic highlighted the need for public health authorities to design optimal mitigation policies for large populations of interacting agents who pursue their own objectives within a game-theoretical framework, rather than adhering perfectly to imposed social distancing or vaccination policies. However, finding equilibria in such large-scale games is notoriously difficult due to the complexity of agent interactions, and the inclusion of a principal and population heterogeneities further intensifies these challenges.\n\nIn this talk, we approximate equilibrium epidemic dynamics under various policies using mean field games (MFG). Inspired by SIR-type models, individuals play a non-cooperative game, controlling their transition rates between health states by adjusting their social contact and vaccination levels to minimize their non-compliance, treatment and vaccination costs. We characterize the equilibrium with forward backward differential equations and prove the theoretical results such as existence and uniqueness of solutions. We focus on a multi-population setting to stratify the population according to their socioeconomic heterogeneity, using real-life survey data to parameterize differences in behavior, authority and risk perception, and access to resources. This modeling enables a more realistic and equitable analysis of policy impacts across diverse population segments. Finally, we discuss a model where the vaccination costs are modeled in linear form. We show that this feature creates a bang-bang type of vaccination control for the individuals.", "id": "Paper/70948", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70948"}, {"title": " A Spatially-Aware Multimodal Deep Learning Framework with Graph Neural Network-Concept Bottleneck Fusion for Interpretable Wound Classification ", "webprogram_exclude": "0", "session_ids": ["Session/19338"], "source_sha256": "4c810a3385a1aa956f7f3cbc7cebce7c3092173215b107ffd4bcec947aeeebb4", "withdrawn": "", "abstract": "Chronic and acute wounds impose a growing burden on health care systems worldwide. Accurate automated wound-type classification supports timely, evidence-based treatment. Previous deep learning methods rely mainly on standalone convolutional encoders or simple late fusion of image and location features, with limited explainability and robustness across morphologically similar wounds. We propose a multimodal, spatially aware Graph Neural Network-Concept Bottleneck Model (GNN-CBM) that integrates wound appearance and anatomical context, exposing latent clinical prototypes before classification. We compared seven visual backbones: ResNet-50, EfficientNet-B0, EfficientNetV2-S, ConvNeXt-Tiny, DenseNet-121, ViT-Base, and Swin-Tiny, using the AZH Wound and Vascular Center dataset (Milwaukee, WI), comprising $N = 311$ unique patients and an augmented set of 830 image-location pairs. Patient identifiers defined groups in 5-fold stratified group cross-validation, preventing images from the same patient from appearing in multiple folds. Swin-Tiny achieved the highest accuracy ($0.809 \\pm 0.014$), macro-F1 ($0.805 \\pm 0.016$), and mean AUC ($0.954$). McNemar's tests with Bonferroni correction across six comparisons showed that Swin-Tiny significantly outperformed five backbones; its difference from ConvNeXt-Tiny was not significant. Ablation of the Domain-Constrained Spatial Penalty Loss reduced the best model's macro-F1 from 0.805 to 0.792 when the anatomical penalty was removed, supporting the value of spatial-plausibility constraints. The framework combines visual and spatial reasoning within single architecture, while the prototype bottleneck exposes an intermediate representation before wound-type prediction. We detail the mathematical framework, anatomical graph construction and density statistics, discuss the interpretability limitations of unsupervised concept bottlenecks and hardware efficiency, and emphasize external, multicenter validation before clinical deployment.", "id": "Paper/70950", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70950"}, {"title": " Two-layer agent based model of cellular dynamics for mammary gland ductal development ", "webprogram_exclude": "0", "session_ids": ["Session/19371"], "source_sha256": "96bf73ecbd74d54711ce899d0bd4658d4f0147d49d5edb2327a4e3938e9b4dbb", "withdrawn": "", "abstract": "Mammary gland development involves the formation of ductal branches necessary for milk production and delivery. Studying development is key for understanding how it may alter in diseases, such as cancer. Research shows that the interactions between the epithelial cells in ducts and collagen fibers in the surrounding extracellular matrix (ECM) is crucial for ductal formation. While it is commonly assumed that collagen directs ductal growth by acting as a mesh the epithelial cells grow onto, preliminary studies show this may not be the case. In fact, early analysis shows there is little to no collagen in front of actively developing ducts. There is, however, collagen along the already developed body of the duct. We hypothesize that actively developing ducts degrade collagen in front of the tip of a duct and fill the space left behind. We also hypothesize that the already developed body of the duct uses collagen to pin itself into place. Testing this process in vivo is complicated and is often done in vitro. However, in vitro experiments are limited because they cannot perfectly replicate the biological environment. Instead, we have opted to develop an agent-based model that simulates the known mechanics in vivo. This allows us to test our hypothesis, as well as a range of other experiments. \n\nTo accurately model the cellular dynamics, we have developed a two-layer agent based model. In layer one, cells and fibers are bonded using simple physics motion equations. In layer two, we use the Laplace equation to model hormone secretion between the cells and fibers. Using flux, we are able to determine regions of degradation in collagen fibers and regions of cellular growth in epithelial cells. This information is brought back into layer 1 to be modelled and visualized. This model is compared to in vivo experiments for validation. \n\nEarly results show possible explanations for the termination of ductal development and the development of ductal bifurcations.", "id": "Paper/70951", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70951"}, {"title": " Isovalent pairs of polynomials over finite fields ", "webprogram_exclude": "0", "session_ids": ["Session/19355"], "source_sha256": "2ce17b483c0de3742dbcb73c98faadd1fdfb45f85433bcfc2f1def8db5e81341", "withdrawn": "", "abstract": "We give a new construction of pairs of isovalent polynomials over a finite field, i.e., polynomials $f,g\\in\\mathbb F_q[X]$ such that, for each $k$, the images $f(\\mathbb F_{q^k})$ and $g(\\mathbb F_{q^k})$ agree as multisets.  We also classify all isovalent pairs of polynomials of certain prescribed degrees.  Our proofs involve group theory and ramification.", "id": "Paper/70954", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70954"}, {"title": " Reinforcement learning to find minimal band decompositions of braids ", "webprogram_exclude": "0", "session_ids": ["Session/18130"], "source_sha256": "d18fed867271405869be2c886175a12779af5aa7375e69d3237c1b79244f295b", "withdrawn": "", "abstract": "The band rank of a braid is the length of its shortest decomposition into conjugates of Artin generators and their inverses. Finding such a decomposition is a search problem over a fixed set of moves, which makes it a natural candidate for reinforcement learning. In this talk I will describe our setup, discuss which enhancements improved performance and where the approach stops working, and outline two techniques that complement it: dynamic programming in the free group, and lower bounds computed in finite quotients.", "id": "Paper/70956", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70956"}, {"title": " Stochastic Wolbachia Dynamics: persistence, invariant measures, and probability-based released strategies ", "webprogram_exclude": "0", "session_ids": ["Session/18095"], "source_sha256": "23b9b350d5faa574131fc14311d59328546a2dad00667fbe19497e6218d9998b", "withdrawn": "", "abstract": "We develop a stochastic discrete-time framework for \\textit{Wolbachia}\ninvasion in mosquito populations under environmental variability. Starting\nfrom a deterministic frequency-dependent difference equation with an\nAllee-type threshold, we consider the random iteration\n\\[\nX_{n+1}=F_{\\Theta_n}(X_n),\n\\]\nwhere $\\Theta_n$ represents fluctuations in fitness cost, cytoplasmic\nincompatibility, and maternal transmission. We establish existence,\nuniqueness, positivity, forward invariance of $[0,1]$, continuity, and\npathwise order preservation, and formulate the model as a random dynamical\nsystem. Under independent environmental forcing, the process is Markovian;\nthe associated Markov operator is Feller, and compactness of the state space\nimplies the existence of invariant probability measures.\n\nLocal behavior near extinction is characterized by the stochastic Lyapunov\nexponent\n\\[\n\\lambda\n=\n\\mathbb{E}\\!\\left[\n\\log\\bigl((1-M)(1-S_f)\\bigr)\n\\right],\n\\]\nwith $\\lambda<0$ yielding local exponential stability of the Wolbachia-free\nstate. We further introduce finite-horizon establishment probabilities and\nprobability-based release thresholds, whose monotonicity follows from the\npathwise comparison principle. Numerical simulations show how the magnitude,\nsource, and dependence structure of environmental variability affect invasion\nprobabilities and release requirements. The framework combines nonlinear\ndifference equations, random dynamical systems, Markov operators, invariant\nmeasure theory, and stochastic stability in a unified analysis of\nthreshold-dependent \\textit{Wolbachia} invasion.", "id": "Paper/70959", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70959"}, {"title": " Graduate Teaching Assistant Development in Mathematics: From Discussion Section Leader to Instructor of Record Cohort Member ", "webprogram_exclude": "0", "session_ids": ["Session/18091"], "source_sha256": "e128f145a7f3793b15f5aad1d990b2f04f5d18626279140459f6c7df06e92854", "withdrawn": "", "abstract": "Institutions have many differing models of responsibility for graduate students in mathematics as well as their pedagogical development. Here we will discuss a two-year model being implemented at a large research university in the Mid-Atlantic where graduate students enter a semester-long seminar in undergraduate mathematics education pedagogy in their first semester while serving as discussion section leaders in various courses. In their second year, the graduate students then move as a cohort to teach their first course as instructor of record in a coordinated course setting. The discussion will include the use of both institutional and national grants to fund the development of the cohesive model, examples of graduate teaching assistant pedagogical development activities, curriculum for the first-year seminar, and feedback from the graduate teaching assistants. Qualitative coding analysis results regarding improvements in affect seen in the graduate teaching assistants through the two-year model will be shared as well as views to further extension of development.", "id": "Paper/70961", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70961"}, {"title": " Tor Algebra Classification for Rings from General Points ", "webprogram_exclude": "0", "session_ids": ["Session/18318"], "source_sha256": "1ab30be05c8418d338e7c1bd767ae5f1141ac050420cb44fd8b19baba7f67ae1", "withdrawn": "", "abstract": "Any ring that comes as a quotient of a regular local or graded ring has an associated Tor Algebra, which has a unique multiplication structure that in some cases can be fully classified. We will consider coordinate rings of general points in $\\mathbb{P}^3$  and their Artinian Gorenstein quotients and classify their Tor algebra structures.", "id": "Paper/70963", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70963"}, {"title": " An irreducible real projective plane in the 4-sphere ", "webprogram_exclude": "0", "session_ids": ["Session/18344"], "source_sha256": "2cbeb517e8c3f2cb1408e0639565e5e29c1155c96e17855963b03b7f8f898165", "withdrawn": "", "abstract": "A smoothly embedded surface in S^4 is called reducible if it can be expressed as a connected sum with an unknotted surface other than a 2-sphere. In this talk I will describe the construction of an irreducible projective plane in S^4. This gives a counterexample to the Kinoshita conjecture, which asserts that every knotted projective plane is reducible. The construction uses a variation of spinning classical knots, together with a generalized knot surgery along an unknotted Klein bottle. I will then explain how the peripheral subgroup of the complement detects irreducibility, and discuss related consequences, including the existence of an irreducible Klein bottle with extremal normal Euler number. This is joint work with Seungwon Kim, Maggie Miller, and Gheehyun Nahm.", "id": "Paper/70966", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70966"}, {"title": " Dynamics of a Charged Particle in Piecewise Constant Magnetic Fields ", "webprogram_exclude": "0", "session_ids": ["Session/18241"], "source_sha256": "6414e3250026955087125640f9be5cbfe76d6470b08a872f5d379acd1db90730", "withdrawn": "", "abstract": "Consider a strictly convex set $\\Omega$ in the plane, and a homogeneous, stationary magnetic field orthogonal to the plane whose strength is $B_0$ inside $\\Omega$ and $B_1$ on the complement of $\\Omega$. The trajectories of a charged particle in this setting are concatenated circular arcs of Larmor radii $\\mu$. We examine the trajectories of such a particle as $B_0$ and $B_1$ vary in both positive and negative value and generate maps to describe them according to angle and arc length. The maps and relationships that follow are made with respect to standard Birkhoff billiards and magnetic billiards both exterior and interior in setting to $\\Omega$. We will focus on the $\\pi$-rational periodicity of the magnetic billiard as well as the extension of the magnetic field to an arbitrary amount of concentric strictly convex sets. Consider the composition of two maps for a charged particle, one directed interior and the latter exterior to $\\Omega$. The composite map can be taken recursively until the particle returns to its original state. This allows us to describe the relationship between the geometry of the trajectory of a charged particle and its period. Additionally, consider the strictly convex sets $\\Omega_1, \\Omega_2,\\dots,\\Omega_n$ in the plane with corresponding homogeneous, stationary magnetic fields orthogonal to the plane with strengths $B_{i-1}$  on $\\Omega_i$. With this construction, we can study the non-grazing conditions required for a trajectory to involve traveling through $i$ magnetic fields, and map the trajectory. Ultimately, we extend to examining trajectories for elliptical orbits.", "id": "Paper/70969", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70969"}, {"title": " A History of Mathematics at Indiana University, 1890-1990 ", "webprogram_exclude": "0", "session_ids": ["Session/18373"], "source_sha256": "a22968632d6b980fdb4795086c8cab6aa0539c9327acc9fe89888439bd174a7c", "withdrawn": "", "abstract": "The Department of Mathematics at Indiana University was founded in 1890 amid a larger shift in higher education in the United States, away from a generalized liberal arts education towards specialization of mathematical and scientific study, in addition to a greater focus on research over teaching in higher academic institutions. In 1912, the first PhD in mathematics at Indiana University was awarded to Cora B. Hennel. Following her graduation, the department awarded a handful of both master's and doctorate degrees. In addition to an expanding graduate program, the department increased involvement in mathematics communities and associations dedicated to the exchange and promotion of mathematical research. Historically this period included international conflict and the Atomic Age, two societal shifts that had a large impact on the world of mathematics. We present and analyze archival materials from the late 19th and 20th century from the mathematics department to track changes in the motivations and work of the mathematicians at Indiana University, in order to construct a historical narrative demonstrating an example of the larger shift in mathematics departments in the United States away from teaching and pedagogical focuses towards a greater focus on research mathematics. Additionally, we consider demographic changes in the department and shifting attitudes around demographics and diversity in the mathematics department. In the early 20th century, the mathematics department had one of the highest percentages of women undergraduate students out of the science degrees. We consider the attitudes towards women and other minorities in mathematics and academia in order to show how these are connected to larger shifts and trends in mathematics.", "id": "Paper/70970", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70970"}, {"title": " What to Teach to How to Teach: Learning Assistants as Catalysts for Instructional Change ", "webprogram_exclude": "0", "session_ids": ["Session/17971"], "source_sha256": "535f43d72a9f767ad882a235777c9d1cfb85e10d6175af7f4a6329174453815c", "withdrawn": "", "abstract": "Large-enrollment mathematics programs are often coordinated around content coverage and common assessments, yet improving student learning also requires sustained attention to pedagogical practices. While common pacing, assessments, and grading policies provide important consistency for students, they also create opportunities to foster effective teaching practices across sections and instructors. This presentation describes how a foundational mathematics program at Florida State University leveraged its existing coordination structures to support instructor development and evidence-based teaching practices. We discuss how these structures provided a foundation for implementing Learning Assistants and facilitating the adoption of active learning strategies across multiple sections. Learning Assistants served as a catalyst for instructors to reexamine classroom practices and adopt more student-centered approaches to instruction. Coordinated course structures also provided a venue for instructors, particularly new instructors, to collaborate, share teaching practices, and receive mentoring in partnership with a campus teaching center. Together, these efforts broadened the focus of course coordination from what students should learn to how they learn most effectively. We will share practical strategies, challenges, and lessons learned for departments seeking to strengthen pedagogy while maintaining consistency across large-enrollment, multi-section mathematics courses.", "id": "Paper/70971", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70971"}, {"title": " Hamiltonian Primal Dual Policy Reinforcement Learning for Derivative-Free Model-Based Control ", "webprogram_exclude": "0", "session_ids": ["Session/19322"], "source_sha256": "4ad0cce399844d7587b9b6e27a964d1887b15f20e3e2539a1e1e6577072816de", "withdrawn": "", "abstract": "Optimal control provides a principled framework for controlling dynamical systems, but many finite-horizon problems involve models that can be simulated reliably while remaining difficult or impossible to differentiate. This occurs in nonsmooth systems, black-box simulators, and Neural ODE models with non-differentiable components. We propose Hamiltonian Primal–Dual Policy Optimization (HPDPO), a model-based reinforcement learning framework for systems with reliable forward simulation but unavailable or unreliable model gradients. For a prescribed initial state, the control sequence is represented as a finite-horizon time-indexed policy. Candidate policies are evaluated through forward rollouts of the transition model, while the control objective is augmented by a regularized Hamiltonian dual formulation. Rather than computing multipliers from backward adjoint equations that require model derivatives, HPDPO alternates sequential policy updates with block-coordinate updates of the dual multipliers. We evaluate the method on two nonsmooth benchmark control problems with exact solutions, a nonlinear biomarker cascade model with analytical and learned ReLU dynamics, and an amyloid Neural ODE trained from longitudinal ADNI observations. Across these experiments, HPDPO produces control policies, trajectories, and objective values that closely match exact solutions or smooth derivative-based baselines. The results show that deterministic model-based rollouts combined with Hamiltonian dual structure provide an effective approach to finite-horizon control when forward simulation is available but model differentiation is unreliable or infeasible.", "id": "Paper/70973", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70973"}, {"title": " Liouville Operator Learning in Paley–Wiener Spaces for Nonsmooth Dynamical Systems ", "webprogram_exclude": "0", "session_ids": ["Session/17703"], "source_sha256": "e9a560c7a5e55bc62296df965c65c1241a63a5c4a22827fd3f5cb4d3f89acfa1", "withdrawn": "", "abstract": "We introduce a data-driven framework for approximating continuous-time dynamical systems using Liouville operators on Paley–Wiener spaces. The approach combines occupation-kernel methods with sinc-based reproducing kernels, providing a natural function space for band-limited approximations of observables and dynamical quantities. This perspective is particularly useful for systems whose vector fields exhibit nonsmooth or piecewise-defined behavior, where standard smooth kernel dictionaries may provide inadequate representations.\n\nUsing trajectory data, a finite-rank approximation of the Liouville operator is constructed through occupation kernels without requiring pointwise numerical differentiation of the state measurements. The resulting operator representation can be used to reconstruct observables, approximate the underlying vector field, and generate predicted trajectories. We investigate the method on several nonsmooth and piecewise-smooth dynamical systems, including piecewise-stiffness and discontinuous oscillators, and also examine its performance on higher-dimensional fluid-flow data through reduced-order coordinates. Numerical experiments demonstrate the potential of Paley–Wiener kernels for representing nonsmooth dynamics while retaining the operator-theoretic structure of continuous-time data-driven modeling.", "id": "Paper/70974", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70974"}, {"title": " Spacetime discreteness and the weight function in a continuous measurement quantum theory ", "webprogram_exclude": "0", "session_ids": ["Session/18321"], "source_sha256": "a3db3d8055c47eb3cd9bf2fbcff1528311028dee2abfd149d9e929cbb6b3e104", "withdrawn": "", "abstract": "In Mensky's “quantum measurement and decoherence” a system of restricted path integrals was developed for first quantization. Adrian Kent in arXiv:1305.6565 developed weighted path integrals for a continuous measurement model of quantum field theory. Sverdlov and Bombelli in arXiv:1306.1948 (2013), and Phys. Rev. D 90: 125020 (2014) showed how the weighted path integral approach can arise from making the iɛ term in quantum field theory propagators finite. In this talk, the latter model will be developed in the discrete spacetime context of causal set theory.", "id": "Paper/70975", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70975"}, {"title": " Teaching statistics using a resampling-based approach ", "webprogram_exclude": "0", "session_ids": ["Session/18064"], "source_sha256": "0123e1e97e96ad4a5e87881f92f4a718922a8d233927a3e3662e8f29375e84d3", "withdrawn": "", "abstract": "Statistics is one of the most important aspects of undergraduate education in the Life Sciences. No matter the career on which students embark, they will be faced with understanding and interpreting statistical results in the literature, and will often be tasked with selecting and applying the correct statistical approaches in their own work. This talk will discuss the overall structure of a new class in statistics that we’ve developed at UCLA that focuses on modern, nonparametric resampling-based approaches. These methods relax many of the assumptions and limitations of traditional, formula-based techniques, and as such produce more reliable, robust results that are more broadly applicable. In addition, we have found that this resampling paradigm is more pedagogically effective, allowing students to directly engage with notions like sampling from a distribution and calculating “statistical significance.” I will discuss the general structure of the class, its computational labs, and focus on several key examples that highlight both the generality of the resampling framework and the ways in which it helps students overcome common misconceptions about the meaning and application of statistical results.", "id": "Paper/70976", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70976"}, {"title": " Overview of geometric structure of Orlicz-Lorentz spaces ", "webprogram_exclude": "0", "session_ids": ["Session/17782"], "source_sha256": "5061dc1c9e5fcdee373fc819b5daae55dd28c6b8aad845ad3a3fdf45c15aa68f", "withdrawn": "", "abstract": "I will present basic and more advance topics in Orlicz-Lorentz spaces", "id": "Paper/70980", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70980"}, {"title": " Fast Simultaneous Matrix Multiplication by Aggregation of Tensor Contractions ", "webprogram_exclude": "0", "session_ids": ["Session/16950"], "source_sha256": "adebd0d9236ed8165f3f018247e66299853eb5867d7a2348dbd42d7d999adda8", "withdrawn": "", "abstract": "We present an interpretation of the fast matrix multiplication algorithms of Coppersmith and Winograd as aggregations of tensor contractions. This point of view provides a direct connection to older constructions by Pan and to more recent work on bilinear algorithms for symmetric tensor contraction. Further, we provide a new simple approach for exact aggregation of tensor contractions, each one yielding an independent matrix-matrix product. These constructions and border rank adaptations thereof do not come close to improving the best known bounds on $\\omega$ (the matrix multiplication exponent), but provide explicit moderate-size fast matrix multiplication algorithms that achieve a better exponent than Strassen and have potential practical value. Finally, we give improvements to the best known bounds on the rank and border rank of constructions corresponding to a fixed number of independent square matrix-matrix products.", "id": "Paper/70981", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70981"}, {"title": " A parity obstruction for Neumaier graphs with <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"9.275ex\" height=\"2.343ex\" style=\"vertical-align: -0.505ex;\" viewBox=\"0 -791.3 3993.5 1008.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">e = s-2</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-73\" d=\"M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-65\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-3D\" x=\"744\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-73\" x=\"1800\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2212\" x=\"2492\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-32\" x=\"3493\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/19354"], "source_sha256": "0b39e50bc20468826a9e0d67627c89b7551999196d57c39d935c7254c82bf18f", "withdrawn": "", "abstract": "A Neumaier graph is a non-complete edge-regular graph containing a regular clique; it is strictly Neumaier if it is not strongly regular. We study Neumaier graphs whose parameters satisfy $e = s-2$, where $s$ is the size and $e$ the nexus of the regular clique. We show that this condition forces the vertices outside the clique to split, in the complement, into $\\binom{s}{2}$ classes of equal size indexed by the pairs of an $s$-set, so that the whole class is a two-parameter family indexed by $(s,\\mu)$ with $\\mu = v-2k+\\lambda$. Analysing the local structure, we prove that the number of edges between two classes sharing an index is completely determined by the distribution of a certain perfect matching, and that the resulting integrality conditions give a parity obstruction: if $\\mu$ is odd, then $4 \\mid s$. In particular, there is no Neumaier graph with parameters $(10\\mu+5, 6\\mu+4, 3\\mu+3; 3, 5)$ for any odd $\\mu$. This answers a question of Abiad, De Boeck and Zeijlemaker, who observed computationally that these parameter sets are eliminated with unexpected ease and suggested there might be an underlying theoretical reason. Using the forced edge counts to prune an exhaustive search, we eliminate five further parameter sets left open in their table, namely $(28,15,6;2,4)$, $(34,18,7;2,4)$, $(40,21,8;2,4)$, $(45,28,15;3,5)$ and $(46,24,9;2,4)$. Together, these results settle the family $(10\\mu+5, 6\\mu+4, 3\\mu+3; 3, 5)$ for all $\\mu \\le 5$. All evidence is consistent with the conjecture that the unique strictly Neumaier graph on $16$ vertices is the only one with $e = s-2$.", "id": "Paper/70982", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70982"}, {"title": " Explicit Solutions to a Classic IVP on Various Discrete Time Scales ", "webprogram_exclude": "0", "session_ids": ["Session/19357"], "source_sha256": "36ca9ae1a1976787f1787f9bf722fc6df2ec7ea2c8be968b2bdd502497cd8f0f", "withdrawn": "", "abstract": "In this talk we give an explicit formula for the solution to the IVP $(\\nabla^m F)(t) = f(t)$ subject to the $m$ initial conditions $F(t_a) = (\\nabla F)(t_a) = \\ldots =  (\\nabla^{m-1}F)(t_a) =0$ where $f(t)$ is a function on an isolated time scale and $\\nabla^m$ is the backward difference operator of integer order $m$.  We consider how the formula for this solution simplifies for some specific time scales for which the graininess is not constant but follows a pattern.\\\\", "id": "Paper/70990", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70990"}, {"title": " Controlling the skips of arithmetic sets ", "webprogram_exclude": "0", "session_ids": ["Session/18589"], "source_sha256": "1138192f3fe84eee6ef425b255b0f5d617738bd131551c2f5f4543979356b7b1", "withdrawn": "", "abstract": "The notion of \\emph{cototality} has connections with various areas of mathematics including group theory, symbolic dynamics, and computable analysis. The \\emph{skip}, a fundamental feature within the structure of enumeration degrees, exhibits a strong connection with cototality. Andrews, Ganchev, Kuyper, Lempp, Miller, A. Soskova, and M. Soskova asked whether skip-cototality coincides with weak cototality. We show that the answer is negative by constructing a $\\Pi^0_2$ set whose skip does not have a cototal degree. We further adapt this construction to obtain additional results on the iterated skips of a set. We prove that for each odd $n$, there is a $\\Pi^0_{n+1}$ degree whose $n$-iterated skip does not have a cototal degree.", "id": "Paper/70992", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70992"}, {"title": " Only finitely many modular Jacobians are supersingular modulo any given prime ", "webprogram_exclude": "0", "session_ids": ["Session/19367"], "source_sha256": "3fd6e41c0a83a66a95264ea131ef937352000dc0514e5be39deaf77b6b5d9f5d", "withdrawn": "", "abstract": "We study the supersingularity of modular Jacobians $J_0(N)$ and abelian varieties $A_f$ of $\\text{GL}_2$-type from both the vertical perspective (where the prime $p$ is fixed, and the level $N$ varies) and the horizontal perspective (where the newform $f$ is fixed, and the prime $p$ varies). Vertically, we prove that for any given prime $p$, $J_0(N)$ is supersingular modulo $p$ for only finitely many levels $N$. Horizontally, we show that for sufficiently large $p$, the reduction of $A_f$ modulo $p$ is supersingular if and only if it isogenous to a power of a supersingular elliptic curve.", "id": "Paper/70993", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70993"}, {"title": " Down the Rabbit Hole of Order 4 Magic Squares ", "webprogram_exclude": "0", "session_ids": ["Session/18234"], "source_sha256": "3785241595ee7c557aa968ef2a72c023279208bf80b6ff02f3cf072b7113d4d8", "withdrawn": "", "abstract": "The 4x4 magic squares, with 880 unique solutions, provide a \"Goldilocks\" opportunity for investigation — more interesting than the 3x3 case (only one solution) and more manageable than higher orders (for example, there are 275,305,224 unique magic squares of Order 5). The 16 numbers in each 4x4 magic square can be represented by colored shapes (or expressed graphically in another number base system) in order to illustrate certain magical properties of the square. The 880 magic squares of order 4 can be grouped into just a dozen basic types based on diagrams of complementary number pairs. Furthermore, the “magic path” diagram for each specific magic square provides interesting insights into the underlying structure of the square. In this talk, I will present several of my recent artworks based on exploring the various properties of Order 4 magic squares and expressing them visually.", "id": "Paper/70999", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/70999"}, {"title": " Dispersive Equations with Combined Nonlinearities: Well-Posedness, Blow-Up, and Simulations. ", "webprogram_exclude": "0", "session_ids": ["Session/19357"], "source_sha256": "fc51d2aec667b8b6b0e43653ba454ffd785845e93d2c263add54489327c0fa7b", "withdrawn": "", "abstract": "We will discuss a local and global well-posedness approached based on weighted\nsobolev spaces for the NLS type equations with combined nonlinearities; emphasizing the flexibility of the technique. In some cases we also prove scattering for initial data with a quadratic phase and discuss a possible threshold for the global vs finite time existence. We then present some simulation examples and comment on how the same\nquadratic phase can lead to blow up solutions by showing numerical examples for exponential type nonlinearities, which are then backed up by analytical results", "id": "Paper/71000", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71000"}, {"title": " Identifiability of Skeletal Path Linear Compartmental Models ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "87fbb632ca2304be74cb5732c341f62936bfd95fce21fac9667b44b38090935a", "withdrawn": "", "abstract": "Linear compartmental models (LCMs) describe the flow of material between compartments and are widely used in fields such as pharmacokinetics, epidemiology, biology, and systems engineering. An LCM consists of an underlying weighted, directed graph, where the weights represent flow rates between compartments, the input represents what enters the system, and the output represents active measurements taken at a particular compartment. Every LCM also has a corresponding system of differential equations, which can be simplified in various ways to yield an equation in only known variables, called an input-output equation.\nA central challenge is determining when all of a model's flow rates can be identified, which is the study of identifiability. Several recent results address identifiability for various families of strongly connected models. In this work, we consider non-strongly connected models, specifically those built on a one-way flow path. Our results build on recent work by Bortner et al., who developed new machinery for generating input-output equations directly from the underlying graph structure. To our knowledge, these are among the first identifiability results for non-strongly connected models.\nThis work was supported by the NSF LEAPS grant DMS-2532620.", "id": "Paper/71001", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71001"}, {"title": " \"The Corridor of Autonomy\": Mathematical Frameworks for Bounded Operating Envelopes ", "webprogram_exclude": "0", "session_ids": ["Session/18323"], "source_sha256": "1ef8f35545102092e82acb0408001213126f8e761c6ee430c17a345637ebdddf", "withdrawn": "", "abstract": "Traditional flight safety certification in the U.S. Department of War (DoW) relies on evaluating a platform against established standards to characterize and mitigate risk. Airworthiness authorities issue flight clearances by accepting residual risk, relying on a human operator to remain accountable for vehicle safety. As the DoW moves toward fielding autonomous Uncrewed Aerial Systems (UAS) operating without a human in or on the loop, this foundational paradigm fails. Certification officials now require mathematically rigorous guarantees that non-deterministic autonomous behavior will remain provably safe. To bridge this gap, research explores bounded operational envelopes managed by Run-Time Assurance (RTA) frameworks. Using complex maneuvers like probe-and-drogue autonomous aerial refueling as a primary use case, an RTA monitor dynamically evaluates vehicle state. Within a certified \"Corridor of Autonomy,\" non-deterministic algorithms are permitted; if a boundary is approached, control deterministically reverts to a verified fail-safe recovery maneuver. Defining and certifying these dynamic safety margins requires mathematical tools beyond conventional empirical flight-testing. This presentation serves as an open call to the mathematical community to help advance rigorous paths to solve this national security challenge. Key areas of interest include formal methods for online verification, computational reachability analysis (such as Hamilton-Jacobi backward reachable sets), Control Barrier Functions (CBFs) for real-time safety constraints, stochastic control, and mathematical abstractions for high-dimensional state spaces We outline the operational certification challenge, showcase current RTA formulations, and highlight explicit open mathematical problems where theoretical advancements can directly enable the safe fielding of autonomous defense systems.", "id": "Paper/71007", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71007"}, {"title": " Optimal decay constant for complete manifolds of positive scalar curvature with quadratic decay ", "webprogram_exclude": "0", "session_ids": ["Session/17803"], "source_sha256": "78287d7d870c1df510cf4056028ab372af79c915d94e2120b749668c9ed877f4", "withdrawn": "", "abstract": "We prove that if an orientable 3-manifold $M$ admits a complete Riemannian metric whose scalar curvature is positive and has at most $C$-quadratic decay at infinity for some $C > \\frac{2}{3}$, then it decomposes as a (possibly infinite) connected sum of spherical manifolds and $\\mathbb{S}^2\\times \\mathbb{S}^1$ summands. Consequently, $M$ carries a complete Riemannian metric of uniformly positive scalar curvature. The decay constant $\\frac{2}{3}$ is sharp, as demonstrated by metrics on $\\mathbb{R}^2 \\times \\mathbb{S}^1$. This improves a result of Balacheff, Gil Moreno de Mora Sarda, and Sabourau, and partially answers a conjecture of Gromov. The main tool is a new exhaustion result using $\\mu$-bubbles.", "id": "Paper/71008", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71008"}, {"title": " On Enveloping Real C*-Algebras for a Real Symmetric lmc*-algebras ", "webprogram_exclude": "0", "session_ids": ["Session/19342"], "source_sha256": "45a68df6e919ca0aea24811a8bf86e75fd9da60f2d15e6e1eddaa89d5c1488ad", "withdrawn": "", "abstract": "In the previous work we have constructed enveloping real locally C^{∗}-algebra A for a real hermitian lmc^{∗}-algebra B, and establish connections with respective complexifications of the aforementioned algebras, as well as have given several necessary and sufficient conditions for the algebra A to be a real C^{∗}-algebra. In the present sequel we show among other things that a real Fréchet lmc^{∗}-algebra B has a real C^{∗}-enveloping algebra iff every operator representation of B maps B into the algebra of bounded linear operators.", "id": "Paper/71010", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71010"}, {"title": " Bound States in Exactly Solvable Polaritonic Models ", "webprogram_exclude": "0", "session_ids": ["Session/17804"], "source_sha256": "acdad8f69c3837acf43b27994deab594ec469b45631dcd68d019eedf3bfedb7a", "withdrawn": "", "abstract": "We investigate the bound states of a one-dimensional matrix Hamiltonian describing an effective-mass field coupled to a continuum of two-level atoms with spatially varying density. In the single-excitation subspace, elimination of the atomic component reduces the eigenvalue problem to an energy-dependent Schrödinger equation. For constant atomic density, the spectrum is purely continuous and consists of two bands separated by an upper and a lower gap.\n\nUsing a Birman–Schwinger type argument, we prove that compactly supported  increases in the atomic density produces a discrete eigenvalue in the lower gap. Conversely, a compactly supported decrease that preserves positivity of the total density produces an eigenvalue in the upper gap. We then analyze several exactly solvable perturbations, including single and double point interactions and finite square wells and barriers. \n\nThis is joint work with Sam Johar and Ryogo Katahira.", "id": "Paper/71015", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71015"}, {"title": " Observable Clocks for Sequential Recovery in Tensor PCA ", "webprogram_exclude": "0", "session_ids": ["Session/19370"], "source_sha256": "f15b10fc9d5c0d266756a20a528c04bec3e67221ed98f9702439ebafa23ef85a", "withdrawn": "", "abstract": "For online orthogonal tensor principal component analysis, sequential recovery is naturally described through correlations between the iterates and unknown signal directions. These correlations, however, are latent and therefore cannot be monitored directly. We ask whether the successive recovery stages can nevertheless be located using quantities observable along the stochastic gradient descent trajectory.\n\nFor fixed tensor order and rank with known positive spike weights, we construct observable reporting rules based on fresh tensor observations and spectral information from a transverse Hessian. Under independent sub-Gaussian noise, positive initialization, and explicit separation and stepsize conditions, we prove that these rules report the recovered columns in the same order as the latent correlation dynamics, with probability tending to one as the ambient dimension grows. More precisely, each observable report interval is asymptotically equivalent to the duration of the corresponding latent recovery stage: their ratio converges to one in probability.\n\nThe proof builds on the sequential recovery dynamics of Ben Arous, Gerbelot, and Piccolo and develops uniform observation estimates that remain valid at the random reporting times. It also controls competing correlations from one reported stage to the next, allowing the argument to be iterated through the full sequential recovery process. The resulting clocks locate otherwise unobservable recovery stages over a polynomial time horizon, while making no claim of certifying a prescribed reconstruction accuracy at the reporting times.", "id": "Paper/71016", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71016"}, {"title": " A characterization of all graphs cospectral to the double star <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"7.947ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 3421.6 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">P_2(1,n)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-50\" d=\"M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-50\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-32\" x=\"908\" y=\"-213\"></use>\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"1096\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-31\" x=\"1485\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2C\" x=\"1986\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-6E\" x=\"2431\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"3032\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18299"], "source_sha256": "bf2b5747ddbcfead22bde08037291d533e271319a9f479e11dff4b8978c84417", "withdrawn": "", "abstract": "We examine the adjacency spectrum of trees with diameter three, also referred to as double stars. Using $P_2(a,b)$ to denote a double star with $ a$ and $b$ leaves at its respective endpoints, we discuss graphs which are cospectral to double stars for various parameters $a$ and $b$. In particular, we give constructions for graphs cospectral to $P_2(1,2k)$ for integers $k$.  Lastly, we show that the double star $P_2(1,n)$  is determined by its spectrum when $n$ is odd. That is, if a graph $G$ cospectral to $P_2(1,n)$ for odd $n$, then $G$ is isomorphic to $P_2(1,n)$.", "id": "Paper/71018", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71018"}, {"title": " Distinct Distances Between Two lines in <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.029ex\" height=\"2.843ex\" style=\"vertical-align: -1.005ex;\" viewBox=\"0 -791.3 873.5 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\ell _p</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2113\" d=\"M345 104T349 104T361 95T369 80T352 59Q268 -20 206 -20Q170 -20 146 3T113 53T99 104L94 129Q94 130 79 116T48 86T28 70Q22 70 15 79T7 94Q7 98 12 103T58 147L91 179V185Q91 186 91 191T92 200Q92 282 128 400T223 612T336 705Q397 705 397 636V627Q397 453 194 233Q185 223 180 218T174 211T171 208T165 201L163 186Q159 142 159 123Q159 17 208 17Q228 17 253 30T293 56T335 94Q345 104 349 104ZM360 634Q360 655 354 661T336 668Q328 668 322 666T302 645T272 592Q252 547 229 467T192 330L179 273Q179 272 186 280T204 300T221 322Q327 453 355 590Q360 612 360 634Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-70\" d=\"M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-2113\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-70\" x=\"590\" y=\"-213\"></use>\n</g>\n</svg> Norms ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "2e8e0e6f7ba354b95fc04312fa6cb6f172a89dfb93b5f6fe6ddd3771b09dd03e", "withdrawn": "", "abstract": "\\emph{Distinct distances between two lines} is a well-studied problem in combinatorial geometry. In this problem, $\\ell_1$ and $\\ell_2$ are lines in the plane. Let $P_1$ and $P_2$ be sets, each of $n$ points, respectively on $\\ell_1$ and $\\ell_2$. Let $D$ be the set of distances spanned by pairs of points from $P_1\\times P_2$. When the lines are parallel or orthogonal, it is possible for $D$ to have only $n$ distances. Otherwise, it is known that $|D|> c n^{3/2}$, for some fixed constant $c$.\n\nWe generalize the above problem from the Euclidean distance to all $\\ell_p$ distances. Our proof relies on a mix of tools from combinatorial geometry, basic algebraic geometry, and model theory.", "id": "Paper/71025", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71025"}, {"title": " The bouquet-of-spheres conjecture ", "webprogram_exclude": "0", "session_ids": ["Session/18072"], "source_sha256": "42c0e2dfc81911514f57a8e7928b750b08152e0b26e9e7013f6a6531a6ca7599", "withdrawn": "", "abstract": "Many naturally arising simplicial complexes and posets are homotopy equivalent to wedge sums (or ``bouquets'') of spheres. Researchers in topological combinatorics have often asked if there is any good reason why. Over 20 years ago, a conjecture was made that, for a certain easy to define measure, a random simplicial complex is homotopy equivalent to a bouquet of spheres with high probability. This would provide a measure-theoretic explanation for the prevalence of bouquets of spheres.  \n\nWith assistance from generative AI, I was recently able to prove this conjecture. In this talk, I will outline the proof.", "id": "Paper/71026", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71026"}, {"title": " Diagonal modules with short linear resolutons ", "webprogram_exclude": "0", "session_ids": ["Session/18318"], "source_sha256": "fa185fe971f3b8c76957cf131c48f0915d7c8176b2527af70549fe3d8b0c728d", "withdrawn": "", "abstract": "In the last few years we have seen a couple of techniques for resolving the diagonal of normal toric varieties via combinatorial methods. I will present work that pulls ideas from a variety of free resolutions of the diagonal to construct modules for the diagonal which have short linear resolutions. These new resolutions connect ideas on quiver algebras inspired by the work of Favero and Huang more directly with the work on the ceiling stratification in my joint paper with Berkesch, Cranton Heller, and Smith.", "id": "Paper/71027", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71027"}, {"title": " Explicit Solutions to a Classic IVP on Various Isolated Time Scales ", "webprogram_exclude": "0", "session_ids": ["Session/17446"], "source_sha256": "99bd3ee7bf701b48d0f9a700c00de7dfee16008ad643469e6a75e60a97ced91e", "withdrawn": "", "abstract": "In this talk we give an explicit formula for the solution to the IVP comprised of the difference equation $(\\nabla^m F)(t) = f(t)$ and the $m$ initial conditions $F(t_a) = (\\nabla F)(t_a) = \\ldots =  (\\nabla^{m-1}F)(t_a) =0$ where $f(t)$ is a function on an isolated time scale and $\\nabla^m$ is the backward difference operator of integer order $m$.  We consider how the formula for this solution simplifies for some specific time scales for which the graininess is not constant but follows a pattern.\\\\", "id": "Paper/71028", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71028"}, {"title": " On Quasisymmetric Magnetohydrostatic Vector Fields with Prescribed Flux Surfaces ", "webprogram_exclude": "0", "session_ids": ["Session/18104"], "source_sha256": "9721f8ba343ccf58fd10cc7125ff1a825d32f3adf3d2f259b3f2e7fe0ca3160e", "withdrawn": "", "abstract": "An open question in stellarator design is the existence of quasisymmetric (QS), magnetohydrostatic (MHS) vector fields with toroidal flux surfaces. This talk will present current work towards resolving this existence question using moving frames and exterior differential systems (EDS). We uncover that there is at most a finite number of QS, MHS vector fields for a chosen foliation of flux surfaces and that any such $B$ field can be constructed in terms of finitely many derivatives of geometric invariants associated to the flux surface foliation. Moreover, we find that a complicated PDE arises as a necessary condition for the foliations, which may tightly constrain the geometry of the flux surfaces.\n\nThis work arose from various conversations with Nathan Duignan, Joshua Burby, James Meiss, and Wrick Sengupta.", "id": "Paper/71030", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71030"}, {"title": " Restriction Trees for Sparsity and Applications ", "webprogram_exclude": "0", "session_ids": ["Session/18090"], "source_sha256": "666336c1da877a6a090608655bfbaa2c0c41587d282ecc9be5e7798a6cd1d3ab", "withdrawn": "", "abstract": "We study the sparsity of real polynomial representations of Boolean functions in the De Morgan basis. We introduce a new combinatorial characterization, called max-degree restriction trees, that provides local certificates of large sparsity. Using this characterization, we show that approximating a Boolean function, rather than computing it exactly, does not lead to substantially sparser representations: there is only a polynomial advantage on the logarithmic scale, up to polylog(n) factors. This is a sparsity analogue of the celebrated relation between exact and approximate degree established by Nisan and Szegedy (STOC, 1992).\n\nI will then explain how this structural understanding can be used to study AND-lifted functions, where a Boolean function is applied to the coordinate-wise AND of two distributed inputs. Using a restriction-and-averaging argument, the restriction-tree structure yields lower bounds on approximate matrix norms associated with these functions. Combined with known upper bounds in terms of De Morgan sparsity, this implies that classical and quantum communication complexity are polynomially related for all AND-functions.", "id": "Paper/71032", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71032"}, {"title": " Quantity vs Quality, and There are Limits to the Power of Both ", "webprogram_exclude": "0", "session_ids": ["Session/18024"], "source_sha256": "74c5fa18460201f35377087ed7916464e6423041cde771e7d9564daa5ddc2926", "withdrawn": "", "abstract": "A variety of Monte Carlo studies were conducted to show the power\nof data quantity for accurately determining a system’s true characteristics, with\nthe hypothesis that a high quantity of data can overcome noise in the measurements.\nFor simplicity’s sake, all noise was distributed symmetrically around the\n“correct” result. The effect of increased measurements were compared with the\neffect of increased measurement accuracy. In all cases, increasing the amount of\nmeasurements increased the accuracy of the final result but only to a point, at\nwhich additional data had no effect. Before this plateau was reached, each experiment\nshowed that reducing the error of each sample is far more powerful than\nincreasing the amount of data. Three simple rules can help balance the costs of\nincreasing measurement accuracy with the costs of increasing the number of experiments;\n1) the accuracy of the result is proportional to the accuracy of the data, 2)\nthe accuracy of the result is proportional to the square of the amount of data, and\n3) increasing the number of data points will increase the accuracy of the result, but\nonly to a limit that is proportional to the accuracy of the data and the accurate\ncharacterization of the population characteristics of the dat", "id": "Paper/71035", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71035"}, {"title": " How do you plan your Math Circle, and why? A Mad Veterinarian explains. ", "webprogram_exclude": "0", "session_ids": ["Session/18212"], "source_sha256": "b2994eff03e00be22ab33af672eeb3612e8e6df27ed19e3edb7988bc8029e17a", "withdrawn": "", "abstract": "This talk will address three main points: what the goals of a Math Circle might be; how to prepare your Circle, depending on your goals; and a walkthrough of these approaches to preparation in the specific case of Mad Veterinarian problems. Our focus will be on how planning works in Math Circles where there is no specific plan, and the participants are asked to take greater ownership over their exploration. Our hope is to break down the barrier to leading this kind of Circle by charting an attainable course to preparing one yourself, with Mad Vet as a case study.", "id": "Paper/71036", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71036"}, {"title": " Enumerations of Row Complete Latin Squares ", "webprogram_exclude": "0", "session_ids": ["Session/19354"], "source_sha256": "113a79fb78c1f0dac0d802b8d22c3d16ffcd1bde21fcef332dda86bddfec7003", "withdrawn": "", "abstract": "Enumeration techniques for Row Complete Latin Squares (RCLS) and certain subsets of RCLS will be presented.", "id": "Paper/71039", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71039"}, {"title": " Fixed perimeter analogues of several partition results related to parity ", "webprogram_exclude": "0", "session_ids": ["Session/17968"], "source_sha256": "28e8ae8c96be366c1e808c5d100f23a730cec8bf32a2b315a649171d7644b2a2", "withdrawn": "", "abstract": "In 2016, Straub proved that Euler's classic partition identity holds true for partitions with largest hook (perimeter) $n$. This inspired further study of the relationship between classical partitions and fixed perimeter partitions. We extend the study of parity bias inequalities, first introduced by Kim, Kim, and Lovejoy in 2020, to the fixed perimeter setting and show using combinatorial methods that fixed perimeter analogues of many classical parity bias results can be proven and generalized. We also extend these methods to prove similar inequalities for the fixed perimeter analogues of PED and POD partitions. We additionally develop recursive formulas for the number of perimeter $n$ partitions with odd parts distinct and even parts unrestricted and with even parts distinct and odd parts unrestricted.", "id": "Paper/71042", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71042"}, {"title": " Fashion Changes but Style Endures: Modeling the Cyclical Dynamics of Trends ", "webprogram_exclude": "0", "session_ids": ["Session/18260"], "source_sha256": "fd320ba89290384735d995d8955175ca7b8859fd770801222fcea07b3835c2c1", "withdrawn": "", "abstract": "Many people have experienced firsthand the idea that \"fashion comes back,\" from bell-bottom jeans to mini-skirts. Historically, a lack of quantitative data posed a barrier to explicit mathematical study of fashion; however, newly digitized historical records now make such work possible. We construct and analyze a database quantifying neckline, waistline, and hemline for women's dresses using over 35,000 images from 1920-2022. Our analysis demonstrates that trends exhibit roughly 20-year cycles, consistent with fashion industry knowledge.  We also observe clustering, with hemlines undergoing an apparent bifurcation from one to two clusters in the mid-1980s, and an increase in variance over time. These phenomena are consistent with the predictions of an ``optimal distinctiveness'' model we propose in which agents strive to be different, but not too different, from the past, from an absolute reference point, and from other agents. Large-scale social phenomena such as fashion trends are of intrinsic interest themselves, but a better understanding of this fashion system will contribute to elucidating the interplay of creativity, differentiation, conformity, and diffusion of ideas in broader human systems.", "id": "Paper/71046", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71046"}, {"title": " Dynabase: A Database of Extreme Examples in Algebraic Dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/17755"], "source_sha256": "86498a98d06a50f14da3cfd69eebb705b68472bfd7e2bcb26e09af335c6560d2", "withdrawn": "", "abstract": "This is a report on a preliminary live version of Dynabase: a database of interesting algebraic dynamical systems. The talk will cover how the examples are curated, what data is contained in the database, and how to access the information within it.", "id": "Paper/71049", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71049"}, {"title": " Optimal Biocontrol of Aphids with Piecewise-deterministic Predator Dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/18248"], "source_sha256": "1690b5d88645f6069b1116d0a3534bfd1c12c5f1051ce12ef127d64c0adb6ccb", "withdrawn": "", "abstract": "Aphids are a pest affecting many commericial crops. Due to the abundance of natural predators, biocontrol via managed or seeded predator populations is an area of active interest. Previous models have assumed that managed predator populations disperse or diffuse continuously in space and time. Here, we investigate the impact of of random predator dispersal times on the effectiveness of aphid management strategies. We model this via optimal control of a piecewise-deterministic Markov process and find optimal policies numerically using methods from dynamic programming. We compare continuous and random dispersal via numerical simulations.", "id": "Paper/71052", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71052"}, {"title": " A Modeling Framework for Predicting Hawaiian Leafhopper Population Responses to Climate Change Using Short-Term Experiments ", "webprogram_exclude": "0", "session_ids": ["Session/19353"], "source_sha256": "fdfa1269dcda2280f1d4df7cb9383270a6adead8ce504487d0f682d3765196ed", "withdrawn": "", "abstract": "The endemic Hawaiian leafhoppers (Hemiptera: Cicadellidae: Nesophrosyne) comprise over 200 species distributed across the archipelago. Species are narrowly adapted to distinct host plants and climatic zones (coastal lowlands to subalpine mountain tops), making them sensitive indicators of the health of a broad range of ecosystems. Understanding how temperature shifts influence the populations of various species, including leafhoppers, will enable land managers to anticipate potential biodiversity loss resulting from climate change. As efforts to conserve Hawai'i’s biodiversity continue, there is a need for conservation tools that translate short-term fitness assay experiments into long-term predictions of population persistence and vulnerability to temperature change. Here, we developed an age-structured population mathematical model to quantify how temperature conditions influence the dynamics of leafhopper generations. The model was fitted on fitness and survival assays using a tractable laboratory leafhopper population (Macrosteles quadrilineatus) reared for one month under moderate to severe predicted climate change scenarios. Based on historical and projected temperature data from the National Oceanic and Atmospheric Administration, we determined the projected temperature changes over the island of Maui and then applied our model to predict the resulting population shifts. As a result, we created geographic maps that highlight vulnerable areas, giving land managers tools to inform conservation and policy decisions and enabling early interventions to reduce biodiversity loss.  Our work highlights the ability to integrate short-term fitness assay experiments and mathematical models to predict population outcomes for conservation efforts, while building a framework that can be applied to other species.", "id": "Paper/71053", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71053"}, {"title": " Deterministic approximation of the permanent ", "webprogram_exclude": "0", "session_ids": ["Session/18002"], "source_sha256": "230376804dac3ca388a79c0f5fcf75946afbbc73ad944f2d682d29501b42e79b", "withdrawn": "", "abstract": "A celebrated result of Jerrum, Sinclair, and Vigoda gives an FPRAS for the permanent of a nonnegative matrix, but obtaining strong deterministic approximations remains open. I will discuss two recent results in this direction. \n\nFirst, if the support graph of an $n\\times n$ nonnegative matrix has girth at least $g$, we show that the Bethe permanent approximates the permanent within a factor $2^{2n/g}$. This is best possible. \n\nSecond, for an arbitrary $n\\times n$ nonnegative matrix and any $\\varepsilon > 0$, we give a deterministic polynomial-time algorithm to approximate the permanent within a factor $(1+\\varepsilon)^n$.\n\nBased on joint works with Dingding Dong (Caltech).", "id": "Paper/71054", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71054"}, {"title": " Weight Space Symmetries and Functional Dimension of Transformer Architectures ", "webprogram_exclude": "0", "session_ids": ["Session/17835"], "source_sha256": "925517546692d89e38e0220f345e1a0296613439173151bcba9bb3058801cd4b", "withdrawn": "", "abstract": "Transformer architectures have non-unique parameterizations where continuous families of distinct weights can induce the same input-output map. This talk studies this non-identifiability and its consequences for the dimension of the represented function families.\n\nWe begin with multi-headed SoftMax attention, describing generic fibers of its parameterization. We then extend the proof strategy to deep transformers under progressively fewer architectural assumptions, culminating in a proof of the functional dimension of the OLMoE transformer architecture using AI assistance in Lean.\n\nUnder explicit genericity hypotheses, we compare functional dimensions after removing or modifying architectural components. We find that removing skip connections reduces the functional dimension far more than replacing SoftMax with linear attention or removing the Swish activation from SwiGLU to obtain a bilinear MLP. Together with experiments, these results illustrate how functional dimension can help quantify the contributions of individual architectural components to transformer expressivity in practical settings.", "id": "Paper/71055", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71055"}, {"title": " A Riemannian optimization algorithm for quantum optimal control ", "webprogram_exclude": "0", "session_ids": ["Session/19337"], "source_sha256": "19c67fcc3a5fd62509bc7ace7c69cf3be1f5a4151a9f1c6c08051b32d72d26e7", "withdrawn": "", "abstract": "Theoretical treatments of quantum computing usually take an algebraic point of view, wherein circuits built from discrete sets of unitary gates are the main objects of study, but at lower levels of abstraction, the physical implementation of  quantum computation resides in the continuous setting. Realizing an operation on a quantum device requires steering the solution of a controlled Schr\\\"odinger equation on a Lie group to a target group element, and the resulting evolution depends highly nonlinearly on the controls. Although geometric control theory addresses the theoretical existence and regularity of optimal controls, the numerical methods used in practice to design control inputs for quantum devices can be unreliable and come with little convergence theory. Viewed through the Riemannian structure natural to the compact Lie groups arising in our applications, the problem of constructing approximate controls has rich structure that can inform both the design of geometric optimization algorithms and their analysis. We discuss progress toward a convergence theory for these methods, and present numerical results for a preliminary algorithm demonstrating substantial improvements over existing approaches.", "id": "Paper/71056", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71056"}, {"title": " Fubini Rankings in the Orbits of the <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.095ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 471.5 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\zeta</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-3B6\" d=\"M296 643Q298 704 324 704Q342 704 342 687Q342 682 339 664T336 633Q336 623 337 618T338 611Q339 612 341 612Q343 614 354 616T374 618L384 619H394Q471 619 471 586Q467 548 386 546H372Q338 546 320 564L311 558Q235 506 175 398T114 190Q114 171 116 155T125 127T137 104T153 86T171 72T192 61T213 53T235 46T256 39L322 16Q389 -10 389 -80Q389 -119 364 -154T300 -202Q292 -204 274 -204Q247 -204 225 -196Q210 -192 193 -182T172 -167Q167 -159 173 -148Q180 -139 191 -139Q195 -139 221 -153T283 -168Q298 -166 310 -152T322 -117Q322 -91 302 -75T250 -51T183 -29T116 4T65 62T44 160Q44 287 121 410T293 590L302 595Q296 613 296 643Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-3B6\" x=\"0\" y=\"0\"></use>\n</g>\n</svg> Map ", "webprogram_exclude": "0", "session_ids": ["Session/19346"], "source_sha256": "f32bb94c2bde173dec9947918e6f03c7a775719a18515ff6fbf83958c841ec81", "withdrawn": "", "abstract": "The $\\zeta$ map is a famous bijective self-map for the set of Dyck paths, or equivalently the set of weakly increasing parking functions. A weakly increasing Fubini ranking is a structured type of weakly increasing parking function in which the corresponding Dyck path returns to the diagonal immediately after each run of consecutive North steps. In this work, we study weakly increasing Fubini rankings in the pre-images and orbits of the $\\zeta$ map.  We enumerate the sets of weakly increasing Fubini rankings whose images are (and are not) Fubini rankings. Symmetrically, we enumerate the sets of weakly increasing parking functions that are not Fubini rankings and whose images are (and are not) Fubini rankings.  Finally, we extrapolate patterns in the pre-image that determine whether the image is or is not Fubini.  The aforementioned enumerations include the Eulerian numbers and a sequence derived from the Catalan numbers.", "id": "Paper/71058", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71058"}, {"title": " The Matrix in the Commutant ", "webprogram_exclude": "0", "session_ids": ["Session/19356"], "source_sha256": "d109b47ea6a9ca1df33a1c21b3f70aa132216df70ef14a6433b5302595da7a65", "withdrawn": "", "abstract": "\\documentclass{amsart}\n\\usepackage{hyperref}\n\n\n\\begin{document}\n\n\n\n\\textbf{The Matrix in the Commutant}\\\\\n\n\n\n\n\\bigskip\n\n An old result by P. R. Halmos on invariant subspaces of square matrices asserts that they are kernels of\nelements in the commutant of the matrix. \nThis presentation gives an explicit,  constructive formula to determine the matrix  in the commutant and then uses it to realize the  complete invariant subspace lattice for any given $n \\times n$ matrix.\n\n\n\\end{document}", "id": "Paper/71059", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71059"}, {"title": " On Subclasses of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.716ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 1169.4 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">C_{0}</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-43\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-43\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-30\" x=\"1011\" y=\"-213\"></use>\n</g>\n</svg>-Semigroups, Linear Operators and Evolution Systems ", "webprogram_exclude": "0", "session_ids": ["Session/17782"], "source_sha256": "fe98b9661e24f53444c7585faacbab4f9a1b6076790700212116ebbd9ad6dc43", "withdrawn": "", "abstract": "\\begin{document}\n\\bibliographystyle{amsplain}\n\n\\begin{center}\n{\\large\\textbf{On Subclasses of $C_{0}$-Semigroups, Linear Operators and Evolution Systems}}\n\\end{center}\n%\\smallskip\n\\medskip\n\n\\begin{center}\n{\\large\\textbf{Abstract}} \n\\end{center}\n\n\\noindent This presentation focuses on the properties of $C_0$-semigroups associated with $\\omega$-order-reversing partial contraction mappings. We examine the fundamental properties of these mappings and explore their relationship with the generation and behaviour of $C_0$-semigroups. Particular attention is given to mild solutions arising from the associated evolution problems, including homogeneous and inhomogeneous cases, as well as the regularity of the solutions.\n\\vspace{.3cm}\n\n\\noindent The presentation further discusses the analyticity of the resulting semigroups and the behaviour of the linear operators generated by the mappings. These results provide insight into how order-reversing partial contraction properties can be used within the concept of semigroup theory to analyse evolution systems.\n\\vspace{.3cm}\n\n\\noindent Finally, we highlight applications of the obtained results to evolution equations and stable families of generators. The discussion covers homogeneous, inhomogeneous and regularity initial value problems, demonstrating how the developed approach can contribute to the analysis of existence, regularity, stability and qualitative behaviour of solutions to evolution systems.\n\\vspace{.3cm}\n\n\\noindent \n\\vspace{.6cm}\n\n\\end{document}", "id": "Paper/71060", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71060"}, {"title": " Mathematical modeling reveals neutrophil-endothelium interactions as a mechanism of vessel occlusion in sickle cell disease ", "webprogram_exclude": "0", "session_ids": ["Session/18309"], "source_sha256": "ee648a182410c836e059261e082c44ceb492a5652067ed187264d7abd8812b37", "withdrawn": "", "abstract": "Vaso-occlusive events (VOE) are acute conditions experienced by Sickle Cell Disease (SCD) patients, wherein blood cells form occlusive aggregates in the microvasculature which can lead to painful crises. These occlusions develop when sickled red blood cells (sRBCs) adhere to neutrophils that have attached to venous vasculature as part of the innate immune response. Recent failures in clinical trials aimed at inhibiting neutrophil interactions with the endothelium have highlighted a gap in our mechanistic understanding of how aggregates form over clinically relevant timescales. In this talk, we will present a dynamical systems model of occlusion in a single vessel that combines deterministic ODEs with a stochastic influx of neutrophils. This model emphasizes the long-term, cumulative interactions between circulating cells and the endothelium. Passing neutrophils not only roll and adhere to the endothelium but also trigger the upregulation of endothelial adhesion receptors through chemical signaling. Full vessel occlusion is subsequently driven by the attachment of circulating sRBCs to firmly adhered neutrophils. We show that upregulation of adhesion molecules by neutrophils leads to a positive feedback mechanism that drives occlusion and negatively impacts inhibitor efficacy. The time to occlusion depends nonmonotonically on wall shear rate, with slow flow limiting the influx of neutrophils and fast flow limiting the likelihood that a neutrophil will remain adhered. Our findings establish a mechanistic framework for evaluating potential of therapeutics and suggest that optimal dosing and half-life requirements must account for dynamic, neutrophil-driven receptor upregulation.", "id": "Paper/71061", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71061"}, {"title": " Small Scale Quantum Ergodicity in Rational Polygons ", "webprogram_exclude": "0", "session_ids": ["Session/17999"], "source_sha256": "c6d288b686b338b004ee3fc843f34b6cff522b39029ebc6c48b089cb127a22c0", "withdrawn": "", "abstract": "Marklof and Rudnick proved that for any rational polygon, a density-one subsequence of Laplace eigenfunctions equidistributes in configuration space, despite the absence of ergodicity of the full billiard flow in phase space. (If the flow were truly ergodic, equidistribution would follow from an extension by Zelditch and Zworski of the well known quantum ergodicity theorem to manifolds with boundary). I will discuss a quantitative refinement of the Marklof-Rudnick theorem and present a polynomial rate of decay for the quantum variance with respect to the frequency parameter. This leads to new results on small scale equidistribution for Laplace eigenfunctions on rational polygons and translation surfaces. The proofs use new estimates for the classical rate of ergodicity and some microlocal analysis to deal with conical singularities.", "id": "Paper/71065", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71065"}, {"title": " Unbounded bunching of saddle connections ", "webprogram_exclude": "0", "session_ids": ["Session/17902"], "source_sha256": "fc735cccf3d94d6d9d96ad3dcc40d064ea449c4f94fc4e34605f7b239ff0a6f1", "withdrawn": "", "abstract": "Given a translation surface, its set of saddle connection periods gives an interesting, and still somewhat mysterious, discrete subset of the complex plane.  In this talk I will discuss how far from uniformly discrete this set can be, focusing on the Golden L translation surface.", "id": "Paper/71067", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71067"}, {"title": " Improved upper bounds for Schur-like numbers ", "webprogram_exclude": "0", "session_ids": ["Session/18339"], "source_sha256": "0a72f6e37bb96dec15f49e0bde51139fca4d9bf06fb383f5bd399f919c7afd1f", "withdrawn": "", "abstract": "Schur’s theorem states that in any coloring of $\\{1,2,3,\\dots,N\\}$ using $k$ colors there must exist integers $x, y$ and $z$, all of the  color, satisfying the equation $x+y=z$, provided $N$ is sufficiently large in terms of $k$. The Schur number $S(k)$ is defined as the smallest integer $N$ for which this property holds. Schur’s original proof gives the upper bound $S(k) = O(k!)$, and it remains an open problem even after over a hundred years to improve the order of this upper bound. This has led to the study of Schur-like numbers $S_m(k)$ which are defined analogously for longer equations of the form $x_1 + ... + x_m = y_1 + ... + y_{m+1}$. In this talk, I will present on a recent joint work with A. Lott, G. Petridis, and N. R. Ponagandla, in which we prove an upper bound of the form $S_m(k)\\le 3^k(k!)^{1/m}$. In the regime where we let the number of variables grow at least logarithmically as a function of $k$, our bound takes the form $3^{k+o(k)}$, which is qualitatively optimal. Our work builds on ideas from a recent breakthrough work of Axenovich et al. on odd-cycle Ramsey numbers.", "id": "Paper/71068", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71068"}, {"title": " Higher order hamiltonians: The biharmonic NLS equations ", "webprogram_exclude": "0", "session_ids": ["Session/18337"], "source_sha256": "25836a8b8d15c8462088c447c4eacd24022fcb78fec58aadb95a1f65be51bcff", "withdrawn": "", "abstract": "Soliton phenomenon for higher-order PDE arises in wave propagation in intense laser beams for quasi-particles in magnetic medium, and plasma, deep water, optical communications, vortex filaments as well as beam mechanism. We will primarily address the construction of ground states solutions for the Fourth-order NLS equations. Then, we will also present a brief review concerning the stability problem for such solitons via variational methods. The proof relies on profile decomposition and an inhomogeneous version of the sharp Gagliardo-Nirenberg inequality in the setting of  the fourth-order PDE. Part of the work is joint with Marius Beceanu and Tingjian Luo.", "id": "Paper/71069", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71069"}, {"title": " Topological properties of fine curve graphs and their automorphism groups ", "webprogram_exclude": "0", "session_ids": ["Session/19358"], "source_sha256": "fabbf82ba217a954ccecad6d14bc98de9d8c656279c49a9046b693ed57e0af42", "withdrawn": "", "abstract": "Let $\\Sigma$ be a closed orientable hyperbolic surface. The fine curve graph $\\mathcal{C}^{\\dagger}(\\Sigma)$ is the graph whose vertices are the essential simple closed curves in $\\Sigma$ and whose edges connect pairs of disjoint curves. Long, Margalit, Pham, Verberne, and Yao proved that the natural homomorphism $\\mathrm{Homeo}(\\Sigma)\\rightarrow\n\\mathrm{Aut}\\bigl(\\mathcal{C}^{\\dagger}(\\Sigma)\\bigr)$\nis an isomorphism of groups.\n\nThe group $\\mathrm{Homeo}(\\Sigma)$ is canonically a (Polish) topological group with the compact-open topology. We ask whether $\\mathrm{Aut}\\bigl(\\mathcal{C}^{\\dagger}(\\Sigma)\\bigr)$ admits a natural topology for which the algebraic isomorphism with $\\mathrm{Homeo}(\\Sigma)$ becomes an isomorphism of topological groups. In joint work with Roberta Shapiro, we answer this question affirmatively. We consider three natural topologies on $\\mathcal{C}^{\\dagger}(\\Sigma)$: the Hausdorff metric topology coming from any compatible metric on $\\Sigma$; the quotient topology induced by the compact-open topology on the space of embeddings $\\mathbb{S}^{1}\\hookrightarrow\\Sigma$ with essential image; and a combinatorial topology arising from the graph structure. Each induces compact-open and pointwise-convergence topologies on $\\mathrm{Aut}\\bigl(\\mathcal{C}^{\\dagger}(\\Sigma)\\bigr)$. We prove that, with any of these induced topologies, the natural homomorphism $\\mathrm{Homeo}(\\Sigma)\\rightarrow\\mathrm{Aut}\\bigl(\\mathcal{C}^{\\dagger}(\\Sigma)\\bigr)$ is an isomorphism of topological groups.\n\nWe also prove that the quotient topology is Polish and is compatible with the graph structure, in the sense that the adjacency relation is open in $\\mathcal{C}^{\\dagger}(\\Sigma)\\times\\mathcal{C}^{\\dagger}(\\Sigma)$. Consequently, $\\mathcal{C}^{\\dagger}(\\Sigma)$ is a Borel graph. Finally, we show that the Hausdorff metric and combinatorial topologies generate the same Borel structure as the quotient topology on $\\mathcal{C}^{\\dagger}(\\Sigma)$. We conclude by discussing natural questions in combinatorics and descriptive set theory arising from the Borel graph structure on $\\mathcal{C}^{\\dagger}(\\Sigma)$.", "id": "Paper/71070", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71070"}, {"title": " Stable Constant Mean Curvature Hypersurfaces in Hyperbolic Space ", "webprogram_exclude": "0", "session_ids": ["Session/17871"], "source_sha256": "d22003d678a1e65123059a574c6f83219568541ca69a5bf3142ac5af65e3f95d", "withdrawn": "", "abstract": "I will discuss recent progress on the existence of stable constant mean curvature hypersurfaces in hyperbolic space. This is joint work with Rafe Mazzeo and Ivan Miranda.", "id": "Paper/71073", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71073"}, {"title": " Multiscale Data Integration for Modeling Permafrost Vulnerability in a Changing Climate ", "webprogram_exclude": "0", "session_ids": ["Session/18327"], "source_sha256": "40aef3ad8d40e1fbe5911d0bfadce9b23bdcf30c3569013b35834faa40c48db0", "withdrawn": "", "abstract": "Permafrost thaw is an important consequence of Arctic warming, affecting landscapes, hydrology, ecosystems, and greenhouse-gas dynamics. This project develops a data-driven framework for integrating remote sensing and geospatial observations to characterize permafrost vulnerability.\n\nOur initial work examined land-surface temperature and addressed missing observations through statistical imputation. We are extending this analysis by incorporating topographic and environmental information at multiple spatial resolutions. IfSAR elevation products and available LiDAR data can provide features such as elevation, slope, curvature, roughness, and drainage characteristics. Additional variables may include snow coverage, vegetation, land cover, hydrology, and SAR observations.\n\nBecause these datasets differ in spatial and temporal resolution, a central challenge is constructing a common representation through feature engineering and multiscale data integration. We will compare statistical and machine-learning approaches and investigate which combinations of environmental features provide the most information about permafrost conditions.\n\nFuture work may incorporate thermokarst landscape change and methane observations where compatible data are available. The project connects mathematical modeling, statistical learning, and remote sensing to study climate-sensitive Arctic systems.", "id": "Paper/71074", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71074"}, {"title": " Bulk-edge correspondence for Z_{2}-topological insulators with curved interfaces ", "webprogram_exclude": "0", "session_ids": ["Session/18292"], "source_sha256": "609790158b592c41917b590139ed020e3080318e9a122d13376a1e0ab6b1ee61", "withdrawn": "", "abstract": "Topological insulators refers to phases of matters that are classified by certain topological index. For instance, the $\\ZZ$-valued Chern numbers can be used to characterize the most classical Chern insulators. One of the key phenomenon for topological insulators is the bulk-edge correspondence. It says that when two insulators with distinct topological index are joint together, the material becomes a conductor. This phenomenon is expected to be robust under deformations and random perturbations. In this talk, we present the bulk-edge correspondence for another type of topological insulators - the time-reversal invariant topological insulators under deformation. These types of topological insulators are classified by a $\\ZZ_2$-valued time-reversal-invariant topological index. This talk is based on a joint work with Alexis Drouot and Jacob Shapiro.", "id": "Paper/71075", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71075"}, {"title": " The largest common subtree of two random trees ", "webprogram_exclude": "0", "session_ids": ["Session/18002"], "source_sha256": "dc059847be439aa4beb07570fd95b9758c2e71e1fb64a555662ffc2a9d9dd3ab", "withdrawn": "", "abstract": "Given two large random graphs, what is the size and structure of their largest common induced subgraph? This question has been a growing topic of interest in the probability and combinatorics communities in recent years, with the problem having been studied for a few different models of random graphs. In this talk, we will discuss the case where the two graphs are independent Bienaymé-Galton-Watson trees with finite-variance offspring distributions, conditioned to have size $n$. The main result is a scaling limit for the size of the largest common subtrees of two such random trees, under some light moment assumptions.", "id": "Paper/71077", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71077"}, {"title": " The competing effects of nonlinear diffusion and density-dependent emigration on population persistence in a reaction-diffusion model ", "webprogram_exclude": "0", "session_ids": ["Session/19369"], "source_sha256": "dc257679522c9ad5bc370d5dbd8ae645b6e885762e08ce7e0393bd38ddd6ac25", "withdrawn": "", "abstract": "We investigate population persistence in a finite habitat patch, with particular emphasis on how habitat patch size and density-dependent movement influence the ability of a population to survive. We consider a reaction-diffusion model incorporating logistic population growth, density-dependent movement within the habitat, and density-dependent emigration across habitat boundaries. Specifically, we analyze positive steady states of the two-point boundary value problem\n$$\n    \\begin{cases}\n        -(\\phi(u)u')'=\\lambda u\\tilde f(u) ~;~ x\\in(0,1) \\\\\n        -u'(0)+\\sqrt{\\lambda}\\gamma G(u(0))u(0)=0 \\\\\n        u'(1)+\\sqrt{\\lambda}\\gamma G(u(1))u(1)=0,\n    \\end{cases}\n$$\nwhere \\(\\lambda>0\\) represents habitat patch size, \\(\\phi\\) characterizes density-dependent movement, \\(\\tilde f\\) describes population growth, and \\(G\\) characterizes density-dependent emigration at the habitat boundaries. We examine how patch size, nonlinear movement, population growth, and boundary emigration interact to determine the existence and structure of positive population distributions. In particular, we identify conditions under which a habitat patch can sustain a viable population and characterize the critical patch size and bifurcation structure associated with population persistence. Our results highlight the role of habitat size and density-dependent dispersal and emigration in determining population persistence in spatially limited and fragmented habitats.", "id": "Paper/71079", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71079"}, {"title": " Learning observation-equivariant diffusion geometry from data ", "webprogram_exclude": "0", "session_ids": ["Session/18353"], "source_sha256": "9a2fcdb80a32033d99ee851c2ad3a3a5be48e396e4af2cba2ba3bde9a41405a7", "withdrawn": "", "abstract": "Classical kernel and graph-based methods for computational geometry equip data with the induced geometry of the ambient space it is observed in. However, observations of scientific data are rarely canonical, so this geometry is rarely the natural one. In this talk, I will discuss a range of new, scalable methods to learn the data geometry with neural networks. Crucially, we can exploit the \\textit{ordered} structure of point clouds, like time series, to recover the intrinsic geometry of the system, independent of the observation map. Specifically, we will learn the intrinsic \\textit{carré du champ} operator of the data, with which we can model the data geometry using \\textit{diffusion geometry}. I will discuss applications to molecular dynamics simulations and studying the structure of image and video datasets.", "id": "Paper/71089", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71089"}, {"title": " Symmetry-Aware Dimension Reduction ", "webprogram_exclude": "0", "session_ids": ["Session/18273"], "source_sha256": "fbea047220c39baad69927fb50f38d03c0a5d28cfc8dc38dda761029d427d441", "withdrawn": "", "abstract": "In this talk I will present two ways to exploit known symmetries in high-dimensional datasets when performing dimensionality reduction.  In graph Laplacian based manifold learning, using a group invariant kernel function results in an improvement in sample complexity according to the dimension of the group.  In principal component analysis, implicit data augmentation reduces the computational complexity from $O(N^9)$ to $O(N^4)$ when performing PCA with $N \\times N \\times N$ volumes.  Both methods take motivation from the applied problem of mapping molecular conformation spaces in cryo-electron microscopy.  Based on joint works with a number of collaborators to be named in the talk.", "id": "Paper/71091", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71091"}, {"title": " Explicit Corrector Results for Nonlinear Electrostatic-Elastic Systems ", "webprogram_exclude": "0", "session_ids": ["Session/17850"], "source_sha256": "68768f6987519e6e0a76b84309bb64e06bb89ce36b1593d9d1c46d531280b9bb", "withdrawn": "", "abstract": "In this talk, a rigorous periodic homogenization of a weakly coupled electrostatic system, accounting for both nonlinear electrostatic equations and elastic structures enriched with electrostrictions, will be presented. Unlike previous models that rely on linear constitutive laws or high regularity assumptions, our approach addresses nonlinear, monotone operators, where the standard gradient estimate fails. The “effective” macroscopic response of these composites is derived by employing two-scale convergence. The method discussed also allows one to obtain an explicit corrector result for the homogenization of monotone operators with minimal regularity assumptions. These results can provide a mathematical foundation for designing the next generation of smart materials with optimized electromechanical couplings.", "id": "Paper/71092", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71092"}, {"title": " Syzygies in Nonstandard Graded Settings ", "webprogram_exclude": "0", "session_ids": ["Session/18253"], "source_sha256": "3b7846b2ea5df9ac934bb896d8beb2a7d3ac3d173496d8947c38980b28df9a2d", "withdrawn": "", "abstract": "In this talk, I will discuss some recent advancements extending classical syzygetic results to nonstandard graded settings. In particular, I'll detail a recent result that leverages methods developed by Ein, Erman, and Lazarsfeld to establish an asymptotic classification of the nonvanishing syzygies of Veroneses of weighted projective spaces of the form $\\mathbb{P}(1^n,2)$.", "id": "Paper/71094", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71094"}, {"title": " On the Gonalities of Generalized Kneser Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/19360"], "source_sha256": "e28338187db73fe4bea5a070147dbbc4d8a96e4a35a20ae004dab7d3c822c755", "withdrawn": "", "abstract": "The Kneser graphs $\\KG(n,k)$ are a classically studied family of graphs. One known invariant of graphs is gonality (also called divisorial gonality), which is the minimum degree of a rank 1 divisor on the graph.\n\nUsing known bounds on gonality of simple, connected graphs, one may obtain that the gonality of $\\KG(n,k)$ is bounded above by $\\binom{n-1}{k}$.\nIn 2014, Harvey and Wood showed that the treewidth (a lower bound on gonality) for $\\KG(n,k)$ is $\\binom{n-1}{k}-1$ for $n\\geq 4k^2-3k+2$. In this presentation, using scramble number, another lower bound on gonality, we improve this polynomial bound and show that the gonality of $\\KG(n,k)$ is exactly $\\binom{n-1}{k}$ for $n\\geq \\frac{3k^2+k+2}{2}$, and conjecture an even stricter polynomial bound using the uniform edge scramble. We then extend our argument to the family of generalized Kneser Graphs, computing the scramble number and gonality using the same polynomial bound.", "id": "Paper/71099", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71099"}, {"title": " Continued Fractions, Torsion Order and Moduli Space ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "a8e2c8f71f30dcbf2349b9bd1a5836d3b4d513e4de3fd51ecd3161aed8fd770e", "withdrawn": "", "abstract": "For elliptic curves over the rationals, we know which curves have finite torsion n, but what about hyperelliptic curves?    In the literature there are scattered results, including: For genus g=2 and torsion order 3, there has been work done connecting curves with these specific torsion order to homogeneous polynomials (Hunt 1996);   for g=2 and n= 5,  in 2025  Elkies gave parametrization of curves that have torsion order 5.  \n\nA hyperelliptic curve y^2= f(x) with f(x) of even degree has a `divisor at infinity' of  finite torsion order n if and only if y has a periodic continued fraction expansion (over the function field Q(x) ).  The general, shape of a continued fraction expansion that has torsion order n over genus g is known. For small g, n we then find the exact set of corresponding f(x).   In genus 2 and small n, we apply the Igusa invariants to determine the set of curves up to isometry.", "id": "Paper/71103", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71103"}, {"title": " Partition-theoretic model of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"4.536ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 1953 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\pi (n)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-3C0\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"573\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-6E\" x=\"963\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"1563\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/19361"], "source_sha256": "2699c2d9f29cd1824a1d9ce58b13c55477f9b2522f208758895b79a8d9f95a16", "withdrawn": "", "abstract": "We describe a deterministic model of prime number distribution derived from first principles related to properties of integer partitions, that naturally predicts the prime number theorem.  The model states that, for $n\\geq 2$, $$p_{n}\\  =\\  1\\  +\\  2\\sum_{j=1}^{n-1}\\left\\lceil \\frac{d(j)}{2}\\right\\rceil\\  +\\   \\varepsilon(n),$$ where $p_k$ is the $k$th prime number, $d(k)$ is the divisor function, and $\\varepsilon(k)$ is an explicit error term that is negligible asymptotically. We invert the error term to give estimates of $\\pi(n)$ similar to those provided by the logarithmic integral, and much more accurate than $\\operatorname{li}(n)$ up to  $n=100{,}000$ where the estimates are almost exact.", "id": "Paper/71104", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71104"}, {"title": " Scattering solutions of a class of magnetic Schrödinger operators ", "webprogram_exclude": "0", "session_ids": ["Session/18292"], "source_sha256": "ef5f10ef3683c59b1c821f5ad438673ec2157e8f0303a3a946a0a27218b43c7c", "withdrawn": "", "abstract": "Consider the Schr\\\"odinger operator $H_{A,V}:=-\\Delta+V_E+ iA\\cdot\\nabla$, where $V=E\\cdot x$, $E\\in \\mathbb{R}^n$ and $A=M x$, $M$ a skew-symmetric matrix.   \nWe analyze the spectral properties for the operator  $H_{A,V}$ with certain linear and nonlinear perturbations. \nAs an application, we derive the local existence for the nonlinearly damped focusing NLS equations  with such class of potentials $(A,V)$.  Furthermore, we prove the $\\log$-$\\log$ law for the system when the initial data is slightly above the ground state.   \nScattering solutions are obtained when the initial data is below the ground state.  \n\nThis study demonstrates the spectral and structural stability for the NLS type equations under the perturbation of unbounded potentials and a damping term.", "id": "Paper/71106", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71106"}, {"title": " Statistical Foundations of Operator Learning ", "webprogram_exclude": "0", "session_ids": ["Session/18446"], "source_sha256": "203029a7be912bcd2c771981b5ea5595804fa9119c84272b45254d7bb8d4bd89", "withdrawn": "", "abstract": "Operator learning is an emerging paradigm at the intersection of scientific computing and\nmachine learning. Its central objective is to learn operators between infinite-dimensional\nfunction spaces from data. Although operator learning has found broad applications across\nscience and engineering, its theoretical foundations remain underdeveloped. In this talk, I\nwill present recent progress on the statistical and computational limits of operator learning,\nfocusing on several fundamental operator classes: bounded linear operators between\nSobolev spaces, pseudo-differential operators central to the analysis of partial differential\nequations (PDEs) and mathematical physics, and Fourier integral operators associated with\nhyperbolic systems and wave propagation. Across these settings, a common multiscale\nframework yields minimax-optimal statistical rates together with computationally efficient\nestimators. These results contribute to a unified theory of operator learning at the interface\nof analysis and PDEs, computational mathematics, statistics, and data science.", "id": "Paper/71108", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71108"}, {"title": " A \"Boss Battle\" in Math and Dragons ", "webprogram_exclude": "0", "session_ids": ["Session/18235"], "source_sha256": "00fde6f77514796783043f72b6f6b19296f3898e390e53ba7ca3835838d819a9", "withdrawn": "", "abstract": "All first year students at Mount Holyoke College take a designated first-year seminar course, a small discussion-based course where the emphasis is on practicing the ability to think analytically and critically by questioning assumptions, evaluating evidence, and articulating well-reasoned arguments. The courses themselves are spread among departments and have no topical pre-requisites. As part of the program, I designed a course called Math and Dragons where students would examine both some of the mathematics that goes into and the cultural impact of tabletop-roleplaying games (TTRPGs), like Dungeons and Dragons. Along the way, students play through various TTRPG scenarios to discuss mathematics and practice storytelling. They also learn how to use R to perform various tabletop-roleplaying game simulations and analyze them. In this talk, I will present an activity from our probability unit where students practiced coding in R to complete an in-class “boss battle.” I will discuss the structure of the activity, what went well, and what I would like to improve in future iterations.", "id": "Paper/71110", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71110"}, {"title": " Fibonacci Numbers in Music ", "webprogram_exclude": "0", "session_ids": ["Session/18233"], "source_sha256": "7942291c15b375d5c1d5949159d2647c790475688fa0a5e625190152a9555638", "withdrawn": "", "abstract": "We examine the way numbers in Fibonacci's famous sequence and the related golden ratio appear in several musical compositions, either intentionally or unintentionally, as methods for structuring pivotal divisions in a piece or as intervals for creating melody.  We examine works by Mozart, Debussy, and Bartok, and we present an original composition for solo piano based on Fibonacci numbers.", "id": "Paper/71111", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71111"}, {"title": " Degree growth of curves under iteration ", "webprogram_exclude": "0", "session_ids": ["Session/17755"], "source_sha256": "4d775026f515e75fc18779936d7d5b017de6d54c7ab1c88db85d967e4d926f8d", "withdrawn": "", "abstract": "In this talk, we study the growth of the bidegree of an ample irreducible curve in $\\mathbb{P}^1 \\times \\mathbb{P}^1$ under iteration by a product polynomial endomorphism $\\varphi=(f,g)$, assuming that at least one of $f$ and $g$ is non-exceptional. We will discuss functional transcendence properties of B\\\"ottcher coordinates and how they can be used to show that if a curve $C$ is not preperiodic under $(f^a,g^b)$ for any $a,b\\geq 1$, then the bidegree of $\\varphi^n(C)$ is asymptotic to $(\\deg(g)^n,\\deg(f)^n)$. Using this exponential growth, we establish a geometric analogue of Silverman’s theorem on the finiteness of $S$-integral points in orbits, formulated in terms of the intersection points of the forward images of one curve with another.", "id": "Paper/71112", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71112"}, {"title": " A note on Jacobson-Rickart-Kadison theorem for locally C*-algebras. II. ", "webprogram_exclude": "0", "session_ids": ["Session/19342"], "source_sha256": "189a4067ff74577617cfdb1fba6f189245c9ff092812a3ea04e8d651dbbad5d2", "withdrawn": "", "abstract": "In the previous work we have extended the results of Jacobson-Rickart and Kadison to show that a Jordan *-homomorphism from one locally C*-algebra onto another locally C*-algebra preserves commutativity. In the present sequel we continue our study of Jordan *-homomorphism and show that every Jordan *-isomorphism of one locally C*-algebra onto another locally C*-algebra is a sum of a *-isomorphism and a *-anti-isomorphism.", "id": "Paper/71113", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71113"}, {"title": " Generalized trace tests and restrictions ", "webprogram_exclude": "0", "session_ids": ["Session/18356"], "source_sha256": "e39ad141af5cc5d30d934697b35fcd376186e6e86b7a5865f8bd89e05fe4755b", "withdrawn": "", "abstract": "A trace test is an algorithm in numerical algebraic geometry which determines whether a subset of a fibre of a branched cover is the entire fibre. A well-known trace test is the classical trace test, where the fibre involved is a zero-dimensional slice of an irreducible affine variety. In the classical trace test, we are concerned with whether the sum of points in a subset acts as a linear function. Here, we generalize the notion of trace tests to branched covers by rewriting the test as a check on whether a function on the fundamental groupoid descends to a function on the regular locus of the branched cover. This generalization reveals that many functions, not just the trace, can be used to create such tests. We introduce a generalized restricted trace test, which simplifies the function that needs to descend by a restriction of the branched cover. The sparse trace test is an example of a restricted trace test for sparse polynomial systems.", "id": "Paper/71117", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71117"}, {"title": " Multi-Experiment Equation Learning for Identifiable Model Discovery in Agent-Based Systems ", "webprogram_exclude": "0", "session_ids": ["Session/18127"], "source_sha256": "95000f563704cf763605879cc6bdc1076f5db7f4247602fbf935454b3ede54e6", "withdrawn": "", "abstract": "Learning governing equations directly from data is a powerful alternative to hand-derived mechanistic models, but a fundamental obstacle is identifiability: equations fit to a single experiment or parameter setting may be weakly constrained, with multiple structurally distinct models fitting the observed data similarly well. In this talk, I present Multi-Experiment Equation Learning (ME-EQL), a framework for learning governing equations from agent-based model data by training simultaneously across experiments in which a model parameter is systematically varied. This multi-experiment approach provides additional constraints on the learned equations and substantially reduces error in parameter recovery relative to single-experiment equation learning. I will discuss how ME-EQL reduces ambiguities that arise when equations are learned from individual experiments, and demonstrate its performance on an agent-based birth-death system. In particular, I show that the learned equations can be used to reconstruct the parameters used to generate the simulations, illustrating how ME-EQL surrogate models can support parameter inference.", "id": "Paper/71118", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71118"}, {"title": " Structure-Preserving Tensor Train Methods for the Lindblad Equation ", "webprogram_exclude": "0", "session_ids": ["Session/18247"], "source_sha256": "214324849b060f7005d9518041bf638c491ba739967078643124c11293e56bbd", "withdrawn": "", "abstract": "We propose a family of low-rank, positivity- and trace-preserving schemes for the Lindblad equation, a common model for open quantum systems. Low-rank representation is employed at two levels: the density matrix is factorized into the product of tall-skinny matrices, and the columns of these matrices are further represented using the tensor train (TT) format, also know as matrix product states (MPS). This two-level low-rank format fits naturally into our existing Kraus is King scheme for the Lindblad equation, whose underlying operations are arithmetic on the columns of the tall-skinny matrices. We show how these operations can be performed efficiently in the TT/MPS format, with particular emphasis on density matrix rank-truncation. We conclude with numerical experiments demonstrating the convergence of this scheme and its efficiency in simulating systems with up to $10^{19}$ degrees of freedom using only modest compute resources.", "id": "Paper/71119", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71119"}, {"title": " The Homicidal Microswimmer: Pursuit and Evasion in a Viscous Fluid ", "webprogram_exclude": "0", "session_ids": ["Session/19343"], "source_sha256": "463d01ee74b58cc6672e38f335d1966c926cab7023b3b3ff184d03a8b084fb2f", "withdrawn": "", "abstract": "The homicidal chauffeur problem is a classic differential game in which a fast pursuer with a finite turning radius chases a slower but more agile evader. We revisit the problem in a viscous fluid, where the pursuer's disturbance flow advects the evader, and the players are no longer kinematically independent. The flow substantially reshapes the capture dynamics, generically requiring the pursuer to follow a far more complex approach trajectory. Optimal strategies are explored analytically and numerically, revealing singular surfaces across which the optimal strategy switches abruptly. The results have implications for predator-prey interactions among microorganisms, and control problems for synthetic particles in viscous environments.", "id": "Paper/71121", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71121"}, {"title": " Mathematical discovery by voice: AI and the 2-adic absolute Galois group ", "webprogram_exclude": "0", "session_ids": ["Session/18208"], "source_sha256": "bedd71b1a0e0491b6e02c23e4596583de37755e3c9bc3d947dade4a0913fb9c1", "withdrawn": "", "abstract": "I will describe how I used my voice to direct AI research on a decades-old problem: finding an explicit presentation of the absolute Galois group of the 2-adic numbers, despite not understanding the underlying Galois theory.\n\nResearch routines I had already developed produced a candidate during a roughly 26-hour autonomous run; subsequent review and correction led to a 60-page proof manuscript. David Roe then obtained a Lean formalization in about a week, largely by delegating tasks to coding agents, with established results from the literature taken as explicit assumptions.\n\nDrawing on this joint work with Roe, I will discuss how spoken instructions could organize sustained mathematical exploration, how the resulting claims were checked, and where other expertise entered the process. The case raises a broader question about participation in mathematical discovery: what does it mean to contribute when the research one can initiate exceeds the mathematics one understands?", "id": "Paper/71122", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71122"}, {"title": " The Linear Prefix Theorem in Linear Size ", "webprogram_exclude": "0", "session_ids": ["Session/17756"], "source_sha256": "4a0e454c4f80bf4c521537c25676fc8ee8baa1789491df4e301e330ce9b98988", "withdrawn": "", "abstract": "A common problem in mathematical logic is to study what properties can be expressed using certain types of statements. The Linear Prefix Theorem of Walkoe states that given two distinct strings of quantifiers $p$ and $q$ of the same length  $n$, there exists a sentence beginning with $p$ that cannot be expressed as any sentence beginning with $q$. For example, there is some sentence beginning with $\\forall\\exists\\forall$ that is not equivalent to any sentence beginning with $\\forall\\forall\\exists$. Walkoe originally proved this theorem by constructing uncountably large structures using infinite Ramsey theory. Shortly after, Keisler and Walkoe reproved this result using finite structures from finite Ramsey theory, obtaining models whose sizes grow superexponentially in $n$. A natural question to ask is if this result holds over smaller models, and this is the focus of our work. We explicitly construct structures with size linear in $n$, using modified Ehrenfeucht-Fraïssé games to verify that they separate the quantifier strings $p$ and $q$. In this way, we prove that Walkoe's Linear Prefix Theorem holds over structures with size linear in $n$, greatly tightening previous bounds and working towards generalizations to broader cases.", "id": "Paper/71124", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71124"}, {"title": " Analyzing a Structurally Identifiable Model for Tuberculosis Using Data from Bangladesh ", "webprogram_exclude": "0", "session_ids": ["Session/19359"], "source_sha256": "aac95f86d00eb32d619cbe68d86bb2189fe706ae2a80a2fcdb059a4f4bd4330f", "withdrawn": "", "abstract": "Tuberculosis (TB) remains a major public health challenge in Bangladesh and around the world, exacerbated by the emergence of multidrug-resistant strains (MDR-TB). The mathematical model is a system of differential equations describing TB infection, progression, treatment, recovery, and reinfection.  The model was shown to be structurally identifiable.  Stability of the model was analyzed by identifying the basic reproduction number using the next generation method.  A practical identifiability analysis was conducted with TB data from Bangladesh.  The model analysis and results will be presented in this talk.", "id": "Paper/71129", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71129"}, {"title": " Invariant Theory Based Approach to Equivariant Learning ", "webprogram_exclude": "0", "session_ids": ["Session/17835"], "source_sha256": "d2b26e7bf52de5a034eeae514d41b5e34f6da3a33655ade81292e195a47532ed", "withdrawn": "", "abstract": "In this talk I will introduce new neural network architectures for learning equivariant functions.  The approach is based on invariant theory, and replaces part of the learning task with algebraic precomputations performed before training.  In an application to fluid dynamics, we encounter old problems in the invariant theory of binary forms, and extend calculations of Gordan and his contemporaries.  The neural networks produced achieve competitive accuracy, while enjoying an improvement in interpretability and a substantial reduction in the number of trainable parameters.  Based on joint works with Sahil Kommalapati and Robert Moser as well as Michael Liu.", "id": "Paper/71131", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71131"}, {"title": " Learning About AI Through Play: Exploring Vector Embeddings and Responsible Use of AI ", "webprogram_exclude": "0", "session_ids": ["Session/17961"], "source_sha256": "98cea68c43988e8723e2d7a9d27b54c536624d9bf584751786d8252afceb785e", "withdrawn": "", "abstract": "As artificial intelligence (AI) becomes increasingly integrated into education and everyday life, students need opportunities to understand both how AI works and the implications of using it. This interactive activity integrates two equally important goals: introducing middle school students to vector embedding, one of the mathematical techniques underlying modern AI systems, and developing critical awareness of the benefits, limitations, and consequences of AI use. \n\nThrough game-based exploration, students investigate how information and their own responses can be represented as vectors, how similarity can be described mathematically, and how AI uses numerical representations to identify relationships, group information, and support applications such as recommendations. These concepts are interwoven with scenarios that encourage students to examine AI’s potential to support learning, creativity, productivity, and problem-solving while considering concerns such as overreliance, effects on independent learning and critical thinking, environmental costs, bias, and the limitations of AI-generated responses and recommendations. By connecting an understanding of how AI works with reflection on its uses and consequences, the activity encourages students to recognize AI’s power rather than viewing it simply as a convenient tool, while developing the knowledge and critical judgment needed to question its outputs and use it thoughtfully and responsibly.", "id": "Paper/71132", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71132"}, {"title": " Murmuration of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"3.603ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 1551.3 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">_3F_2</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-46\" d=\"M48 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H742Q749 676 749 669Q749 664 736 557T722 447Q720 440 702 440H690Q683 445 683 453Q683 454 686 477T689 530Q689 560 682 579T663 610T626 626T575 633T503 634H480Q398 633 393 631Q388 629 386 623Q385 622 352 492L320 363H375Q378 363 398 363T426 364T448 367T472 374T489 386Q502 398 511 419T524 457T529 475Q532 480 548 480H560Q567 475 567 470Q567 467 536 339T502 207Q500 200 482 200H470Q463 206 463 212Q463 215 468 234T473 274Q473 303 453 310T364 317H309L277 190Q245 66 245 60Q245 46 334 46H359Q365 40 365 39T363 19Q359 6 353 0H336Q295 2 185 2Q120 2 86 2T48 1Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-33\" x=\"0\" y=\"-213\"></use>\n<g transform=\"translate(453,0)\">\n <use xlink:href=\"#E1-MJMATHI-46\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-32\" x=\"910\" y=\"-213\"></use>\n</g>\n</g>\n</svg> Hypergeometric families ", "webprogram_exclude": "0", "session_ids": ["Session/18370"], "source_sha256": "a32386e0614d7d13a8b59e85f264c3282a101656a3a4b8ab9ea7767f4934d1a1", "withdrawn": "", "abstract": "Elliptic curves are fundamental objects in number theory, drawing connections between polynomial equations and concepts involving prime numbers. Using machine learning methods, He, Lee, Oliver, and Pozdnyakov (2022) have found a ``murmuration\" phenomenon concerning the unexpected oscillatory behavior that emerges when point counts on elliptic curves over finite fields are averaged over families of elliptic curves. These sorts of patterns have been observed more generally among certain $L$-functions. Sawin and Sutherland (2025) proved a variant of the murmuration phenomenon for elliptic curves over $\\mathbb{Q}$ ordered by naive height, establishing an explicit limiting formula. Their proof uses a Voronoi summation formula (a tool for transforming difficult sums into ones that are easier to analyze) together with an analysis of the resulting local factors. In this talk, we extend this approach to the symmetric squares of the Legendre family of elliptic curves. These are related to values of a certain $_3F_2$ hypergeometric function with rational parameters. We set up an analogous sum so that we are able to apply a $GL(3)$ Voronoi summation formula. We then average this transformed sum over the family, allowing us to achieve a smooth murmuration behavior. We will also present the numerical approximation of our murmuration phenomenon.", "id": "Paper/71134", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71134"}, {"title": " Words Go Viral: Epidemic Models of Neologism Adoption on Twitter ", "webprogram_exclude": "0", "session_ids": ["Session/19365"], "source_sha256": "e666475e4636711039e509b0e86a04d87f007555ab74ec4beec569aa88ccc077", "withdrawn": "", "abstract": "Everyone has experienced the sudden spread of a new slang word through their social circle. We treat this phenomenon as an epidemic process, applying compartmental ODE models from mathematical epidemiology to study how new words spread through a population. We track fifty neologisms, previously identified from their 2013–2014 Twitter dynamics, through sixteen years of Twitter data and find qualitatively different fates: some die out, others spike and plateau, and still others show multiple waves of revival. We fit a hierarchy of models to this data: SIR, SIRS, time-inhomogeneous transmission-rate variants, and a two-island migration SIR/SIRS system. We estimate parameters via best fit and compare using the Akaike Information Criterion (AIC). The two-island model captures a 'Herald wave': an initial burst of adoption followed by a second wave once a new pool of potential users is reached. Model comparison shows that different neologisms rely on different spread mechanisms, with some driven by reinfection or transient bursts of attention and others by cross-community influence.", "id": "Paper/71136", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71136"}, {"title": " Combinatorial & Topological Results on the Ramification Spectrum of Isosceles Triangles ", "webprogram_exclude": "0", "session_ids": ["Session/18241"], "source_sha256": "69b283b5c2f7826cd72fdd72e5deb949e7fb6a3a23a0bcbb0780080ead8266c0", "withdrawn": "", "abstract": "For a triangle whose angles are rational multiples of $\\pi$, its ramification density is the proportion of spherical triangles in its Galois orbit. We study the ramification spectrum of isosceles triangles, consisting of these densities and their limit points. We first present a combinatorial classification theorem that determines the densities for a particular family of isosceles triangles. We then prove that the full isosceles spectrum is homeomorphic to the ordinal space $\\omega^2+1$. The proof uses limits of Galois orbits and their relation with lines and planes in the moduli space. These geometric limits correspond to two successive levels of accumulation: the spectrum has infinitely many accumulation points, and those points have $\\frac12$ as their unique accumulation point.", "id": "Paper/71142", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71142"}, {"title": " Active particles in anisotropic fluids: bifurcations and pattern formation ", "webprogram_exclude": "0", "session_ids": ["Session/19351"], "source_sha256": "b333d4c7cb467c6be295765a02c17a31c7d0767fa58274e59a2f3d3eb0727767", "withdrawn": "", "abstract": "Active particles drive flows in a variety of complex biological fluids. Such fluids on their own commonly exhibit viscoelasticity and anisotropy, which can rectify the motion of the active immersed particles. To explore the coupling of an active suspension and environment anisotropy, we develop a kinetic theory and examine it numerically and analytically. We identify a family of steady states, tuned by a competition between particle anchoring to the environment and rotational diffusivity. Through linear and weakly nonlinear stability analyses, we predict a host of different bifurcations and emergent patterns.", "id": "Paper/71143", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71143"}, {"title": " The Future of Mathematics and Media: An Uncensored Perspective ", "webprogram_exclude": "0", "session_ids": ["Session/18322"], "source_sha256": "5f03fb733a8604a4ba2b791c1b7c141dbe6638ff86c7fc2d16982116fc5ff2ea", "withdrawn": "", "abstract": "In this talk, the hosts of the podcast Mathematically Uncensored, Dr. Pamela E. Harris and Dr. Aris Winger, reunite to discuss what lies ahead for Mathematics and the Media.  Motivating their discussion during the talk is the question “What happens when we (as a community) do mathematics without attending to who is doing the mathematics and how they experience the doing of mathematics?” With the podcast in evergreen mode, the speakers will continue the tradition of being real, complex, and never discreet (discrete) as individuals. The Question and Call to Action Remains:  Who will lead our discipline and media to address the inequity of access to joyful and meaningful mathematical experiences?", "id": "Paper/71144", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71144"}, {"title": " Reclaiming Mathematics: Hidden Histories of Disability, Neurodivergence, Illness, and Trauma ", "webprogram_exclude": "0", "session_ids": ["Session/17472"], "source_sha256": "3f04b60bd45f904df4e80983465746fa407aca90aeb528156ac58680af511cb5", "withdrawn": "", "abstract": "Mathematics is often presented as an abstract body of knowledge. Yet mathematics is created and understood through our bodies, minds, and life experiences. Many important mathematicians have lived with disability, neurodivergence, chronic illness, or trauma, but conventional histories often erase these parts of their lives or reduce them to stories of overcoming adversity. Drawing on these hidden histories, my own lived experiences, and the concept of disability gain, I explore how human difference has shaped mathematical creativity.", "id": "Paper/71149", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71149"}, {"title": " NUMERICAL INTEGRATION OF GEODESIC SHOOTING EQUATIONS FOR INVARIANT SOBOLEV METRICS ON CURVE AND SURFACE SPACES ", "webprogram_exclude": "0", "session_ids": ["Session/19344"], "source_sha256": "65736173eb48b04268ea78fc94a1045e4a40dabe04be9bacfa094929b4631379", "withdrawn": "", "abstract": "In this work, we address the issue of numerically computing geodesics in the shape space of parametrized curves/surfaces when equipped with an invariant Sobolev metric. This family of Riemannian metrics has a long standing history, notably in the field of shape analysis, and has played an important role in multiple applications to areas such as computer vision, computational anatomy or shape optimization. Despite significant advances on the mathematical study of these metrics' properties and of their corresponding geodesics, there has been comparatively less extensive work on numerical aspects. Most of the proposed approaches for integrating the initial value problem associated to the geodesic equations have been derived from the principles of discrete geodesic calculus. They typically require solving high-dimensional nonlinear systems of equations at each time step, which can become computationally expensive and possibly unstable in high sampling regimes. While parametric representations (Fourier, splines $\\ldots$) have been considered to alleviate this issue, this concurrently limits its generality and flexibility. The approach we propose instead directly operates over curve or surface meshes, by relying on the discrete Hamiltonian geodesic equations, whose solutions can then be obtained via adequate time integrators. Beyond solving the initial value problem, we derive a geodesic shooting scheme for the boundary value problem, and illustrate how these methods can further be used to approximate parallel transport or perform geodesic regression in shape spaces. Extensive numerical experiments on curve and surface data are provided as empirical validation for each of the proposed schemes.", "id": "Paper/71152", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71152"}, {"title": " Mixing Times of Toggle Markov Chains ", "webprogram_exclude": "0", "session_ids": ["Session/19370"], "source_sha256": "36aa5ec1b9c55c1db40a5213105392d087fdf1f96af46be34d1d6f9ca34a90bc", "withdrawn": "", "abstract": "The notion of \\textit{rowmotion}, a bijective operator on the distributive lattice $J(P)$ of order ideals of a finite poset $P$, was first defined in 2012 by Striker and Williams. Since then, a substantial body of work has explored both the algebraic and combinatorial properties of rowmotion. In 2023, Defant, Li, and Nestoridi defined \\textit{rowmotion Markov chains} $\\mathbf{M}_{J(P)}$ by considering stochastic transitions on $J(P)$. Building on Striker’s generalization of rowmotion to the toggle operator, they further introduced \\textit{toggle Markov chains} and initiated the study of mixing times in such chains. One of their results concerning the mixing of toggle Markov chains on Boolean lattices is generalized in this work.\n\nIn this paper, our main results address an open question posed by Defant, Li, and Nestoridi, concerning the mixing of two natural classes of toggle Markov chains $\\mathbf{T}$ which we term \\textit{lower-$k$} and \\textit{upper-$k$} chains, where the integer $k$ pertains to a constraint imposed on the state space of $\\mathbf{T}$. Respectively conditioned on $k$ or $n - k$ being constant, where $n = \\lvert P \\rvert$, we show the mixing time is $\\Theta(n^2)$ for both chains. For more general $k$, we provide broader asymptotic bounds.\n\nIn our work, we also discuss an interesting connection between bounded-$k$ toggle chains and a variant of the stochastic box-ball system. The box-ball system is a discrete cellular automaton introduced by Takahashi and Satsuma in 1990, and it was first considered in a stochastic setting by Keating, Kim, Loeser, and Lyu in 2025. The box-ball interpretation of bounded-$k$ chains provides an intuitive framework under which parts of our main results are proven.", "id": "Paper/71156", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71156"}, {"title": " Machine Learning Enhanced Optimal Control for Sustainable Energy Systems ", "webprogram_exclude": "0", "session_ids": ["Session/19337"], "source_sha256": "874ba1788b14b49b417cc3b644616bdd5e1242abd98b83b34d6e5bb6f105c6b0", "withdrawn": "", "abstract": "The increasing use of renewable energy introduces new challenges in balancing energy supply, storage, and demand. These challenges naturally lead to optimal control problems in which decisions must be made over time while accounting for system constraints and changing operating conditions. In this work, we consider a mathematical model for energy management and formulate the problem as a constrained optimal control problem. The objective is to determine a control strategy that improves the use of available energy while reducing operating cost and unnecessary energy loss. We then incorporate a machine learning model to approximate the relationship between system states and optimal control decisions. The learning based solution is compared with a classical numerical optimal control approach in terms of accuracy and computational efficiency. Particular attention is given to how the learned control behaves when system parameters and energy demand vary. This study provides a framework for combining mathematical optimal control with machine learning and explores its potential for efficient decision making in sustainable energy systems.", "id": "Paper/71158", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71158"}, {"title": " MATHEMATICAL MODELING OF THE BEHAVIORAL RESPONSES TO MAMMALIAN GRAZING EXPOSING INSECT HERBIVORES TO AVIAN PREDATION ", "webprogram_exclude": "0", "session_ids": ["Session/17383"], "source_sha256": "39a5d8ddea52c96b8786d7aac16628e282dc06e4e2962ae4ae412cd4bd4e0803", "withdrawn": "", "abstract": "Grassland birds have experienced some of the steepest population declines among North American birds. Grazing-induced changes in vegetation are widely implicated in these declines, yet the pathway linking grazing to species-specific bird responses remains empirically untested. This study develops and analyzes a system of ordinary differential equations (ODEs) describing the indirect, vegetation-mediated effects of mammalian grazing on grassland-bird abundance. The model links grazing intensity, vegetation structure, litter depth, and bird abundance and is parameterized using field data from the northern tallgrass prairie of North America. The system is non-dimensionalized to reduce parameter redundancy and facilitate scalable analysis. Equilibria are derived, and local stability is assessed using eigenvalue analysis. Parameters are estimated from three field seasons (2011–2013) by matching integrated areas under the curve. The model identifies a unique, locally asymptotically stable coexistence equilibrium. Species-specific recovery rates also consistently rank the three focal species across years. The framework provides a transparent and replicable approach for quantifying vegetation-mediated grazing effects and informing grazing management in grassland ecosystems experiencing bird declines.", "id": "Paper/71163", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71163"}, {"title": " The Vibes are Skewed: Using AI to Develop an Immersive Environment for Plane-and-Sphere Constructions ", "webprogram_exclude": "0", "session_ids": ["Session/17461"], "source_sha256": "277c582249a113ea20333c3b209365dee63c52e4357b4e8ae1c6b052c81a1058", "withdrawn": "", "abstract": "How could analogs of compass and straightedge constructions create opportunities for students to explore three-dimensional space? And how is AI helping to realize those opportunities? We report on the design and development of HandWaver, a three-dimensional, immersive virtual environment where players investigate the geometric figures that can be constructed from the intersections of planes and spheres. The environment allows players to spawn points in space; construct lines through any two points; construct planes though any three points  or two lines; and construct spheres.   HandWaver provides a spatial canvas where learners can explore questions about spatial geometry by using virtual tools to inscribe interactive, three-dimensional diagrams. For example, learners could explore how to construct a tetrahedron, a plane tangent to a sphere, or the common perpendicular of two skew lines.  Such constructions are rarely considered in secondary or tertiary mathematics education. Yet, the extension of compass and straightedge constructions into three-dimensions creates new possibilities for students to explore three-dimensional geometric concepts by investigating novel problems. HandWaver was designed by a team of mathematicians and learning scientists and then developed through iterative, agent-based vibe-coding. We will consider how HandWaver provides an example of how AI is opening up new areas for mathematics education, innovation, and research.", "id": "Paper/71164", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71164"}, {"title": " Structured systems of nonlinear equations ", "webprogram_exclude": "0", "session_ids": ["Session/18039"], "source_sha256": "3fab7afed7499f361e02e5e323b8fb10765842cc90bb735987e8c1021a1179da", "withdrawn": "", "abstract": "The engineering literature has well developed a theory of structured matrices that began in the field of control theory. While that theory was originally about linear systems, in this talk I will develop a corresponding nonlinear theory. Consider a system of equations $F(x)=c$,  where\n$F:\\mathbb{R}^N \\to \\mathbb{R}^N$, and write $F(x)=(F_1(x_1,\\ldots,x_N), \\ldots, F_N(x_1,\\ldots,x_N))$.\nIn many applications, each coordinate function $F_j$ depends only on a restricted set of $x_j$'s. One way to say this, is that for certain $i$ and $j$, $\\frac{\\partial F_i}{\\partial x_j}(x)$ is identically zero for all $x$. The ``structure'' of the system is a matrix $A=(a_{i,j})$ where each $a_{i,j}$\nis either zero or $*$ which means any value is permitted. \n\nI will talk about the generic properties of structured systems. In the engineering literature, it is shown that almost every (in the sense of Lebesgue measure) matrix that respects a given structure has the same rank. I have extended this result to nonlinear structured systems, using the concept of prevalence (the analogue of Lebesgue measure for infinite dimensional vector space of functions). I will show that ``almost every'' (in the sense of prevalence) nonlinear function that respects a given structure has the same rank.\n\n\nFor some structures $A$, the rank of the matrix $(\\frac{\\partial F_i}{\\partial x_j})$ is always less than $N$. We call such a structure $A$ ``non-robust''. \nI will describe our bottleneck theorem which gives a necessary and sufficient criterion for a structured system to be robust.", "id": "Paper/71165", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71165"}, {"title": " New Family of Low-Rank Tensor Decompositions ", "webprogram_exclude": "0", "session_ids": ["Session/18302"], "source_sha256": "ff4d9da822d2ca578211479d2ce52654113443dc570ab2c133979dee16813b08", "withdrawn": "", "abstract": "In this talk I will define a new family of tensor decompositions, and give quasi-optimal approximation algorithms for computing them.  Underlying the framework is a fresh algebraic perspective on what structures tensors are encoding.  Numerical results will compare the performance of the new tensor decompositions with existing ones.  Joint work with Paulina Hoyos.", "id": "Paper/71167", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71167"}, {"title": " Multiplication by Sunlight: The Design and Fabrication of an Interactive Mathematical Sculpture ", "webprogram_exclude": "0", "session_ids": ["Session/18234"], "source_sha256": "2c95f6e5a413e92af4faae7d9fd6a6ad61eefe59fce9b429461c4cc6cda4d61e", "withdrawn": "", "abstract": "How can a geometric definition of multiplication—where the products of magnitudes are constructed via compass and straightedge—be embedded in an interactive, physical tool? We report on the design and fabrication of the second iteration of the SunRule, an interactive mathematical sculpture that models multiplication by stretching or shrinking beams of light. A SunRule harnesses the apparent parallelism of sunlight to model multiplication as a continuous scaling operation that is normed to a specific unit. SunRule2.0 is a 32” stainless steel disk that is encircled by a cylindrical cuff that is 10” high. The disk/cuff assembly is mounted to a stainless steel post that allows the disk to be rotated (through a complete turn) and tilted (along any axis). The disk is etched with concentric circles that are spaced 1” apart. The cuff has a series of narrow slits that vary in height. Each slit is offset from the disk by the same amount, and this offset functions as the multiplicative identity. By swiveling the disk, the SunRule can be used to represent a range of multiplicands. By tilting the disk, any slit can be acted on by a range of multipliers. In effect, the tilting action of the SunRule varies the angle of the sun’s (apparently) parallel rays: tilt the disk toward the sun, the sun’s altitude increases, and the beam of light shrinks; tilt the disk away from the sun, the sun’s altitude decreases, and the beam of light stretches. Our project is a collaboration between learning scientists, mathematics educators, sculptors, teachers, and engineers. We will report on the mathematical design of the sculpture and demonstrate how it harnesses the apparent parallelism of sun rays to represent products and quotients. We consider the implications of the SunRule for teaching and learning and present plans to co-design instructional activities for the SunRule with mathematics and science teachers.", "id": "Paper/71174", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71174"}, {"title": " Quantitative Reasoning in a First Course in Linear Algebra ", "webprogram_exclude": "0", "session_ids": ["Session/17855"], "source_sha256": "fd0b0b6e1c3a299934965ce9ff0b77e69fdea99a73bdf763a6ae25baa9d445d3", "withdrawn": "", "abstract": "While quantitative reasoning (Thompson, 1993) has been shown to play a significant role in student learning from introductory mathematics through calculus, its impact in post-calculus courses is far less understood. In this talk, I will discuss the valuable role it can play in a first course in linear algebra. I will present an approach that begins on day one grounded in quantities, naturally giving rise to vectors and linear combinations. I will then illustrate how sustained engagement with three categories of quantities (day-to-day, disciplinary, and intrinsic algebraic) promotes deep sense-making and fosters productive mathematical attitudes.", "id": "Paper/71177", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71177"}, {"title": " Are classical enveloping algebras of semisimple lie algebra also quantum groups? ", "webprogram_exclude": "0", "session_ids": ["Session/18372"], "source_sha256": "facab2e6ddb582d440b620d2a275b898343e28f50873e865b066b9c0617b11cb", "withdrawn": "", "abstract": "Quantum groups are very important Hopf algebras associated to a semisimple lie algebra. They are deformations of their enveloping algebras given by a parameter q.\n\nA remarkable fact discovered by Majid is that these Hopf algebras can be recovered completely from their positive part, via a Braided drinfeld double construction. This positive part is a universal object associated to a braided vector space. So in a sense, a braiding and a universal property encode all the complicated relations of the quantum group, including the quantum Serre relations.\n\nA natural question then, is that if the normal (non quantum) Serre relations can be recovered from this point of view in some way. Are they also consequence of an universal construction related to a braided vector space?\n\nWe propose a braided vector space associated to the cartan data of g, without any deformation parameter q, and compute its Nichols algebra. Relations similar to the classical Serre relations appear as a consequence of the braiding. And the corresponding braided double U (The associated analogue of the quantum group) is a Hopf algebra that fits in an abelian exact sequence, and has as a Hopf quotient the classical enveloping algebra U(g). In particular the Serre relations are exact modulo a Hopf ideal generated by a commutative subalgebra. This object then connects the classical algebra U(g) with the theory of Nichols algebras, braided vector spaces and quantum groups.", "id": "Paper/71179", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71179"}, {"title": " Developing Modeling Portfolios in a Mathematical Modeling Class Using Data From In-Class Experiments ", "webprogram_exclude": "0", "session_ids": ["Session/18088"], "source_sha256": "b24da87c13e1b714e96df4b47fbc103110dd75acc6b65d5e2011140b73cc3c33", "withdrawn": "", "abstract": "In our mathematical modeling class, students perform experiments primarily developed at another institution.  Students are presented an initial mathematical model, though not necessarily the best model for the experiment.  Students are divided into groups to perform the experiments and see how well the model represents the data.  Each group is expected to identify a model improvement, and then present the results in both oral and written forms.  Then each individual student is required to further refine/improve the models and submit for their midterm and final grades.  Additionally, students have the option of taking the feedback from the individual projects or use the ideas learned over the course of the semester to further refine and possibly improve their results.  This can create an iterative process for trying to improve the mathematical model while receiving feedback multiple times.  The collection of model improvements forms a model portfolio for each student.  The results of the model portfolio development from the Fall 2026 class will be discussed in this talk.", "id": "Paper/71180", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71180"}, {"title": " Learning from the Life of Dr. Michael Barrus ", "webprogram_exclude": "0", "session_ids": ["Session/18141"], "source_sha256": "53f60d331c1de5077108e935359670f752ed1cea9465aa12cfc45104a3abce71", "withdrawn": "", "abstract": "Dedicated to the researcher and teacher, Michael David Barrus, Jr. (1980-2025), this talk will reflect on experiences that shaped his character, explore his mathematical and lesser-known pastimes, and celebrate his influence as a beloved husband, father, professor, and mathematician.", "id": "Paper/71185", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71185"}, {"title": " Atiyah’s Conjecture on Configurations of Five Points ", "webprogram_exclude": "0", "session_ids": ["Session/19356"], "source_sha256": "5a25f599358d317819a0eb0242d32a39948556acbf4bbffd68c1653095fecd53", "withdrawn": "", "abstract": "Proceeding in the vein of Malkoun's Gram matrix approach, we claim to show Atiyah's conjecture on configurations of points holds for the case of five points. The case of three points was shown by Atiyah, while the case of four points was shown by Eastwood-Norbury, Khuzam-Johnson, and Malkoun. A computational verification of the five-point case was presented by Svrtan at the 8th Croatian Mathematical Congress, though no peer-reviewed proof of this case has yet to arise. We revisit Malkoun's four-point construction and provide an alternative argument for this case, which makes the five-point case more accessible.", "id": "Paper/71186", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71186"}, {"title": " Modeling Healthcare Accessibility for Dengue Fever Patients in Nepal ", "webprogram_exclude": "0", "session_ids": ["Session/19353"], "source_sha256": "044c7b7080be054436c1b160fe8c1caab8f42cc66972d60d551c880cd3e66ce8", "withdrawn": "", "abstract": "Dengue fever is a vector-borne disease highly prevalent in tropical and subtropical regions. In Nepal, dengue affects many people each year, and in severe cases, timely access to healthcare facilities is essential for appropriate treatment and care. However, due to differences in population distribution, transportation networks, and challenging terrain, geographic proximity to healthcare facilities alone may not adequately represent accessibility. In this study, we develop a mathematical model to estimate healthcare accessibility for dengue fever patients across Nepal. We integrate population distribution, healthcare facility locations and capacity, road networks, land cover, and elevation to estimate travel times between populations and healthcare facilities. These travel times are incorporated into a travel-time-dependent decay function that represents decreasing access to healthcare resources as travel time increases. Healthcare supply is then considered relative to spatial and temporal demand for care, including monthly dengue burden, to quantify accessibility across regions. Using this framework, we produce spatially resolved estimates of healthcare accessibility and identify areas with comparatively low access to care. By integrating geospatial, epidemiological, and healthcare data within a mathematical modeling framework, this work aims to characterize spatial inequities in healthcare access and identify areas that may warrant further consideration in healthcare planning.", "id": "Paper/71187", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71187"}, {"title": " The Galois module structure of Deligne–Lusztig varieties for <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"9.531ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 4103.5 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbf {G} = \\mathrm {GL}_3</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAINB-47\" d=\"M465 -10Q281 -10 173 88T64 343Q64 413 85 471T143 568T217 631T298 670Q371 697 449 697Q452 697 459 697T470 696Q502 696 531 690T582 675T618 658T644 641T656 632L732 695Q734 697 745 697Q758 697 761 692T765 668V627V489V449Q765 428 761 424T741 419H731H724Q705 419 702 422T695 444Q683 520 631 577T495 635Q364 635 295 563Q261 528 247 477T232 343Q232 296 236 260T256 185T296 120T366 76T472 52Q481 51 498 51Q544 51 573 67T607 108Q608 111 608 164V214H464V276H479Q506 273 680 273Q816 273 834 276H845V214H765V113V51Q765 16 763 8T750 0Q742 2 709 16T658 40L648 46Q592 -10 465 -10Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-47\" d=\"M56 342Q56 428 89 500T174 615T283 681T391 705Q394 705 400 705T408 704Q499 704 569 636L582 624L612 663Q639 700 643 704Q644 704 647 704T653 705H657Q660 705 666 699V419L660 413H626Q620 419 619 430Q610 512 571 572T476 651Q457 658 426 658Q401 658 376 654T316 633T254 592T205 519T177 411Q173 369 173 335Q173 259 192 201T238 111T302 58T370 31T431 24Q478 24 513 45T559 100Q562 110 562 160V212Q561 213 557 216T551 220T542 223T526 225T502 226T463 227H437V273H449L609 270Q715 270 727 273H735V227H721Q674 227 668 215Q666 211 666 108V6Q660 0 657 0Q653 0 639 10Q617 25 600 42L587 54Q571 27 524 3T406 -22Q317 -22 238 22T108 151T56 342Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-4C\" d=\"M128 622Q121 629 117 631T101 634T58 637H25V683H36Q48 680 182 680Q324 680 348 683H360V637H333Q273 637 258 635T233 622L232 342V129Q232 57 237 52Q243 47 313 47Q384 47 410 53Q470 70 498 110T536 221Q536 226 537 238T540 261T542 272T562 273H582V268Q580 265 568 137T554 5V0H25V46H58Q100 47 109 49T128 61V622Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAINB-47\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-3D\" x=\"1182\" y=\"0\"></use>\n<g transform=\"translate(2238,0)\">\n <use xlink:href=\"#E1-MJMAIN-47\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-4C\" x=\"785\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-33\" x=\"1995\" y=\"-213\"></use>\n</g>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/19367"], "source_sha256": "e4dae4f6b626f69cd2b3cc2912877809440ddb414465c6cf44dfb2c1fe00176c", "withdrawn": "", "abstract": "Deligne and Lusztig defined a finite \\'etale cover \\(Y(w) \\to X(w)\\) of varieties which is attached to any connected reductive group \\(\\mathbf{G}\\) defined over a finite field \\( k = \\mathbb{F}_q \\), with an isogeny \\(F\\) whose some positive power is a Frobenius endomorphism, and a Weyl group element \\(w \\in W\\). We consider the  ramified Galois covers  \\( \\overline{Y}(w)\\rightarrow  \\overline{X}(w) \\) of the natural compactifications of these Deligne-Lusztig varieties. Our goal is to calculate the Lefschetz numbers for the action of the covering group, which is given by the rational points \\(\\mathbf{T}^{wF}\\) of a torus, on the coherent cohomology of the structure sheaf of \\( \\overline{Y}(w)\\). \nThe full collection of Lefschetz numbers determine the virtual representation of \\(\\mathbf T^{wF}\\) on the alternating sum of these cohomology groups.  In the two cases of Deligne--Lusztig surfaces of type \\(A_2\\) and \\(^{2}A_2\\) for \\( \\mathbf{G} = \\mathrm{GL}_3 \\), we give explicit formulas for the Lefschetz numbers for a generator of the stabilizer of an irreducible component of \\(\\overline{Y}(w)\\) . It follows that the equivariant Euler characteristic class\n\\(\n[ \\chi_{\\mathbf T^{wF}}\n\\bigl(\\overline Y(w),\\mathcal O_{\\overline Y(w)}\\bigr) ] \n\\)\nis not an integral multiple of the regular representation class\n\\([\\bar k[\\mathbf T^{wF}]]\\) in \\(K_0(\\bar k[\\mathbf T^{wF}])\\).", "id": "Paper/71188", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71188"}, {"title": " Fairness and Temporal Generalization in Student Dropout Prediction: A Single-Institution Study ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "58ac2adcd4741a2ddf48527da252bb76fa68fd27650aeb6511ab7c8a7e8d7d0d", "withdrawn": "", "abstract": "Predictive models are increasingly used to identify students who may be at risk of dropping out, but overall predictive accuracy does not necessarily imply equitable performance across student groups or reliable performance over time. We examine predictive performance, fairness, and temporal generalization in a single-institution student success dataset.\n\nOur analysis includes 2,241 students observed from Fall 2022 through Spring 2026, including 593 students who experienced dropout and 1,648 who persisted. After removing potential sources of information leakage and reducing correlated predictors, we used 51 academic, demographic, and enrollment-related features to train a LightGBM classification model. Model performance was evaluated using repeated cross-validation and a held-out test set. We compared subgroup performance using area under the ROC curve (AUC), false negative rate, demographic parity, equal opportunity, and calibration. Bootstrap confidence intervals and paired permutation tests with Benjamini-Hochberg correction were used to quantify uncertainty and assess differences across groups.\n\nThe model achieved a cross-validated AUC of 0.968 (SD = 0.015) and a held-out test AUC of 0.976. On the locked test set, the false negative rate was 0.048 for URM students compared with 0.191 for non-URM students, and 0.032 for first-generation students compared with 0.236 for non-first-generation students. The URM pattern was observed across four within-institution cohort replications, while the first-generation pattern was less consistent. Temporal validation revealed a substantial reduction in predictive performance on later cohorts, with AUC decreasing to 0.861.\n\nThese results illustrate that predictive accuracy, subgroup fairness, and temporal generalization can tell different stories about the same predictive system. Evaluating all three dimensions provides a more complete statistical assessment of data-driven decision systems.", "id": "Paper/71189", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71189"}, {"title": " Siegel-Veech constants for solvable torus covers ", "webprogram_exclude": "0", "session_ids": ["Session/17902"], "source_sha256": "c76abdac4d8cc1850a5bdbe76a8b3879c3ff1f677fdf63a311acc25f40dd9179", "withdrawn": "", "abstract": "We present work to determine Siegel-Veech constants for generic branched torus covers with solvable deck groups. This is a continuation of previous work on Siegel-Veech constants for branched cyclic covers of generic translation surfaces done by Aulicino, Calderon, Matheus, Salter and the presenter.  We will look at a specific example supporting ideas for a general formula and properties of the Siegel-Veech constants. This is work in progress with David Aulicino (CUNY).", "id": "Paper/71190", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71190"}, {"title": " Nonlocal Korn inequalities in linear and nonlinear continuum models ", "webprogram_exclude": "0", "session_ids": ["Session/17883"], "source_sha256": "3f1dd1d04edacc3c96078b20a811dcbd5678bdca80695b0b75f1a0c98b182933", "withdrawn": "", "abstract": "Motivated by nonlocal models in continuum mechanics, we present several nonlocal analogues of Sobolev rigidity relations for vector fields. In the setting of linearized continuum mechanics, we show that a class of vector field spaces whose semi-norm involves the magnitude of ``directional'' difference quotients is in fact equivalent to the class of vector fields characterized by a semi-norm involving the full difference quotient. This equivalence can be considered a Korn-type characterization of nonlocal Sobolev spaces. The form and strength of the inequality we obtain depends on the scaling of the nonlocal interactions in the models. In certain regimes, the inequalities are genuinely nonlocal, in the sense that no local counterpart exists. We apply these inequalities to obtain quantitative statements for variational problems arising in peridynamics and dislocation models. In the nonlinear setting, nonlocal Poincar\\'e-Korn inequalities have a distinct character from local analogues; nevertheless they can be used to justify the linearized continuum setting.", "id": "Paper/71191", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71191"}, {"title": " Ising disks: topology-preserving Glauber dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/19359"], "source_sha256": "843a5ec9d88673d292dc4c924978104f2ccabb504f5dcc56d10d4665e2080833", "withdrawn": "", "abstract": "I will introduce a dynamic model of finite, contractible unions of unit cubes without pinches or other local singularities. Its moves add or remove one cube while preserving these constraints. Although contractibility is global, we prove that whether a move is permissible can be decided from a fixed neighborhood of that cube. The dynamics thus resemble Eden growth with an added topological constraint. In dimension two, these conditions are equivalent to the union being homeomorphic to a disk. Our strongest results are in this planar case. We prove a stronger version of a question of Pach: every state can be reduced to any prescribed square using only permissible removals. Reversing these reductions connects any two states and makes the associated continuous-time Markov chain irreducible. The chain has addition rate $p_{\\uparrow}$ and removal rate $p_{\\downarrow}$, and their ratio $\\beta$ is a fugacity parameter controlling growth. The boundary of a planar state is a self-avoiding polygon, and states with $n$ squares correspond to such polygons of area $n$. For the exponential growth factor $\\kappa$ of self-avoiding polygons, we prove ergodicity for $\\beta<1/\\kappa$, with stationary probability proportional to $\\beta^n$. We also study unusually large states in equilibrium. We count each excursion from the single-square state that reaches size $T$ as one rare event, avoiding repeated crossings within that excursion. After the natural time rescaling, these event times converge in distribution as $T$ grows to a homogeneous Poisson point process of unit intensity. I will conclude by extending this model to distorted disks, lattice models of immersed disks whose polygonal boundaries may self-overlap. They provide discrete random-metric-space models with disk topology motivated by Jackiw-Teitelboim gravity. I am developing local-move Markov chains on these objects and studying removability, irreducibility, and ergodic regimes. This is joint work with Yuliy Baryshnikov.", "id": "Paper/71192", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71192"}, {"title": " The Lie Functor: A Categorical View of Classical Lie Theory ", "webprogram_exclude": "0", "session_ids": ["Session/18242"], "source_sha256": "c7d15aa846aa2f80a191ebd4ac3706ead84aa0201af6d01267e2a2c1c2c1121a", "withdrawn": "", "abstract": "Despite their shared name, Lie groups and Lie algebras are distinct mathematical objects. Lie groups are smooth manifolds with group structure, whereas Lie algebras are vector spaces equipped with a bracket operation. Categorical constructions such as zero objects, equalizers, and quotients in the categories of Lie groups and Lie algebras reveal interesting structural results. For instance, each category has a version of the first isomorphism theorem. We analyze how the categorical framework also reveals a deeper relationship through the functor $\\mathrm{Lie}\\colon \\mathbf{LieGrp}\\longrightarrow \\mathbf{LieAlg}$,\nwhich assigns to each Lie group its tangent Lie algebra. We study how the Lie functor preserves local information but may lose global topological information. Finally, we interpret Lie’s three theorems categorically to show that restricting the Lie functor to connected, simply connected Lie groups yields an equivalence with the category of finite dimensional Lie algebras.", "id": "Paper/71194", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71194"}, {"title": " Double (the) Categories: Applying Categorical Logic to Applied Categorical Modeling ", "webprogram_exclude": "0", "session_ids": ["Session/18324"], "source_sha256": "4809318929933152069776cfafa33ccba9f5d7189a7d3e9515e5a03cbbb4fe96", "withdrawn": "", "abstract": "Category theory is such a natural yet rigorous setting in which to study processes and relationships that researchers from fields as diverse as epidemiology and aerospace engineering are drawn to the subject, yearning to reap its benefits to synthesize complex data and model evolving dynamics. Yet there is a dearth of modeling software that fully leverages the interoperability and abstraction that categorical techniques permit. To build such a tool, we would need to formally encode the desired categorical structures in a way that still exposes their compositionality and universal properties for us to work with. It turns out the most suitable lens for formally study of category theory is category theory itself, particularly the theory of double categories. These have morphisms along two dimensions, providing an abundant framework for the categorical logic needed to capture and fine-tune categorical foundations at the level necessary for application. In ongoing joint work with Evan Patterson, we lay the mathematical groundwork upon which categorical modeling platforms like the Topos Institute’s (open source and under development) CatColab may be built.", "id": "Paper/71195", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71195"}, {"title": " A Low-Rank Structure-Preserving Semi-Lagrangian Algorithm for a Hybrid Plasma Model in a Magnetized Setting ", "webprogram_exclude": "0", "session_ids": ["Session/18247"], "source_sha256": "92fe0e69e826265ae75f85b68740606db7057bde2148e73cb3d62493a6d63153", "withdrawn": "", "abstract": "Accurately simulating plasmas for fusion applications requires 6D kinetic models, but this high-dimensional setting limits the size and resolution achievable with traditional numerical methods. This talk presents a tensor-train (TT) solver for the 6D Vlasov kinetic equation in a magnetized plasma setting. By exploiting low-rank structure, the TT representation mitigates the curse of dimensionality, enabling efficient computation in six-dimensional phase space. We combine a semi-Lagrangian method with TT-Cross to adaptively evolve a low-rank representation of the distribution function over time. We highlight a key practical challenge: preserving the underlying structure under aggressive rank truncation, and describe a low-rank correction scheme that efficiently restores it.", "id": "Paper/71196", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71196"}, {"title": " Solving Null Controllability Problems via Feedback Control governed by Riccati Equations. ", "webprogram_exclude": "0", "session_ids": ["Session/19337"], "source_sha256": "bb04c3ca67568f9e8e985daaa9f301270fa60a44c9afb0e7324ebd34b0319cbf", "withdrawn": "", "abstract": "Null controllability of PDE systems by means of appropriate Riccati equation will be discussed. Riccati equation naturally occurs when solving linear quadratic regulation problem in Hilbert Spaces. Null controllability can also be approached by solving suitable optimal control problem with a small parameter -say \\epsilon >0. For each given value of \\epsilon one has a suitable feedback mechanism represented by a solution of Riccati equation. This equation becomes singular at the end point when $\\epsilon tends to zero. \n\nThe algorithm applies for dynamical systems exhibiting infinite speed of propagation. This includes dynamics like heat transfer or dynamics of vibrations in plate systems with boundary or localized controls. Null controllability can be achieved in an arbitrary short time due to the infinite speed of propagation using the limit obtained [under certain observability conditions] from Riccati equation. As a consequence new feedback controller mechanism is proposed via solution of singular Riccati equation.", "id": "Paper/71199", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71199"}, {"title": " Tying primes out of knots ", "webprogram_exclude": "0", "session_ids": ["Session/18100"], "source_sha256": "c939118d5de2691af485a8178e07a8d1f6b92670ad5fceb10521b20a9b4fa826", "withdrawn": "", "abstract": "How do you draw $\\textrm{Spec}(\\mathbb{Z})$? What about the spectrum of rings of integers of other number fields? I will show some drawings of these spaces inspired by arithmetic topology. In this world, $\\textrm{Spec}(\\mathbb{Z})$ is like a three-manifold, and primes are knots tied in that manifold.", "id": "Paper/71201", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71201"}, {"title": " A quantum group that doesn’t have deformation parameter for a semisimple lie algebra. ", "webprogram_exclude": "0", "session_ids": ["Session/17907"], "source_sha256": "ebe41f2884425fa7e5d139951eaf0e99ff5c550597fea0fc04649da402ddd342", "withdrawn": "", "abstract": "Quantum groups are very important Hopf algebras associated to a semisimple lie algebra. They are deformations of their enveloping algebras given by a parameter q.\n\nA remarkable fact discovered by Majid is that these Hopf algebras can be recovered completely from their positive part, via a Braided drinfeld double construction. This positive part is a universal object associated to a braided vector space. So in a sense, a braiding and a universal property encode all the complicated relations of the quantum group, including the quantum Serre relations.\n\nA natural question then, is that if the normal (non quantum) Serre relations can be recovered from this point of view in some way. Are they also consequence of an universal construction related to a braided vector space?\n\nWe propose a braided vector space associated to the cartan data of g, without any deformation parameter q, and compute its Nichols algebra. Relations similar to the classical Serre relations appear as a consequence of the braiding. And the corresponding braided double U (The associated analogue of the quantum group) is a Hopf algebra that fits in an abelian exact sequence, and has as a Hopf quotient the classical enveloping algebra U(g). In particular the Serre relations are exact modulo a Hopf ideal generated by a commutative subalgebra. This object then connects the classical algebra U(g) with the theory of Nichols algebras, braided vector spaces and quantum groups.", "id": "Paper/71206", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71206"}, {"title": " Counting PCF Maps Using Hurwitz Spaces ", "webprogram_exclude": "0", "session_ids": ["Session/18365"], "source_sha256": "93103f1cbe06a99c684a0167f85d96643b569d5dc80d610935d1ad526f009ad0", "withdrawn": "", "abstract": "In complex dynamics, a self map of $\\mathbb{P}^1$ is called post-critically finite (PCF) if the forward orbit of its critical points is finite. A generic self map will not satisfy this, but when it does, the dynamics of this finite set tells us about the dynamics of the map. \n\nThe dynamics of a PCF map on its post-critical set yields a ramification portrait. A natural question then arises: Under what conditions an abstract ramification portrait can be observed via a rational (or even topological) map of $\\mathbb{P}^1$? Many families of abstract ramification portraits are known to be realizable via rational maps, for instance, as in the work of Floyd-Kim-Koch-Parry-Saenz. However, the question is still generally open. I will talk about these ideas from a Hurwitz space approach using the combinatorial boundary stratification of a Hurwitz space.", "id": "Paper/71217", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71217"}, {"title": " Reflection of two student teams’ experience with MCM \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18066"], "source_sha256": "2f06c98028d01dc77ffc2e8810bf9821de0e0c3c5e79162b0f02cb6554c967c3", "withdrawn": "", "abstract": "We took on this challenge following a conversation with Professor Watson where we expressed wanting to gain a more hands-on experience with the application of mathematics and industrial engineering to real-world scenarios. In the process of completing this challenge we were challenged to translate my fluency with mathematics into a tool for problem-solving and communication. Beyond the competition this followed me in my coursework as we had a more effective understanding of mathematical modelling.", "id": "Paper/71228", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71228"}, {"title": " Free quantum groups and the wild category ", "webprogram_exclude": "0", "session_ids": ["Session/18371"], "source_sha256": "5c41d45da131551dfff51a136ab4796f88efa4c93bc2419e1095c3ed6b0a21c8", "withdrawn": "", "abstract": "In a recent result, we showed that the category lf(n) of locally finite representations of the free algebra A on n letters is hereditary and completely determined by its Ext quiver, which is can be very explicitly described. This free algebra is also a Hopf algebra, and in fact a type of free quantum group. It turns out that the category of representations of the group algebra of the free group, as well as any pointed finitely generated free Hopf algebra, as constructed by Takeuchi, are all isomorphic to such a free category lf(n) for some n. While the quantum group can be reconstructed from additional tensor category information, this shows that even in this rigid case of a free quantum group they cannot be reconstructed only from its raw abelian category. However, we conjecture this reconstruction problem has an affirmative answer in the world of free groups, give a partial answer and show how it relates to other reconstruction problems of a similar flavor, such as the free von-Neumann factor isomorphism problem. Part of this is based on joint work with Ryan Bianconi.", "id": "Paper/71231", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71231"}, {"title": " Sharpening models of ice melting via the pinnacle problem ", "webprogram_exclude": "0", "session_ids": ["Session/19343"], "source_sha256": "52926129f31ffaa8d9b4d9558cf43bf68f2cbc5d29f2ee1a294b74128209c5e8", "withdrawn": "", "abstract": "Ice melting is a major factor in the climate system and one that interacts with many other processes across scales. Even at the fundamental scale of an ice-water interface, melting involves coupled complexities arising from the fluid dynamics of thermal convection, the physics of phase transitions, and the mathematics of moving boundaries and evolving shapes. Such effects are conventionally studied in isolation, and there remains a need for unifying frameworks that combine the relevant factors and whose predictions can be quantitatively tested. Here we conduct precision laboratory experiments on the pinnacle problem and use the findings to validate a phase-field model of ice melting and corresponding computational simulations. Experiments on upright spikes of immersed ice reveal a family of finely-tipped structures that are attractors of the melting dynamics and whose geometries differ from recent theoretical predictions. A phase-field model whose parameters are tuned on one set of experimental conditions is shown to accurately reproduce experimental findings over widely ranging scales. Analysis of the results indicate that microscopic effects linking the interfacial curvature, temperature, and melt rate lead to macroscopic effects on the morphology and dynamics. More generally, this work provides a validated computational framework that solves for the coupled dynamics of heat, flow, phase and shape and which therefore should prove useful for a broader class of related problems.", "id": "Paper/71233", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71233"}, {"title": " Wild number for spanning trees in complete and bipartite graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17841"], "source_sha256": "899d8d77529b262f9dee1b6d603e9fa1122d0b6f2a481181a5874a84edeb636f", "withdrawn": "", "abstract": "We study the wild number of an edge-colored graph, a parameter measuring  the minimum number of edges which must belong to every color class so that every color class contains a spanning tree. We investigate the wild number of complete graphs and complete bipartite graphs under two common edge colorings, equitable $2$-colorings and minimum proper colorings. For an equitable $2$-coloring, the ranges of possible wild numbers of a complete graph and a complete bipartite graph are determined, and constructions for a complete graph show that every wild number within the range is attainable by some equitable 2-coloring. For minimum proper colorings, the lower bound of the wild number of a complete graph is established, and we conjecture that the upper bound corresponds, while the wild number of a complete bipartite graph is determined. We also investigate how this parameter behaves for subgraphs and for Cartesian products.", "id": "Paper/71235", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71235"}, {"title": " Disordered Matrix Product States for 1D Spin Chains ", "webprogram_exclude": "0", "session_ids": ["Session/18296"], "source_sha256": "4fc7ebce82424d402c6ab703a7dc86573cc9bf0642de6130db7f46bd22dfb0fb", "withdrawn": "", "abstract": "In 1991, Fannes, Nachtergaele, and Werner introduced the notion of a \"finitely correlated state\" for a translation invariant 1D spin chain, generalizing the structure of the AKLT state. In this talk, we will discuss a recent extension of the FNW theory to states with homogeneous disorder.  In the disordered context, a new phenomenon arises: there are states with exponential clustering that are inherently gapless, in the sense that they have no gapped finite-range parent Hamiltonian.  A disordered generalization of the AKLT state with this property will be presented. This state has a gapless nearest neighbor parent Hamiltonian and exponential clustering. We call such a state \"quasi-gapped.\" Time permitting, several open questions about quasi-gapped states will be presented. (Joint work with Eric Roon.)", "id": "Paper/71236", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71236"}, {"title": " Covering the Numerical Range of Operators with Berezin Ranges on Subspaces of the Hardy Space ", "webprogram_exclude": "0", "session_ids": ["Session/19368"], "source_sha256": "58f095885c99098bcbf6eab570a502cea1dd24629da2ed5637ae5bb376fb1085", "withdrawn": "", "abstract": "The numerical range of a bounded operator $T$ on a Hilbert space $\\mathcal{H}$ is defined as $$\\operatorname{W}(T) = \\left\\{\\langle Tx, x \\rangle \\mid \\lVert x \\rVert = 1,~ x \\in \\mathcal{H} \\right\\}.$$\nWhen $\\mathcal{H}$ is a reproducing kernel Hilbert space (RKHS) with normalized reproducing kernels $k_p$, $p\\in X$, the Berezin range of $T$, which is a subset of the numerical range of $T$ is given by \n\\[\n\\operatorname{Ber}(T) = \\left \\{ \\langle Tk_p,k_p \\rangle \\mid \\, p \\in X \\right \\}.\n\\]\nThe weighted shift operator on the space of polynomials of degree $2$ or less, $P_2(\\mathbb{D}) \\subset H^2(\\mathbb{D}),$ is defined by $T(1) = 0,~T(z)=a,~T(z^2)=bz,$ where $a, b \\in \\mathbb{C}.$ We show that the Berezin range of a unitary conjugate intersects the boundary of $\\operatorname{W}(T)$ in at most $4$ points. Consequently, $\\operatorname{W}(T)$ cannot be covered by a countable union of Berezin ranges of its unitary conjugates; instead, an uncountable union is required. We also show that the standard shift in $P_3(\\mathbb{D}),$ defined $T(1) = 0,~T(z)=1,~T(z^2)=z,~T(z^3)=z^2$ similarly requires an uncountable union. In $P_1(\\mathbb{D}),$ it is known that three unitary conjugates will suffice for a weighted shift.\n\nAdditionally, we show that if $T$ has a finite-dimensional proper reducing subspace $M$ with $\\operatorname{W}(T|_{M^\\perp}) \\cap \\partial \\operatorname{W}(T) = \\emptyset$, where every $\\dim(M)+1$ reproducing kernels (at distinct points) are linearly independent, then an uncountable union of Berezin ranges of unitary conjugates is required to cover $\\operatorname{W}(T)$ provided that any choice of $\\dim(M)+1$ reproducing kernels is linearly independent. Notably, operators on $H^2(\\mathbb{D})$ or $P_n(\\mathbb{D})$ with $n \\geq 2$ would satisfy that final condition. \n\nRank one operators can be expressed in the form $Tf = \\langle f, g \\rangle h,$ where $\\lVert h \\rVert = 1.$ A useful corollary of the previous result is that, for a rank one operator $T$ with $g \\neq ch,$ we use the reducing subspace $M = \\operatorname{span}\\{g, h\\}$ to show that it requires the union of uncountably many Berezin ranges of unitary conjugates of $T$ to cover $W(T).$ In contrast, if $g = ch,$ then it is known that two unitary conjugates will suffice; in this case, $\\operatorname{int}(\\operatorname{W}(T)) = \\emptyset.$", "id": "Paper/71238", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71238"}, {"title": " Optimal Spectral Algorithms for Correlated Two-view Models in High Dimensions ", "webprogram_exclude": "0", "session_ids": ["Session/18002"], "source_sha256": "abfd977f4b2622490c2ba1e8cf7d2a16cd04d1e722db170f1e4bd42deb2b5e32", "withdrawn": "", "abstract": "We study high-dimensional inference in correlated two-view models, focusing on spectral methods for strong detection and weak recovery. We introduce a general framework, motivated by a TAP type heuristic from statistical physics, that provides a unified treatment of three canonical models: high-dimensional canonical correlation analysis, and the correlated spiked Wigner and Wishart models. Our main contribution is to construct explicit spectral algorithms in all three settings, that achieve strong detection and weak recovery down to the corresponding thresholds, where we prove matching information-theoretic lower bounds. Furthermore, our spectral procedures operate without knowledge of the model parameters, relying solely on the observed data. This demonstrates the optimality of spectral methods in these models and the broad statistical applicability of the framework.", "id": "Paper/71243", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71243"}, {"title": " What is the Probability that a Random Graph is Characterized by its Generalized Spectrum? ", "webprogram_exclude": "0", "session_ids": ["Session/19370"], "source_sha256": "55c3e0c29d12d765956607f9a0112e4c65aa5882e80f192dc97fc8eb9fcdcc56", "withdrawn": "", "abstract": "In a series of papers, Wang and his collaborators found sufficient arithmetic conditions for a graph to be uniquely characterized by its generalized spectrum. It is natural to ask how often these conditions are satisfied for an Erdos-Renyi random graph. We rephrase this problem as a question about the distribution of the cokernel of a certain random matrix. We give the first specific conjecture on how frequently Wang's condition is satisfied, by analyzing a related, but more tractable random matrix model. This is joint work with Alexander Van Werde.", "id": "Paper/71246", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71246"}, {"title": " Mathematical Modeling and Reconstruction of Environmental Disturbances in Undersea Fiber Optic Cables ", "webprogram_exclude": "0", "session_ids": ["Session/19353"], "source_sha256": "cf89af5cf9a30e0b79c64475a8240189e141740e8e53a0482e63428fc446743a", "withdrawn": "", "abstract": "Undersea fiber-optic cables, traditionally used for telecommunications, can also function as distributed sensors by detecting environmental disturbances through changes in backscattered optical signals. In this work, we develop a mathematical framework for modeling and reconstructing such disturbances using fiber-optic sensing. The optical fiber is modeled as a continuous distribution of Rayleigh scattering centers, while external disturbances are represented by spatially and temporally varying phase perturbations. We formulate the relationship between an interrogation signal, the fiber response, and the resulting backscattered signal and use matched filtering and phase comparison between baseline and disturbed measurements to recover the induced phase perturbation. The framework is applied to simulated environmental disturbances, including whale vocalizations, seismic activity, and temperature fluctuations. We further compare different interrogation signals and investigate the effects of laser noise on phase recovery. Our analysis shows that uncertainty in phase measurements increases with propagation distance and that averaging multiple interrogation signals can reduce the effects of noise. This framework provides a basis for studying the use of undersea fiber-optic infrastructure for environmental sensing and motivates further investigation of interrogation-signal design and reconstruction in the presence of realistic noise.", "id": "Paper/71247", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71247"}, {"title": " Physical Scalar-Longitudinal Modes in Extended Electrodynamics ", "webprogram_exclude": "0", "session_ids": ["Session/18321"], "source_sha256": "6f6ad7e634bf156b68f7b064dce6ce485a24e706071fca905b768409216462ca", "withdrawn": "", "abstract": "We consider an extension of electromagnetism in which the term involving the four-divergence of the electromagnetic potential is treated as part of the physical dynamics rather than solely as a gauge-fixing term. The resulting field equations contain an additional scalar-longitudinal sector. For conserved currents, this additional degree of freedom satisfies a massless wave equation, while the usual transverse electromagnetic modes are retained.\n\nAfter reviewing the relation of this formulation to conventional gauge-fixed electrodynamics, we investigate the coupling of the scalar-longitudinal sector to matter. Particular attention is given to the constraints imposed by local current conservation and to identifying conditions under which the additional degree of freedom can produce observable longitudinal electromagnetic effects. We consider generalized material response and effective-current models, derive the corresponding propagation equations, and examine boundary conditions at interfaces between media.\n\nThe analysis provides a framework for distinguishing genuine propagating scalar-longitudinal excitations from gauge or pure-potential solutions and for determining what modifications of the matter sector are required for such modes to interact with material systems. Possible applications to systems in which longitudinal electromagnetic effects have been proposed are discussed.", "id": "Paper/71250", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71250"}, {"title": " Duffin–Schaeffer examples, real residue systems, and Bohr set primes ", "webprogram_exclude": "0", "session_ids": ["Session/18256"], "source_sha256": "54acbf43405c72dac024412833f8012543a0e07f6c1ee9d534008fdb7dca1e8b", "withdrawn": "", "abstract": "I will discuss joint work with Stefan Hesseling, where we construct functions $\\psi:\\mathbb{N}\\to [0,\\infty)$ so that the associated sets of inhomogeneously $\\psi$-approximable numbers meet given measure specifications. (``Duffin--Schaeffer examples.'') The work relies on natural generalizations of two familiar ideas from number theory: the distribution of primes lying in arithmetic progressions, which we generalize to primes lying in Bohr sets; and the asymptotic density of unions of arithmetic integer sequences (``residue systems''), which we generalize to the setting where the residues can be arbitrary real numbers.", "id": "Paper/71251", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71251"}, {"title": " Beyond the the Code: Explorations using AI in Data Science courses ", "webprogram_exclude": "0", "session_ids": ["Session/17461"], "source_sha256": "d6f3ca9607b31533ec23cc0831c82e922770f204f100e21577b7f1625ce00d79", "withdrawn": "", "abstract": "Long before the emergence of AI, software libraries; particularly in R and python, allowed one to train complex machine learning models without a deep understanding the underlying models. Though this still required some \"coding\", the dictum \"if you can code it, you understand it\" no longer applied-at least not in quite the same way. Now that AI can perform all the steps of a data science workflow, how much coding should we require of students, and how do we  develop intuition and habits of mind required to interrogate data sets and models, ask the right questions, and check data quality? This talk reports on experiences using a mix of traditional approaches and AI; including pencil and paper mathematics, from-scratch coding of simple models, coding assistants, and  chat based AI, in a graduate and undergraduate data science courses.", "id": "Paper/71260", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71260"}, {"title": " Mean-Variance Stackelberg Games with Asymmetric Information ", "webprogram_exclude": "0", "session_ids": ["Session/17800"], "source_sha256": "6819d7ce2c0fb8e96d5b839d7887828c97b297b6ae3ff64c771ec17af4e46060", "withdrawn": "", "abstract": "We consider two investors who perform mean-variance portfolio selection under asymmetric information: investor 1 knows the true stock dynamics, while investor 2 has to infer the true dynamics from observed stock evolution. Their portfolio choices are connected through relative performance concerns, i.e., each investor is concerned about not only the individual terminal wealth, but also how it compares to the average terminal wealth of both investors. We model this as Stackelberg competition: investor 2 (the ``follower'') observes actual trading of investor 1 and decides his trading strategy accordingly; anticipating investor 2's reaction, investor 1 (the ``leader'') selects a trading strategy that best suits her objective. As investor 2 only observes investor 1's actual trading (without knowing its dynamics), he performs {\\it pathwise} optimization, i.e., solving his mean-variance problem under every fixed path of trading actions investor 1 may take, which yields an intrapersonal equilibrium strategy depending linearly on investor 1's trading actions. Anticipating investor 2's use of this strategy, investor 1 aims to randomize her trading actions (to better conceal her private information from investor 2) via a stochastic policy, selected under an {\\it entropy-regularized} mean-variance objective, where the entropy regularizer quantifies the randomness from a policy. Our main result obtains an intrapersonal equilibrium strategy of investor 1, which is a Gaussian policy depending on investor 1's private information and strategic internalization of investor 2's strategy. The tuple of the two investors' respective intrapersonal equilibrium strategies then forms a Stackelberg equilibrium between them.", "id": "Paper/71263", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71263"}, {"title": " Moduli of Representations of Strongly Simply Connected Algebras of Polynomial Growth ", "webprogram_exclude": "0", "session_ids": ["Session/18371"], "source_sha256": "a379464e29fb5366f2a0b7e3dfeb39cbe290410a06e06d5cf0c42a16b9012880", "withdrawn": "", "abstract": "We prove irreducible components of moduli spaces of semistable representations of strongly simply connected algebras of polynomial growth are isomorphic to products of projective spaces. This is achieved by using multicoil structure to show that Kuranishi obstructions disappear after taking invariants and that the resulting moduli spaces are smooth and normal. The main theorem extends the analogous product-of-projective-spaces phenomenon for special biserial and tame tilted algebras.", "id": "Paper/71267", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71267"}, {"title": " Random Matrix Theory in C* algebra’s ", "webprogram_exclude": "0", "session_ids": ["Session/18381"], "source_sha256": "d1b9df0c8593034969079ca4760147ff7a9722cfda54aa970cd7533da1a4f125", "withdrawn": "", "abstract": "We will talk about various recent applications of random matrix theory to various problems in C* algebras.", "id": "Paper/71270", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71270"}, {"title": " Amenability and random walks on non-locally compact topological groups. ", "webprogram_exclude": "0", "session_ids": ["Session/18383"], "source_sha256": "1a7bfbc3a07c091c5aea6e31b9b25eb73f71ddd1dab264448eea06a46a1ebe89", "withdrawn": "", "abstract": "We discuss two notions of amenability for non-locally compact topological groups and their implications for the behavior of random walks on topological groups. In particular, we show that a generalized version of Kesten's theorem holds for all amenable topological groups with small invariant neighborhoods and all locally generated skew-amenable groups. Moreover, we describe the connection of this topic with countable Borel equivalence relations and its applications in the discrete setting. The talk is based on a joint work with Kate Juschenko and Friedrich Martin Schneider.", "id": "Paper/71271", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71271"}, {"title": " A half-constant upper bound for Chowla’s cosine problem ", "webprogram_exclude": "0", "session_ids": ["Session/19368"], "source_sha256": "c0ad8e4b6c55e31abecadb7a1b0362b76803a884b196c2b7c4bd66ba53227071", "withdrawn": "", "abstract": "For a finite set $A \\subset \\mathbb{N}$, let $f_A(x) = \\sum_{a \\in A} \\cos(ax)$, and let $\\lambda(n)$ be the least value of $-\\min_x f_A(x)$ over all $n$-element sets $A$. Chowla conjectured that $\\lambda(n) \\gg \\sqrt{n}$; the best lower bound is now polynomial, due to recent work of Bedert and of Jin, Milojević, Tomon, and Zhang, while the classical Sidon-set construction gives $\\lambda(n) = O(\\sqrt{n})$, with explicit constant $\\sqrt{2}$ due to Mercer. We improve the leading constant in the upper bound to $1/2$, proving $\\lambda(n) \\le \\tfrac12\\sqrt{n} + O(n^{1/4}\\sqrt{\\log n})$. The starting point is a two-sided square identity: for a Sidon set $S$ of size $k$, an explicit set $A(S)$ of $k(k-1)$ frequencies, built from the differences and shifted sums of $3S$, satisfies $f_{A(S)} = \\rho^2 - k/2 - g/2$, where $\\rho$ and $g$ are cosine sums over $S$ alone. This identity already gives constant $1$, and the remaining task is to choose $S$ so that $g$ is small wherever $\\rho$ is small. We take $S$ to be a random tent-weighted subset of a centred Singer perfect difference set, so that the relevant exponential sums are close to a Fejér kernel. The dangerous point $x = \\pi/3$, where the kernel controlling $g$ peaks while the one controlling $\\rho$ vanishes, is handled by deleting a block of odd offsets near the centre, which biases $\\rho$ to be positive there. A uniform concentration bound, together with a lower bound on the probability that the random set has exactly $k$ elements, produces a set with $\\min_x f_A(x) \\ge -k/2 - O(\\sqrt{k \\log k})$, and subadditivity of $\\lambda$ extends the bound from $n = k(k-1)$ to all $n$.", "id": "Paper/71273", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71273"}, {"title": " Predicting CATH Protein Classifications Using Entanglement-Based Descriptors ", "webprogram_exclude": "0", "session_ids": ["Session/19358"], "source_sha256": "14e668e61c1c402c32e7b91f4f6dcad07c4d1de2e409908f55a11f2121577fbe", "withdrawn": "", "abstract": "The CATH (Class , Architecture, Topology, Homology) database organizes protein structures using sequence similarity, fold organization, and structural alignment methods. We use the CATH hierarchy as a benchmark to ask how much information about protein structural organization is encoded by mathematical entanglement descriptors. Proteins are represented as piecewise-linear curves whose vertices are their CA atoms, and we employ three entanglement metrics as structure descriptors: the Writhe, the second Vassiliev measure (v2) and the third Vassiliev measure (v3). We show that a simple Multi-Layer Perceptron classifier, using writhe, v2, v3 and length as input features, predicts the dominant CATH classes of all single domain proteins in the Protein Data Bank with high accuracy, without any sequence information or structural alignment. Furthermore, we find that the descriptors contribute differently across the hierarchy: the Writhe and length contribute the most while predicting at the class level, whereas the second and third Vassiliev measures substantially improve classification at the architecture, topology and homologous superfamily levels. Together, these results show that these entanglement measures can capture complex protein structural organization.", "id": "Paper/71274", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71274"}, {"title": " Oriented spectral sequences ", "webprogram_exclude": "0", "session_ids": ["Session/18209"], "source_sha256": "12cc5c58128492ed6cd1fc96e774e2245cf39463f8e061bedaf897efe0862b61", "withdrawn": "", "abstract": "Building on work of Gepner-Heine on Postnikov towers of (\\infty,\\infty)-categories and forthcoming work of Zahrer on oriented t-structures, we introduce oriented spectral sequences (for stable oriented categories with t-structure), which for ordinary stable \\infty-categories recover ordinary spectral sequences. Joint work with Alexander Zahrer.", "id": "Paper/71275", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71275"}, {"title": " Translation symmetry-enforced long-range entanglement in mixed states ", "webprogram_exclude": "0", "session_ids": ["Session/17925"], "source_sha256": "1774926b3bebfaa78ab31caad5980dbdc9b465b1703f969de58a08fe380184b6", "withdrawn": "", "abstract": "We show by a counting argument that even though translation symmetry admits symmetric short-range entangled (SRE) eigenstates, there are not enough such SRE eigenstates to span the zero momentum sector. This means that the fixed point strong-to-weak spontaneous symmetry breaking state of translation symmetry is long-range entangled: it cannot be written as a mixture of SRE states. This is a subtle form of long-range entanglement in mixed states that cannot be detected by long-range connected correlation functions.", "id": "Paper/71276", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71276"}, {"title": " Decomposing multiscale locomotor coordination via morphology-informed graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17383"], "source_sha256": "531f4fb5bcdfae0a5d5c439b38b6620f8b04b09350cb2b53fe36cf1c7be9579f", "withdrawn": "", "abstract": "Coordinating locomotor structures is fundamental to organismal motility, from multiciliated microorganisms to multi-legged animals. While quantitative high-speed videography captures this coordination at unprecedented spatiotemporal scales, understanding the collective dynamics of locomotion and extracting the underlying control principles that reliably generate motion across environments and species remain challenging. Here, we introduce a morphology-informed graph framework to quantify multiscale coordination. By representing an organism’s body plan as a graph, with anatomical landmarks as nodes and morphologically relevant connections as edges, we construct a sparse orthogonal basis over this graph. Rather than treating individual joints or limbs independently, we project postural dynamics onto this orthogonal basis to decompose movement into interpretable modes, ranging from organism-wide motion through inter-limb coupling to local joint movements. We demonstrate the framework across scales: revealing a conserved coordination pattern during take-off among jumping spider genera and identifying distinct motility states in a multiciliated microorganism. Because this representation is defined by anatomical connectivity, the decomposition provides a principled basis for comparing locomotor dynamics among living and robotic systems.", "id": "Paper/71277", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71277"}, {"title": " Continuous eigenvector propagation under nonlinear N-body dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/18300"], "source_sha256": "e1e2255c6f4ba55a986fc5426e5b034283614ff02dc3dfd6ab75bb22812c8290", "withdrawn": "", "abstract": "Power series are a powerful tool to understand dynamical systems. Here we use them to approximate the continuous in time evolution of eigenvectors. Specifically, we are interested in the non-linear evolution and capturing high fidelity nonlinearities of the covariance of observational or processed data, while avoiding limitations of the inherently linear state transition matrix.", "id": "Paper/71282", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71282"}, {"title": " Ecological Dynamics and Spatial Patterns on Large Metapopulation Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17383"], "source_sha256": "782a6932c69f5e198c304a8969afc393babc3e33d915f5768c9b719a9fd87cc5", "withdrawn": "", "abstract": "In this presentation, we discuss reaction-diffusion models for predator-prey dynamics in patch-structured populations with between-patch dispersal on large graphs. We aim to unify two classical\napproaches for studying spatial dynamics in ecological systems: spatially-continuous models where\ndispersal typically follows a local diffusion operator and spatially-discrete patch models with more\ngeneral network connectivity between the patches. Making use of the recently-developed formalism\nof graph limits, or graphons, we derive a continuum analogue of patch reaction-diffusion models\nwhich can describe the role of dispersal in the presence of non-local connectivity schemes like\nsmall-world or power law networks. A useful feature of these continuum limits is that one can find\nthreshold quantities for the onset of pattern formation in predator-prey models in terms of the non-local dispersal kernel, and therefore the qualitative behavior\nof these metapopulation dynamics is intricately linked to the topology of the dispersal network. We\nwill place particular emphasis on the nonlinear stability of patterned states and regimes in which\npatterned steady states can coexist bistably with spatially uniform states.", "id": "Paper/71284", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71284"}, {"title": " Partition-Valued Hook Count Differences on <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"0.84ex\" height=\"2.009ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -719.6 361.5 865.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">t</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-74\" d=\"M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-74\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Cores ", "webprogram_exclude": "0", "session_ids": ["Session/19321"], "source_sha256": "c8ccdea401083d83d03d0905ddadbf80ae53ad5907406418d63c244327f65d0b", "withdrawn": "", "abstract": "For fixed \\(t\\ge2\\), a \\(t\\)-core is a partition with no hook length divisible by \\(t\\).\nLet \\(X_{t,h}(\\lambda)\\) denote the number of hooks of length \\(h\\) in a \\(t\\)-core \\(\\lambda\\).\nFor increasing \\(\\boldsymbol h=(h_j)_{j\\ge0}\\), consider\n\\[\n \\bigl(X_{t,h_j}(\\lambda)-X_{t,h_{j+1}}(\\lambda)\\bigr)_{j\\ge0}.\n\\]\nWhenever this sequence is nonincreasing and nonnegative, we regard it as an integer partition.\nWe obtain complete classifications for these partitions from different perspectives.", "id": "Paper/71286", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71286"}, {"title": " New Directions in Irrationality ", "webprogram_exclude": "0", "session_ids": ["Session/18261"], "source_sha256": "6782f9ad953ef61c3c0b95f2d8eb87e58fbe214b8d0c56c4255f727b47e1ec84", "withdrawn": "", "abstract": "Although almost every real number is irrational, proving that a specific\nconstant is irrational, or obtaining a strong bound on its irrationality\nmeasure, is often nontrivial. Landmark results such as Ap\\'ery's proof\nof the irrationality of $\\zeta(3)$, as well as many efforts to bound irrationality\nmeasures, including those of Rhin and Viola, Hata, Marcovecchio, Zudilin,\nand Zeilberger, have relied on constructions tailored to each constant,\nmost often based on Beukers-type integrals. Such\nconstructions are found sporadically and cannot be used for a systematic\nsearch.\n\nHere we show that Conservative Matrix Fields (CMFs) generalize these approaches:\nBeukers-type integrals and their hypergeometric generalizations all appear as\ntrajectories inside CMFs. We use CMFs to embed known formulas into searchable\nfamilies of rational approximation sequences. Different trajectories in the\nsame CMF can approximate the same constant with very different arithmetic\nquality, allowing us to search systematically for better trajectories.\n\nFor rational approximations $p_n/q_n$ to $L$, we measure their quality by $\\delta=-1-\\limsup_{n\\to\\infty}\\frac{\\log|L-p_n/q_n|}{\\log|q_n|}$.\nLarger $\\delta$ means a better approximation, and $\\delta>0$ proves\nirrationality. We recover the best-known formulas for\n$\\zeta(2)$, $\\zeta(3)$, $\\zeta(5)$, $\\log 2$, $\\pi$, and Catalan's constant\nas CMF trajectories.\n\nFor $\\zeta(2)$, a search in the ${}_4F_3$ CMF gives\n$\\delta=0.2745$, improving upon the previous best bound of $\\delta=0.2441$.\n\nFor Catalan's constant, Nesterenko's formula with $\\delta=-0.4757$ and the\nRamanujan Machine record with $\\delta=-0.4325$ both appear in the same\n${}_3F_2$ CMF. Extending the search to a ${}_4F_3$ CMF yields\n$\\delta=-0.2759$, \\textbf{a new world record}. For\n$\\zeta(2)+\\zeta(3)$, we improve the previous best bound from\n$\\delta=-0.1329$ to $\\delta=-0.0002$, and for\n$L(2,\\chi_{-3})$, we improve the previous best bound from\n$\\delta=-0.4765$ to $\\delta=-0.0579$.", "id": "Paper/71287", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71287"}, {"title": " High-Order Weak Galerkin Finite Element Methods for Biot’s Consolidation Model: Stability, Error Analysis, and Numerical Validation ", "webprogram_exclude": "0", "session_ids": ["Session/19344"], "source_sha256": "3357f7a91b832f3e2f3f6128c16fbe3138e5e90d20c46bcabc7bd5b86a088728", "withdrawn": "", "abstract": "This research presents a new high-order Weak Galerkin finite element method for Biot's consolidation model, a coupled poroelasticity system describing the interaction between solid deformation and fluid flow in porous media. The proposed formulation employs weakly defined differential operators and arbitrary-order polynomial approximation spaces for the displacement and pressure variables. For the fully discrete scheme, a backward Euler method is used for temporal discretization, while the spatial discretization is based on the Weak Galerkin framework. Existence and uniqueness of the fully discrete solution are established, and stability and error estimates are derived for the coupled displacement-pressure system. Extensive numerical experiments are presented to validate the theoretical findings. The computed convergence rates agree with the predicted error estimates and demonstrate optimal order of convergence in energy-norm together with higher-order interior accuracy in $L^2$. The results confirm the stability, robustness, and high-order accuracy of the proposed method.", "id": "Paper/71289", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71289"}, {"title": " CANCELLED Inverse Reciprocal Compatibility and the Golden Ratio \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/19369"], "source_sha256": "a91d1c01b7c6370cd92251f94851a9a8caa23a8b95fdbf0c041fe3e116d7cba8", "withdrawn": "i", "abstract": "We introduce an inverse--reciprocal compatibility construction for differentiable functions based on normalized primitives associated with a function, its inverse, and its reciprocal. For the power family \\(f(x)=x^p\\), the corresponding reduced quantities satisfy\n\\[\nG_I[x^p]=p^3,\\qquad G_R[x^p]=\\frac{p+1}{p-1}.\n\\]\nRequiring inverse and reciprocal compatibility yields\n\\[\np^3=\\frac{p+1}{p-1},\n\\]\nand hence\n\\[\n(p^2+1)(p^2-p-1)=0.\n\\]\nThus the compatible exponents are \\(p=\\pm i\\), \\(p=\\phi\\), and \\(p=-1/\\phi\\), where \\(\\phi=(1+\\sqrt{5})/2\\) is the golden ratio. A reduced formulation expresses the compatibility problem through logarithmic second-derivative quantities \\(U''/U\\) and \\(V''/V\\), placing the power-family factorization within a broader differential framework. The construction provides an exact setting in which the golden ratio emerges algebraically from compatibility between inverse and reciprocal operations.", "id": "Paper/71290", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71290"}, {"title": " How Do Competing Honey Bee Colonies Survive? A Mathematical Model ", "webprogram_exclude": "0", "session_ids": ["Session/19353"], "source_sha256": "043068f2dc4a9d65f5ac8db2f8fdd27bd0ec33f2ef7ed11f88c63b6a7bac5c08", "withdrawn": "", "abstract": "Honeybee colonies located in the same environment may compete for shared floral resources, and this competition can influence foraging activity, worker survival, and the long-term persistence of the colonies. We develop a nonlinear ordinary differential equation model to investigate the dynamics of two honeybee colonies sharing a common foraging environment. Each colony is divided into non-foraging and foraging worker populations, with transitions between these groups determined by recruitment and return from foraging. The model incorporates worker mortality and additional mortality associated with competition between foragers from neighboring colonies.\n\nWe investigate how colony-specific demographic parameters, foraging behavior, mortality, and inter-colony competition influence population dynamics. The mathematical analysis includes the determination of biologically feasible equilibria, conditions associated with their existence and uniqueness, and the local stability of the resulting steady states. We also examine how changes in model parameters affect coexistence and the relative population sizes of the two colonies. Numerical simulations complement the analytical results and illustrate possible long-term behaviors under different biological and competitive conditions.\n\nThe model provides a framework for exploring how interactions between neighboring honeybee colonies can shape colony survival and coexistence in a shared environment.", "id": "Paper/71291", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71291"}, {"title": " Gromov–Hausdorff distance between Euclidean Unit Balls ", "webprogram_exclude": "0", "session_ids": ["Session/19321"], "source_sha256": "fb172b69cbad3fc2cb881b9a955fbb52dbc4b3ec7ea1c58effac79eb4ed6de8f", "withdrawn": "", "abstract": "What is the Gromov--Hausdorff distance between Euclidean unit balls of different dimensions, denoted by $d_{GH}(B^m,B^n)$, for $m>n$? Note that the lower bound coming from the stability of persistent homology is zero, since all balls possess identical (trivial) persistent homology. To establish non-trivial lower bounds, we exploit the Borsuk--Ulam theorem. For any $n \\ge 1$, we prove that $d_{GH}(B^m,B^n)\\ge \\frac{\\sqrt{n+1}}{\\sqrt{n+1}+\\sqrt{n}} > \\frac{1}{2}$ for $m>n$, and that $d_{GH}(B^m,B^n)\\to 1$ as $m\\to \\infty$. Finally, we prove that $d_{GH}(B^m,B^n)<1$ for all finite $m>n\\geq 1$.", "id": "Paper/71292", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71292"}, {"title": " Design of Experiments for Identifiable Sparse Model Discovery in Systems Biology ", "webprogram_exclude": "0", "session_ids": ["Session/18220"], "source_sha256": "8dcc8a5dcb51bb0180c894eaf39fcc25a7c9fafb7948d6dc93ab6807288e7c5a", "withdrawn": "", "abstract": "Library-based model discovery methods such as sparse identification of nonlinear dynamics (SINDy) recover governing equations for biological systems, including chemical reaction networks, ecological systems, and gene regulatory circuits, directly from time-series data, but recovered model structure is often unstable under measurement noise and can be incorrect when sampled trajectories fail to capture a sufficient range of a system's behavioral regimes. This instability reflects sloppiness in the underlying regression: some combinations of candidate library terms are orders of magnitude less sensitive than others, becoming practically non-identifiable under realistic sampling. These sloppy directions in parameter space result from multicollinearity among library terms; we therefore treat sampling design as a direct intervention on the conditioning of the candidate library. Using information-theoretic criteria, we test strategies for selecting sampling times, initial conditions, and perturbation protocols that visit regions of state space in which collinear library terms become distinguishable, guiding the construction and pruning of the SINDy library prior to regression. We discuss these design principles in the context of biological experiments, including constraints arising from limited admissible perturbations, conserved quantities, and timescale separation.", "id": "Paper/71295", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71295"}, {"title": " Handlebody diagrams of 6-dimensional Weinstein Manifolds ", "webprogram_exclude": "0", "session_ids": ["Session/18218"], "source_sha256": "a38936593bd8ceaab636f42f55e621daecc772c30727b3007548392a8f294617", "withdrawn": "", "abstract": "Weinstein manifolds are symplectic manifolds with a handle decomposition via model symplectic handles. In low enough dimension, the attaching information of handles can be captured diagrammatically featuring Legendrians. In dimension 4, these diagrams consisting of primarily knots have been used to compute invariants and find equivalences between different manifolds. In fact, in a project which started at WiSCon 2019, we (Acu, Capovilla-Searle, Gadbled, Marinkovic, Starkston, W.) showed a way to produce handle diagrams for complements of smoothed divisors. In dimension 6, explicit diagrams are harder to come by. Now, in joint work with Orsola Capovilla-Searle and Laura Starkston, we build explicit Weinstein handlebody diagrams of various 6-dimensional manifolds including cotangent bundles of any closed orientable 3-manifolds, and prove some results regarding the isotopies of Legendrian surfaces in the 5-dimensional boundaries of 6-dimensional subcritical Weinstein domains.", "id": "Paper/71297", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71297"}, {"title": " The orchard-planting problem for fifteen points ", "webprogram_exclude": "0", "session_ids": ["Session/19321"], "source_sha256": "30a96e6543132a58bc924e07312b9d094544880c29bdf0a0e4775785cc78291d", "withdrawn": "", "abstract": "Let $t_3(n)$ be the maximum number of lines containing exactly three points of a set of $n$ points in the real plane. The values $t_3(n)$ are known for $n \\le 12$ and for $n = 16$, the values for $n = 13, 14$ have been announced from an unpublished computation, and it has been known since 1974 that $t_3(15) \\in \\{31, 32\\}$. We prove that $t_3(15) = 31$: fifteen points determine at most $31$ three-point lines, so $15$ is not a sporadic exception to the Burr--Grünbaum--Sloane formula $\\lfloor n(n-3)/6 \\rfloor + 1$ (the known exceptions are $n = 7, 11, 16, 19$). By the same method we confirm $t_3(13) = 22$ and $t_3(14) = 26$. For arrangements of pseudolines (equivalently, rank-$3$ oriented matroids) the answer is already different at $n = 13$: there is an arrangement of $13$ pseudolines with $23$ triple points, so the pseudoline maximum is $t_3^{ps}(13) = 23 > 22$, and likewise $t_3^{ps}(14) = 27 > 26$. The proof reduces the question to the exact realizability of every partial Steiner triple system on $15$ points with $32$ blocks whose leave is a $9$-edge graph with all degrees even. We enumerate these systems up to isomorphism ($7{,}955{,}290$ classes, organised by $13$ leave types) and show that none has a realization in the real projective plane with exactly the prescribed collinearities, using the Pappus and Desargues theorems as combinatorial filters and exact Gröbner-basis computations for the rest. Every rejection is valid over every field of characteristic $0$. The enumeration is checked against the $80$ Steiner triple systems of order $15$, and the rejections are cross-checked on all systems for $n = 13$ by an unfiltered algebraic run, and on random samples for $n = 15$ by both this run and a SAT encoding of rank-$3$ oriented matroids.", "id": "Paper/71299", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71299"}, {"title": " Complementary Course Design: Computational Linear Algebra Within a Data Analytics Master’s Curriculum ", "webprogram_exclude": "0", "session_ids": ["Session/17855"], "source_sha256": "4190e039df8b7336920e2184a440a7c94ec781886e7af81c215b887a8c225e00", "withdrawn": "", "abstract": "In the Master of Science in Data Analytics for Science at Carnegie Mellon University,\nComputational Linear Algebra is taught in the same semester as a machine learning course\nand a large-scale computing course, so that principal component analysis is introduced in\nall three within the same few weeks. This paper examines what the mathematics course\ncontributes to the collective learning objectives, and identifies three areas: computational\ncritical thinking about when a method applies, where it fails, and at what cost; an\nintegrated treatment of related matrix methods that allows students to transfer reasoning\nacross them; and mathematical motivation for the large-scale algorithms implemented\nelsewhere in the program. We describe two supporting practices, explicit cross-referencing\nbetween instructors and collective project mentoring, and report\non implementation and student responses.", "id": "Paper/71307", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71307"}, {"title": " Persistent Homology and Capillary Waves of Fluctuating Chemical Phase Boundaries ", "webprogram_exclude": "0", "session_ids": ["Session/18304"], "source_sha256": "c4224a123b6f22f63e01bc991e3501ab19c39af6c17143e24da4cb4816518339", "withdrawn": "", "abstract": "Liquid-gas and liquid-liquid phase boundaries are fluctuating surfaces, that may, at any point in time, be approximated as a combination of sine and cosine functions via a Fourier series (known as capillary wave theory). The work functional describing the distortion of the surface from the flat plane has several forms, and may be written in terms of the Fourier expansion, or in geometric terms like bending rigidity and Gaussian curvature (the Helfrich Hamiltonian). From an energetic standpoint, the surface structure (in terms of either the capillary wave spectra or the geometric terms in the Helfrich Hamiltonian) can be predicted from the energy minimization of the work functional. Here we compare and contrast the encoding of the surface via capillary wave theory, the Helfrich geometry, and persistent homology that identifies the distributions of the surface critical points. Complementing this spatial understanding of the surface, we are also interested in the temporal fluctuations of these descriptors so as to learn how the spatial structure is related to the dynamics (in essence, the time-dependent Hamiltonian).", "id": "Paper/71313", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71313"}, {"title": " The Köthe Conjecture ", "webprogram_exclude": "0", "session_ids": ["Session/17949"], "source_sha256": "32b2f635bccb33ee6a0c39257707f9f7e36fd50f37e3c34ff9a8ae64b3668f5f", "withdrawn": "", "abstract": "We give a short construction refuting the K\\\"othe Conjecture, joint with King and Vendramin. The construction is based on the point module approach to the problem, introduced by Easton, Ford, King, and myself, over a year ago. One of the missing pieces of the puzzle was completed with the assistance of AI, and we will describe precisely what AI assistance was used within the human strategy for the solution.", "id": "Paper/71317", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71317"}, {"title": " Effects of plaque buildup on blood flow. ", "webprogram_exclude": "0", "session_ids": ["Session/19343"], "source_sha256": "a22db505a8a82938ca42a138d20ea03782592d666597b7fef8ea13e8c407a592", "withdrawn": "", "abstract": "This research investigates whether the shape of obstacles has a significant impact on blood flow behavior. The researchers used the Navier-Stokes equations to simulate blood flow using Direct Numerical Simulation. Several numerical tests were done for three main obstacle shapes, namely square, semi-circle, and hyperbolic.  One such test is the classical flow past a full-step test problem to simulate laminar flow through horizontal arteries, where different shapes are used instead of the step, and vortex forming is observed. Similarly, the simulations are done for pulsating flow and computation the wall shear stress using FreeFEM++.", "id": "Paper/71318", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71318"}, {"title": " PAGOTAS: Partially AGgregatable One-Time Adaptor Signatures ", "webprogram_exclude": "0", "session_ids": ["Session/18307"], "source_sha256": "e33eae80226cba14debe82ee4113429b0fd9a3ea3a7515e13a4dd98f934b5807", "withdrawn": "", "abstract": "We define PAGOTAS (Partially AGgregatable One-Time Adaptor Signatures) for authenticated release of witnesses. We describe a lattice-based instantiation built from the one-time aggregatable signatures of Boneh and Kim and note that a discrete-logarithm analogue is straightforward to construct. Our PAGOTAS are useful if Alice wants to learn Bob's witness for a certain public statement, and Bob wants Alice to give a one-time authentication to him in exchange. She pre-signs a message bound to Bob's statement, and Bob uses his witness to complete her pre-signature without knowing her signing key. By publishing the completed signature, Bob reveals enough information such that Alice can extract a witness from the signature-pre-signature pair. In discrete logarithm settings, the extracted witness is exact, and in lattice settings, the extracted witness is from a relaxed relation which can be parameterized to be cryptographically hard.  Pre-signatures and signatures are publicly verifiable, and we discuss one-time unforgeability and witness extractability. The signature component admits aggregation, but individual witness extraction uses the signature and the pre-signature. Thus, the total representation remains linear in the number of signers, but authentication alone can be compactly represented, which is useful in blockchain applications.", "id": "Paper/71319", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71319"}, {"title": " Action-angle and complex coordinates on non-compact toric manifolds ", "webprogram_exclude": "0", "session_ids": ["Session/17691"], "source_sha256": "98cd50c9c940898f29af863f8d05821f9188dc939b1e9e2a7053a91364e2144a", "withdrawn": "", "abstract": "In the string-theory inspired duality of mirror symmetry, manifolds come in pairs. The symplectic geometry on one corresponds to the complex geometry on the mirror. We will describe how to equip a mirror manifold with a symplectic form, reviewing the joint work arXiv:2103.08714. In particular, we consider a non-compact example, as these are mirrors to manifolds with first Chern class positive or negative.", "id": "Paper/71321", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71321"}, {"title": " Real-Rooted Edge Cover Polynomials ", "webprogram_exclude": "0", "session_ids": ["Session/17900"], "source_sha256": "87e4f7f233b8c63e17f0b6f3637352c1f6953e69da3c1eb7e3eec17f765810c3", "withdrawn": "", "abstract": "An edge cover of a graph is a subset of the edges that covers all vertices of the graph. The edge cover polynomial is the generating polynomial for edge covers. We establish real-rootedness of the edge cover polynomial for several families of graphs, extending the well-known cases of paths and cycles. These include certain subfamilies of tadpole and spider graphs, as well as double cycle graphs, which provide examples with minimum degree at least two. We also show how a graph decomposition method can be used to construct larger graphs with real-rooted edge cover polynomials from smaller graphs with this property.", "id": "Paper/71322", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71322"}, {"title": " State- and Observable-aware Shadow Quantum Singular Value Transformation ", "webprogram_exclude": "0", "session_ids": ["Session/18246"], "source_sha256": "ff9035dc00d9bee724e50990e58037581b0e1e8e1ad3c0a05ec8965558ceae79", "withdrawn": "", "abstract": "We introduce a state- and observable-aware framework for quantum linear systems (QLS), Hamiltonian simulation, and, more broadly, quantum singular value transformation (QSVT). Briefly, given an input state \\(|\\psi\\rangle\\), a block encoding of a Hermitian matrix \\(H\\), a polynomial \\(f\\), and a collection of observables \\(\\{O_1,O_2,\\ldots,O_m\\}\\), shadow QSVT estimates the quantities $\\langle\\psi|f(H)O_i f(H)|\\psi\\rangle$\nfor all \\(i\\). By tailoring the computation to the input state and target observables, this framework aims to mitigate worst-case dependence on the condition number and polynomial degree while avoiding the unnecessary synthesis of the full output state or unitary transformation. \n\nIn this talk, we will present our recent results on shadow QSVT algorithms, demonstrate advantages over existing algorithms, and discuss their potential for early fault-tolerant quantum computing", "id": "Paper/71323", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71323"}, {"title": " High quantum local differential privacy breaks entanglement ", "webprogram_exclude": "0", "session_ids": ["Session/19338"], "source_sha256": "5b0b3eff8d53804c0a44793f610f96ebea8410a47740d9ae6b16776d9c91d4e9", "withdrawn": "", "abstract": "Differential privacy provides a mathematical framework for guaranteeing privacy for sensitive data. Given that the utility of many protocols, and often the presence of a quantum advantage, relies on quantum resources such as entanglement, it is crucial to understand when a privacy requirement for a quantum channel is compatible with the channel's ability to preserve entanglement. We study this question for quantum local differential privacy (QLDP). \n\nOur main result shows that every $\\varepsilon$-QLDP channel with a $d$-dimensional input is entanglement-breaking whenever $\\varepsilon \\leq \\log \\frac{d}{d-1}.$ We also prove an approximate version for $(\\varepsilon,\\delta)$-QLDP, where channels in the same high-privacy regime are close in diamond norm to an entanglement-breaking channel. We further prove a composition result for a collection of private quantum channels having entangled inputs and global measurements in the high-privacy regime. \n\nFinally, we apply our results to private quantum learning theory. We prove that any learning protocol using arbitrary quantum memory on copies of the output of an entanglement-breaking channel can be simulated by a protocol that measures the corresponding unprocessed input copies one at a time while storing only classical information. Combining this result with our high-privacy entanglement-breaking theorem, we show that under sufficiently private local noise, a learning protocol with quantum memory for purity testing and bipartite product testing is subject to the sample complexity lower bounds for protocols with single-copy measurements on the noiseless tasks. We also obtain stronger sample complexity lower bounds when a single highly private channel acts on the entire multipartite input.", "id": "Paper/71326", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71326"}, {"title": " The  Middle Books  before and after Naṣīr al-Dīn al-Ṭūsī: Writing Histories of Spherical Geometry in the Islamciate World ", "webprogram_exclude": "0", "session_ids": ["Session/18373"], "source_sha256": "25ec972991946305d1378c3783975e0eef7315190736ddd982d7f363a64fd763", "withdrawn": "", "abstract": "The \\textit{Middle Books} (\\textit {Kitāb al-Mutawassiṭāt}) were a compilation of mathematical (mostly geometrical) texts that were meant to transition one from Euclid and Ptolemy.  The \\textit{Middle Books} have their origins in a late antique curricular grouping called the \\textit{Little Astronomy}, but in the Islamicate world, they expanded from a set pedagogical progression to an expandable mathematical “canon.”  Scholarship on Arabic mathematics remains organized around studies of single texts, and for this reason, the \\textit{Middle Books} are rarely treated as a coherent object of study. The \\textit{Middle Books} were a distinct subset of mathematical compilation: a unified but dynamic multi-text Arabic manuscripts that were centered around the theme of spherical geometry and applied spherical geometry—the chief application of which is the study of astronomical phenomena (which affects both the heavens and the earth) and optics. The most famous “version” is by the thirteenth-century polymath Naṣīr al-Dīn al-Ṭūsī (1201-1274), who wrote his own commentaries on many of the most common texts; scholars have since falsely attributed the \\textit{Middle Books} to al-Ṭūsī as a text itself, of which we have very few surviving copies. But, if we expand our search to look more broadly, there are many extant manuscript witnesses in libraries around the world that have been dismissed as mere miscellany.  In this talk, I first trace the evolution of the \\textit{Middle Books} from the \\textit{Little Astronomy} through important changes made by al-Ṭūsī (focusing on the example of Menelaus’ Theorem). I then present my survey of post-classical Arabic manuscripts of the \\textit{Middle Books}, expanding the number of known witnesses from ~30 to 82 in order to demonstrate the ways in which the \\textit{Middle Books} continued to evolve after al-Tusi. Ultimately, I argue that by looking at the case of the \\textit{Middle Books}, we see that spherical geometry in the Islamicate world was not only quite sophisticated by contemporary standards, but also self-conscious about the limits of Euclidean geometry.", "id": "Paper/71327", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71327"}, {"title": " Four years (so far!) of MaCSS Scholars: Lessons Learned and Next Steps ", "webprogram_exclude": "0", "session_ids": ["Session/18200"], "source_sha256": "34f5a6182a5da56f68d27d740e7bb86f9296e018315c17b56a4774373028e63e", "withdrawn": "", "abstract": "MaCSS Scholars (Math, Computer Science, and Statistics) is an NSF S-STEM grant (DUE-2221516). Two-thirds of the way into its grant life, we have both lessons and outcomes to share, as well as an optimistic look at our final two years. We’ll share our experience applying for and directing an S-STEM grant, challenges faced, solutions found, and key outcome data from our Year 4 annual report. Finally, we’ll share what’s next for MaCSS Scholars and what we hope to accomplish in the last two years of the grant.", "id": "Paper/71331", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71331"}, {"title": " Seasonal Duration Shapes Bat Persistence under White-Nose Syndrome ", "webprogram_exclude": "0", "session_ids": ["Session/18220"], "source_sha256": "4f70d578814b12db5f1ba6b408338001ba1c9b84eea38ec1aaaea7b6ec48a85a", "withdrawn": "", "abstract": "White-nose syndrome (WNS), caused by the fungal pathogen Pseudogymnoascus destructans (Pd), has caused severe declines in North American bat populations. We develop a discrete seasonal model for a colony of little brown bats (Myotis lucifugus) exposed to Pd, in which population dynamics are tracked across biologically distinct seasonal phases and model coefficients depend explicitly on season length. The resulting annual dynamics are described by a two-dimensional discrete map, capturing susceptible and infected/exposed bats. To account for uncertainty in transmission pathways, we consider different levels of bat-to-bat and environment-to-bat transmissions throughout. We characterize how ecological and disease-related model parameters, as well as season length, affect the stability of the extinction and disease-free equilibria. We further investigate how changes in season length affect regions of quasi-extinction, focusing on hibernation and birthing, which emerge as particularly influential seasons. Our results demonstrate how seasonal duration and transmission pathways interact to shape long-term bat population dynamics and extinction risk through increased oscillations caused by a Neimark-Sacker bifurcation of the endemic equilibrium.", "id": "Paper/71334", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71334"}, {"title": " Rethinking Mathematical Practice and Assessment in the Age of Generative AI ", "webprogram_exclude": "0", "session_ids": ["Session/17461"], "source_sha256": "bb1064e4052169f4e198b07ec8949bdde2487ec4e3ca920cf56f963b2168431a", "withdrawn": "", "abstract": "Generative AI raises new questions about the roles of homework, grading, and feedback in undergraduate mathematics. When students can obtain complete solutions with AI assistance, how should instructors support productive practice while assessing independent understanding? Drawing on selected literature and examples of assessment design, this talk explores how instructors can respond to student AI use and set appropriate expectations based on course level and learning objectives. I discuss ways to combine AI-supported practice with opportunities for students to explain, verify, and independently apply mathematical ideas. I also consider instructor-facing uses of AI, including the development of autograder code and test cases for computational assignments. The discussion emphasizes instructor validation, useful feedback, and the limits of automated grading. Rather than treating homework as obsolete or AI as a replacement for teaching, the talk explores how assignments and assessments can be redesigned to support mathematical reasoning while making thoughtful use of AI.", "id": "Paper/71335", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71335"}, {"title": " On the domination polynomial of a graph ", "webprogram_exclude": "0", "session_ids": ["Session/18206"], "source_sha256": "6a51650420f77f237485875a6d8e95a8d6d8981ff6b881549cfd88bcb71c62c1", "withdrawn": "", "abstract": "The domination polynomial enumerates the dominating sets of a graph according to cardinality. We will begin by reviewing several complementary interpretations of this polynomial, including a broken-neighborhood analogue of Whitney's broken-circuit theorem for chromatic polynomials, an inclusion-exclusion formula, and formulations of the polynomial in terms of the dominance complex and the closed-neighborhood hypergraph. Subsequently, we will report on progress made on the tree unimodality conjecture. This is joint work with Joshua Birns.", "id": "Paper/71339", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71339"}, {"title": " Multimodal sequences and their generating functions ", "webprogram_exclude": "0", "session_ids": ["Session/18276"], "source_sha256": "b87df1ab6865eb27e674e5c9a37b87439c1653bb23c44a8e857997fd09c83bc9", "withdrawn": "", "abstract": "We define integer multimodal sequences, which are generalizations of unimodal sequences having multiple local peaks of equal size. The generating functions for multimodal sequences represent novel types of $q$-series that combine generating functions for both integer partitions and integer compositions. We show that multimodal sequence generating functions become finite series at roots of unity much like the ``strange'' function of Kontsevich, quantum modular forms, and other known examples of this finiteness phenomenon in the modular forms literature; and we generalize some of these previous examples.", "id": "Paper/71341", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71341"}, {"title": " When Computation Is Not Proof: GenAI-Supported Exploration of Hadamard Matrices ", "webprogram_exclude": "0", "session_ids": ["Session/17461"], "source_sha256": "72debf69e879d28d43a3b16da5dc04bb613f933e4c0320f13f8eb88a38f946a7", "withdrawn": "", "abstract": "This chapter examines how two undergraduate computer science students, both retaking discrete mathematics, built and tested mathematical claims while exploring Hadamard-style matrix problems in \\emph{Matrix Explorer}, a web applet that pairs an interactive matrix workspace with an embedded genAI partner, \\emph{ZhengGPT}. The three-hour session took place at Sichuan University; students investigated a parameterized near-Hadamard problem involving matrices with entries in \\(\\{-1,1\\}\\), without being told its connection to the Hadamard conjecture. By modifying matrix entries and comparing patterns of row orthogonality, inner products, Gram matrices, and determinants, students encountered ideas that connect discrete mathematics with introductory linear algebra. Read through critical AI literacy, cognitive offloading, and hybrid intelligence, the data show students treating the interactive matrix workspace as their primary source of evidence and \\emph{ZhengGPT} as a translator and methodological guide. Three findings emerged. Students often treated a growing collection of successful matrix examples as sufficient evidence for a general claim, even when \\emph{ZhengGPT} cautioned that finite computation does not establish existence in all cases. Mathematical vocabulary—including orthogonality, inner product, determinant, and equivalence of matrices—had to be negotiated, often through \\emph{ZhengGPT}. Finally, the matrix workspace and \\emph{ZhengGPT} played complementary roles: one anchored experimentation and visual evidence, while the other supported interpretation, mathematical language, and connections between numerical patterns and general statements. GenAI-mediated inquiry shifted the work from answer production toward conjecture formation and claim testing, while the open-ended matrix setting created opportunities to connect computational experimentation with foundational ideas from both discrete mathematics and linear algebra. At the same time, the study shows that interactive design and genAI support alone do not prevent students from overstating what finite computational evidence can establish.", "id": "Paper/71342", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71342"}, {"title": " Large Almost-Equidistant Sets from Triangle-Free Strongly Regular Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/19366"], "source_sha256": "34babd8997afa13d5dc579f2ee66af632eb1f1340d702059b536f1836b934b95", "withdrawn": "", "abstract": "A set of points in $\\mathbb{R}^d$ is \\emph{almost-equidistant} if among any three of them some two are at distance $1$. Let $f(d)$ be the largest size of an almost-equidistant set in $\\mathbb{R}^d$. The best lower bound previously recorded for every $d \\ge 10$ was $f(d) \\ge 2d+4$, and the main structured construction in the literature was the $16$-point set of Larman and Rogers in $\\mathbb{R}^5$ built from the Clebsch graph. We observe that every connected regular triangle-free graph on $n$ vertices whose second largest eigenvalue $\\lambda_2 > 0$ has multiplicity $m$ yields an almost-equidistant set of $n$ points on a sphere in $\\mathbb{R}^{n-1-m}$, and that two spherical almost-equidistant sets can be combined by an orthogonal direct sum whenever their squared radii sum to $1$. Applied to the triangle-free strongly regular graphs (Petersen, Clebsch, Hoffman--Singleton, Gewirtz, $M_{22}$, and Higman--Sims), and complemented by an extension lemma based on Delsarte-tight cocliques, this gives $f(10) \\ge 26$, $f(20) \\ge 58$, $f(21) \\ge 78$, $f(22) \\ge 100$, $f(22+j) \\ge 100+2j$ for $1 \\le j \\le 8$, and $f(31) \\ge 120$; hence $f(d) > 2d+4$ for all $20 \\le d \\le 57$, and $f(22) \\ge 100 > 4.5 \\cdot 22$. The Higman--Sims set is a two-distance almost-equidistant set of $100$ points in $\\mathbb{R}^{22}$; in connection with a question of Polyanskii, it shows that some triangle-free graph on $100$ vertices with $\\lambda_2 > 0$ has $\\mathrm{rank}(A - \\lambda_2 I) \\le 23$. All constructions are certified by an exact, dependency-free verification script.", "id": "Paper/71343", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71343"}, {"title": " A New Upper Bound for the Polylog Exponent of the Diameter of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"8.218ex\" height=\"3.009ex\" style=\"vertical-align: -1.005ex;\" viewBox=\"0 -863.1 3538.4 1295.7\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathrm {SL}_{2}(\\mathbb {Z}_{p})</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-53\" d=\"M55 507Q55 590 112 647T243 704H257Q342 704 405 641L426 672Q431 679 436 687T446 700L449 704Q450 704 453 704T459 705H463Q466 705 472 699V462L466 456H448Q437 456 435 459T430 479Q413 605 329 646Q292 662 254 662Q201 662 168 626T135 542Q135 508 152 480T200 435Q210 431 286 412T370 389Q427 367 463 314T500 191Q500 110 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y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/19356"], "source_sha256": "d42f3bd5474349d5a23666e41f300119ec9e9aadc40b5bdb2718c480a91f2f23", "withdrawn": "", "abstract": "The Solovay-Kitaev algorithm (see Dawson and Nielsen) gives a poly-log bound of order $\\mathcal{O}(\\log^{\\alpha}(1/\\epsilon))$ for approximating quantum gates in $\\mathrm{SU}(2)$ and $\\mathrm{SU}(d)$ to a precision of $\\epsilon$ with exponent $\\alpha<4$. Dinai extended this result to $\\text{SL}_{2}(\\mathbb{Z}_p)$ with identical exponent. Here, we introduce $p$-adic analogues of techniques on Elkasapy words from Kuperberg to $\\text{SL}_{2}(\\mathbb{Z}_{p})$, improving the poly-log diameter bound from Dinai to exponent $\\alpha > \\log_{\\phi}(2) \\approx 1.44042\\ldots$ arbitrarily close. This technique can be used to bound the diameter of matrix groups on finite fields.", "id": "Paper/71345", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71345"}, {"title": " Fukaya category of a symplectic Landau-Ginzburg model ", "webprogram_exclude": "0", "session_ids": ["Session/17105"], "source_sha256": "c0148fae3e0c7f09bcff4d2514e182acb816d7c39fa855c15ba41e9523bb849a", "withdrawn": "", "abstract": "Certain symplectic fibrations, known as symplectic Landau-Ginzburg models, are mirror to complex manifolds of positive and negative first Chern class. Mirror symmetry is a string theory-inspired duality between pairs of manifolds, specifically the complex geometry on one manifold and the symplectic geometry on the mirror. We will review the methods developed in arXiv:2312.00973 for computing symplectic invariants of these models. Then we will apply them to the example from arXiv:2508.06379.", "id": "Paper/71348", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71348"}, {"title": " Coordinating Early Mathematics Courses for Human Flourishing ", "webprogram_exclude": "0", "session_ids": ["Session/17971"], "source_sha256": "d022d5b54bf0c68c073b2a00060c5b636a4e914f74ff15423842bd8e75f747ed", "withdrawn": "", "abstract": "At a large public university, consistency among multiple sections of early mathematics courses is desired by many departments, leading to a significant amount of course coordination. We coordinate two large undergraduate mathematics courses that serve students on the pathway to Calculus. With a large and diverse instructional team—including part-time lecturers, graduate students, and, unusually, undergraduate teaching assistants—it can be tempting to view course coordination as a mechanism for standardization. We have instead asked whether coordination can create the conditions for people to flourish.\n\nOur approach centers on three principles. First, support instructors at the human level, particularly part-time and non-tenure-track lecturers who often receive the least institutional support, visibility, and professional development. Second, make belonging a primary goal for students and instructors by creating opportunities for human-to-human community. Third, make the structures of the course transparent through clear organization and communication, frequent feedback, transparent assessments and pedagogy, and explicit attention to study skills and metacognition.\n\nThese principles have shaped our approach to administration, assessment, professional development, recitation teaching, and student support. We work to empower instructors rather than simply direct them, providing shared resources while preserving autonomy and encouraging experimentation. We treat undergraduate TAs as instructional leaders and change agents, giving them meaningful agency to develop relationships and initiatives with students. We also coordinate with other departments serving many of the same students.\n\nWe have observed changes in the instructional culture: instructors feel more supported and less isolated, TAs take greater ownership, experimentation spreads, and students become more willing to seek help and participate in mathematics. These experiences have also informed our thinking about student attitudes toward mathematics and persistence in STEM.\n\nOur central lesson is that coordination need not make everyone the same. It can instead create the conditions for agency, belonging, growth, and a healthy relationship with mathematics for students, instructors, and administrators.", "id": "Paper/71349", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71349"}, {"title": " Perfectoid Shimura Varieties of Exceptional Type ", "webprogram_exclude": "0", "session_ids": ["Session/19367"], "source_sha256": "e372dfb981acdebaa97d589e95d57f08136a31462b988dbf6c032d9d38305b12", "withdrawn": "", "abstract": "We develop a group-theoretic analogue of the theory of canonical subgroups which works uniformly for integral canonical models of Shimura varieties, with bounds on its overconvergence radii in terms of group-theoretic Hasse invariants. This is achieved using prismatic Dieudonné theory. We apply this to prove that all minimally compactified Shimura varieties at infinite level are perfectoid spaces, including those of exceptional type for sufficiently large primes.", "id": "Paper/71350", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71350"}, {"title": " From Play to Proof: Building an Undergraduate Research Program Around the Snake Cube Puzzle ", "webprogram_exclude": "0", "session_ids": ["Session/18062"], "source_sha256": "e651f103de69067b937bbd114617141a1852a619e286ec68d895e282ce1f4741", "withdrawn": "", "abstract": "The snake cube is a recreational puzzle consisting of a chain of $n^3$ small cubes that must be folded into an $n\\times n\\times n$ larger cube. Some snakes of cubes have no solution; deciding whether an arbitrary snake can be folded into a cube is NP-complete. Over several years, I have used this puzzle as the starting point for a sequence of undergraduate honors and NSF-funded research projects. Students have modeled solutions as Hamiltonian paths in cubic grid graphs, established bounds on the number and arrangement of straight pieces in solvable puzzles, developed algorithms to enumerate solutions and investigate puzzle difficulty, and studied the role of symmetry in counting distinct foldings. Later projects explored topological variants obtained by identifying opposite faces of the cube to form solid and higher-dimensional tori and exploring new solvability criteria that led unexpectedly to generalized Fibonacci sequences.\n\nThese projects have built on each other while exploring different directions, based on student interest and background, leading to undergraduate presentations at the Joint Mathematics Meetings and other conferences. In this talk, I will survey the undergraduate research results and the research process, illustrating how investigations of the cube move undergraduates from play and experimentation to computation and conjecture, culminating in theorem and proof.", "id": "Paper/71355", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71355"}, {"title": " A Size-Structured Predator-Prey Model: Well-posedness, Numerical Approximation and Dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/18023"], "source_sha256": "74acf8fbcad0189f04ba99e84abaf0a6852f379eb9957d17326ec84146531508", "withdrawn": "", "abstract": "We develop a size-structured predator–prey model together with a first-order finite-volume scheme for approximating its solutions. We first establish uniqueness of weak solutions. Then, using the numerical scheme and a compactness argument, we prove the existence of bounded-variation weak solutions to the predator–prey system and use uniqueness to establish convergence of the numerical scheme to the unique weak solution of the model. We then demonstrate that the model exhibits a limit cycle arising through a Hopf bifurcation.", "id": "Paper/71356", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71356"}, {"title": " On the Geographic Spread of Chikungunya between Brazil and Florida: A Multi-patch Model with Time Delay ", "webprogram_exclude": "0", "session_ids": ["Session/19359"], "source_sha256": "cd9c21d2ce5f94c26ed60ff53989aecda4a14c33ff5451bce5b7751fecae52a3", "withdrawn": "", "abstract": "Chikungunya (CHIK) is a viral disease transmitted to humans through the bites of Aedes mosquitoes infected with the chikungunya virus (CHIKV). CHIKV has been imported annually to Florida in the last decade due to Miami's crucial location as a hub for international travel, particularly from Central and South America including Brazil, where CHIK is endemic. This work addresses the geographic spread of CHIK, incorporating factors such as human movement, temperature dependency, as well as vertical transmission, and incubation periods, for different patches. Central to the model is the integration of a multi-patch framework and the inclusion of human movement between endemic Brazilian states and Florida in the numerical analysis. We establish crucial correlations between the mosquito reproduction number $R_m$ and the disease reproduction number $R_0$ with the disease dynamics in a multi-patch environment, encompassing not only from a theoretical perspective but also from numerical simulations. After establishing the well-posedness of the multi-patch model problem, we present conditions to ensure the uniform persistence of the disease. Using real population and temperature data we are able to determine all parameters that are temperature-dependent for both Brazil and Miami-Dade county and apply a two-patch model to calibrate the CHIK data from Brazil and Miami-Dade county. Finally, via sensitive analysis we discuss the disease dynamics under different scenarios and make future projections, offering insights for potential effective control strategies, as well as addressing the timing for these strategies to be adopted.", "id": "Paper/71358", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71358"}, {"title": " Letter Frequencies and Entropy in Pattern-Avoiding Binary Words ", "webprogram_exclude": "0", "session_ids": ["Session/19346"], "source_sha256": "8218f265d0d5a77f8ca2b3da262099e9560de5d5eb13b3743fbde57d0be538ea", "withdrawn": "", "abstract": "We study the exponential growth of binary words subject to local pattern-avoidance rules and global composition constraints. For a finite forbidden set of binary patterns and an asymptotic proportion of one symbol, we consider the entropy density of admissible words with fixed composition. Under standard irreducibility and mixing hypotheses, we use weighted transfer matrices and a classical variational formula to relate this entropy to the spectral radius of a parameter-dependent matrix. We work out the classical case in which consecutive $A$'s are forbidden, giving exact fixed-composition counts and an explicit entropy density. We also analyze the system forbidding both $AA$ and $ABA$, deriving an exact counting formula and the corresponding constrained entropy. These examples show how stronger local exclusion rules narrow the admissible composition interval and alter the exponential growth rate. We conclude by outlining a connection to recent questions of Bóna, Maga, and Richey concerning letter frequencies in binary words avoiding a forbidden pattern, highlighting the relationship between entropy-maximizing compositions and limiting symbol frequencies.", "id": "Paper/71362", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71362"}, {"title": " Order, Chaos, and What’s Next: A Brainstorming Session ", "webprogram_exclude": "0", "session_ids": ["Session/18348"], "source_sha256": "8d62a3eefa55520e326dffdb3ae981e69f758713479f16f0075120559826c4c2", "withdrawn": "", "abstract": "This interactive session builds on the open problems and research directions presented earlier, providing a collaborative forum to explore the broader future of the coexistence problem in dynamical systems. Rather than solely reviewing established questions, the discussion will emphasize identifying critical gaps, connecting disparate subfields, and articulating unexamined problems. Beginning with brief framing remarks by the speaker, participants will collectively brainstorm high-impact questions, necessary technical breakthroughs, and emerging intersections. The goal is to establish a creative, forward-looking space where researchers can synthesize perspectives, refine new ideas, and lay the groundwork for future research.", "id": "Paper/71366", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71366"}, {"title": " Fully-Dualizable <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.934ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 1263.1 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">E_n</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-45\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-6E\" x=\"1044\" y=\"-213\"></use>\n</g>\n</svg>-Algebras and Segalification ", "webprogram_exclude": "0", "session_ids": ["Session/18209"], "source_sha256": "2a28d00ce31e056a12aa056023c94796ced429d8d3bd20e488d06d69d0460f0d", "withdrawn": "", "abstract": "In a remark in his Cobordism Hypothesis paper, Lurie conjectured a characterization of fully-dualizable objects in the $(\\infty,n+1)$-category of $E_n$-algebras. Brochier, Jordan, Safronov and Snyder later formulated a conjecture about which $E_n$-algebras are further invertible. After proving some folklore results on adjoints in $(\\infty,n+1)$-categories, these conjectures come down to some computations in factorization homology. Establishing these folklore results relies on a good formula for Segalification, as provided by Barkan and Steinebrunner's work. We discuss how these formulas can be improved.", "id": "Paper/71370", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71370"}, {"title": " The Rainbow Number for <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"10.569ex\" height=\"2.843ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -934.9 4550.4 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">x + y = z^2</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-78\" d=\"M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 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xlink:href=\"#E1-MJMAIN-32\" x=\"620\" y=\"355\"></use>\n</g>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "e7e0b9882f4ed2214e30f8816363832a6ff5cb809dc070600ca095ffd3a37f86", "withdrawn": "", "abstract": "The rainbow number $\\mathrm{rb}(S,\\ eq)$ for an equation $eq$ defined on a set $S$ is the minimum number $r$ such that any partitioning of $S$ into $r$ non-empty sets (an ``$r$-coloring\") contains a solution to $eq$ where each variable is contained in a different set. We give the rainbow number for $x + y = z^2$ in $\\cyc{p^2}$ and $\\cyc{p^3}$ for prime $p$. We additionally provide lower bounds for this rainbow number in $\\cyc{p^k}$ and $\\cyc{p_1 \\cdots p_n}$ for distinct primes $p_1, \\dots, p_n$.", "id": "Paper/71371", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71371"}, {"title": " When AI Changes What We Want: Stability and Agency in Adaptive Learning Systems ", "webprogram_exclude": "0", "session_ids": ["Session/18272"], "source_sha256": "6ed6dcd9c9a33958206d49aade44ef88760f833bb83d6be6ce4b0ad1adcc5e21", "withdrawn": "", "abstract": "What does it mean for AI to serve human preferences when interaction with AI changes those preferences? This question turns alignment into a problem in coupled adaptive dynamics: people learn from algorithms, algorithms learn from people, and both reshape the environment in which future preferences develop.\n\nI will outline a proposed stochastic framework for human-AI systems in which beliefs, preferences, and interaction networks evolve together. The framework distinguishes the persistence of a collective state from the wellbeing and agency of its participants. A stable attractor need not be desirable, and increasing reported satisfaction need not imply increasing freedom to choose or leave.\n\nThe mathematical focus is on metastability, transition rates, hysteresis, and control in systems with endogenous preferences. Three questions motivate the programme. When does adaptive feedback stabilize cooperative behaviour, and when does it create lock-in? Which observations or interventions can distinguish improved wellbeing from adaptation to restricted alternatives? Can changes to interaction rules make beneficial states more persistent while preserving the ability to escape harmful ones?\n\nConnecting stochastic dynamics with performative learning and evolutionary games, I will discuss a minimal human-AI information-network testbed and the assumptions needed to make its predictions identifiable and falsifiable. The goal is a tractable research programme for studying stability, human wellbeing, and agency as distinct, coupled properties of learning systems.", "id": "Paper/71374", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71374"}, {"title": " Generic Identifiability for Level-2 Phylogenetic Networks ", "webprogram_exclude": "0", "session_ids": ["Session/18115"], "source_sha256": "b3c7bd3bd83ffd1b06d58db7a246572a703e777e01674f61367a832f6e62f66e", "withdrawn": "", "abstract": "In statistical evolutionary biology a common research question is whether we can infer past evolutionary events from observable genetic data. Usually this means fitting a tree-based probability model to our data which describes some set of evolutionary events. These models can tell us how species evolved together and how long ago they split off from common ancestors. Phylogenetic networks extend tree-based models to allow for hybridization, horizontal gene transfer (the movement of DNA between organisms that don’t share a parent-offspring relationship) and other non-treelike processes. However, the space of such models is huge, and in many cases different topologies can give the same probabilities of observing our data, making the true model unidentifiable.\n\nWe prove generic identifiability for a class of networks under the Jukes-Cantor model using tools from computational algebraic geometry and combinatorics. In this talk I will show how the network topology is recoverable with any number of leaves, so long as we only allow up to two hybrid events per biconnected component, and we don’t allow three-cycles or hybrid events that lead directly into another hybrid event. These results clarify when it is possible to reconstruct complex evolutionary histories from genetic data.", "id": "Paper/71379", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71379"}, {"title": " Travel Bans vs. Other Disease Mitigation Measures: A Mathematical Analysis ", "webprogram_exclude": "0", "session_ids": ["Session/19364"], "source_sha256": "e2b327c992355b6285874917588ff702622c799ebd6bfe61e0402487aace1da5", "withdrawn": "", "abstract": "As the world grows increasingly connected, infectious disease transmission and outbreaks have become a pressing global concern for public health officials and policymakers. While policy interventions to contain and prevent the spread of disease have been proposed and implemented, there has been little rigorous quantitative analysis of the effectiveness of such interventions. In this paper, we\nstudy the susceptible-infected-recovered (SIR) infection process on a dynamic network model that models two communities with travel between them with the infection starting in one of them. In particular, we consider two Erd\\H{o}s--R\\'enyi graphs where edges are dynamically changing based on node travel between the graphs. We characterize the time evolution of the outbreaks in both communities and pin down the time for when the infection first reaches the second community. Finally, we analyze two types of interventions--travel bans and intra-community interventions in the second community--and prove that travel bans are not effective unless implemented early, while the second type are effective even without travel bans, provided they sufficiently reduce the effective reproduction number. We complement our analytic results by numerical simulations on large networks with  realistic degree distributions and disease recovery times, showing that these results are robust, and hold for settings that model actual contact networks and disease spread more closely.", "id": "Paper/71380", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71380"}, {"title": " A Hybrid Global-Optimization and Physics-Informed Learning Approach to Modeling Tumor–Immune Dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/19365"], "source_sha256": "f0bd4bbc888d6f3b24b260f95d1a4121efbe07878e63910b4c92794d37e81ecf", "withdrawn": "", "abstract": "Mathematical models of cancer typically describe the interaction between a growing tumor and the immune system as a system of ordinary differential equations. Such models are interpretable and biologically meaningful, but their usefulness depends on parameters that must be inferred from clinical data, and clinical data are sparse, noisy, and incomplete. This talk presents a two-stage approach to this problem in which global evolutionary search first identifies a promising region of parameter space. From there, rather than simply fitting the data, the network is trained to produce trajectories that also satisfy the differential equations, with the model parameters treated as learnable quantities. While the study is limited to synthetic data and does not establish clinical applicability, it demonstrates the computational feasibility of integrating global optimization with physics-informed learning for inverse problems in mechanistic cancer models.", "id": "Paper/71381", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71381"}, {"title": " Stability and Bifurcation in a Coupled Malaria–Economic Model ", "webprogram_exclude": "0", "session_ids": ["Session/18260"], "source_sha256": "26819a1ff5ee1c21662ad07759b8ef2832288282d4a492979c706e7c209df7c3", "withdrawn": "", "abstract": "We analyze a nonlinear host-vector malaria model to investigate stability, bifurcation, and threshold dynamics associated with persistent disease and potential malaria–poverty traps. Disease-free and endemic equilibria are characterized analytically, and their local stability is determined from the Jacobian eigenvalue structure. Bifurcation analysis identifies parameter regimes in which multiple stable equilibria coexist. Numerical simulations demonstrate bistability between disease elimination and endemic persistence, with outcomes depending on initial disease burden and parameter values. Two-parameter analyses further delineate regions of disease-free, endemic, and bistable behavior. The results provide a dynamical-systems framework for examining how nonlinear feedback and threshold effects can sustain persistent malaria and potentially contribute to poverty-trap dynamics.", "id": "Paper/71385", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71385"}, {"title": " Inverse Identification of Viscosity in Time-Dependent Navier–Stokes Flows Using Adaptive Physics-Informed Neural Networks ", "webprogram_exclude": "0", "session_ids": ["Session/19322"], "source_sha256": "36786755ba476bd02010056adcae25989bfe9114a738d83716077b53a61c8f17", "withdrawn": "", "abstract": "We present an adaptive physics-informed neural network (PINN) framework for the inverse identification of viscosity in time-dependent incompressible Navier–Stokes flows. The inverse problem seeks to recover an unknown viscosity parameter from observations of the evolving velocity and pressure fields while simultaneously enforcing the governing momentum and incompressibility equations. The proposed formulation incorporates the Navier–Stokes residuals, initial and boundary conditions, and available observational data within a unified physics-informed loss function. To address the imbalance among competing loss components during training, adaptive weighting is employed to dynamically regulate their contributions to the optimization process. The forward problem is first solved to generate synthetic flow observations, which are subsequently used in the inverse problem without directly providing the viscosity to the inverse model. Numerical experiments consider time-dependent channel flow with an obstacle and examine the ability of the proposed approach to reconstruct the flow dynamics and identify viscosity from spatiotemporal measurements. Particular attention is given to the sensitivity of viscosity recovery to the strength of the viscous effects, observation density, and noise in the data. The study provides a computational investigation of both the capabilities and challenges of PINN-based coefficient identification in nonlinear, time-dependent fluid-flow problems.", "id": "Paper/71386", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71386"}, {"title": " Lyapunov spectra, stability, and learning in recurrent neural networks ", "webprogram_exclude": "0", "session_ids": ["Session/17703"], "source_sha256": "7da68055de2e210d091e92f8254cf76e16b9a7561f43211e92bbf1224eb2d65c", "withdrawn": "", "abstract": "I will discuss how Lyapunov spectra can be used to understand both dynamical stability and learning in recurrent neural networks. For recurrent dynamics $h_{t+1}=F_\\theta(h_t,x_t)$, products of state Jacobians describe how small perturbations grow or shrink along a trajectory. Their asymptotic growth rates define the Lyapunov spectrum. The same products of Jacobians also appear in backpropagation through time, which connects the stability of the forward dynamics to exploding and vanishing gradients.\n\nI will first present results on the full Lyapunov spectrum of chaotic random recurrent networks, including its relation to entropy production and attractor dimensionality. I will then turn to gradient flossing, an approach for directly controlling the tangent dynamics of recurrent networks during learning. More specifically, by differentiating through QR-based calculations of Lyapunov exponents, selected exponents can be regularized toward zero. This creates directions in tangent space in which perturbations grow or shrink only slowly and improves the propagation of learning signals over long time horizons.\n\nI will also consider how the same dynamical-systems perspective can be extended to other forms of recurrent computation, including systems in which the same nonlinear transformation is applied repeatedly over time or computational depth.", "id": "Paper/71387", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71387"}, {"title": " A Two-species Competition Model on a Compact Metric Graph for the Invasion and Competition of  Aedes Aegypti  and  Aedes Albopictus  Mosquitoes in Florida ", "webprogram_exclude": "0", "session_ids": ["Session/18009"], "source_sha256": "f9c1f4a335fcf97f8b0685cf5362f04ca80f3a210f28d51e19eaeb5a2c80b7d5", "withdrawn": "", "abstract": "Motivated by the invasion of \\textit{Aedes albopictus} mosquitoes and the interspecific competition between \\textit{Aedes aegypti} and \\textit{Aedes albopictus}  in Florida, we formulate a two-species competition model on a compact metric graph. This model accounts for the species' ability to inhabit and traverse along the graph's edges. In the scenario of weak-strong competition, we prove that solutions of the competition model converge uniformly to a semi-positive equilibrium, where either \\textit{Aedes albopictus} survives while \\textit{Aedes aegypti} goes extinct, or vice versa. Whereas for weak-weak competition, the solutions converge uniformly to a positive equilibrium, enabling the coexistence of both \\textit{Aedes aegypti} and \\textit {Aedes albopictus}. We conduct numerical simulations on the two-species competition model along Route 441 in Florida, aiming to illustrate the invasion dynamics and competitive interactions of  \\textit {Aedes aegypti} and \\textit {Aedes albopictus}.", "id": "Paper/71388", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71388"}, {"title": " Applying Directed Topology to Multi-Parameter Persistence Modules ", "webprogram_exclude": "0", "session_ids": ["Session/17998"], "source_sha256": "6a4ee176a8ad9836dccaa23fd4f30bb8a72d54d11b51da39236ff8c8f5ebfad7", "withdrawn": "", "abstract": "In topological data analysis, multi-parameter persistence modules (MPMs) are used to tackle the issue of ordinary persistent homology not being robust.  However, a challenge arises of choosing an appropriate invariant for MPMs analogous to the barcodes in the $1$-parameter case. We generalize the fibered barcode, which is a partial invariant. Given a $k$-critical bifiltration, we build a directed Euclidean cubical complex  $C$  whose directed paths each restrict the bifiltration to a $1$-parameter filtration. We show that removing certain cubes from $C$ yields a subcomplex on which dihomotopic paths induce simplicially equivalent filtrations (and hence combinatorially equivalent barcodes).", "id": "Paper/71389", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71389"}, {"title": " A Course Coordination Model that Engages Instructors in Continuous Improvement of Curricula ", "webprogram_exclude": "0", "session_ids": ["Session/17971"], "source_sha256": "9e0879049b4b1515382b2920c95370bf2cb8be457a597b0c289fc8fd60dcfb68", "withdrawn": "", "abstract": "Over the past 10 years, a group of mathematics faculty at the University of Delaware have developed a course coordination model centered on continuous improvement of course curricula. This model has been employed in five courses ranging from Intermediate Algebra to Calculus. In each course, a shared curriculum has been collaboratively developed consisting of 1) a student workbook containing guided lecture notes and active learning activities for each class, and 2) instructor lesson plans that provide guidance on pacing, student thinking, and implementation of active learning opportunities.\n\nCourse instructors meet weekly to debrief on lessons taught and plan for upcoming lessons. Most importantly, these meetings serve as a forum to solicit lesson-level feedback from instructors to systematically improve the curriculum over time so that it better supports student learning. Feedback ranges from ideas for revising problem sets, to adjusting activity pacing, to adding more support to instructor lesson plans. Thus, the instructors’ role shifts from designing their own lectures and class activities to contributing to the improvement of the shared curriculum.\n\nData indicate that our course coordination model is effective. DFW rates are low, and student feedback from surveys administered each semester indicate that students greatly appreciate the course workbook and other features of the model. In this session we will briefly describe our course coordination model and highlight key benefits and challenges for course coordinators and participating instructors.", "id": "Paper/71391", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71391"}, {"title": " An almost-always measure of the failure of unique factorization ", "webprogram_exclude": "0", "session_ids": ["Session/19356"], "source_sha256": "73d1bac5cb5b0a5754c31bc1c7f97b5b4061d918f2ab1c3c42e72888b1da99c8", "withdrawn": "", "abstract": "Let $K$ be a number field. For each nonzero, nonunit element $\\alpha$ in the ring of integers $\\mathcal{O}_K$ of $K$, the elasticity $\\rho(\\alpha)$ of $\\alpha$ is defined as the largest possible ratio $m/n$, where $m$ and $n$ range over the lengths of factorizations of $\\alpha$ into irreducible elements of $\\mathcal{O}_K$. A celebrated theorem of Narkiewicz, Steffan, and Valenza shows that the maximum value of $\\rho(\\alpha)$ admits a simple description in terms of the Davenport constant of the class group of $K$. Less well known is that the values $\\rho(\\alpha)$ tend to concentrate around a single real number, denoted $\\rho_{\\mathrm{typ}}(\\mathcal{O}_K)$, as shown by Narkiewicz and Śliwa. In this talk, we describe $\\rho_{\\mathrm{typ}}(\\mathcal{O}_K)$ in terms of a combinatorial game played on the class group of $K$, and we analyze this game for two new families of groups.", "id": "Paper/71392", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71392"}, {"title": " Generic <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.852ex\" height=\"2.509ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -934.9 1228 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">C^2</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-43\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-43\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-32\" x=\"1094\" y=\"513\"></use>\n</g>\n</svg> Spline Dimensions via Defect Modules and Deformation ", "webprogram_exclude": "0", "session_ids": ["Session/19342"], "source_sha256": "ff875fa1e2cc228f262d4a8cf4e53d1785a6782551d83917a8cf0712072aa4be", "withdrawn": "", "abstract": "We study planar $C^2$ spline dimensions through graded defect modules and deformations of vertex coordinates. For an explicit infinite family of triangulations obtained from split bipyramids, we aim to prove that every quartic spline on a generic realization is a global polynomial. We also derive a conditional first-order criterion for eliminating degree-six cofactor generators, illustrated by an exact rational calculation. These results address specific families and deformation mechanisms within the higher-smoothness generalization of Strang’s spline dimension problem.", "id": "Paper/71395", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71395"}, {"title": " Extending Assessment Past End of Semester Deadlines ", "webprogram_exclude": "0", "session_ids": ["Session/18440"], "source_sha256": "29558ebb24f99877bf9ab1a1ee33db384c9fd31b73c1c9305b12f64d5f12fc1d", "withdrawn": "", "abstract": "College Algebra at FIU has undergone a series of changes over the last decade which includes redesigning the class as a hybrid course, eliminating the pre-requisite course and embedding just-in-time, weekly prerequisite modules directly into the learning management system. The most recent reform involved creating a modified mastery-based grading structure allowing students the opportunity to reassess throughout the semester on content they had not yet mastered. Concurrently, a post-semester recovery program was implemented that allows students to complete missed work or learning outcome targets during a shortened 4-week course called a stretch semester. \n\nIn this presentation we will discuss the assessment framework for College Algebra and how this connects with the post-semester opportunity. We will provide data for student outcomes from this work and compare it to some historical student outcomes in the course. We will also provide some summary qualitative student data derived from an end of semester survey administered to students in gateway courses like College Algebra to compare student perceptions of the course in general to those who choose to attend a stretch section.", "id": "Paper/71401", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71401"}, {"title": " Categorical representations and higher traces ", "webprogram_exclude": "0", "session_ids": ["Session/18210"], "source_sha256": "864aa746bb798ca0fc7f317394cae34d13fae72f09c75c626c9507728edfbd79", "withdrawn": "", "abstract": "I will give an overview of the theory of categorical representations of algebraic groups and relate them to\nordinary representations via higher categorical trace. I will explain how the theory of iterated traces\napplied to an appropriate (\\infty,3)-category gives a conceptual proof of the character formula for\nDeligne-Lusztig representations of finite groups of Lie type. This is joint work with D. Gaitsgory and Y.\nVarshavsky.", "id": "Paper/71404", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71404"}, {"title": " CANCELLED-Low Discrepancy Sequences that Are Good for Arbitrary Sample Sizes \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/19352"], "source_sha256": "b0dcfe57f7f59e8a5bcc6369a6f4c5ff30b8e576773cd9f00671177bc7da2709", "withdrawn": "", "abstract": "Low discrepancy sequences tend to have preferred sample sizes to ensure their low discrepancy behavior.  We present and discuss new constructions of Kronecker sequences and lattices that are good for all sample sizes.", "id": "Paper/71405", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71405"}, {"title": " Langrangian Dual Sections and the Unbalanced Procrustes Problem ", "webprogram_exclude": "0", "session_ids": ["Session/18302"], "source_sha256": "0a61c321e91d85016f02a129d727b336cce226204019d920349feb343ccde48c", "withdrawn": "", "abstract": "The unbalanced Procrustes problem is a basic optimization problem, and asks one to find the element of the Stiefel manifold (i.e. an orthogonal projection) which approximately maps a given high dimensional data set onto a given lower dimensional data set. Formally, the objective is given by $\\|AX-B\\|^2$, where $A \\in \\mathbb{R}^{d \\times n}$, $B \\in \\mathbb{R}^{d \\times m}$, and $X$ constrained to be in the Stiefel manifold. While this problem has received much attention, its complexity was unknown until recently. We will discuss the hardness of this problem in general and polynomial time algorithms when the dimensional of the lower dimensional space is fixed. We will then discuss how this problem fits into a more general class of manifold optimization problems that can be analyzed using the theory of Lagrangian dual sections, which is a topological tool that can show that a given optimization problem has an equivalent convex reformulation.", "id": "Paper/71407", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71407"}, {"title": " College Students’ Creation and Use of Exam Note Sheets in Intermediate Algebra ", "webprogram_exclude": "0", "session_ids": ["Session/18068"], "source_sha256": "7430aa46af6f84592c390bb49100d4be09774a9c804ab457d5cb5ef99d1a2200", "withdrawn": "", "abstract": "Preparing a sheet of notes to bring to a math exam can help students study.  While creating their note sheet, students may identify key information that could be tested, evaluate their understanding as they decide what to include, and make connections between ideas while organizing information on the page. However, some students may not be preparing their note sheets in ways that help them learn the material. I surveyed 603 college students in Intermediate Algebra about how they created an exam note sheet and used it during the exam. Students reported a variety of approaches to creating their sheet. The vast majority (85 percent or more) reported that creating their note sheet helped them study and reduced their anxiety about the exam. Analysis of variance showed that students who reported spending one hour or less making their note sheet scored significantly higher on the exam than those who reported spending longer creating their sheet. Additionally, students who reported using their sheet one to five times during the exam scored significantly higher than those who reported using it more frequently. Findings from this study shed light on students’ approaches to creating and using exam note sheets and can help instructors develop guidance for students on how to prepare note sheets in ways that help them study and learn the material.", "id": "Paper/71410", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71410"}, {"title": " Stabilizer codes and entropies associated with orbits of finite groups ", "webprogram_exclude": "0", "session_ids": ["Session/19362"], "source_sha256": "39f7cab1e2d5058c62daa9d517aba2ea34d8d8c4e778671057835c5ebffbe8d1", "withdrawn": "", "abstract": "The number of $[[n,k]]_q$ stabilizer codes, which correspond to totally isotropic subspaces of dimension $n-k$ in the symplectic space $\\mathbb{F}_q^{2n}$, grows as $q^{n^2 H_L(1-\\kappa,\\kappa)+o(n^2)}$ at rate $\\kappa=k/n$, where $H_L$ is a new entropic functional that we call Lie entropy; in particular, a stabilizer code drawn uniformly at random has rate close to $1/3$. This is one instance of a general relation between symmetry and information. The orbits of the symmetric group acting on words have multinomial cardinalities, asymptotically related to Shannon entropy; quotients of general linear groups over $\\mathbb{F}_q$ by parabolic subgroups correspond to flags of subspaces, counted by $q$-multinomial cardinalities asymptotically related to the Tsallis 2-entropy. We extend this picture to the other finite reflection groups and to the split classical groups over finite fields, of types $B_n$, $C_n$ and $D_n$. The treatment is uniform, based on classical invariant theory: by Solomon's formula, quotients of Poincaré polynomials count at once the cosets of parabolic subgroups (at $t=1$) and the $\\mathbb{F}_q$-points of the flag varieties $G/P$ (at $t=q$), which for the symplectic group are isotropic flags, i.e. nested stabilizer groups. The series $B_n$, $C_n$, $D_n$ are linked to new entropic functionals: a reflective entropy $H(P)+(1-p_k)\\ln 2$, which is the Shannon entropy of memoryless sources over signed alphabets, and the Lie entropy $H_L(P)=\\tfrac12\\bigl(1-\\sum_i p_i^2\\bigr)+\\tfrac12(1-p_k^2)$. Each satisfies its own chain rule, and both chain rules are asymptotic shadows of a single identity between Poincaré polynomials. Joint work with Ryan Leal and Jingtong Sun.", "id": "Paper/71411", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71411"}, {"title": " On the choice of viscous discontinuous Galerkin discretization for entropy correction artificial viscosity methods ", "webprogram_exclude": "0", "session_ids": ["Session/19344"], "source_sha256": "2de556553fe5be12993d5c1794afc1299ab5ff1934e0beee21749e5d532b1ee7", "withdrawn": "", "abstract": "Entropy correction artificial viscosity (ECAV) is an approach for enforcing a semi-discrete entropy inequality through an entropy dissipative correction term. The resulting method can be implemented as an artificial viscosity with an extremely small viscosity coefficient. In this work, we analyze ECAV when the artificial viscosity is discretized using a local discontinuous Galerkin (LDG) method. We prove an $O(h)$ upper bound on the ECAV coefficient, indicating that ECAV does not result in a restrictive time-step condition. We additionally show that ECAV is contact preserving, and compare ECAV to traditional shock capturing artificial viscosity methods.", "id": "Paper/71412", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71412"}, {"title": " Homological Properties of (Locally) String Algebras ", "webprogram_exclude": "0", "session_ids": ["Session/18371"], "source_sha256": "cde6b74fdea11bf2e059930ff51f79cc7cc2cf1360d0653cd635171ee2e6a1b1", "withdrawn": "", "abstract": "\\noindent String algebras are finite-dimensional monomial algebras defined by quivers with relations satisfying certain combinatorial conditions. Recent work of Xin–Zhang and Liu–Liu–Zhang gives combinatorial descriptions of their global and self-injective dimensions, respectively. Locally string algebras generalize string algebras by allowing their infinite-dimensional counterparts. In this talk, we discuss how these descriptions extend to locally string algebras and explore related structural questions.", "id": "Paper/71415", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71415"}, {"title": " Hierarchical Reinforcement Learning for Sparse-Reward Search in Commutative Algebra ", "webprogram_exclude": "0", "session_ids": ["Session/18130"], "source_sha256": "6276615ec5f8cbb541621242f4f9b5970e72a6fea4d25549db22126dddcfffaa", "withdrawn": "", "abstract": "Applying machine learning techniques to solving long-standing mathematical conjectures can be particularly challenging due to their extreme reward sparsity. As an illustrative example, we consider Kalai's algebraic Hirsch conjecture and recast the construction of linearly presented square-free monomial ideals $I$ of degree $d$ whose associated graphs $G_I$ have large diameter $\\mathrm{diam}(G_I)>d$ as a sparse-reward reinforcement learning problem on graphs. In this talk, we will discuss results from our ICML 2026 paper (arXiv:2606.22922), where we propose a constrained options-based HRL framework with an equivariant graph neural network policy, which allows us to learn useful temporal abstractions for this task. We evaluate our approach over a wide range of degrees and demonstrate that it consistently outperforms classical RL algorithms as well as greedy search. By exploiting the hierarchical structure of the problem, we effectively provide a first-of-its-kind application of HRL to a problem in commutative algebra.", "id": "Paper/71416", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71416"}, {"title": " Surprising Historical Methods in Calculus that Foster Understanding and Lead to Numerical Methods ", "webprogram_exclude": "0", "session_ids": ["Session/17713"], "source_sha256": "d439119839631523096ba45aaee170d3278c13983dfd6cd45a087cbe32af946e", "withdrawn": "", "abstract": "In the early history of calculus, interpolation, extrapolation, and series were extensively used by Napier, Wallis, and Newton. These surprising forgotten methods can solve or approximate solutions to problems for which the algebraic methods of calculus cannot give closed form solutions. These mathematicians usually did not give proofs, but supported their results with arguments on the consistency of patterns, and often calculations to a great degree of precision.\nModern calculus students are usually left with the impression that algebraic methods in calculus, derivatives and integrals, will solve every problem. In fact, most integrals do not have closed form antiderivatives. The methods to approximate solutions are more usefully visualized in tables or spreadsheets, rather than algebra, and lead to the numerical algorithms used in most modern applied mathematics. Students should see these methods early, and faculty should understand how they fit into mathematics.\nDetails may be found in the book Connecting History to Secondary Mathematics Education by Carrejo, Dennis, and Addington.", "id": "Paper/71417", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71417"}, {"title": " Perfect Partitions and Disjoint Perfect Sets of Regular Bipartite Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/19354"], "source_sha256": "fab74d841c4ef936ffa492ac3b127de2c3ff9a6511c1ac498bf8769ea0b2e0ea", "withdrawn": "", "abstract": "Let $I_{n,n}$ be a fixed perfect matching of a labeled complete bipartite graph $K_{n,n}$, and let $L_{n,1}=K_{n,n}-I_{n,n}$. A \\emph{perfect set} of $L_{n,1}$ is a $1$-factorization of $L_{n,1}$, that is, a set of $n-1$ pairwise edge-disjoint perfect matchings whose union is $E(L_{n,1})$; a \\emph{perfect partition} of $L_{n,1}$ is a partition of the set of all perfect matchings of $L_{n,1}$ into perfect sets. Brualdi, Chiang, and Li (2005) asked whether $L_{n,1}$ admits a perfect partition. Identifying both sides of the bipartition with $[n]=\\{1,2,\\ldots,n\\}$, the perfect matchings of $L_{n,1}$ are exactly the derangements of $[n]$, the perfect sets correspond bijectively to the reduced Latin squares of order $n$, and the perfect partitions are exactly the perfect matchings of the $(n-1)$-uniform hypergraph whose vertices are the derangements of $[n]$ and whose edges are the perfect sets. We first give, for every $n$, a constructive lower bound on the maximum number of pairwise disjoint perfect sets of $L_{n,1}$. We then show that $L_{5,1}$ has exactly $42$ perfect partitions and that $L_{6,1}$ has at least $82$; these are the first examples showing that perfect partitions need not be unique. Finally, through a computational search, we prove the existence of two distinct perfect partitions of $L_{7,1}$, resolving the $n=7$ open problem raised by Li, Soosiah, and Yu (2012).", "id": "Paper/71419", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71419"}, {"title": " Mathematical Modelling of Dual Oncolytic Virus and CAR-T Cell Against Solid Tumors: A Validated Model of Subcutaneous Melanoma in Mice ", "webprogram_exclude": "0", "session_ids": ["Session/17972"], "source_sha256": "3caad7cdf11c3804942d10c6b7c145aed6a3585bf6629eddbbcb90de26477735", "withdrawn": "", "abstract": "Solid tumors such as pancreatic, breast, and ovarian cancers, glioblastoma (an aggressive brain tumor), and metastatic melanoma remain challenging to treat in part due to the immunosuppressive tumor microenvironment and limited penetration by therapeutic agents. A number of oncolytic virus (OV) and Chimeric antigen receptor (CAR)-T cell immunotherapies are being used on their own to treat cancers in a limited capacity with limited efficacy. OVs are engineered or naturally occurring virus that selectively prefer to infect, replicate inside, and lyse cancer cells, while sparing normal healthy cells and simultaneously triggering an antitumor immune response. CAR-T cells are T cells that are genetically engineered to bind to specific proteins on the surface of cancer cells, thereby activating targeted T cell-mediated killing of cancer cells. Although theses have demonstrated limited efficacy when administered individually, the synergistic effects of combining OV and CAR-T cell therapies have emerged as a promising approach for improving treatment outcomes in solid tumors. Moreover, this combination therapy is actively being explored in early-phase clinical trials. We develop a mathematical model of OV and CAR-T cell combination therapy against a solid tumor model of melanoma in immunocompetent mice and validate the model using published longitudinal datasets from tumor-bearing mice treated with oncolytic vesicular stomatitis virus encoding mouse-specific IFN$\\beta$ (VSVmIFN$\\beta$), an oncolytic virus currently undergoing clinical evaluation, and CAR-T cells. Furthermore, we use analytical, theoretical, and computational approaches to investigate mechanisms underlying the interactions between the tumor microenvironment, the OV therapy, and the CAR-T cell therapy to identify treatment strategies that may enhance the therapeutic efficacy of the combination therapy against solid tumors.", "id": "Paper/71424", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71424"}, {"title": " An algorithmic solution to the tropical Schottky decision and recovery problems ", "webprogram_exclude": "0", "session_ids": ["Session/18302"], "source_sha256": "44ccd9e4f00e2080714d922f851b74553c4614750fd4a019efccd3b1f5d68dbe", "withdrawn": "", "abstract": "Given a positive-definite quadratic form, how can we decide whether it is the period form of a metric graph, and recover such a graph and its edge lengths when it is? These are the tropical Schottky decision and recovery problems. I will present an algorithmic solution in arbitrary genus using conorms, quantities obtained by a discrete Fourier transform of the minimum values of the quadratic form in each parity class of the lattice.\n\nThe main result is that a positive-definite quadratic form has nonnegative conorms if and only if it is matroidal, resolving a conjecture of Dutour Sikiri\\'c and Kummer. Under this nonnegativity hypothesis, the support of the positive conorms represents a regular matroid. The quadratic form comes from a graph exactly when this matroid is cographic. I will explain how this connection between lattice geometry and matroid theory yields exact algorithms for decision and recovery, answering a question of Chua, Kummer, and Sturmfels.", "id": "Paper/71425", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71425"}, {"title": " Structured Matrix Learning from Matrix-Vector Products ", "webprogram_exclude": "0", "session_ids": ["Session/18447"], "source_sha256": "04280db042f35563f786702bd707230825dddcc87e2f7e27780bfcf02a5afc06", "withdrawn": "", "abstract": "I will discuss the problem of approximating an arbitrary target matrix A with a structured matrix, given access to just a limited number of adaptively chosen matrix-vector products with A. This general problem is ubiquitous in computational science, both in algorithmic applications and, more recently, as an important special-case of the operator learning problem in Scientific Machine Learning.\n\nFor common structures, like low-rank matrices, the number of matrix-vector products required to obtain a near-optimal approximation to A is well understood. Indeed, optimal results are obtained by the randomized singular value decomposition (RandSVD) and related methods. However, for a number of other important structures, like sparse or hierarchically structured matrices, results have been more elusive. I will present recent work that makes progress on matvec-efficient algorithms for these structured classes and others. I will also discuss my group's work on trying to develop a general theory for the complexity of structured matrix learning. \n\nThis talk presents joint work with Noah Amsel, Pratyush Avi, Paul Beckman, Tyler Chen, Prathamesh Dharangutte, Chinmay Hegde, Feyza Duman Keles, Diana Halikias, Cameron Musco, David Persson, and Indu Ramesh.", "id": "Paper/71426", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71426"}, {"title": " Normal Cores, Fourier Escape, and Central Sequences in Crossed Products ", "webprogram_exclude": "0", "session_ids": ["Session/18383"], "source_sha256": "caebfd24933004382878796646035b7ca7da30e546171a79a4c2faa78c9ba060", "withdrawn": "", "abstract": "Let a countably infinite amenable group $G$ act freely on a nonempty compact metrizable space $X$ with the uniform Rokhlin property. For $L\\leq G$, set $A=C(X)\\rtimes_r G$, $B_L=C(X)\\rtimes_r L$, and $N=\\operatorname{core}_G(L)$. We characterize when central sequences for $A$ supported in $B_L$ can be represented in $B_N$. The corresponding relative central sequence algebras coincide if and only if $N$ is an intersection of finitely many conjugates of $L$. This equivalence holds for each such action, both in norm and in the uniform tracial ultrapower formed using traces of $A$.\n\nIf finite detection fails, the core expectation has infinite probabilistic index. For each prescribed $G$-invariant probability measure, we construct a normal contraction in the uniform tracial relative centralizer whose image in the associated tracial ultrapower is a Haar unitary with all nonzero powers having zero expectation onto the core relative centralizer. The proof combines coset dispersion, continuous cyclic matrices, and Rokhlin induction.\n\nWe also establish support-preserving local order-zero lifting from tracial to norm central sequences for arbitrary countable groups, assuming that subgroup Fourier expectations preserve the chosen traces. A complementary dichotomy shows that the tracial relative centralizer contains unital copies of every matrix algebra exactly when $L$ is normalish, meaning that every finite intersection of its conjugates is infinite; otherwise it is abelian. The core criterion distinguishes Fourier support even when both relative centralizers contain every matrix size. Finally, we obtain sharp finite-detection bounds for finitely generated nilpotent groups and exhibit an almost finite $\\mathbb{Z}^2$-action showing that ambient tracial matrix structure need not imply Jiang--Su absorption of the intermediate inclusion.", "id": "Paper/71427", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71427"}, {"title": " Curvature corrects contextual embeddings: Ollivier–Ricci flow on the hypersphere and the categorical–continuous structure of word meaning ", "webprogram_exclude": "0", "session_ids": ["Session/18354"], "source_sha256": "6dfaa03a7f4abbf3b1f8eb390fade0351f4808ebd5488ac9ca89b43a0b7df318", "withdrawn": "", "abstract": "Trott and Bergen (2023) argue that word meaning is both continuous and categorical: the cosine similarity of contextual language-model embeddings predicts both human relatedness judgments and performance in an associated psycholinguistic task, but an exogenous deformation of these distances based on ground-truth sense labels improves all these predictions. We ask whether there is an intrinsic mechanism for this deformation, derived from the geometry of the embedding space, and answer with a graph-free version of Ollivier's coarse Ricci curvature, computed directly on the unit hypersphere where normalized embeddings lie. Each token carries a probability measure on its neighbors in an ambient corpus cloud, and one step of Ricci flow corrects the distance between two usages to $d_\\varepsilon=(1-\\varepsilon)\\,d_{\\mathrm{chord}}+\\varepsilon W_1$, an explicit convex interpolation between the embedding distance and the Wasserstein-1 distance between the two neighborhood measures. We explain why this works: because transport lengths concentrate in high dimension, $W_1$ is, to first order, a smooth reparametrization of neighbor overlap, with a second-order correction that carries the geometry. On human relatedness norms, this label-free metric matches, and slightly exceeds, the supervised transform given the ground-truth sense boundary (although the largest gains come from the choice of neural representation, not from the correction). Iterating the flow traces a continuous–categorical frontier: indexed by flow time, a density-blind neighborhood sharpens graded relatedness early, while a density-sensitive one crystallizes the polysemy/homonymy contrast later, a label-free dynamical realization of the thesis that meaning is both continuous and categorical.", "id": "Paper/71428", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71428"}, {"title": " Transverse invariants in cyclic branched covers ", "webprogram_exclude": "0", "session_ids": ["Session/19358"], "source_sha256": "ff4fccada91c30a6b57d472ef46ed9950549ef5c81d33d19a4e865e6c737b557", "withdrawn": "", "abstract": "In this work, we develop a new family of invariants for transverse knots in the standard tight contact $3$-sphere, $K\\subset (S^3,\\xi_{std})$, by studying their cyclic branched covers. Transverse knots admit a combinatorial description via grid diagrams. From these diagrams, Ozsv{\\'a}th, Szab{\\'o}, and Thurston defined the GRID invariant $\\theta(K)$, represented by a distinguished element in the combinatorial knot Floer homology. This invariant has been used to show that several knot types, including $10_{132}$ and the $(2,3)$-cable of the trefoil, are transversely non-simple. Adam Levine constructed a combinatorial model for the knot Floer complex of the lift $\\widetilde{K} \\subset \\Sigma_m(K)$. Using this lifted grid diagram, we define new invariants of transverse knots, $\\theta_m(K)$, by identifying a distinguished element analogous to $\\theta(K)$, and we prove their invariance under commutation and (de)stabilization of the underlying grid diagram. We further discuss prospects for using these invariants to detect transverse non-simplicity in knots not distinguished by $\\theta$ alone.", "id": "Paper/71429", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71429"}, {"title": " Ungrading measure-theoretic probability: weekly reports, portfolios, and self-assigned grades in an upper-division course ", "webprogram_exclude": "0", "session_ids": ["Session/18081"], "source_sha256": "6181de023beb6753da9fef3732bc14a8e875c9350f7b0c75003c212c590f6777", "withdrawn": "", "abstract": "I report my experience teaching an upper-division course on measure-theoretic probability at Caltech, taken by a very heterogeneous population of undergraduates and graduate students, under an all-feedback, no-grades system. I had to adapt several approaches discussed in the book \\emph{Ungrading} (edited by Susan D. Blum) both to mathematical content (where the notion of ``correctness'' is particularly important) and to the expectations of STEM students. The resulting methodology combined self-reflection and self-evaluation with peer review and collaborative problem solving. Each week students submitted solutions to the two most challenging problems they had solved, with a report documenting their work and learning process. Particular emphasis was placed on reflecting on the feedback received from the instructor and from peers, and on improving as a result. At midterm and at the end of the term, students prepared a portfolio in which they reviewed all their work, assessed their progress toward the learning goals they had set at the start of the term, and proposed a grade for themselves, discussed afterwards in a short individual conference. I reserved the right to disagree with the proposed grade, but seldom did, and every change I proposed was a single step (e.g., A- to A). I will describe the design and how it interacted with the course structure (lectures, collaborative problem-solving in small groups, and sessions devoted to students' difficulties); what students reported in midterm and end-of-term evaluations, where every student expressed a positive opinion of the system (sometimes against their initial expectations) and students described how the absence of grades let them attempt harder problems without fear and pursue understanding rather than points; and what the experience suggests about students' capacity for serious self-assessment in a proof-based course. I will also discuss the limits of this evidence (a single offering, self-reported outcomes).", "id": "Paper/71431", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71431"}, {"title": " Square and overdetermined polynomial systems in parameter estimation for ODE models ", "webprogram_exclude": "0", "session_ids": ["Session/18319"], "source_sha256": "c081305189d452488a33a57280953237df4f3e2e5924482ae1869b20bc9a3e17", "withdrawn": "", "abstract": "Parameter estimation from data is a key to using ODE models with unknown parameters. There are many different approaches to parameter estimation. One of the main challenges is to have a reliable method that can guarantee the correctness of the answer. Differential algebra based methods for parameter estimation are promising in terms of this kind of robustness. One of such methods is based on differentiation and polynomial system solving. This method has its own challenge of solving square vs over-determined polynomial systems, which we will address in this presentation.", "id": "Paper/71432", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71432"}, {"title": " Tilings in Outer Billiards ", "webprogram_exclude": "0", "session_ids": ["Session/18365"], "source_sha256": "ac938b677c8df38eb80163706a74f7cd5d6278ce265842d9ff19cf05fdb4936d", "withdrawn": "", "abstract": "Applying polar duality to the billiard on a sphere gives a new dynamical system: the outer billiard. This game can be played in the Euclidean and hyperbolic planes, too, although honest duality with the inner billiard is no longer present. The outer billiard map, introduced by Day and Neumann in the middle of the last century and popularized by Moser, remains an object of active research, with connections to chaotic dynamics, symplectic geometry, and number theory. In this talk, I will use interactive visualizations to give a sense of this beautiful map. In particular, I will highlight a family of polygonal outer billiards which produce tilings of $\\mathbb{R}^2$, $\\mathbb{H}^2$, and $\\mathbb{S}^2$.", "id": "Paper/71433", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71433"}, {"title": " Theoretical and computational properties of traces of algebraic varieties. ", "webprogram_exclude": "0", "session_ids": ["Session/18356"], "source_sha256": "b4fef50cf15da384325d5228c673a7aa1d709281a6c111ebce0d84bdf0a41081", "withdrawn": "", "abstract": "The trace of a zero-dimensional variety is the sum of its points.  Classically, the trace test was introduced in numerical algebraic geometry to decide if a numerical calculation to \nfind solutions to a zero-dimensional polynomial system had successfully found all of them.  In this talk, I will separate the trace from from its original application, and present many of its properties.  Through examples, I will discuss both theoretical and computational aspects of the trace function.", "id": "Paper/71439", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71439"}, {"title": " From Bird Viremia to Bird Surveillance: Identifiability in a Multiscale Vector-Borne Model of Usutu Virus Infection ", "webprogram_exclude": "0", "session_ids": ["Session/18303"], "source_sha256": "caeab98963362d41af9fd19b82aa01b74fa5b09f1c55301e5a9c2042a270956d", "withdrawn": "", "abstract": "Usutu virus is an emerging mosquito-borne flavivirus, maintained through an enzootic cycle involving wild birds and mosquitoes, with occasional spillover to humans. Understanding how interactions across these biological scales shape transmission dynamics is essential for predicting outbreaks and improving surveillance strategies. In this study, we developed a multiscale vector-borne model of Usutu virus infection that links within-host viral kinetics in birds, the per-bite probability of mosquito infection, and population-level mosquito–bird transmission dynamics. Model parameters were validated using two laboratory datasets collected under an optimally designed experimental framework and one surveillance dataset from wild bird populations. Structural and practical identifiability analyses were conducted to evaluate parameter robustness under varying levels of measurement noise. We found that simultaneous multiscale fitting to integrated datasets improved parameter identifiability and robustness. These results highlight the importance of combining microscale and macroscale data to enhance the predictive reliability of vector-borne disease models and demonstrate the broader utility of multiscale modeling frameworks for understanding the transmission dynamics of emerging arboviruses.", "id": "Paper/71442", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71442"}, {"title": " The Role of Group-Level Competition in PDE Models of Cross-Scale Evolutionary Dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/18289"], "source_sha256": "f031887a5c653ab120afa1903f3bba1b4485081bc1a72eecc0b3641e794a37dd", "withdrawn": "", "abstract": "Natural selection often operates simultaneously at multiple levels of biological organization, with evolutionary forces at each level potentially creating a tug-of-war between individual-level incentives to cheat and a collective incentive of maintaining cooperation. In this talk, we will discuss a stochastic framework for describing nested birth-death processes in group-structured populations with selection operating within and among competing groups, presenting simulations of the stochastic models and deriving ODE and PDE models that arise by successively taking the limit of an infinite number of groups and infinite group size. By comparing different possible update rules for individual-level and group-level replication events, we will be able to explore how forms of frequency-dependent competition at each level of selection can help shape the long-time support for cooperation by multilevel selection in both finite and infinite populations.", "id": "Paper/71444", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71444"}, {"title": " Dedekind Cuts Associated with Selective Ultrafilters ", "webprogram_exclude": "0", "session_ids": ["Session/18589"], "source_sha256": "b30bf7c428cc3f9658c41854c580c3c2665789f12ee1c39b7bb3ef60a3272371", "withdrawn": "", "abstract": "A map from an ultrafilter to a countable set determines a Dedekind cut in an ultrapower of the natural numbers. We study these cuts for ultrafilters associated with the topological Ramsey space \\(\\mathcal R_1\\). We show that selectivity for \\(\\mathcal R_1\\) implies that every proper associated cut is standard, extending the corresponding result for Ramsey for \\(\\mathcal R_1\\) ultrafilters. We also discuss what can happen when selectivity is replaced by p-pointness and the existence of a cofinal \\(\\mathcal R_1\\) base.", "id": "Paper/71445", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71445"}, {"title": " Open Learning as Infrastructure for Mathematics: Generation, Dissemination, and Preservation ", "webprogram_exclude": "0", "session_ids": ["Session/18101"], "source_sha256": "85d8b3c53dc8b4cc9f3b58d911da1fbd515d2948a6d8b34bbcd30a1f832ab9f6", "withdrawn": "", "abstract": "Drawing on work and experience in open learning, I will explore how we might expand access to meaningful mathematics for the learner in everyone, and more broadly how mathematics might be cultivated across communities at scale. This may point toward an infrastructure that integrates the generation, dissemination, and preservation of mathematical knowledge, formal or informal, with our mathematical community growing together with public understanding of mathematics.", "id": "Paper/71450", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71450"}, {"title": " Weak mixing of the transposition rule for IID list update ", "webprogram_exclude": "0", "session_ids": ["Session/18002"], "source_sha256": "af4daa37ae284b1eadce96591b7a5cc01cd14cc5808871382a2d4ef8b5418355", "withdrawn": "", "abstract": "We study the list update problem, where a set of items is maintained in a list and are requested.  Requests arrive iid according to some probability vector $p$ supported on the set of items.  The optimal configuration is to order the items by decreasing probability $p_1 \\geq p_2 \\geq \\cdots \\geq p_n$, with each query having an expected cost of $\\mathsf{OPT} = \\sum_j j p_j$.  However, $p$ is generally unknown, and so this cannot generally be done.\n\nWe study the transposition rule, where whenever an item is requested, it is moved forward 1 spot.  The stationary distribution of this Markov chain has expected cost $\\mathsf{OPT}+1$.  However, for arbitrary $p$, the mixing time can be arbitrarily slow.  We prove that for any $p$, after polynomially many steps, the expected cost is $\\mathsf{OPT} + O(1)$.", "id": "Paper/71453", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71453"}, {"title": " Collaborative Course Coordiunation - The \"Bus-driver\" model ", "webprogram_exclude": "0", "session_ids": ["Session/17971"], "source_sha256": "d25e9e03dd98b8353c7b2bcc3dee9a5e928cca3f758bf82e61ef176f71958ab5", "withdrawn": "", "abstract": "We will describe our collaborative approach to course coordination, which we call the “Bus-driver model”, which we used to develop and refine high-quality, cohesive course lesson plans and materials in the span of less than two years as part of a HHMI Success in STEM effort to redesign coordinated calculus courses at Rice University.  This collaborative approach allowed us to sustainably achieve much more than what we could have done working individually.", "id": "Paper/71456", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71456"}, {"title": " Fermat Active Laplace Learning for Semi-supervised Hyperspectral Image Classification ", "webprogram_exclude": "0", "session_ids": ["Session/19345"], "source_sha256": "8d2f95f0c34110df0ac1a14badc9e7a03d158573713126eb4c606f09b60342bb", "withdrawn": "", "abstract": "Two active learning algorithms for hyperspectral image (HSI) classification are proposed that combine density-aware Fermat distances with Poisson-reweighted harmonic label propagation. Our methods actively query points using an uncertainty-based acquisition function, extending \\textit{Poisson ReWeighted Laplace Learning} (PWLL). Our first algorithm, \\textit{Fermat Active Laplace Learning} (FALL), builds an affinity matrix using Fermat distances between all data points. Then, PWLL is run with a diagonal perturbation using the minimum-norm acquisition function. In contrast, \\textit{Approximate FALL} (A-FALL) computes Fermat distances between each data point and landmark pixels selected via farthest-point sampling and constructs the affinity matrix using landmark multidimensional scaling. After several query rounds, A-FALL selects the Fermat exponent $p$ using a leave-one-out cross-validation variant. FALL and A-FALL leverage Fermat distances and subsequent harmonic label propagation to provide a density-aware estimation of the data manifold, improving labeling accuracy. Experiments on Salinas A and Pavia show the effectiveness of FALL and the scalability of A-FALL to large HSI scenes.", "id": "Paper/71462", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71462"}, {"title": " Designing collaborative mixed reality experiences to foster discipline-specific learning: The case of TriO ", "webprogram_exclude": "0", "session_ids": ["Session/18235"], "source_sha256": "0aecb238895d9bfd79f3ed6e0f02e2b736e63c35f186a41110c6f847a6d0d0db", "withdrawn": "", "abstract": "How can virtual and augmented reality experiences be leveraged to teach specific mathematical concepts? We report on the design and development of TriO, a multiplayer collaborative experience that allows learners to explore three-dimensional cartesian space by coordinating movement. The environment consists of a series of colored handles (red, blue, green); a collection of numbered, glowing orbs (1-8); and a small, white object defined by the orthogonal intersections of three unit disks (tri-disk). The handles are fixed to (invisible) orthogonal axes that span $R^3$ and the orbs are arranged in a cubical pattern. Each player slides their handle to control one coordinate of the tri-disk's position.  The three players work together to move the tri-disk through the cubical course, moving from numbered vertex to numbered vertex, while working together to achieve the shortest path. After they complete one course, the cubical pattern is reconfigured and the coordination demands change. TriO is played in collaborative mixed reality--rendered environments where players wear headmounted displays that blend co-located digital objects into a shared physical space. Each player sees the red, blue, and green handles (for example) in the same place in the room, as if they were any other physical objects. TriO has been continually co-designed by an ongoing multidisciplinary collaboration among high school mathematics teachers and researchers in mathematics education and learning science. We report on the results of this ongoing design collaborative. In particular, we describe how teachers imagined connecting explorations in TriO to topics in vector calculus, trigonometric functions, parametric equations, and spatial thinking more generally.", "id": "Paper/71464", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71464"}, {"title": " Area and Addition Formulas in Polynomial Trigonometry ", "webprogram_exclude": "0", "session_ids": ["Session/19368"], "source_sha256": "6021efacd620bd180793bd872ebeadb0eb0137fc78dffce57815bef256ca669f", "withdrawn": "", "abstract": "The tangent function satisfies the differential equation \\(u'=1+u^2\\). Replacing \\(1+u^2\\) by a real polynomial \\(P(u)\\), positive near zero, gives a construction of generalized sine and cosine functions. We describe this construction and show that its parameter measures swept area. We then show that the resulting pair admits a local bilinear addition formula precisely when \\(P\\) has degree at most two. Examples illustrate the construction and the distinction between a curve and its parametrization.", "id": "Paper/71465", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71465"}, {"title": " Geometry from arithmetic: computing Hilbert modular forms ", "webprogram_exclude": "0", "session_ids": ["Session/17808"], "source_sha256": "d1939509902110e7a6ad2c88ed1864274abec93339eebc196b02958f45450ee0", "withdrawn": "", "abstract": "Modular forms are holomorphic functions on the upper half-plane satisfying certain symmetries and growth conditions. Hilbert modular forms are generalizations of modular forms, and are functions on a product of complex upper half-planes. In recent years, there have been several developments in algorithms and implementations for the explicit computation of Hilbert modular forms. In this talk, we will review the current state-of-the-art, and then discuss two ways in which computations of Hilbert modular forms can be used to understand and compute geometric objects. First, they allow us to provably compute explicit models for a class of interesting complex algebraic surfaces called Hilbert modular surfaces. Second, Galois representations associated to ``interesting'' Hilbert modular forms contribute -- at least conjecturally -- to the \\'etale cohomology of ``interesting'' algebraic varieties, and thereby offer insight into their geometry.", "id": "Paper/71466", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71466"}, {"title": " The Artistic Origins of Geometric Dilations and Their Use in Improving Student Understanding of Similarity ", "webprogram_exclude": "0", "session_ids": ["Session/18233"], "source_sha256": "1755104e71f87dd8aa3a61a68982d8c6b46b23c1a51743c2dab58e43eb11b89b", "withdrawn": "", "abstract": "Art sometimes precedes the development of new technologies, followed by science, and then mathematics tidies up the theory afterwards. Ideas in Euclid’s Optics and the Renaissance practice of perspective drawing prefigure the definition of the dilation transformation in the 19th century.  Dilations only recently entered the U.S. middle and high school curriculum. Students often are given a mixture of an Euclidean treatment of similarity (e.g. the Angle-Angle criterion for similar triangles), along with a disconnected study of transformations, leading to many misconceptions. \nThese historical ideas lead to activities that help students connect the two styles of treating similarity. Lessons for preservice secondary (grades 6-12) math teachers will be presented.\nDetails may be found in the book Connecting History to Secondary Mathematics Education by Carrejo, Dennis, and Addington.", "id": "Paper/71467", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71467"}, {"title": " Block Links and Character Triple Isomorphisms ", "webprogram_exclude": "0", "session_ids": ["Session/17832"], "source_sha256": "09072ae71402e7437740727c1774a95a734c242b7595aee04c6707352d624ff8", "withdrawn": "", "abstract": "Character triple isomorphisms are an important tool in the representation theory of finite groups and occur naturally in the inductive conditions for local-global conjectures. Classically, such isomorphisms and their block-theoretic refinements are described using projective representations and associated factor sets.\n\nIn previous work, we introduced links between character triples, which realize character triple isomorphisms intrinsically by irreducible characters of certain subgroups of direct products. In this talk, I will discuss a block-theoretic analogue. We introduce block links and show that they characterize block isomorphisms of character triples. Thus, the projective-representation and block-compatibility data defining a block isomorphism can be encoded by a single irreducible character. I will also discuss connections with Dade’s ramification groups and applications to the character-triple conditions arising in inductive local-global conjectures.\n\nThis is joint work with Robert Boltje.", "id": "Paper/71468", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71468"}, {"title": " Which Systems of ODEs Share This Input-Output Equation? ", "webprogram_exclude": "0", "session_ids": ["Session/18319"], "source_sha256": "e373237d2ace48ea5586553411838a293a20c515b1ebe3fde855edbec9826e09", "withdrawn": "", "abstract": "Two systems of polynomial ODEs are said to be indistinguishable if they induce identical input-output equations. For a system of interest, a natural question can be asked: what is the set of systems that produce the same input-output equation? In other words, which other systems are indistinguishable from ours? When we constrain ourselves to a parameterized class of ODEs, we can treat the map of an ODE to its input-output equation as a morphism of algebraic varieties. From this perspective, the set of models with a given input-output equation is a fiber of this morphism. This fiber is a variety whose defining ideal can be studied through the tools of computational commutative algebra (in particular, Groebner basis techniques) as well as numerical algebraic geometry. In this talk, we will analyze some enlightening examples, and discuss general strategies.", "id": "Paper/71469", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71469"}, {"title": " Which Randomized Apportionment Method is the Best? ", "webprogram_exclude": "0", "session_ids": ["Session/18310"], "source_sha256": "6442ad51cc551aecabf09b140a139d597f2f9ea94f6651adc44e0275e52fcc47", "withdrawn": "", "abstract": "Democracies around the world apportion seats in their legislatures according to party vote shares (or in some cases population sizes, as in the US House of Representatives). Since it is impossible to allocate a fraction of a seat, an apportionment method must inevitably decide who gets rounded up and who gets rounded down. It is well-known that there is no canonical solution to this problem, with classic impossibility results holding that all deterministic methods suffer from paradoxes. Allowing randomness opens the door to a much larger class of methods that can avoid some of these paradoxes while introducing new ones. I will discuss two recent papers that seek to refine this vast space of randomized apportionment methods by imposing additional desirable axiomatic properties:\n(1) Requiring that joint selection probabilities be monotone in the vote shares.\n(2) Minimizing order reversals between vote shares and seat shares.", "id": "Paper/71470", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71470"}, {"title": " Information-theoretic inequalities versus geometric inequalities on volumes ", "webprogram_exclude": "0", "session_ids": ["Session/18442"], "source_sha256": "a7a5d5313e9e11c66bdcb448890707484a531a8fed1e58c57260396154129324", "withdrawn": "", "abstract": "Entropy inequalities not only specialise to but also provide useful interpretations of geometric inequalities on volumes for bodies in multidimensional Euclidean space. As one example, Shearer’s lemma in its version from information theory can be used to deduce and provide a natural interpretation of the Loomis-Whitney inequality.\r\r\nWe will focus on the converse direction: whether for a given geometric inequality on volumes, there really is an entropy inequality that mildly generalises it, hence providing not only another proof but also a useful explanation of the geometric inequality.", "id": "Paper/71472", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71472"}, {"title": " The Role of Singular Modes in Image Reconstruction and Recognition ", "webprogram_exclude": "0", "session_ids": ["Session/17849"], "source_sha256": "c046e07f92a47c0da2a8f6fe1caca7948f205262beb4023976ad85cf537e2619", "withdrawn": "", "abstract": "Singular value decomposition (SVD) allows us to decompose an image matrix and reconstruct the image using selected singular modes. In this study, we use SVD to investigate how reducing the number of singular modes used in image reconstruction affects whether an image can still be recognized by TinEye, a reverse-image search tool. Three images were converted to grayscale and decomposed using SVD. The images were then reconstructed using progressively fewer singular modes, producing different levels of image distortion, in what we call a noised image. The images were then entered into TinEye to determine an overall range at which the images were no longer matched to the original. Across the three images tested, the lower recognition margin ranged from approximately 4 to 10 retained modes. Our results demonstrate how SVD can be used to systematically reduce the information retained in an image and examine the relationship between singular-mode selection, image reconstruction, and reverse-image matching.", "id": "Paper/71473", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71473"}, {"title": " Construction and Periodicity of Minimal Resolution Graphs of Suspension Singularities ", "webprogram_exclude": "0", "session_ids": ["Session/19356"], "source_sha256": "89030825f0fe9a7a0c0895f4a813511b0107e71de84bba15c00692da349fe411", "withdrawn": "", "abstract": "We introduce a Magma program that implements Nemethi's algorithm as a computational tool for constructing the minimal resolution graphs of suspension singularities. The program outputs the resulting resolution graph of a given suspension singularity as structured graph data, encoding the vertices, edges, and decorations of the graph. The output can be further directed to the accompanying SageMath program that produces visual representations of the resolution graphs, facilitating their analysis. \n\nAdditionally, for three families of suspension singularities, we prove that the corresponding minimal resolution graphs are periodic, with periods equal to the orders of the corresponding monodromy factorizations. Some additional Magma programs for generating compactified resolution graphs of suspension singularities and checking graph isomorphisms over a specified range of parameters are also presented.", "id": "Paper/71477", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71477"}, {"title": " Isospectrality for Periodic Schrödinger Operators ", "webprogram_exclude": "0", "session_ids": ["Session/18296"], "source_sha256": "119d01bf47797ef6c8fe34af17ed177a1076f203c076890a299e1dee7c6d77e6", "withdrawn": "", "abstract": "In this talk we will discuss some recent progress on regarding the study of Fermi and Floquet isospectrality for discrete periodic Schr\\\"odinger operators. We focus our discussion on various recently proven rigidity theorems regarding Fermi and Floquet isospectrality for the discrete Laplacian on \\mathbb{Z}^d with nearest neighbor edges. This talk will focus on two recent works of the author, one with Brysiewicz and Liu, and another with Cobb and Kretschmer.", "id": "Paper/71478", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71478"}, {"title": " A Century Later, Numerical Ranges Go Finite ", "webprogram_exclude": "0", "session_ids": ["Session/18205"], "source_sha256": "81ad7479a333e7e193582c56b8c768206ca18dadc4858288da859f5b29de6cb4", "withdrawn": "", "abstract": "In 1918, Otto Toeplitz introduced the numerical range of a matrix. In 1932, Francis D. Murnaghan proved that the numerical range of a $2\\times 2$ complex matrix is an elliptical disk whose foci are the eigenvalues of the matrix. Slightly less than a century later, inspired by research started at REUF 2011, our collaborators, Patrick Rault and Douglas Knowles, began investigating the numerical range of matrices whose entries come from finite fields. In the ensuing decade, we and our students have been working to classify the numerical ranges of such matrices. In this talk, we will present our progress on this problem.", "id": "Paper/71482", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71482"}, {"title": " Fostering Mathematical Curiosity Through Math Jamboree Activities ", "webprogram_exclude": "0", "session_ids": ["Session/18211"], "source_sha256": "3b1a5c2b3abcc989956aacb8473b33942f571ae443b3b61975e9468b2483cdef", "withdrawn": "", "abstract": "The Math Jamborees, organized by the Panamanian Foundation for the Promotion of Mathematics (FUNDAPROMAT), are interactive, hands-on activities hosted in public spaces like parks, museums, malls, and libraries. By shifting the perception of mathematics through joyful discovery, these initiatives engage both children and adults while fostering collaboration among students. This talk explores FUNDAPROMAT's successful outreach models, detailing specific interactive activities designed to break down barriers to math education and cultivate an inclusive, community-wide appreciation for mathematics. Furthermore, participants will discover the free teaching resources offered by the non-profit.", "id": "Paper/71485", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71485"}, {"title": " Exhaustive Weakly Wandering Sets for Group Actions ", "webprogram_exclude": "0", "session_ids": ["Session/19357"], "source_sha256": "ab811596165beddcc34d11e097144c4d386aef5dc61248436fd2d83a3f3b5cdf", "withdrawn": "", "abstract": "We study exhaustive weakly wandering sets for nonsingular group actions not admitting a finite invariant measure. We prove for a large class of groups that every infinite measure-preserving ergodic action admits an exhaustive weakly wandering set, generalizing the analogous result of Jones and Krengel from the classical setting.", "id": "Paper/71488", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71488"}, {"title": " \"Micro-Coordination\": Mentors as Facilitators of Coordination Activities ", "webprogram_exclude": "0", "session_ids": ["Session/17971"], "source_sha256": "aeaf3b4798a9efa172aba6aee42a7821c855453ddb3bae216f6f61b502a3b5dc", "withdrawn": "", "abstract": "We have an extensive course coordination structure in our introductory courses, in which coordinators seek to address both resource management and humanistic growth in their courses.  More recently we have adopted a training model in which new graduate students teach a section of calculus in a large team-learning room with three to four other sections also taught by new graduate student instructors, and an experience faculty mentor or lead instructor.  The team of instructors collaboratively plans and delivers active-learning lessons to all sections in the room (90 to 120 students in total) that are centered around short lectures and extensive group work.  This is an mportant training ground for graduate student instructors, and that training is a significant part of the humanistic growth goals of our coordination structure more broadly.  In this talk we will discuss some of the coordination-adjacent and coordination-supplementing duties that our faculty mentors take on, especially in the context of humanistic growth, share mentors' experiences about the required skills and support needed for such a position, and reflect on the impact of this instructional model.", "id": "Paper/71496", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71496"}, {"title": " Constructions of Colorable Tri-Plane Diagrams ", "webprogram_exclude": "0", "session_ids": ["Session/18384"], "source_sha256": "f2c13601ec2102c6b217be848ca6dc6cdfceb6e08e34cdad8b681cf3e06ea0f6", "withdrawn": "", "abstract": "A knotted surface in the 4-sphere can be described by a tri-plane diagram: 3 trivial tangles whose pairwise unions form unlinks.  There is a notion of $p$-colorings for tri-plane diagrams, similar to Fox $p$-colorings of knot diagrams. The number of $p$-colorings of a tri-plane diagram is an invariant of the corresponding knotted surface. We introduce techniques for constructing $p$-colorable tri-plane diagrams, and build families of p-colorable tri-plane diagrams.", "id": "Paper/71497", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71497"}, {"title": " Dynamic Exchange: Community Networking and Open Problems ", "webprogram_exclude": "0", "session_ids": ["Session/18065"], "source_sha256": "2b30616c95377a3833bb376c858259f51e03b1485bb9002d40ec2d938375a4d0", "withdrawn": "", "abstract": "Designed to build community and spark collaboration, this interactive session addresses the coexistence of regular and stochastic behavior in smooth dynamical systems. The session will begin with a structured networking segment for participants to introduce themselves, share current projects, and map out the research landscape. The second half will center on open problems and future directions, beginning with a brief highlight of open questions followed by an open discussion of key challenges facing the field. We especially encourage graduate students, early-career researchers, and scholars new to the field to participate alongside established researchers.", "id": "Paper/71498", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71498"}, {"title": " Watch Your Own Thinking: Math Puzzles That Replay a Learner’s Reasoning, and an AI That Only Asks ", "webprogram_exclude": "0", "session_ids": ["Session/17461"], "source_sha256": "8214cf31ad3fbeed4beee3145df7cfda19a14ee1af4784d06204c711a93377c7", "withdrawn": "", "abstract": "A well-made puzzle carries a mathematical idea, but the reasoning that solves it vanishes the moment the grid is filled. This talk presents three browser puzzles built for a mathematics course for prospective PK-5 teachers that keep that reasoning, and an AI that makes students defend it. Metadoku (Calcudoku, constraint deduction), Metaplete (delete cells to hit row and column targets, hypothesis testing), and Metagons (arithmagons, inverse reasoning) record every move with a timestamp. When the puzzle is done, the learner scrubs back through the solve, attaches notes where the real reasoning happened, and writes a thinking analysis in their own words: which clue forced which cell, when they knew and when they guessed.\n\nThen the analysis goes to an AI configured to ask and never answer. One question per turn, about the learner's own account: \"You say that cell was forced. Forced by what?\" It will not solve, hint, or grade, and it stops when the learner can say why. The design comes from an earlier study in which an unconstrained AI tutor wrote eleven words for every one a student wrote; here the student does the explaining and the AI does the pressing. We report the questions the AI asks, how learners revise their analyses in response, and what the transcripts reveal about how novices reason under constraints.\n\nThe AI also built the tools. All three apps were vibe-coded by a teacher working with an AI assistant, engine and all. We name the moves the AI could not make and a teacher had to: choosing puzzles that hold an idea, deciding what to record, and designing the replay so a student studies reasoning rather than admires a score. We close with a working method for teachers who want to build, rather than buy, the tools their students need.", "id": "Paper/71499", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71499"}, {"title": " Models of occlusion progression in ECMO ", "webprogram_exclude": "0", "session_ids": ["Session/18122"], "source_sha256": "947da06e75c65c14cf9ea5f8490ada385a5f3cd43b38739c99a70ae8f3482209", "withdrawn": "", "abstract": "Extracorporeal Membrane Oxygenation (ECMO) is a life-saving procedure providing cardiac and respiratory support to patients with severe and potentially fatal heart or lung conditions. The dynamics of blood flow inside the oxygenator are in part determined by the patient’s physiology and blood characteristics, as well as the oxygenator geometry. Hemodynamic factors that have proven to influence blood coagulation also promote clot formation occluding the oxygenator, which is of significant concern for optimal ECMO circuit performance. The current paradigm for assessing clotting includes making clinical decisions based on pressure measurements used as a surrogate for clot-induced resistance, but this does not account for full system dynamics. We developed several dynamic models that simulate the interactions between ECMO blood pressure and flow, using patient hemodynamics and oxygenator geometry, with the goal of predicting the real-time progression of occlusion.", "id": "Paper/71501", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71501"}, {"title": " Online Van Der Waerden Numbers ", "webprogram_exclude": "0", "session_ids": ["Session/18339"], "source_sha256": "6e48980eda44cf68a1c31f565356662e5253b09b219066e821c25832de18a180", "withdrawn": "", "abstract": "For $r, k \\in \\mathbb{N}$, the Van der Waerden number $W(r,k)$ is the least $n$ such that every $r$-coloring of $\\{1, 2, \\ldots, n\\}$ contains a monochromatic $k$-term arithmetic progression. The best known lower bounds for $W(r,k)$ are exponential, while the upper bounds are of tower type, leaving a substantial gap between the two.\n\nIn this talk, I will present a game-theoretic variant of this problem. Consider a game played between two players, Builder and Painter. Builder presents integers one at a time, aiming to force a monochromatic $k$-term arithmetic progression, while Painter colors each integer with one of the $r$ colors as it is presented, aiming to delay this outcome. Let $\\widetilde{W}(r,k)$ denote the minimum number of turns sufficient for Builder to force a monochromatic $k$-term arithmetic progression, regardless of Painter's strategy. Van der Waerden's theorem immediately gives $\\widetilde{W}(r,k) \\leq W(r,k)$; however, we prove that Builder can do much better than this. This is joint work with S. Hegde, P. Horn, D. King, B. Lidick\\'y, G. McCourt, F. Pfender, and S. Zerbib, started at the 2025 Graduate Research Workshop in Combinatorics (GRWC).", "id": "Paper/71504", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71504"}, {"title": " Oral Quizzes in Honors Multivaraible Calculus ", "webprogram_exclude": "0", "session_ids": ["Session/18476"], "source_sha256": "af2685c646b6ed09766f82b8ecd37e427aade67d6dc61af4863659122504179d", "withdrawn": "", "abstract": "We will describe the implementation of oral and video quizzes in MATH 232, Honors Multivariable Calculus at Rice University.  These assessments were designed to help students develop their mathematical communication and collaboration skills, with a particular focus on their ability to explain and defend their prior written work and ideas.  These quizzes were used in conjunction with in-person summative written exams.", "id": "Paper/71505", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71505"}, {"title": " Absolute character sums and involution factorizations in the symmetric group ", "webprogram_exclude": "0", "session_ids": ["Session/19366"], "source_sha256": "5ff3232be665bda293b9712b70a067431a91b9d8b2489b8278e6ee9decba9fa6", "withdrawn": "", "abstract": "Let $\\mu$ be a partition of $n$ corresponding to the cycle type of a permutation in the symmetric group $S_n.$ Write $N(\\mu)$ for the number of ways to write a fixed permutation of type $\\mu$ into the product of two involutions, and let $A(\\mu)=\\sum_{\\lambda\\vdash n}|\\chi^\\lambda_\\mu|$ be the sum of absolute values of irreducible characters of the symmetric group evaluated at that same permutation. In their paper \"How to write a permutation as a product of involutions (and why you might care),\" Petersen and Tenner asked for which $\\mu$ does $A(\\mu)=N(\\mu)$. We show first that $N(\\mu)$ is the irreducible-degree sum of the centralizer of a permutation of type $\\mu$. The centralizer is abelian when the parts of $\\mu$  are distinct, and so column orthogonality identifies equality with the condition that $\\mu$ be a sign partition, meaning that the irreducible characters take values of 0, 1, or -1. Morotti’s classification of the sign conjugacy classes then gives a complete answer in this case, as we will see in this talk. We will also show that $A(\\mu) \\neq N(\\mu)$ for most permutations.", "id": "Paper/71507", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71507"}, {"title": " Bringing Algorithms to the Algorithm: How I Teach Math on Social Media ", "webprogram_exclude": "0", "session_ids": ["Session/18074"], "source_sha256": "06f2cb183d67f78f2a681264e84567862059a8d5e67315fbef01fd5e0a1c3d48", "withdrawn": "", "abstract": "In a world of infinitely scrollable brainrot, who would stop and watch a video about math? Millions of people, apparently. Scroll back through my post history and you’ll see that my math content creation journey has been extremely nonlinear, and not just in terms of video production quality: what started as a tutoring series for kids struggling with math during the first pandemic summer has evolved into an exploration of the intersection between math and pop culture (especially Taylor Swift). In this talk, I’ll share my own “mathfluencer” journey, my current production process, and the dos and don’ts of content creation that I’ve learned the hard way. If you’ve ever wanted to make your own math TikToks/Reels/Shorts, wondered what it’s like behind the scenes as a math creator, or considered yourself a fellow Swiftie in STEM, this talk is for you!", "id": "Paper/71508", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71508"}, {"title": " Scientific American Math Puzzles as a Gateway to Mathematical Exploration ", "webprogram_exclude": "0", "session_ids": ["Session/17961"], "source_sha256": "e63c980ed08a0efeeb853defd81ead9e370e30bbe2431b74619dc15d1fc3c11f", "withdrawn": "", "abstract": "Scientific American publishes weekly math puzzles that are challenging, engaging, and generally require little specialized mathematical background. Topics range across combinatorics, number theory, graph theory, probability, logic, and more. These puzzles are often too difficult as stated for a single Math Circle or classroom session, while their given solutions don’t always do justice to the rich math behind the puzzles. In this talk, we’ll look at a few favorites and explore ways to turn them into low-floor, high-ceiling, collaborative investigations. Students can compute examples, look for patterns, make and test conjectures, discover connections to deeper mathematical ideas, and ask questions of their own. In this way, a single puzzle can introduce a mathematical topic, develop mathematical habits of mind, or even lead to an accessible research project.", "id": "Paper/71509", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71509"}, {"title": " Behavior-Induced Oscillations and Hopf Bifurcation in a Game-Theoretic Model of Household Mosquito Control ", "webprogram_exclude": "0", "session_ids": ["Session/19353"], "source_sha256": "5b15eb71b17c6b0d115cbe6749d78c157036f119c5e984a526523bede86f4a47", "withdrawn": "", "abstract": "Mosquito-borne diseases remain an important public-health challenge, and control of mosquito populations relies on sustained household participation in removing breeding sites. While environmental drivers of mosquito oscillations have been extensively studied, the role of spontaneous household decision-making on mosquito population dynamics remains poorly understood. We introduce a game-theoretic model in which the proportion of households performing breeding site control evolves through imitation dynamics, driven by perceived risks that can depend on mosquito prevalence. We assume that household behavior regulates the carrying capacity of the aquatic mosquito stage, creating a feedback between control actions and mosquito population growth. We show that when the perceived risk of not controlling breeding sites depends on mosquito prevalence, the system admits an equilibrium with partial household engagement. We derive conditions under which this equilibrium undergoes a Hopf bifurcation, yielding sustained oscillations arising solely from the interaction between mosquito abundance and household behavior. Numerical simulations confirm our\nanalytical results by delineating the parametric regions of local stability for each steady state. Our study demonstrates that spontaneous household decision-making alone can generate nontrivial dynamics in mosquito populations, offering insights into the interplay between risk perception and vector ecology. From a public health perspective, recurrent peaks in mosquito abundance may translate into periodic surges in cases, and effective interventions may therefore target the perceived risks that drive household participation in controlling breeding sites.", "id": "Paper/71510", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71510"}, {"title": " A Full Characterization of Basic Weights on <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.962ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 1275.1 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">A_n</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-41\" d=\"M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-41\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-6E\" x=\"1061\" y=\"-213\"></use>\n</g>\n</svg>-type Root Systems ", "webprogram_exclude": "0", "session_ids": ["Session/19362"], "source_sha256": "f61ff415e4beb3b9a1bd608cb062bb8540224a3ac9fd0b18a95d4368bd911dd3", "withdrawn": "", "abstract": "The Galois side of the categorical local Langlands program involves representations of complex matrix groups. Combinatorially, such representations are determined by weights. This paper investigates weight functions on root systems of type $A_n$, which map the basis weights to either $0$ or $2$. As it turns out, certain weight functions admit \\textit{basic weights} and \\textit{cuspidal weights}, which lie on the boundary and the interior of the cuspidal polytope determined by the weight function, respectively.\n\n\nIn this paper, we build upon our previous work (presented at the 2026 JMM PME poster session), where we established that all weight functions that contain basic weights must take a certain form, which we called the ``hike\" property. We begin by demonstrating that all hike functions contain at least one basic weight, showing that the ``hike\" property is both a necessary and sufficient condition for the existence of basic weights. Furthermore, we go on to describe and enumerate the basic weights for any given hike function, completely characterizing the existence of basic weights in $A_n$-type root systems. Finally, we also illustrate a potential correspondence between a class of basic weights (those with central character $0$) and ladder representations and explore the consequences of such a correspondence.", "id": "Paper/71513", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71513"}, {"title": " Hypergraphs in Biological Discovery ", "webprogram_exclude": "0", "session_ids": ["Session/18282"], "source_sha256": "92fb251c1a7c9da2b13ca3a780f0011c07c00f3bbb1b1ed5292aae6d90d10066", "withdrawn": "", "abstract": "Complex biological systems rely on multi-way interactions that traditional pairwise graphs fail to capture. By extending network representations to hypergraphs, computational models can preserve higher-order relationships across molecular pathways, cellular networks, and complex disease mechanisms. This talk synthesizes recent advancements from machine learning and foundational algorithmic approaches to demonstrate how hypergraph frameworks enhance representation learning, feature extraction, and predictive accuracy for high-dimensional biological data. This talk will provide a clear overview of how higher-order graph architectures translate intricate, multi-variable biological signals into actionable computational insights.", "id": "Paper/71514", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71514"}, {"title": " Coverings and rank lower bounds beyond the slice rank ", "webprogram_exclude": "0", "session_ids": ["Session/18294"], "source_sha256": "2a33af4d0962cfb6d14876f4e8e018d40aa277c584a4f06d9d346597109bf0ff", "withdrawn": "", "abstract": "A result of Sawin and Tao states that for tensors supported in an antichain, the slice rank of the tensor is equal to the smallest number of slices that suffice to cover its support. After showing how various naive generalisations of that identity fail for more general notions of rank, we shall describe how the rank lower bounds behind that principle can nonetheless be extended from the slice rank to a significantly wider class of rank notions on tensors that we shall describe.", "id": "Paper/71517", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71517"}, {"title": " Web-Based Tools for Transforming Mathematical Thinking and Learning ", "webprogram_exclude": "0", "session_ids": ["Session/18092"], "source_sha256": "779f37f9fdc3b341735f51390d71a213632e0ea7fc3a69b8ef2d0797851542f6", "withdrawn": "", "abstract": "In this talk, we will explore some of the web-based tools used by the Panamanian Foundation for the Promotion of Mathematics (FUNDAPROMAT) to transform mathematical thinking and learning. These online spaces foster collaboration, shared problem-solving, and informal discovery, allowing participants to communicate their reasoning in a safe, inclusive environment. See firsthand how interactive visual manipulatives empower global communities, including students, teachers, and families, to drag, rotate, and manipulate digital objects, while exploring mathematical concepts together through joyful play.", "id": "Paper/71521", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71521"}, {"title": " Gorenstein linkage of Ideals ", "webprogram_exclude": "0", "session_ids": ["Session/18285"], "source_sha256": "a4fc084bc83d21bcd2e1dd4b4b981e8bec5736bbe7ce9fba353aabe566524e7d", "withdrawn": "", "abstract": "Linkage theory, initiated in its modern form by Peskine and Szpiro, studies ideals through residual intersections. If \\(I\\) and \\(J\\) be proper ideals in a Noetherian ring \\(R\\), they are directly linked by a Gorenstein ideal \\(\\mathfrak a\\subseteq I\\cap J\\) when \\(I=\\mathfrak a:J\\) and \\(J=\\mathfrak a:I\\). Restricting \\(\\mathfrak a\\) to complete intersections gives complete-intersection linkage. Linkage has played an important role in the study and classification of perfect ideals. Beyond being an active area of study in its own right, linkage theory has become an important tool in commutative algebra, providing methods for constructing examples and understanding structural obstructions in various contexts. A useful perspective in linkage theory is the following: if a property or conjecture is known to hold for a given ideal, one may ask whether it is preserved throughout its linkage class. Several important conjectures in commutative algebra are known to hold for ideals in the linkage class of a complete intersection.\n\nA central open problem is the study of Gorenstein linkage, \"glicci conjecture\", which asks if every Cohen–Macaulay ideal in a regular ring belongs to the Gorenstein linkage class of a complete intersection. I will describe a module-theoretic approach to this problem based on Bourbaki sequences, and filtration of modules. Using this method, we prove glicci results for several classes of Cohen–Macaulay ideals, including \\(\\mathfrak m\\)-primary ideals over Gorenstein rings, height-three monomial ideals, and monomial ideals admitting clean prime filtrations. \nAnother fundamental question in linkage theory asks whether every unmixed ideal lies in the linkage class of a Golod ideal. We show that this holds when one passes from complete-intersection linkage to the more flexible setting of Gorenstein linkage.", "id": "Paper/71522", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71522"}, {"title": " EvenQuads: From a Card Game to a Research Community ", "webprogram_exclude": "0", "session_ids": ["Session/18235"], "source_sha256": "ac08e136713bb833f48bc41eaf0178de4474fb808c39ec40f060583f49659752", "withdrawn": "", "abstract": "The card game Quads began as a variant of SET and the subject of an undergraduate senior thesis in 2013. It later became EvenQuads, when the Association for Women in Mathematics adapted the game for its 50th anniversary with a deck celebrating women mathematicians and their contributions. But the mathematics kept growing. Since 2020, Quads has inspired a series of summer research groups at Bard College and, since 2024, in the Polymath Jr. program. Starting simply by playing games, computing small cases, looking for patterns, and making conjectures, students have followed questions from finite geometry and linear algebra into unexpected directions such as coding theory and cryptography. Along the way, a research community has grown around the game, bringing together undergraduates, graduate students, former students, and mid-career mathematicians returning to research, with many women among both students and mentors. We will share how a game adapted to celebrate women in mathematics has become a source of new mathematics, new researchers, and new collaborations.", "id": "Paper/71523", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71523"}, {"title": " Quaternionic linear canonical transforms with hyperbolic measures ", "webprogram_exclude": "0", "session_ids": ["Session/18336"], "source_sha256": "5a2f8c3bf5f0cdc49f62412c01f27f18a3f5212732f497323960762325a5c805", "withdrawn": "", "abstract": "Fourier analysis reflects the translation structure of the underlying space. Motivated by this principle, we consider quaternion-valued functions on an open rectangle equipped with a hyperbolic reference measure, where ordinary translations are replaced by Einstein addition and a natural straightening map relates the hyperbolic geometry to the Euclidean one.\n\nWithin this framework, we introduce a two-sided quaternionic hyperbolic linear canonical transform associated with unimodular matrices. The two-sided structure incorporates quaternionic noncommutativity, while the canonical parameters provide a family of transforms that contains the quaternionic hyperbolic Fourier transform as a particular case. We establish its main analytic properties, including translation and modulation relations, a Riemann-Lebesgue lemma, an inversion theorem, and Plancherel and Parseval identities. In the Euclidean limit, the construction reduces to the classical two-sided quaternionic linear canonical transform.", "id": "Paper/71524", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71524"}, {"title": " The Geometry of Learning to Emulate Physics ", "webprogram_exclude": "0", "session_ids": ["Session/18323"], "source_sha256": "bb7074c0e9dbf88c40391125ec79660774404912bfbc5a81b01124a9d93b5c0f", "withdrawn": "", "abstract": "Neural emulators of partial differential equations offer a fast alternative to traditional numerical\nsimulation, but their reliable deployment requires evidence that they have learned the underlying\nphysics, which predictive accuracy on test data alone does not establish. This talk explores how\ngradient geometry can help us determine what these models learn and how that learning extends to\nnew situations, including physically admissible inputs outside the training distribution. Drawing on\nthe PDEGym fluid flow benchmark, I will describe influence functions that measure how learning\nfrom one example helps or hinders performance on another. These measurements reveal relation-\nships among learning, physical symmetries, and prediction across time, providing information that\nforward-pass prediction error alone does not capture. They connect questions about generalization\nto the alignment of gradient directions during training. I will discuss ongoing work exploring how\nthis evolving geometry can inform new training algorithms, including how information from earlier\nupdates is transported as the local geometry changes. The broader aim is to connect mathemat-\nical tools for understanding learning with the development of more reliable models for scientific\ncomputation.", "id": "Paper/71525", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71525"}, {"title": " Five+ Years of Math Visualization ", "webprogram_exclude": "0", "session_ids": ["Session/18074"], "source_sha256": "7dfec4db6cddbeaf0eb543089a4d0afc38141b4e9e94439e9466f291be512315", "withdrawn": "", "abstract": "I've been animating mathematics visualizations, primarily proofs without words, on various social media outlets for nearly six years. I will discuss what led me to start the associated channels, how I go about creating content regularly, and how I plan to move forward. In addition, I'll reflect on some of my past and current challenges and especially explore the difficulties arising from being a \"faceless channel\" during the rise of AI-generated content.", "id": "Paper/71534", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71534"}, {"title": " Insertion algorithms and trees as an analog of Schubert calculus for moduli space of curves <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"7.278ex\" height=\"3.676ex\" style=\"vertical-align: -1.005ex;\" viewBox=\"0 -1150.1 3133.5 1582.7\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\overline {M}_{0,n+3}</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4D\" d=\"M289 629Q289 635 232 637Q208 637 201 638T194 648Q194 649 196 659Q197 662 198 666T199 671T201 676T203 679T207 681T212 683T220 683T232 684Q238 684 262 684T307 683Q386 683 398 683T414 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xlink:href=\"#E1-MJMAIN-2B\" x=\"1379\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-33\" x=\"2158\" y=\"0\"></use>\n</g>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/19366"], "source_sha256": "c24a2067d840d3c91c60b5704b867b0a3b6a198c03fec6c235090e43a08aaea3", "withdrawn": "", "abstract": "Schubert Calculus has been extremely successful in developing combinatorial theories to understand Grassmannians and flag varieties. In recent years, much work has been done with the goal of replicating this success in the context of moduli spaces of curves $\\overline{M}_{g,n}$. In particular, there exist combinatorial rules, analogous to the Littlewood–Richardson rule, for the intersection theory of $\\overline{M}_{g,n}$ and related spaces.\n\nWe illustrate some of these rules on the moduli space of stable genus zero curves with $n+3$ marked points $\\overline{M}_{0,n}$, and resolve a question of Gillespie, Griffin, and Levinson that asks for a combinatorial bijection between two classes of trivalent trees, \\textit{tournament trees} and \\textit{slide trees}, that both naturally arise in the intersection theory of $\\overline{M}_{0,n}$. Each set of trees enumerates the same intersection product of certain pullbacks of $\\psi$ classes under forgetting maps. We give an explicit combinatorial bijection between these two sets of trees using an insertion algorithm that mimics the RSK algorithm for Young tableaux.\n\nAdditionally, we discuss some recent work being done to develop combinatorial intersection rules on \\textit{multicolored spaces}, which generalize $\\overline{M}_{0,n+3}$.", "id": "Paper/71537", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71537"}, {"title": " Diagonal restrictions of Hilbert modular forms ", "webprogram_exclude": "0", "session_ids": ["Session/17903"], "source_sha256": "217f185563a7f07c398e1eeb8211e1b9dde8d9760e2a5e0829048e9e65c921b4", "withdrawn": "", "abstract": "A Hilbert modular form $f(z_1, z_2)$ over a real quadratic field is a function on a product of two complex upper half-planes satisfying symmetries and growth conditions generalizing those of a classical modular form. Given a Hilbert modular form, restriction to the diagonal $z_1 = z_2$ yields a classical modular form, and if $f$ has weight $(k_1, k_2)$, the restriction $g(z) := f(z, z)$ is a classical modular form of weight $k_1 + k_2$. Restriction to the diagonal is algebraically a somewhat unwieldy operation -- in particular, even if $f$ is a Hecke eigenform, $g$ will generally not be. Nonetheless, the Fourier coefficients of $g$ encode information relating to the central $L$-values of automorphic representations associated to $f$. Recent computations of Hilbert modular forms suggest that in certain settings, a broad class of classical Hecke eigenforms arise as restrictions of Hilbert modular forms. In this talk, we discuss these computations and the mathematics that ensues.", "id": "Paper/71538", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71538"}, {"title": " A min-max principle for matrix completion ", "webprogram_exclude": "0", "session_ids": ["Session/18230"], "source_sha256": "6054263a426109ee8b7851c2f6c0ed74a602c753883805cd25acc15d16b947cc", "withdrawn": "", "abstract": "It is known that the lowest rank that can be attained by changing the diagonal entries of a matrix and the highest rank that can be obtained by restricting the matrix to an off-diagonal submatrix are in a sense two sides of the same coin: they differ by a factor of at most 3 (with the optimal constant in this question appearing to be much less straightforward to determine).\n\n\nThis talk will focus on how the above min-max principle can be extended to other sets of modifiable coefficients than the diagonal. If U is a set of entries, then does the highest rank of U-avoiding submatrices control the lowest rank of the matrix after modification of coefficients in U? As stated, this is far from being true for all sets U, but what is an adequate formulation?", "id": "Paper/71541", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71541"}, {"title": " Engaging Young Minds with Mathematical Magic ", "webprogram_exclude": "0", "session_ids": ["Session/18062"], "source_sha256": "4ce2a20989f71f9e26c07fd41170dda0df2d5b13a868b38738386d5fa4e0fba3", "withdrawn": "", "abstract": "Discover the power of mathematical magic to transform student engagement. In this talk, the Panamanian Foundation for the Promotion of Mathematics (FUNDAPROMAT) reveals how card tricks, number puzzles, and simple props can drive profound mathematical thinking. Join us to explore practical examples of magic tricks that deepen conceptual understanding, elevate your teaching pedagogy, and spark unexpected avenues of research. This talk stems from my participation in the First International Magic & Math Conference hosted by the Brin Math Research Center at the University of Maryland in March 2026.", "id": "Paper/71545", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71545"}, {"title": " Spectral Capping and Nesting in Graph Cutwidth ", "webprogram_exclude": "0", "session_ids": ["Session/19366"], "source_sha256": "d0e0242c78041bcb87247e6892d911793ad1277a7e3e890f6968ff6de123a7fa", "withdrawn": "", "abstract": "The edge-isoperimetric peak $B(G)$ is the maximum, over subset sizes, of the minimum edge boundary (the number of edges leaving that subset). It bounds cutwidth from below but allows the minimizing subsets to be chosen independently, whereas cutwidth requires the subsets to be nested prefixes of a single vertex ordering. A clique with an attached path illustrates how large this gap can become. We study this distinction using capped Laplacians $Q_\\tau$, where $\\tau$ is a cap level and $Q_\\tau$ is formed spectrally by replacing each Laplacian eigenvalue $\\lambda$ with $\\min(\\lambda,\\tau)$. For an ordering, a prefix is its first $k$ vertices. Minimizing, over all orderings, the largest value of $\\mathbf{1}_S^{T}Q_\\tau\\mathbf{1}_S$ over its prefixes $S$ gives a cutwidth lower bound that can exceed $B(G)$. Minimizing separately at each subset size cannot yield such an improvement. Thus the method isolates the obstruction created by requiring low-boundary subsets to occur as the nested prefixes of one layout.\n\nWe report preliminary computational results for all 273,193 connected unlabeled simple graphs on at most nine vertices, using numerical eigendecompositions and subset dynamic programming. We test caps at the distinct positive eigenvalues below the largest eigenvalue. In these computations, a tested cap improves on $B(G)$ in all but 261 of the 159,522 graphs whose cutwidth exceeds $B(G)$. We discuss these exceptions and selected graph families through 18 vertices. We also give exact certificates over real algebraic numbers for representative cases, including recovery of the full cutwidth at a cap below the largest eigenvalue.", "id": "Paper/71548", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71548"}, {"title": " A Deep Learning Framework for Alzheimer’s Disease Classification from Brain MRI ", "webprogram_exclude": "0", "session_ids": ["Session/19345"], "source_sha256": "73575b570ce8a7b9660db4ef99c4baa88255458c669b8bf305488aa7acfc3b69", "withdrawn": "", "abstract": "Alzheimer’s disease (AD) is a progressive neurodegenerative disorder for which accurate MRI-based classification may support earlier clinical assessment and disease management. This study develops a unified deep-learning framework for evaluating three architectures ADD-Net, Bayesian Convolutional Neural Network (BayesianCNN), and U-Net using the OASIS brain MRI dataset. The primary contribution of this work is the integration of class-imbalance correction, uncertainty-aware deep learning, and model interpretability within a common comparative framework for AD classification. SMOTE-Tomek was incorporated to address the highly imbalanced distribution of dementia classes, while Bayesian learning was used to represent uncertainty in model predictions.\nThe three models were evaluated using accuracy, precision, recall, F1-score, and area under the ROC curve, and Gradient-weighted Class Activation Mapping (Grad-CAM) was used to visualize image regions contributing to model decisions. BayesianCNN combined with SMOTE-Tomek achieved the strongest overall performance, with 95.03% accuracy, 0.95 precision, 0.93 recall, and an F1-score of 0.94, compared with 94.16% accuracy for ADD-Net and 84.91% for U-Net. The improvement of BayesianCNN from 91.20% without SMOTE-Tomek to 95.03% with SMOTE-Tomek further demonstrates the value of addressing class imbalance in MRI-based AD classification.\nThese findings suggest that combining Bayesian deep learning with class-imbalance correction can improve MRI-based AD classification while providing a framework for uncertainty estimation. Grad-CAM further enhances model transparency by identifying image regions contributing to predictions. Overall, the results support the potential of interpretable and uncertainty-aware deep learning approaches for assisting Alzheimer’s disease classification from brain MRI, while further validation on independent datasets is needed before clinical implementation.", "id": "Paper/71549", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71549"}, {"title": " From Genes to Cell Types: A Wavelet-Based Multilayer Causal Hypergraph in Alzheimer’s Disease ", "webprogram_exclude": "0", "session_ids": ["Session/19371"], "source_sha256": "aa25c80f9f1bf7a566ffde395e3479d1a4a368ac4c380532adb62824cb3660fd", "withdrawn": "", "abstract": "Alzheimer’s disease (AD) is characterized by complex, cross-level regulatory disruptions that originate in gene-regulatory networks, drive heterogeneous cell-state transitions, and ultimately culminate in system-wide neural circuit failure. Traditional network inference methods typically rely on pairwise correlation, a single structural resolution, or pseudotime-based trajectory tracking, leaving them incapable of capturing multi-scale, higher-order, or abrupt non-linear causal dynamics. To address these limitations, we present a novel computational framework that constructs a multi-layer, higher-order causal hypergraph directly from single-nucleus RNA sequencing (snRNA-seq) data. By utilizing Spectral Graph Wavelet Transform (SGWT), we decompose raw transcriptomic data into five distinct multi-scale resolution views. Within each view, we implement a trajectory-free, double-filter causal inference pipeline combining Interaction Information (II) and nonlinear Additive Noise Models (ANM) to identify and orient directed gene triplets (hyperedges). We then map these gene-level hyperedges to specific cellular phenotypes, integrating them into a multi-layer architecture spanning gene-gene, gene-cell, and cell-cell interaction layers. Applying this framework to human AD and normal control datasets reveals striking disease-specific reorganizations. Notably, in microglia, the framework uncovers an AD-specific shift toward an oxidative stress axis centered on BACH1 and NFE2L2, alongside an inflammatory module (ZFX–MYSM1–ARID5A–NFAT5) that was completely obscured in the baseline data. Furthermore, we show that our framework successfully handles abrupt cell state transitions (e.g., in neurons) where trajectory-dependent methods fail. Ultimately, this framework provides a robust, mathematically rigorous roadmap for dissecting multi-level AD pathology and prioritizing multi-gene synergistic therapeutic targets.", "id": "Paper/71551", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71551"}, {"title": " Shift-invariant aggregation ", "webprogram_exclude": "0", "session_ids": ["Session/18058"], "source_sha256": "97434f701fd563ba9eeda31e61619ce0ffb9c74e5368caa13cb9b4ceecfccc01", "withdrawn": "", "abstract": "We characterize explicitly the path-dependent payoffs that satisfy a shift-invariant aggregation property.", "id": "Paper/71552", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71552"}, {"title": " Topological Data Analysis for Out-of-Distribution Detection ", "webprogram_exclude": "0", "session_ids": ["Session/18323"], "source_sha256": "309b974be7a57a658829af52d0d4e990519310c4188cc333d8650404c8dde6a7", "withdrawn": "", "abstract": "Machine learning (ML) models can perform extraordinarily well in controlled environments. However, out in the “real”-world, performance drops due to the unpredictable nature of the environment. The usual approach to ensure good performance is to obtain a plethora of high-quality labeled data from the relevant environment. However, when working in a Naval setting this is often not practical or even possible. We use tools from Topological Data Analysis (TDA) to help us analyze, understand, and characterize the effects of changes to operating conditions on the performance of Naval ML systems. Specifically, we use the TDA tool, Mapper, to explore the latent space of Naval ML systems.  Mapper, in short, takes a possibly high dimensional dataset and reduces it to a low-dimensional graph, while still preserving information from the original dataset—unlike other dimension reducing techniques. After applying Mapper to the latent space of ML models, we see that there is a qualitative difference between the latent space of in-distribution data to out-of-distribution datasets. To quantify this difference, we have begun investigating a generalized version of Optimal Transport applied to these Mapper graphs. Although this metric appears to be promising, it remains to be shown that it is statistically significant.", "id": "Paper/71553", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71553"}, {"title": " From Conservation of Live Force to the Kinematic Perspective: The Work of Poisson and Thomson on General Fluid Equations and Their Boundary Conditions ", "webprogram_exclude": "0", "session_ids": ["Session/18373"], "source_sha256": "cd68a6ca919a86b1f9bf14e772c3a9fc9dbdc0947017281790589c8d5e566dfd", "withdrawn": "", "abstract": "Since Daniel Bernoulli gave the one-dimensional hydrodynamic equation in 1738 based on the \"conservation of live force\" [conservation of live force: the law of conservation of live force. In Bernoulli’s era in the 18th century, it referred to the energy possessed by a body due to its motion, equivalent to today’s \"conservation of kinetic energy\"], how to provide more general equations, as well as the boundary conditions satisfied by these equations, became a problem of common concern to mathematicians and physicists thereafter. On the basis of the work of d’Alembert, Euler, Laplace, Lagrange, and others on fluid dynamics, Poisson in 1811 further gave relatively complete general fluid equations in terms of variables, and analyzed the fluid surface boundary conditions satisfied by the equations, but Poisson believed that they were not applicable to some complex cases of fluid motion. From 1847 onward, Thomson and Stokes successively published six articles in the \"NOTES ON HYDRODYNAMICS\" series, among which Thomson reinterpreted the problem left over by Poisson, clarifying that the results given by Poisson are applicable to fluids in different states. The work of Poisson and Thomson represents the transmission of two different academic lines of thought, revealing the shift of perspective from dynamics to kinematics.", "id": "Paper/71557", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71557"}, {"title": " Evolving Thinking About Graphs: The Case of Colin. ", "webprogram_exclude": "0", "session_ids": ["Session/18068"], "source_sha256": "e830deee7e3a55094a85ac79cf6a2e344884e9913a0580e8a88fd03457c3574e", "withdrawn": "", "abstract": "This talk documents how one student transitions from one way of thinking to another when reasoning with graphs. We describe students’ understandings of graphs and graphed quantities using the construct of quantitative reasoning (Thompson, 1995). Drawing on constructivist learning theory (von Glasersfeld, 1995), we account for how one student's meanings (Colin's) evolve over the course of a task. We describe Colin’s activity while engaging with the task and highlight key moments that supported his productive shifts in meanings for graphs. We conclude by discussing implications for researchers and instructors.", "id": "Paper/71558", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71558"}, {"title": " A Sabbatical to Observe K-6 Math Classes: Applications to My Own Teaching ", "webprogram_exclude": "0", "session_ids": ["Session/19341"], "source_sha256": "94f758f1bbdd7f8ca46be6d16fc93f0c42fcba55138e4688082ec8c6cfbc6167", "withdrawn": "", "abstract": "I’ve taught the math content sequence for preservice elementary teachers (PSTs) for years.  I am an algebraist, but received training and valuable mentoring specifically in teaching PST content courses early in my career, and I've built on that steadily.  However, post-COVID, I wanted to see what might need to be changed in my approaches with this cohort. \nA yearlong sabbatical afforded the opportunity for regular, in-depth observations in multiple K-6 math classrooms, to see first-hand the diverse experiences children and teachers have while learning, doing, and teaching math.  This presentation shares insights I'm now trying to incorporate into my own classes for PSTs and other students as well.  If you also teach this sequence or have an interest in it, I hope you’ll join in the conversation.", "id": "Paper/71559", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71559"}, {"title": " A Case for The Extrinsic Theory of Surfaces ", "webprogram_exclude": "0", "session_ids": ["Session/17853"], "source_sha256": "dfd6d26aa08de22b4408a7c99c93a96c7208c884f5609f6c4dfab9db5934c05c", "withdrawn": "", "abstract": "Two primary perspectives have shaped discourse about the theory of surfaces (and other manifolds): the intrinsic and the extrinsic viewpoints.  The historically prior {\\it extrinsic} view permits measurement and construction in the ambient environment, keeping the embedding of the surface in mind.  In conversation with accounts of space and time, the {\\it intrinsic} perspective orients away from a presumed ambient (Euclidean or otherwise), and permits only metric considerations from within the surface itself\n\nIn this presentation, I offer an account of how the extrinsic perspective may yet yield fruitful insight for the theory of surfaces, together with implications this perspective may have across other areas of mathematics.  Beyond a philosophical interpretation of existing results, I also offer as evidence a new extrinsic object, the torus of curvature, which answers a 260-year-old question posed by Leonhard Euler.", "id": "Paper/71561", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71561"}, {"title": " Mathematics of micro-swimming through shear-thinning fluids ", "webprogram_exclude": "0", "session_ids": ["Session/18444"], "source_sha256": "63f96c0fab6d28959cbaf6f222758efb7351f7feb86e35815f60131ddf73796d", "withdrawn": "", "abstract": "Both artificial and biological microswimmers frequently come into contact with non-Newtonian rheological fluid environments. Many biological fluids, such as blood and mucus, are particularly shear-thinning. The shear-rate-dependent viscosity in these shear-thinning fluids diminishes as the local strain rate increases, resulting in a nonlinear and spatially variable fluid response to swimmer motion. In this talk, we investigate how different axisymmetric squirmer forms affect movement in a fluid that is shear-thinning. We quantify the effects of particle geometry on swimming speed and energetic cost using numerical simulations and asymptotic analysis. We explain how the swimmer's geometry may be adjusted to better take advantage of non-Newtonian rheological behaviors for more efficient movement in complicated fluids.", "id": "Paper/71563", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71563"}, {"title": " On Notions of Rank for Symbolic Countable Group Actions ", "webprogram_exclude": "0", "session_ids": ["Session/18385"], "source_sha256": "c6ec020a1821ac8d5740037c34c9a7aad036311bae23bb034eab7f1e1583e967", "withdrawn": "", "abstract": "Let $G$ be a countably infinite group. We consider maps from $G$ into $\\{0,1\\}$ and call them $G$-words. We define notions of finite rank on $G$-words, extending symbolic rank one as defined by Gao and Hill, and finite symbolic (spacer) rank as defined by Gao, Jacoby, Johnson, Leng, Li, Silva, and Wu. Rank depends on families of finite subsets of $G$, and for families of F{\\o}lner sets containing recursive monotiles we show separation of finite rank.", "id": "Paper/71564", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71564"}, {"title": " Weyl <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.04ex\" height=\"1.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -576.1 878.5 721.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">m</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-6D\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Functions and Decoupling Asymptotics for the Bessel Plus Harmonic Oscillator Operator ", "webprogram_exclude": "0", "session_ids": ["Session/17804"], "source_sha256": "eb200559a726809d67a7e10d214c5f19588772cb8f983188d8f6e00e4c30ede7", "withdrawn": "", "abstract": "Due to their use in the modeling of molecular phenomena, Bessel plus Harmonic Oscillators acting as $\\tau_{\\gamma,\\omega}=-\\frac{d^{2}}{d^{2}}+\\frac{\\gamma^{2}-\\frac{1}{4}}{t^{2}}+\\omega^{2}t^{2}$ on the positive half-line $t\\in(0,\\infty)$ are frequently studied in the literature (recently by Boyack, Coulam, Derezi\\'nski, Lee, and So, among others).  We compute Weyl--Titchmarsh--Kodaira $m$-functions for these singular Sturm--Liouville operators.  Once obtained, we use these functions to determine spectral properties of the underlyilng operators and to prove trace formulas for differences of resolvents involving different (generalized) boundary conditions.  We also prove limiting results as these Bessel plus Harmonic Oscillator operators undergo decoupling limits ($\\omega\\downarrow 0$) to ordinary Bessel half-line operators.\n\nThis is based on joint work with Stephen L. Clark and Fritz Gesztesy.", "id": "Paper/71566", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71566"}, {"title": " The extremal black hole threshold ", "webprogram_exclude": "0", "session_ids": ["Session/18300"], "source_sha256": "ed3d2c92ec6f4d91cda01a496b26cf007a08839f16051f25010b3394ad623c21", "withdrawn": "", "abstract": "Extremal black holes are special solutions of Einstein’s equations with maximal spin or charge for their mass. In this talk, we consider the moduli space of spherically symmetric solutions to the Einstein-Maxwell equations with a real scalar field. It is known that solutions in this space either collapse to a black hole or do not collapse and remain regular. In the small scalar field regime, we show that the boundary between these two regions of moduli space is a smooth hypersurface consisting of solutions collapsing to asymptotically extremal black holes. This is based on joint work with Yannis Angelopoulos (Crete) and Christoph Kehle (UZH).", "id": "Paper/71568", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71568"}, {"title": " Topoisomerases Distance Table ", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "aa8e0676af860980e162a7e5897126eef07c9ef0c291ada5bf5cc17d2d9aace6", "withdrawn": "", "abstract": "DNA molecules are long polymers. Circular\nDNA can become knotted, which for proper\nbiological function need to be resolved.\nProteins such as topoisomerases play a\ncrucial role in unknotting these molecules.\nThe activity of type II topoisomerases can\nbe thought of as a topological operation:\nthese proteins resolve DNA knots by\nchanging crossings.\nI am calculating distance tables modeling\ntopoisomerase action on knots and links.", "id": "Paper/71572", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71572"}, {"title": " A Space for Wonder: The Cathartic Role of Mathematics within the Human Intellectual Life ", "webprogram_exclude": "0", "session_ids": ["Session/17853"], "source_sha256": "d4e6268bef93f065147a9a75abb340ff3faa2d4af501717898f67e2b9e96d80f", "withdrawn": "", "abstract": "What distinguishes the study of mathematics from other sciences?  In what particular ways, if any, does the process of mathematical inquiry contribute to the human experience?  Seeking to explore the specific role of mathematics within the broader scope of the human intellectual life, this paper examines the nature of mathematical objects, the manner in which we know these objects, and the process of inquiry by which we progress in our understanding of these objects. This exploration is particularly aided by reflecting on the insights of Plato, the medieval philosopher Aquinas, and contemporary mathematicians, such as Reuben Hersh. Developing a deeper understanding of the various facets of mathematics reveals it to be a study particularly suited to the human being as such, insofar as it harnesses both one's sensible and intellectual faculties, and fulfills one's desire to order chaos.\n\nThe ordering of one’s own mind which occurs in the study of mathematics finds an analogy in the classical understanding of catharsis, a process in which one’s emotions are excited and brought to rest through dramatic tragedy. This analogy is strengthened by the insights of Michael Polanyi, who suggests that the study of mathematics excites one’s intellectual passions by a recognition of and appreciation for intellectual beauty. This passionate desire for intellectual beauty manifests itself in an experience of wonder which begets wondering. However, while mathematics’ cycle of wonder follows a pattern of hope and fulfillment, the ongoing nature of this cycle indicates the inability of mathematics to bring about the ultimate fulfillment of human intellectual desires.", "id": "Paper/71573", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71573"}, {"title": " Using Ordinary Classifiers for Uncertainty Quantification ", "webprogram_exclude": "0", "session_ids": ["Session/17705"], "source_sha256": "f904fd2e71769219b9fcb2ef079e027fd2a735f2d03fe20982f933968cc193fd", "withdrawn": "", "abstract": "Class-membership probability is a central object for uncertainty quantification for classification. Many approaches begin by constructing a probabilistic classifier and using its scores to estimate or bound this quantity. This paper studies whether informative confidence intervals can instead be obtained from a finite family of ordinary classifiers by reasoning on positive-probability domains of the feature space.\n\nWe show that weighted ordinary classifiers induce domains of the feature space that naturally separate regions of higher and lower class-membership probability. For weighted Bayes classifiers, these domains yield almost-sure deterministic bounds on the class-membership probability. For classifiers whose classification error is close to the Bayes-optimal error, i.e. classifiers with small Bayes excess risk, we derive finite-sample and asymptotic confidence intervals whose width depends explicitly on the Bayes excess risk. These results provide a framework that links uncertainty quantification directly to Bayes excess risk and, consequently, to the quantity of available training data.", "id": "Paper/71574", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71574"}, {"title": " Duality of Webs is Transposition of Tableaux for <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"8.644ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 3721.7 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\lambda = \\left (1^n\\right )</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-3BB\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-3D\" x=\"861\" y=\"0\"></use>\n<g transform=\"translate(1917,0)\">\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"0\" y=\"0\"></use>\n<g transform=\"translate(389,0)\">\n <use xlink:href=\"#E1-MJMAIN-31\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-6E\" x=\"707\" y=\"557\"></use>\n</g>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"1414\" y=\"0\"></use>\n</g>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18370"], "source_sha256": "f132028ca786231b728ff924ec2e7cc41e9f35ca6e62121e81d0c4a1f26e5c8f", "withdrawn": "", "abstract": "Webs are planar bipartite graphs embedded in a disk representing elements of the $\\lambda$-graded component of the coordinate ring of the Grassmannian $\\mathbb C[\\widehat{\\operatorname{Gr}}(k, n)]_\\lambda$ where $\\lambda\\vdash n$. Fraser, Lam, and Le established a bilinear pairing between this space and the space of tensor invariants and conjectured that duality of non-elliptic web bases corresponds to transposition of their associated semistandard Young tableaux. In this talk, for $\\lambda = \\left(1^n\\right)$, we show that the change of basis matrix from products of Plücker coordinates to a web basis is triangular in the same ordering as its dual. From this, we prove the conjecture of Fraser, Lam, and Le for $\\lambda = \\left(1^n\\right)$.", "id": "Paper/71575", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71575"}, {"title": " AI-Augmented Cartographing, Desedimentation, and Elementarization of Mathematics Across Disciplines ", "webprogram_exclude": "0", "session_ids": ["Session/19341"], "source_sha256": "6595a43cfa55f6058a402451137f82336ba8d02dcb5782b5b100773f618f520d", "withdrawn": "", "abstract": "Mathematical concepts are often taught within disciplinary silos, obscuring the structures that connect mathematics, engineering, chemistry, and physics. This work develops the cartography of mathematics as a framework for mapping the conceptual terrain of mathematical ideas, practices, and relationships across disciplines. The framework employs AI-augmented learning trajectories grounded in the complementary processes of desedimentation and elementarization, through which mathematical knowledge emerges, circulates, and becomes established within disciplinary practice.\n\nDrawing on Felix Klein's conception of elementarization, elementary mathematics is understood as the reconstruction of advanced ideas around their fundamental conceptual structures. Concepts such as transformations, set theory, Fourier analysis, vector spaces, and linear operators were once specialized achievements but have become indispensable tools throughout STEM. Their diffusion reflects the continuing transformation of advanced mathematical ideas into foundational forms of practice.\n\nCentral to the framework is a desedimentation operator that analyzes disciplinary practices, representations, and modeling activities to recover the mathematical foundation. By examining recurring ideas such as symmetry, invariance, conservation, transformation, approximation, periodicity, and equilibrium across engineering, chemistry, and physics, the operator reveals shared mathematical structures often hidden beneath disciplinary conventions. These foundations become candidates for elementarization, supporting learning trajectories that connect practice, conceptual understanding, and formal theory.\n\nFaculty-developed concept maps and textbooks are transformed into network and matrix representations that visualize identified conceptual dependencies and interdisciplinary relationships. Student work from computational notebooks and inquiry tasks refines these maps and identifies conceptual bottlenecks. The resulting cartography portrays mathematics as an evolving landscape of ideas that emerge, migrate, and stabilize across disciplines, providing a scalable model for interdisciplinary curriculum design linking foundational understanding, advanced mathematics, and STEM practice.", "id": "Paper/71577", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71577"}, {"title": " Panel Discussion: Mathematics for Human Learning ", "webprogram_exclude": "0", "session_ids": ["Session/18101"], "source_sha256": "d1bcf1ca8105fa0454e91747f7189a01d77f317bdba7dc7b5837ee23f602695d", "withdrawn": "", "abstract": "This is one of two complementary discussions on the future of mathematical knowledge and mathematical community, public understanding of mathematics, and the relationship to open learning for mathematicians and nonmathematicians alike. In this part, we look more closely at the opportunities and responsibilities surrounding our mathematical knowledge, including how it might be disseminated and preserved for human learning at scale, alongside other timely questions as developments unfold.", "id": "Paper/71579", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71579"}, {"title": " Multiscale Graph-Wavelet Inference of Directed Predictive Hypergraphs for Spatial Transcriptomics ", "webprogram_exclude": "0", "session_ids": ["Session/19371"], "source_sha256": "7d76d03c7320107f75e3bc9bbe310f729ce6523975a3b1e1b4d296d03ee99766", "withdrawn": "", "abstract": "**Multiscale Graph-Wavelet Inference of Nonlinear Causal Hypergraphs for Spatial Transcriptomics**\n\nSpatial transcriptomic data encode gene expression together with tissue geometry, but expression correlations alone cannot establish directional predictive dependence or reveal how relationships vary across spatial scales. We develop a multiscale framework that combines spectral graph wavelet transforms (SGWTs) with directed hypergraphs to characterize gene–gene and gene–cell-state relationships across tissue organization. The framework was applied to three human spatial-transcriptomic datasets: breast cancer Block A Section 1 and pancreatic cancer samples PA11-2 and Pt-13A. Each tissue was analyzed using raw expression and four graph-wavelet representations, with independent clustering and Slingshot trajectory inference. Along the resulting pseudotime trajectories, ridge-regularized cubic B-spline Granger models tested whether source histories improved target prediction, with significance assessed by circular-shift tests and generalization evaluated by rolling-origin prediction. In the PA11-2 benchmark, SGWT representations showed greater mean clustering stability than feature-axis discrete wavelet transforms (DWTs), whereas DWTs remained more similar to raw expression. Directed hypergraph analysis identified the relationships ${\\mathit{IGHG1},\\mathit{MMP1}}\\rightarrow\\mathit{LILRA4}$ and ${\\mathit{GAL},\\mathit{LILRA4}}\\rightarrow\\text{Acinar Cell-Type}$, with joint predictive gains of 0.408 and 0.370 beyond the stronger corresponding single-source model. Backprojection mapped these predictive gains to contributing tissue spots while preserving bin-level totals. Together, the resulting networks provide a multiscale representation of spatially localized, directional predictive relationships along inferred cellular trajectories and generate testable candidates for subsequent biological validation.", "id": "Paper/71580", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71580"}, {"title": " The hypergraph adjacency tensor and its ranks ", "webprogram_exclude": "0", "session_ids": ["Session/19350"], "source_sha256": "2021e782d2f41fa96130582350ee55c9b7a9b3f4d954cdcecfdc06c8ebccefee", "withdrawn": "", "abstract": "Just like an adjacency matrix can be assigned to a graph, an order-d adjacency tensor can be assigned to a d-uniform hypergraph. The notion of rank on matrices likewise extends to several notions of rank on tensors. We shall discuss the interpretation of the ranks of the adjacency tensor and compare this interpretation to that of the rank of the adjacency matrix.", "id": "Paper/71581", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71581"}, {"title": " Panel Discussion: Human Learning for Mathematics ", "webprogram_exclude": "0", "session_ids": ["Session/18329"], "source_sha256": "72c560ef4f972eacab355e80f6382b15add95e616c047b179f5c2d61f2d89621", "withdrawn": "", "abstract": "This is one of two complementary discussions on the future of mathematical knowledge and mathematical community, public understanding of mathematics, and the relationship to open learning for mathematicians and nonmathematicians alike. In this part, we look more closely at the opportunities and responsibilities surrounding our mathematical community, including how it might be nurtured and sustained through human learning at scale, alongside other timely questions as developments unfold.", "id": "Paper/71582", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71582"}, {"title": " Physics informed signal reconstruction ", "webprogram_exclude": "0", "session_ids": ["Session/19369"], "source_sha256": "1c293ac1e9bfd1fc282c5e73f953bb2c84a966b72050ab08b3a1a5ce75b7238b", "withdrawn": "", "abstract": "We develop a theoretical framework for understanding the limits of function reconstruction in cases where the function satisfies a first-order partial differential equation (PDE). Specifically, we derive minimax optimality rates for interpolation and approximation algorithms for a linear transport equation by leveraging the property induced by their characteristic curves. For both uniform and nonuniform linear transport equations, we establish an improved minimax rate, which scales asymptotically with the sample size $n$ as $\\left(\\frac{\\log n}{n}\\right)^{1/(d-1)}$ where $d$ is the dimension of the domain. This is an improvement over the classical minimax rate of $\\left(\\frac{\\log n}{n}\\right)^{1/d}$ known for the class of 1-Lipschitz functions. These findings highlight the significance of prior knowledge of the underlying PDE structure in enhancing the reconstruction of function from sample data. We present numerical results to validate our theoretical findings.", "id": "Paper/71583", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71583"}, {"title": " On Open Borel Orbits in Conormal Bundles to Schubert Cells ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "75d3695524618ad31fae606f09d63cf911b5955b7a1a0c624192719ee825d5dd", "withdrawn": "", "abstract": "Let $C(v)$ denote a Schubert cell in the flag variety $\\GL_n/B$, and let $X(w)$ be a Schubert variety containing $C(v)$. Mellit has conjectured that, if $X(w)$ is smooth, the existence of an open $B$-orbit in the conormal bundle to $C(v)$ in $X(w)$ is equivalent to $C(w_0w)$ being contained in the smooth locus of $X(w_0v)$. We prove a stronger version of this conjecture, requiring only that $X(w)$ is factorial. We prove our result by constructing a sequence of graphs associated to the pair $v,w$ such that the existence of a cycle in one of these graphs is equivalent to the non-existence of such an open orbit.", "id": "Paper/71585", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71585"}, {"title": " Quantum Score Matching and Its Application to Gibbs State Learning ", "webprogram_exclude": "0", "session_ids": ["Session/18113"], "source_sha256": "7984b55f37ade124e8e9907e896f5bc6eaee64c5375c6d355bac1ffd76abde00", "withdrawn": "", "abstract": "Score matching has driven a wave of advances in classical generative artificial intelligence, including diffusion models. At its heart is the idea of learning data statistics by aligning the score functions of a model and the data distribution, avoiding intractable normalization constants. Despite its classical success, a unified theoretical foundation for quantum score matching remains missing. Can the same learning principle translate into protocols for learning quantum states? The answer is not immediate: classical score matching relies on commutative scalar operations, whereas quantum states require noncommutative matrix algebra. In this talk, we provide a positive answer by presenting a quantum score-matching framework that addresses noncommutativity while avoiding partition-function evaluation. By revisiting the mathematical foundations of classical score matching, we establish a noncommutative analogue of the Hyv\\\"{a}rinen identity suitable for quantum learning. We also rigorously study when quantum scores identify the target state and analyze the landscape of the resulting optimization objective. The framework yields explicit learning algorithms with gradient-estimation procedures implementable using quantum circuits with controllable depth. We demonstrate this framework through Gibbs state learning. We prove that, in the high-temperature regime, our protocol achieves information-theoretically optimal state-copy complexity for Hamiltonians of bounded locality and interaction degree. Numerical simulations further show that learning can succeed with inaccurate gradient estimates even under a very limited state-copy budget, supporting its potential for experimental demonstrations on quantum devices in the near future.", "id": "Paper/71589", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71589"}, {"title": " A Website Platform for Surveying Statistics and Data Science Courses ", "webprogram_exclude": "0", "session_ids": ["Session/19364"], "source_sha256": "a69d5ce01f007b90a0f69c326c849ca4c9686d2216152bf5d712ec82e2b638b5", "withdrawn": "", "abstract": "Understanding the role that attitudes play in learning is critical for our ability to engage and empower students. We have developed a family of instruments to measure post-secondary student and instructor attitudes toward statistics and data science, in addition to the course learning environment. Our website (masder.net) provides a model for a streamlined process for distribution, assembly, and analyses of such survey data. Account holders can customize the surveys, generate unique survey links, download their data, and receive automated reports comparing their course to the continually-compiled US national sample. We will discuss the development of the website, including feedback from instructors, as well as how educators can use the website to understand their own students and identify best-practices in statistics and data science education.", "id": "Paper/71602", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71602"}, {"title": " Toward a Multidisciplinary Framework for Undergraduate Data Science Competencies: Progress, Gaps, and Community Input ", "webprogram_exclude": "0", "session_ids": ["Session/18236"], "source_sha256": "e67a245da72c70b257c73a3b47f8434de98326d6e94431bfef64e520d45c71b3", "withdrawn": "", "abstract": "This session reports on progress from the Joint Taskforce on Undergraduate Data Science Competencies, a multi-society initiative ASA/ACM/ADSA/INFORMS/MAA/SIAM) that aims to establish a shared framework for undergraduate data science education. The taskforce defines competencies as an integration of knowledge, skills, and dispositions, organized into structured knowledge areas such as statistical modeling, machine learning, data acquisition, and data storytelling. The framework further maps skills to levels of mastery using Bloom’s taxonomy, providing a coherent basis for curriculum design, instruction, and assessment.\n\nThe taskforce was formed in 2023, with formal work beginning in April 2024 through regular meetings and community-facing presentations. By the end of 2025, a structured set of knowledge areas and units had been established, forming the foundation of the framework. The current phase focuses on refining skills and dispositions and clarifying levels of mastery, with a draft report expected by late 2026. The March 2026 ASA Town Hall represents an important round of community engagement. JSM 2026 occurs at a stage where both consolidation of the framework and broader discussion of its implications are timely.\n\nThis session has three complementary objectives. First, it will present the current state of the proposed framework, including key design decisions and their rationale. Second, it will examine open questions that remain under active development, focusing on the delineation of core versus specialized competencies; approaches to defining competencies, including skills and dispositions. Third, it will invite feedback that can inform the next phase of refinement.\n\nThis session targets a broad audience involved in data science education and practice. It will be particularly relevant to academic statisticians and educators designing or revising curricula, industry practitioners concerned with workforce alignment, professional society leaders contributing to guidelines and accreditation, and early-career faculty and program directors developing new data science programs.", "id": "Paper/71603", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71603"}, {"title": " Forensic Mathematics: 9/11 25 Years Later ", "webprogram_exclude": "0", "session_ids": ["Session/19340"], "source_sha256": "f94afe68f95b4d4b48c02282b3afa6188f49e4af4e3c8c980ca2a3e2a890f254", "withdrawn": "", "abstract": "2026 is the 25th Anniversary of the World Trade Center attack on 9/11. This PowerPoint presentation will cover the events following that day, and detail the Forensic Mathematics developed to identify the 2,977 victims of the attack. The victim identification project was the largest and most complex forensic project in history up to that time. This presentation will describe the events of 9/11 from a forensic perspective and detail the Mathematics of DNA victim identification. These include DNA Fingerprinting, Kinship Analysis and other genetic applications. Moreover, this discussion will include how the Mathematics was adapted to fit the statistical requirements of the medico-legal examiners at the NYC Office of the Chief Medical Examiner. In addition, lessons learned from that project will be discussed, as how the DNA analysis industry has adapted to the various Mathematical approaches. A view of how this work changed the face of DNA identification over the past quarter century.", "id": "Paper/71607", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71607"}, {"title": " Will Farmers Adopt Robotic Weeding? Adoption Dynamics and Herbicide Resistance in a Coupled Human-Natural System ", "webprogram_exclude": "0", "session_ids": ["Session/18327"], "source_sha256": "2f6cf4185d41d5adbb7e090bcb7dc7c97228eb77a2599050a0ffdcfb6d54e452", "withdrawn": "", "abstract": "The widespread reliance on herbicides in agriculture has accelerated the evolution of herbicide-resistant weeds, threatening the long-term effectiveness of weed management. This paper examines how farmers’ adoption of AI-enabled robotic weed management services interacts with weed pressure and resistance dynamics within a coupled natural–human system, generating feedbacks in which ecological conditions shape adoption decisions and adoption decisions reshape future ecological conditions. Using data from a discrete choice experiment of U.S. corn and soybean producers, we estimate heterogeneous preferences for robotic weed management and embed these preferences in a spatially explicit agent-based model that captures weed population and resistance dynamics. Mixed logit estimates show that producers value improvements in weed control effectiveness and are more likely to adopt robotic weed management as herbicide resistance increases, while neighboring weed pressure shifts preferences away from conventional herbicide-based management. Coupled ecological-economic simulations reveal cyclical adoption and disadoption patterns rather than conventional monotonic diffusion. Herbicide resistance on a farmer’s own fields accelerates early adoption, whereas neighboring weed pressure shapes adoption dynamics over time, generating sustained switching between robotic and chemical weed management. These findings demonstrate how feedbacks between farmer decisions and evolving ecological conditions can produce technology diffusion dynamics that depart from conventional adoption patterns, with important implications for regional herbicide resistance management.", "id": "Paper/71612", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71612"}, {"title": " Staggered-Grid Finite Difference (SGFD) Schemes for 2D Acoustics ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "35dc254f5dd7531212983cdf6f1a48f78d6f7a25e0aa82c06beabc6a8809f62f", "withdrawn": "", "abstract": "This project develops and evaluates staggered-grid finite-difference (SGFD) methods for simulating wave propagation governed by the two-dimensional acoustic equations. We implemented a second-order-in-time, fourth-order-in-space SGFD scheme in MATLAB that accommodates variable medium parameters and multipole sources, which represent spatially localized and complex seismic disturbances. To approximate wave propagation in unbounded domains, the computational model incorporates perfectly matched layers that absorb outgoing waves and minimize artificial boundary reflections. We assessed the implementation through numerical experiments examining convergence, stability, and energy conservation. Grid-refinement studies demonstrate the expected fourth-order convergence away from the source when a fourth-order multipole-source approximation is used, while a second-order source approximation limits the observed convergence rate everywhere. Energy tests show that the numerical solution preserves the energy-conservation behavior of the acoustic equations to high accuracy. This implementation provides a foundation for future work on modeling and estimating complex seismic sources.", "id": "Paper/71620", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71620"}, {"title": " Generating Functions of Non-backtracking Walks on Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "90e3d5aaca016a46640fa6b4c50f6e3e3b768d0c2fc173e8a8301b324679b271", "withdrawn": "", "abstract": "We study the asymptotic relationship between the number of closed simple random walks and the number of closed nonbacktracking random walks of length $n$ on a graph. We begin by using a known recurrence formula for the nonbacktracking walk counting matrix to prove a relationship between the generating functions of the number of closed simple and nonbacktracking random walks of length $n$ on regular graphs. This generating function will allow us to compute the asymptotics of nonbacktracking walks on any regular graph without knowing an explicit formula for the number of nonbacktracking walks of a certain length. The eigenvalues of the adjacency matrix will prove useful in the case of regular graphs. We then pose questions and conjectures about what may hold for irregular graphs, including an example of the asymptotic analysis for all complete bipartite graphs.", "id": "Paper/71621", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71621"}, {"title": " A Graph Theoretic Approach to Measuring Connectivity in Districting ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "36b8a00212c1c2d4f0246782229696653cc84b9ab3f45e694624222e2cbc605d", "withdrawn": "", "abstract": "Geometric compactness measures currently offer one of the most commonly used forms of examining districts, but known geometric measures fall short in a variety of different ways. For example, they fail to account for natural boundaries, state borders, or they don’t prioritize shapes that could tile. In this study, we develop an algorithm to build a network that seeks to characterize the connectivity of the population represented within the districts by incorporating road network data from OpenStreetMaps into the network construction. In the network, nodes correspond to census block groups with edges being determined by adjacency and underlying road networks. We then analyze these networks looking at various graph-theoretic measures, particularly the resistance distance, to statistically determine if they represent their respective populations.", "id": "Paper/71625", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71625"}, {"title": " Realistic Modeling of Phylogenetic Trees and Its Implications. ", "webprogram_exclude": "0", "session_ids": ["Session/17953"], "source_sha256": "ee4755efa3c01dc7a037ee5b5e7d710365fbeeb58ef049c67f150720ac14cf8e", "withdrawn": "", "abstract": "In this talk, we review the beta-splitting tree model introduced by David Aldous in 1993, a one-parameter family of recursive random binary trees indexed by a real parameter $\\beta$. At the critical value $\\beta = -1$, which yields the so-called critical beta-splitting tree, this model captures realistic topological features absent from traditional combinatorial ensembles. We discuss structural and statistical properties of these trees that enable the high-probability pseudo-diagonalization of the phylogenetic covariance matrix for large trees in the critical ensemble. This structural behavior provides a theoretical justification for using Haar-like wavelets to identify lineage-associated features in comparative metagenomics that best differentiate between pairs of microbial environments based on the relative abundance of operational taxonomic units (OTUs). \nThis work is in collaboration with my graduate research student, S. Svihla.", "id": "Paper/71628", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71628"}, {"title": " Pattern avoidance in binary lattice and Yamanouchi words ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "f126ac1825237b206980379939f5724fdffa51e81f54eb61a3042ee0439fbaa8", "withdrawn": "", "abstract": "This research focuses on pattern avoidance in binary lattice and Yamanouchi words. For each binary pattern $w$ of size three, we determine the number of such words of size $n$ that avoid $w$. We also characterize the structure of the words that make up these classes.", "id": "Paper/71653", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71653"}, {"title": " Integrated Landslide Susceptibility Modeling in Nepal’s Mid-Hills Using Richards Equation, Infinite Slope Stability, and QGIS ", "webprogram_exclude": "0", "session_ids": ["Session/18327"], "source_sha256": "d2fa787c7b1871af16422fd34920208307352959369c5f47b5421402d5faa08e", "withdrawn": "", "abstract": "Severe landslides in the Himalayas arise from the interaction of steep terrain, fragile geology, and intense monsoon rainfall. This study presents a coupled modeling framework that integrates the Richards equation for unsaturated flow with a modified infinite-slope factor-of-safety formulation to evaluate rainfall-induced slope instability. A mesh-free generalized finite difference method is employed to solve the Richards equation, enabling computation of soil moisture and pore pressure. Topographic and meteorological data are incorporated using QGIS to produce quantitative hazard maps. Simulations for selected sites in the Nepalese foothills demonstrate the model’s capability in assessing landslide susceptibility. \n\nKeywords: Richards Equation, flow in unsaturated soil, meshfree generalized finite difference, shallow landslides, infinite slope stability", "id": "Paper/71660", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71660"}, {"title": " Data Analysis of Water Quality on Whitton Pond ", "webprogram_exclude": "0", "session_ids": ["Session/18554"], "source_sha256": "e9ee014406de9b649a325ac0d841f1848f382ec0046b86fb513aace08325811a", "withdrawn": "", "abstract": "This research adds Whitton Pond to the Lakes Lay Monitoring Program (LLMP), which tracks the water quality and ecosystem health of approximately 50 lakes across New Hampshire. Whitton Pond , located in the towns of Albany and Madison, is a 164-acre fresh-water lake  with an average depth of 12 feet and a maximum depth of 57 feet. We conducted weekly water quality testing, collecting scientific data about the pond’s health. This included water transparency (water clarity informs on algal populations, silt, and water color), temperature (thermal profile assesses the stratification of the water column), chlorophyll (tracks microscopic phytoplankton populations), dissolved water color (the natural background color can track climate-driven browning), phosphorus (the limiting nutrient to growth of algae, indicator of pollution and sediment erosion), cyanobacteria (this algae harms aquatic ecosystems), and alkalinity (informs how water neutralizes acidic pollution from acid rain and snowmelt).\n\nThis talk will share other analysis of the 2026 data from Whitton Pond. Analysis of the data collected from the other bodies of water participating in the LLMP will place Whitton pond into a broader context. All told this analysis provides insight into the natural capacity of the New Hampshire lake system to respond to changing climate conditions.", "id": "Paper/71662", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71662"}, {"title": " Track Reconstruction in a High-Occupancy Gas TPC with Time-Aware Object Condensation ", "webprogram_exclude": "0", "session_ids": ["Session/19345"], "source_sha256": "454598a8f611bffe3b2398fbd5d1f99e1b10f57ac4f056c3a81fa65f0179af83", "withdrawn": "", "abstract": "We reconstruct charged-particle trajectories in a high-occupancy gas time-projection chamber\n(TPC) from a point cloud of detector hits. For every hit, a four-block transformer maps the\nmeasured features to a condensation score, a latent coordinate, and a collision time, attending\nonly within a fixed 32-nearest-neighbour graph to keep training cost bounded. Particles are\nrecovered by greedy seeding and assignment in that latent space—no need for bipartite matching,\npredicting the number of tracks, or enforcing a fixed upper bound. Our contribution is the\ntime coordinate. For each hit we estimate the collision time of the interaction that produced it\nand use the time as the fifth coordinate of the grouping metric. The readout does not measure\nz, the coordinate along the beam and the direction the ionisation drifts: it can be derived\nfrom the drift time only if the collision time is known. Recovering that time therefore recovers\na separation the TPC readout alone cannot give. On a benchmark of ten complete readout\nframes the time-aware model reaches a double-majority reconstruction efficiency of ε50 = 0.948\nat 50% completeness and ε75 = 0.917 at 75% completeness, against 0.930 and 0.901 for the\nsame architecture without the time coordinate, a gain that comes almost entirely from reduced\nmerging. Against a second baseline trained on the realistic momentum spectrum (ε50 = 0.947,\nε75 = 0.884), the improvement is in completeness rather than in the number of particles found.", "id": "Paper/71668", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71668"}, {"title": " Instances of the higher Segal conditions in group theory \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18264"], "source_sha256": "79a2bfa244d386ef60c395959d9de758a6c4a392963837c6a11f3f686dbf45a7", "withdrawn": "", "abstract": "The higher Segal conditions are certain exactness conditions for simplicial sets defined by Dyckerhoff and Kapranov.  Recently, we've been working to understand these conditions for partial groups, which are certain algebraic structures defined by Chermak that can be understood as special types of (symmetric) simplicial sets. I will give a selection of examples of partial groups for motivation, and then try to indicate how to recognize instances of the higher Segal conditions where they come up in group theory.", "id": "Paper/71681", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71681"}, {"title": " Property Gamma Factors from Shift-similar and Houghton-like Groups ", "webprogram_exclude": "0", "session_ids": ["Session/18383"], "source_sha256": "8b4a48d8c1729d902bfa1665d4258115ae7a45834f7781f1c62ab7b628a5bf96", "withdrawn": "", "abstract": "In this talk, I will discuss recent results on a fairly new class of groups called shift-similar groups. These are certain groups of bijections of the natural numbers that are analogous to self-similar groups acting by automorphisms on an infinite regular $d$-ary tree. Given a shift-similar group $G$, one can form a mashup of the Houghton group $H_n$ (the group of eventual translations on the disjoint union of $n$ copies of the natural numbers) to get a Houghton-like group denoted $H_n(G)$. This group is analogous to the R\\\"{o}ver--Nekrashevych group, which is a mashup of a self-similar group with the Higman--Thompson group $V_d$. We will discuss some examples and show that, under a very natural and general amenability condition, both $L(G)$ and $L(H_n(G))$ yield property Gamma factors. This is joint work with Patrick DeBonis.", "id": "Paper/71682", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71682"}, {"title": " Bloch Discriminants of Discrete Periodic Operators \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18042"], "source_sha256": "de4bdcbbb766fd9f11e4ff285a6e309adc1b3dce52117383bb1a808739ed776f", "withdrawn": "", "abstract": "Given an operator on a $\\mathbb{Z}^d$-periodic graph, its Bloch variety encodes its spectrum with respect to the unitary characters of $\\mathbb{Z}^d$. This talk will describe how the Bloch discriminant gives a mapping of the geography of the parameter space that yields a qualitative change in the behavior of the critical points of Bloch varieties for three $\\mathbb{Z}^2$-periodic graphs. This includes determining the number and arrangements of critical points and whether or not they are degenerate as the parameters vary. This is joint work with Frank Sottile and Simon Telen.", "id": "Paper/71683", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71683"}, {"title": " The Integrating Factor as Operator Conjugation ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "610d894fb1462fe9467b3e22e7336629ca650eef1724bbe3d9740ea3bccdbc71", "withdrawn": "", "abstract": "The standard approach to solving higher-order constant-coefficient linear differential equations relies on guessing exponential solutions, with polynomial factors appearing mysteriously for repeated roots. But why do exponentials work? Where does the \"multiply-by-t\" rule come from? How do we know we’ve found all the solutions? We provide answers by uncovering a hidden connection: the integrating factor method for first-order equations is precisely an instance of operator conjugation. This perspective transforms guesswork into derivation: exponentials emerge from conjugation, polynomial factors from the kernel of repeated differentiation, and the direct sum decomposition of the solution space emerges from the conjugated operators. We also discuss an extension of this framework to equations with variable coefficients, revealing why constant-coefficient equations are special: their operators always commute.", "id": "Paper/71684", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71684"}, {"title": " A contact invariant from bordered Heegaard Floer homology \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18218"], "source_sha256": "145fe7d30cb14fdc374b4e9f2d7945029dd243591d478a6dfbde683196bca50f", "withdrawn": "", "abstract": "To a Heegaard diagram presentation for a (closed, oriented) 3-manifold, one can associate a chain complex, whose homology is an invariant of the 3-manifold, called Heegaard Floer homology. Given a contact structure on the 3-manifold, one can refine this construction to obtain a special class in this homology, which is an invariant of the contact manifold. We will begin by outlining this construction. \n\nThe original definition of Heegaard Floer homology involves counting holomorphic curves in a high-dimensional manifold, and as a result the invariant can be hard to compute. Bordered Floer homology is a generalization of Heegaard Floer homology to manifolds with boundary, which provides powerful gluing techniques for computing the Heegaard Floer homology of closed 3-manifolds. \n\nGiven a contact 3-manifold with convex boundary, we describe an invariant which takes values in the bordered Floer homology of the manifold. This invariant satisfies a nice gluing formula, and recovers the Oszvath-Szabo contact class in Heegaard Floer homology. This is joint work with Alishahi, Foldvari, Hendricks, Licata, and Vertesi.", "id": "Paper/71694", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71694"}, {"title": " Flexural scattering from junctions of periodic gratings \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/17702"], "source_sha256": "acbdfa704607956a6b0f991620f45ed7897abee1309887c59f7df62d2bdebb0d", "withdrawn": "", "abstract": "Periodic structures occur widely in the construction of acoustic and electromagnetic applications, including diffraction gratings, sub-wavelength photo-lithography, and meta-lenses. They also provide a computationally tractable proxy for rough boundaries that occur frequently in nature. For this reason, many numerical methods have been developed to simulate scattering off of such structures. Much less attention, however, has been placed on edge effects and the simulation of junctions of these structures. Further, these methods have been generally restricted to second order PDEs, and so have not been applicable to problems involving thin plates, which are widely used to model wave propagation in floating sea ice and in some engineering settings. \n\nIn this talk, I present a method for simulating the flexural, or biharmonic, scattering from junctions of semi-infinite gratings. I begin by demonstrating a novel integral equation method for solving this fourth order flexural scattering problem when the boundary is simply periodic. I then show how this method can be used to find the fundamental solution for the periodic scattering problem and to show that the fundamental solution admits an exponentially decaying analytic extension to the complex plane. I then leverage this fact to rephrase the junction problem into an integral equation on the fictitious boundary between the two gratings. I finish by presenting an efficient discretization scheme and present a few examples.", "id": "Paper/71697", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71697"}, {"title": " Free boundary minimal annuli in convex balls \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/17803"], "source_sha256": "ded2d03151b25ea6fa96b2214ce258886463e36b00d3dbba0c50e34dcc799f77", "withdrawn": "", "abstract": "We construct a $4$-parameter family of properly embedded genus-zero surfaces with at most two boundary components in a Riemannian $3$-ball. The construction is a free boundary analog of the canonical $5$-parameter family of surfaces on the $3$-sphere by Marques-Neves in the proof of  Willmore conjecture. In the Euclidean unit ball, this family realizes the critical catenoid as a Simon-Smith min-max limit.  As applications, we give an upper bound of Almgren-Pitts $4$-width $\\omega_4(\\mathbb{B}^3)$ by the area of the critical catenoid. Moreover, we prove the existence of at least three free boundary minimal annuli in any compact $3$-manifold with nonnegative Ricci curvature and strictly convex boundary.", "id": "Paper/71698", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71698"}, {"title": " Chip-firing and special divisors on the loops of loops metric graph ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "5d795dae33b628403dda4a09d34d31ba68d5e399064c15c6f3aa0d0533beb226", "withdrawn": "", "abstract": "In 2007, Baker and Norine established a groundbreaking result, proving a graph-theoretic Riemann-Roch, thus deepening the connection between combinatorics and algebraic geometry. For a metric graph $\\Gamma$, define the \\emph{Brill--Noether locus} as \n\\[\nW^r_d(\\Gamma)=\\{[D]\\in\\operatorname{Pic}^d(\\Gamma):r(D)\\geq r\\}\n\\]\nwhich parametrize divisor classes of degree $d$ and rank at least $r$. In 2017, Pflueger gave us a complete classification of these loci on generic chains of loops. The next question is to see how these loci behave on other metric graphs. \n\nConsider the metric graph, $L_g$ obtained by joining a chain of loops of genus $g-1$ at it's endpoints. We first show, by result of Chan, that for $g>3$ this graph can never be hyperelliptic. Next, we make steps towards exhibiting that every such graph of even genus has a metric realization which is Brill--Noether special. For $g=4$ such has been done by Lim, Payne, and Potashnik. We have done so for $g=6$, and make effort towards proving the general case.", "id": "Paper/71713", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71713"}, {"title": " Computing Without The Computer: 3D Applications Of Nomography ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "6558a948d212eaf02cfcb46a9623689c4a46eac13d890fdc3b4cff7291803504", "withdrawn": "", "abstract": "Nomographs are paper-based diagrams used to efficiently and accurately calculate solutions to an $n$-variate equation if you know the values for $n-1$ of the variables. Typically, these 2D nomographs model 3-variate equations. Popularized in the 19th and early 20th centuries as portable, easy-to-use ‘calculators’ by engineers, they fell out of favor with the advent of modern computing. That said, modern settings that don’t afford the use of computers still have demand for such technologies (e.g., field work and medicine). Being paper-based, all existing nomographs are 2D and use traditional geometry in their construction. This project investigates extensions into 3D nomographs---ones that typically model 4-variate equations. In particular, we extend two common nomographs: parallel scale and concurrent scale. These extensions warrant the use of methods beyond classical geometry (namely, analytic geometry and barycentric coordinates). We will discuss these extensions and their utility/portability in the modern day.", "id": "Paper/71717", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71717"}, {"title": " On Weighted Ehrhart Series of Order Polytopes ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "ed20da51aa463ba5d60022216955484f96ce7146da745481575719ea45da8709", "withdrawn": "", "abstract": "For a poset $P$, its associated order polytope $\\mathcal{O}(P)$ is the polytope defined by the inequalities $0 \\leq x_{i} \\leq 1$ and $x_{i} \\leq x_{j}$ for $i\\prec_P j$. We derive a formula for the weighted Ehrhart series of $\\mathcal{O}(P)$, which encodes the weighted sum of integer points over integer dilates of $\\mathcal{O}(P)$, in terms of the linear extensions and descent statistics of $P$. Our work generalizes the work of Stanley in the unweighted case. We then derive an alternative but equivalent formulation for the weighted Ehrhart series using a stars-and-bars argument. This latter formula yields an algorithm, now implemented in SageMath, for computing the weighted Ehrhart series that is significantly faster than Normaliz's WeightedEhrhartSeries function on posets with large numbers of linear extensions.", "id": "Paper/71719", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71719"}, {"title": " MULTIPLE DISTANCE RAMSEY BOUNDS FOR GRAPHS IN EUCLIDEAN SPACES ", "webprogram_exclude": "0", "session_ids": ["Session/18242"], "source_sha256": "470c4e3de71ba8d618195e65227b0cf646448d668f72d79a1aeb2689a647cf3c", "withdrawn": "", "abstract": "For a finite set $A \\subset \\R_{>0}$ and a finite graph $H$, let $\\chi_H(\\R^n;A)$ be the minimum number of colors required to color $\\R^n$ while avoiding a monochromatic copy of $H$ whose edges have distances in $A$. Extending the graph-copy framework of Axenovich, Liu, and Sagdeev and a multiple distance theorem of Naslund, we prove for any positive integer $m$,\n\\[\n\\chi_H(\\R^n;m):=\\max_{\\substack{A \\subseteq \\R_{>0} \\\\ |A|=m}} \\chi_H(\\R^n;A) \\geq\n\\left(\\Gamma_{\\chi}\\sqrt{\\frac{m+1}{\\Xi(H)}}+o(1)\\right)^n.\n\\]\nHere, $\\Gamma_{\\chi}$ is a constant and $\\Xi(H)$ is an explicit structural parameter that can be substantially smaller than $|V(H)|-1$, thereby recovering Naslund's similar bound for complete graphs and improving the general bound inherited from the corresponding clique for many graph families. Along the way, we construct a weighted strengthening of the semi-diagonal flattening rank theorem of Correia, Sudakov, and Tomon.", "id": "Paper/71724", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71724"}, {"title": " Graph-Theoretic Optimal Tilings for DNA Self-Assembly of Sun Graph Structures ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "c837962b1c38e862e1b05fadc533767d995f1b18c140223ced96a1be40890224", "withdrawn": "", "abstract": "DNA self-assembly provides a powerful framework for constructing nanoscale structures with applications in biosensing, molecular computation, and targeted drug delivery. Within the flexible tile model, branched junction DNA molecules are represented as graph vertices with complementary cohesive ends corresponding to bond-edges. A central challenge in this setting is determining the minimum number of tile and bond-edge types necessary to realize a target graph while preventing the formation of unwanted alternative structures. In this work, we investigate the family of sun graphs as assembly targets. We establish structural properties of sun graphs that influence tile and bond-edge assignments and derive bounds on the minimum number of required types. Our results contribute to the growing catalog of graph families with known self-assembly parameters and provide additional insight into the relationship between graph symmetry and assembly efficiency.", "id": "Paper/71725", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71725"}, {"title": " Optimal Tiling of Kayak Paddle Graphs Using Self-Assembling DNA ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "36b1021bb72273229e5b8f46b0779a580a16c407a7ebf2c8dadc09ebd58fb32d", "withdrawn": "", "abstract": "The self-assembly of branched DNA junction molecules has emerged as a versatile method for constructing complex nanostructures. Graph theory offers a natural mathematical framework for studying such systems, where vertices represent DNA junctions and edges represent potential molecular connections. An important objective is to minimize the number of distinct molecular building blocks required to assemble a desired target structure. Motivated by this problem, we examine the family of kayak paddle graphs within the flexible tile model of DNA self-assembly. We determine bounds on the minimum numbers of tile types and bond-edge types required to assemble these graphs while excluding undesired lower-order or nonisomorphic structures. We establish lower bounds using graph symmetry and swappability arguments and develop corresponding upper bounds through explicit tile assignments. For several cases, these bounds coincide, yielding optimal values for the associated assembly parameters.  These results further illustrate how graph theory can inform practical design strategies for DNA nanostructure construction.", "id": "Paper/71726", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71726"}, {"title": " Optimal tile-based self-assembly of DNA Sunlet Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "96d8232f3deffbfbea6b1588a41c2a1be8ede7d8002acf802bcdbee7a92e1a77", "withdrawn": "", "abstract": "Recent advances in DNA nanotechnology have increased interest in graph-theoretic models of molecular self-assembly. In the flexible tile model, DNA junction molecules correspond to graph vertices and bond-edge types determine allowable connections between molecules. The design problem is to realize a target graph using as few tile and bond-edge types as possible while preventing the assembly of unintended structures. We investigate this problem for the family of sunlet graphs, a class of graphs formed by appending paths to the vertices of a cycle. By exploiting the highly structured nature of sunlet graphs, we derive efficient assembly schemes and identify conditions under which optimality is achieved. The results extend existing work on graph families arising in DNA self-assembly and demonstrate the utility of combinatorial methods in the design of efficient nanoscale architectures.", "id": "Paper/71728", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71728"}, {"title": " Algorithmic Bounds for Bond-Edge Optimization under Strict DNA Self-Assembly Constraints ", "webprogram_exclude": "0", "session_ids": ["Session/18159"], "source_sha256": "53cf680403894b63b00c03ad4f9f0623ab17c9e2f298434e1bee92694dd03ba6", "withdrawn": "", "abstract": "Graph-theoretic models of DNA self-assembly provide a mathematical framework for designing nanostructures from branched junction molecules. Within the flexible tile model, vertices represent junction molecules and edges represent potential molecular bonds. Under the most restrictive assembly conditions, the objective is to minimize the number of bond-edge types required to assemble a target graph while preventing the formation of both smaller complexes and nonisomorphic competing structures. Determining optimal bond-edge assignments in this setting presents significant theoretical and computational challenges.\n\nIn this work, we develop an algorithmic framework for establishing bounds on the minimum number of bond-edge types required for such assemblies. Our approach exploits the relationship between bond-edge assignments and graph isomorphism through the study of 2-switch operations. We introduce efficiently computable criteria based on local structural changes, including triangle-count arguments, to certify when pairs of edges must receive distinct bond-edge types. These constraints are encoded in an associated conflict graph whose chromatic number provides a computable lower bound on the required number of bond-edge types. Ambiguous cases are resolved through direct isomorphism testing, yielding a refined conflict structure and stronger bounds. The resulting algorithms provide practical methods for analyzing graphs that are beyond the reach of complete theoretical characterization.", "id": "Paper/71729", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71729"}, {"title": " Optimal Self-Assembly of Kayak Paddle Graphs in a Flexible DNA Tile Model ", "webprogram_exclude": "0", "session_ids": ["Session/18159"], "source_sha256": "ccce2ff37daefebc16816a646fb6d34b635d85c164ce8b36fcdb3f7ffc776695", "withdrawn": "", "abstract": "DNA self-assembly provides a powerful approach for constructing nanoscale structures from branched junction molecules. Within the flexible tile model, these molecules are represented as vertices of a graph, while potential molecular connections are represented by edges. A central design objective is to minimize the number of tile and bond-edge types required to assemble a target structure while preventing the formation of undesirable competing assemblies. In this work, we investigate the broad family of kayak paddle graphs as assembly targets. Unlike many previously studied graph families, kayak paddle graphs exhibit substantial structural variation arising from differing cycle lengths and connecting paths, leading to a rich collection of nonisomorphic configurations. We develop graph-theoretic techniques to establish lower and upper bounds on the minimum numbers of tile and bond-edge types required for assembly. While some subclasses admit provably optimal solutions, others present significant theoretical challenges, necessitating the use of pragmatic bounds and constructive assembly strategies. These results highlight both the opportunities and difficulties associated with analyzing highly variable graph families and illustrate the ongoing challenges of determining optimal self-assembly designs.", "id": "Paper/71730", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71730"}, {"title": " Optimal Self-Assembly of Sunlet Graphs Using a Flexible DNA Tile Model ", "webprogram_exclude": "0", "session_ids": ["Session/18242"], "source_sha256": "24fe7e0fb9d0741af2f05a5dab6e93c4cf5195cd997e554bc13347f2ba9244a9", "withdrawn": "", "abstract": "Theoretical approaches to DNA nanostructure design can improve assembly efficiency by reducing the number of distinct molecular components required in laboratory implementations. The flexible tile model captures this problem through graph-theoretic representations of branched DNA junction molecules and their interactions. In this research, we focus on sunlet graphs as assembly targets and analyze their realization under varying assembly restrictions. We characterize the symmetries and structural features of these graphs and use these characterizations to derive bounds on tile and bond-edge requirements. Our findings add to the understanding of efficient DNA self-assembly and provide new examples illustrating the interplay between graph structure and molecular design constraints.", "id": "Paper/71731", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71731"}, {"title": " Mathematically Modeling How Secondary Habitats Impact Pacific Treefrog Population Persistence ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "be2204f10ac56a3b7103fdfcc91296a5c94d2b80b406b92d427f03affa5373ad", "withdrawn": "", "abstract": "Amphibian populations worldwide are declining, but the Pacific treefrog (PTF) remains common. We hypothesize that PTF persistence despite environmental stressors like drought and invasive species in the Santa Monica Mountains (SMM) is driven by their ability as generalist breeders. PTFs can breed opportunistically in various habitats, including streams, side pools, and refuge pools. SMM streams contain invasive red swamp crayfish, which prey on amphibian eggs and larvae. Connected side pools have reduced predation, while distant refuge pools are predator-free and shallower, meaning they may dry up before tadpoles metamorphose.\n\nWe create a discrete stage-structured mathematical model of PTF life cycle dynamics. This includes a patch model that allows adult frogs to move between streams, side pools, and refuge pools. We assume predation in the stream and side pools, while incorporating stochastic drying in refuge pools. Using numerical simulations and sensitivity analysis, our model predicts PTFs will only persist if they have access to breeding spaces with low predation risk, such as side pools and especially refuge pools. This informs the importance of conservation efforts to reduce invasive predators and maintain natural habitat for amphibians.", "id": "Paper/71733", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71733"}, {"title": " Facet-Maximizing Graphs of Symmetric Edge Polytopes ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "591378e226eda2e711c350cb95177f904bf8bdcc54a91c0cd306f1c1417e9850", "withdrawn": "", "abstract": "A symmetric edge polytope is a centrally symmetric polytope formed from a finite, simple graph by taking the convex hull of vectors corresponding to its edges. A common question about these kinds of polytopes is how their facets can be classified, and how certain properties of a graph will determine what its symmetric edge polytope will look like. Previous work on symmetric edge polytopes gives us theorems and methods for counting facets using certain functions and maximal bipartite subgraphs. With these tools, we make progress towards determining which graphs on a given number of vertices and edges will maximize the number of facets in their symmetric edge polytopes.", "id": "Paper/71737", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71737"}, {"title": " Dynamics of cascading failures in biological networks ", "webprogram_exclude": "0", "session_ids": ["Session/18242"], "source_sha256": "6c42c87467c58d2cc4bafe11b0718291e46224834d3574711bfd5f4897f614bc", "withdrawn": "", "abstract": "Gene correlation networks were constructed for three species under various physiological states: normal soybean versus soybean with root rot disease, yeast grown anaerobically versus aerobically, and human prostate cancer versus healthy individuals, based on their respective gene expression profiles. Investigation of these networks using a cascading failure model revealed significant differences in dynamic stabilities across the different states. Structural key genes contributing to these differences were identified, and their biological functions were annotated. These key genes may play a role in the development of root rot disease in soybeans. This research elucidates the relevant functional mechanisms underlying these changes and provides a valuable tool for understanding the mechanisms of various life processes.", "id": "Paper/71740", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71740"}, {"title": " A Recurrence-Based Summation Method for Ultra-Rapidly Diverging Series and Renormalon-Type Expansions ", "webprogram_exclude": "0", "session_ids": ["Session/18242"], "source_sha256": "557126837b1e4edeaf6dd0e3dbd8b8b9c61eae7999b6d959508e8a72ed663ad7", "withdrawn": "", "abstract": "Classical summation methods are often organized around fixed growth regimes: standard Borel summation treats Gevrey-1 series, while higher-order Gevrey behavior typically requires changing the kernel. We introduce a recurrence-based method, called $C$-summation, whose primary input is a first-order inhomogeneous recurrence rather than a prescribed growth class.\n\nSince the recurrence solution is determined only up to a homogeneous term, we pass to a normalized tail, where this ambiguity becomes an additive constant, and define the value by extracting a finite part. The selector is constructed through a Bromwich transform of the normalized tail differences.\n\nUnder a precise $\\mathcal M$-admissibility hypothesis, we prove independence from the chosen recurrence solution and invariance under different presentations of the same formal series, as well as regularity, homogeneity, and limited shift-stability. The method agrees with Borel-Laplace summation on a Borel-summable class, but also applies beyond the classical Borel setting: it sums examples growing faster than any power of the factorial, such as terms of order $e^{n^2/2}$, and assigns a principal-value Ecalle-Borel value to a non-Borel-summable renormalon-type series.", "id": "Paper/71747", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71747"}, {"title": " Modular Reconstruction of Graph Matchings Using Generalized Gaussian Integrals ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "e47da329daf5ea25672a502c1ac327e469ce4f4fcc381838afb5b415ea886fbc", "withdrawn": "", "abstract": "The matching polynomial of a graph tells us the number of ways to choose edges so that no two chosen edges share a vertex. In this project, we investigate whether these counts can be recovered using generalized Gaussian integrals and modular arithmetic. For a finite graph $G$, let $M_G(x)=\\sum_{k=0}^{d}m_k(G)x^k$, where $m_k(G)$ is the number of matchings with $k$ edges and $d=\\nu(G)$ is the maximum matching size. For a positive integer $q$ and a nonnegative integer $r$, we define $F_{q,r}(G)=\\int_0^\\infty x^rM_G(x)e^{-x^{1/q}}\\,dx$. Using a change of variables, we obtain $F_{q,r}(G)=q\\sum_{k=0}^{d}m_k(G)(q(r+k+1)-1)!$, expressing each integral as an integer involving factorials and matching counts. We then examine these values modulo a prime $p$ and use the divisibility of factorials to remove contributions from larger matchings one at a time. Our main result shows that when $p>q(d+1)$, setting $s=\\lfloor p/q\\rfloor-1$ gives a triangular system that can be used to recover all matching counts modulo $p$. Since the empty matching is already known, the remaining counts can be recovered from $d$ integral measurements with shifts $r=s-1,s-2,\\ldots,s-d$. If $p$ is also larger than every matching count, the exact coefficients of the matching polynomial can be recovered. We use path and cycle graphs to demonstrate the method and investigate how changing the Gaussian exponent affects the reconstruction process. We also consider whether certain graph families allow the same information to be recovered from fewer integral values. The results provide a way to recover discrete counting information from generalized Gaussian integrals using factorial identities and modular arithmetic.", "id": "Paper/71749", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71749"}, {"title": " Computational geometry on tangent planes to Veronese varieties ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "9f9c58de124d0bbefdb86cca0a289414775250e0bf53a6e0c33d5d4285c1b48e", "withdrawn": "", "abstract": "Given the Veronese map $v_d:\\mathbb{P}^n\\to\\mathbb{P}^{\\binom{n+d}{d} -1}$ and tangent planes $T_1,\\ldots,T_k$ to the image, we study the dimension of the vector space $[I_{T_1\\cup\\cdots\\cup T_k}]_r$ of degree-$r$ hypersurfaces containing their union. The dimension of this vector space can tell us useful information about how the tangent planes intersect. This can be used to determine whether a degree-$r$ hypersurface is unique. Using SageMath, we calculate dimension counts for various $(n,d,k,r)$.\nThese results motivate various conjectures revealing the relationship between the degree $d$ and ambient space $\\mathbb{P}^n$ of our Veronese map, and the conditions each additional tangent plane imposes. Moreover, We observe and explain many geometric phenomena using the dimension. For example, we observe stabilization cases in which, after sufficiently many tangent planes are added, additional tangent planes will impose no further independent conditions on degree $r$ hypersurfaces. For higher degrees $d$, the relationships and geometric phenomena become increasingly complex. We relate these results to many classical interpolation problems on $\\mathbb P^n$, including the Alexander--Hirschowitz theorem.", "id": "Paper/71750", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71750"}, {"title": " The Most Malicious Maître D’ ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "1fa7c1e62e23d207a566189c2294a9cd57fb69b7701fba8cabad4d57a0c330a1", "withdrawn": "", "abstract": "We present an optimal strategy for the malicious ma\\^{i}tre d’ problem, resolving a problem posed by Peter Winkler in 2004. Diners are seated around a circular table with one napkin between each pair of adjacent seats, and each diner independently prefers the napkin to the left with probability $p$ and the napkin to the right with probability $1-p$. When seated, a diner takes their preferred napkin if it is available and otherwise takes the other one, if available. The ma\\^{i}tre d’, an adaptive adversary who observes all previous choices, chooses where to seat each diner, with the goal of maximizing the expected number of diners who ultimately receive no napkin. We determine an optimal seating strategy for every fixed $p$ and compute its asymptotic performance. In particular, in the symmetric case corresponding to $p=0.5$, the expected proportion of napkinless diners approaches $3/16$ for large tables.", "id": "Paper/71754", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71754"}, {"title": " Effects of Misclassification on Power ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "50ea82f088ca2630d5e78a913dee9b0dadb9096c14a08206dab17b0a270aafdb", "withdrawn": "", "abstract": "Statistical power is fundamental in the practice of inferential statistics.  However, the effects of misclassification and contamination of samples remains largely misunderstood.  This project examines the effects that misclassification has on power, specifically examining the two-sample Z test, pooled t test, and Welch’s t test.  Monte Carlo simulations in R are used to estimate the observed power under conditions of misclassification, sample size imbalances, variance heterogeneity, and nonnormality.  The Monte Carlo powers are then compared with the calculated analytic power over a range of effect sizes.  Performance is evaluated using the average power, root mean squared error, and confidence intervals.  The findings of this project will identify conditions resulting in power loss or gain and clarify the robustness and limitations of commonly used two-sample procedures.  This would allow for practical guidance for selecting tests and planning studies when samples and labels are subject to error.", "id": "Paper/71767", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71767"}, {"title": " Combinatorial Formulas for the Weighted Ehrhart Series of Order Polytopes ", "webprogram_exclude": "0", "session_ids": ["Session/18242"], "source_sha256": "b1c17ca699a504323ce3200ef2490d40bd69b6981f9926854ebed77bf0b599a6", "withdrawn": "", "abstract": "For a poset $P$, its associated order polytope $\\mathcal{O}(P)$ is the polytope defined by the inequalities $0 \\leq x_{i} \\leq 1$ and $x_{i} \\leq x_{j}$ for $i\\prec_P j$. We derive a formula for the weighted Ehrhart series of $\\mathcal{O}(P)$, which encodes the weighted sum of integer points over integer dilates of $\\mathcal{O}(P)$, in terms of the linear extensions and descent statistics of $P$. Our work generalizes the work of Stanley in the unweighted case. We then derive an alternative but equivalent formulation for the weighted Ehrhart series using a stars-and-bars argument. This latter formula yields an algorithm, now implemented in SageMath, for computing the weighted Ehrhart series that is significantly faster than Normaliz's WeightedEhrhartSeries function on posets with large numbers of linear extensions.", "id": "Paper/71770", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71770"}, {"title": " Total Prime Labelings of Various Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "b80ffe31c4c4d0c6cd30b51ff1601b586681080a92398baa02e3b2845f2ca250", "withdrawn": "", "abstract": "A total prime labeling of a graph of order $n$ is an extension of a prime labeling in which we distinctly label the vertices and edges. The goal of the labeling is for adjacent vertex labels to be relatively prime, and for each vertex of degree at least two, the greatest common divisor of the labels on its incident edges is equal to 1. We construct total prime labelings by extending known prime and minimum coprime labelings and by developing new constructions for various classes of graphs.", "id": "Paper/71774", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71774"}, {"title": " Distinct Distances under Well-behaved Norms ", "webprogram_exclude": "0", "session_ids": ["Session/18242"], "source_sha256": "6565ccae96d8405fe39957f9ae0cf1640f46a090b7d190b6dce5a540b7c5dd7c", "withdrawn": "", "abstract": "Alon, Bucic, and Sauermann showed that, for almost any norm, the minimum number of distinct distances spanned by $n$ points in the plane is $n+o(n)$. Their result is nonconstructive, however, and the distinct distances problem remains poorly understood for most specific norms. We establish improved lower bounds on the number of distinct distances under several classes of norms. In particular, for $\\ell_p$ norms with non-integer $p>1$, we improve the best known lower bound from $\\Omega(n^{4/5})$ to $\\Omega(n^{5/6})$. We also obtain more general bounds for o-minimal norms and for certain classes of semi-algebraic norms.", "id": "Paper/71782", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71782"}, {"title": " Negligible cohomology of the cyclic group of order two with a non-trivial action on the coefficients ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "34a8b3e21e3203edfdbb7c4b472dcdd283f9e1fc6f5c955b448081022c11795a", "withdrawn": "", "abstract": "Let $G$ be a finite group that acts compatibly on an abelian group $M$.\nThe group cohomology of $G$ with $M$ coefficients is an algebraic tool that uses the $G$-action on $M$ to study properties of $G$ like central extensions.\nWe compute explicitly the cohomology of $\\mathbb{Z}/2\\mathbb{Z}$ acting trivially and non-trivially on cyclic or elementary abelian coefficient modules. The computations rely on analyzing automorphisms of the coefficient modules and classifying admissible actions.\n\nThe notion of negligible cohomology was introduced by Serre to study the relationship between group cohomology of finite groups and that of absolute Galois groups. Negligible cohomology has mostly been studied with a trivial $G$-action on the coefficient module $M$. Recently, however, negligible cohomology with a non-trivial action was used to answer an open question in number theory. We compute the negligible cohomology of $\\mathbb{Z}/2\\mathbb{Z}$ with cyclic or elementary abelian coefficients with any $\\mathbb{Z}/2\\mathbb{Z}$-action over any field. We rely on long exact sequences to relate the negligible cohomology associated with different coefficient modules.", "id": "Paper/71783", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71783"}, {"title": " Spectral Properties of Weighted Graphs Approximating the Basilica Fractal ", "webprogram_exclude": "0", "session_ids": ["Session/18242"], "source_sha256": "4ae75d383532ea74fb2fbd25c9f5b994b02a1064b4cfa3083534dc53c7c4942b", "withdrawn": "", "abstract": "The Basilica group, a self-similar automata group introduced in the early 2000s by Rostislav Grigorchuk and Andrzej Zuk, was the first example of an amenable but not subexponentially amenable group and remains significant in the study of group theory and complex dynamics. While investigating questions of amenability, Grigorchuk and Zuk became particularly interested in the Basilica group’s spectral properties; thus, they developed techniques to analyze the spectra of the graph Laplacians on the one-parameter family of weighted orbital Schreier graphs of the Basilica group. The existing literature on the Basilica group gives two approaches for characterizing the spectra of the weighted Schreier graphs: the first, Grigorchuk and Zuk’s original method, directly develops a two-dimensional dynamical system for the eigenvalues and edge weights through spectral decimation. The second provides a more macroscopic perspective by establishing a recursion on the characteristic polynomials of the Schreier graphs, taking advantage of their underlying self-similar structure in the process. However, the latter approach has only been applied to unweighted Schreier graphs. \n \nIn our research, we generalize the macroscopic approach for Schreier graphs with any finite, positive edge weight. We develop a recursive construction of the characteristic polynomials of the conformally invariant Laplacians on each weighted Schreier graph, and we find that this recursion is nearly identical to the recursion arising from the unweighted Laplacians previously studied. Additionally, we show the existence of a factorization of the characteristic polynomials corresponding to the homology of the Schreier graphs. We confirm that the microscopic and macroscopic approaches for characterizing the spectra of the weighted Schreier graphs yield consistent results. We show that the limiting behavior of the Laplacian spectra are also consistent for weighted and unweighted graphs: in both cases, the spectra accumulate on a Cantor set. Together, our results show that the spectral properties studied by Grigorchuk and Zuk arise from the homology and self-similar structure of the Schreier graphs of the Basilica group and are invariant for any finite, positive weight.", "id": "Paper/71787", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71787"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/17971"], "source_sha256": "b7d42b31eb289cf7c9d6c2e9f2153a025e7aac98f333831542680db119d7a6c0", "withdrawn": "", "abstract": "", "id": "Paper/71797", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71797"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/17971"], "source_sha256": "7b59ffc40a3cd80bb924c1de855520e07c81a69a3f1125186b252f9befecbbe7", "withdrawn": "", "abstract": "", "id": "Paper/71798", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71798"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/18250"], "source_sha256": "b4c9d1dde4761027e4396bad042f8435bb4a4c4399734b81dd1904b3ce2869a0", "withdrawn": "", "abstract": "", "id": "Paper/71801", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71801"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/18250"], "source_sha256": "c2c564f193c331adddfe314979973f438c140a84934e36cb3fe03f5822acecea", "withdrawn": "", "abstract": "", "id": "Paper/71802", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71802"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/18250"], "source_sha256": "ae826fd10de57fd29cd7c05851503f566e77a0cf6c121ecdb11d259d69352ee5", "withdrawn": "", "abstract": "", "id": "Paper/71803", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71803"}, {"title": "Introductory Remarks", "webprogram_exclude": "0", "session_ids": ["Session/18082"], "source_sha256": "1e95aa61560a54d69747024fc6c3d8a30f5431c17bdd85f4c02c9ebdf5ef7249", "withdrawn": "", "abstract": "", "id": "Paper/71890", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71890"}, {"title": "Introductory Remarks", "webprogram_exclude": "0", "session_ids": ["Session/18379"], "source_sha256": "64fdac8b03943b4f89772e4d4006e6b7e9817b25c2d63894c12ddb912e033b5a", "withdrawn": "", "abstract": "", "id": "Paper/71891", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71891"}, {"title": "Discussion", "webprogram_exclude": "0", "session_ids": ["Session/17963"], "source_sha256": "2fa8ad35a5e7bbfd6812d615a4966e0c92ed3a84ce7c7fb01b8ebaac05625c43", "withdrawn": "", "abstract": "", "id": "Paper/71988", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71988"}, {"title": "Discussion on Labeling Problems", "webprogram_exclude": "0", "session_ids": ["Session/17963"], "source_sha256": "c88b65bb1b536213e125dabfb8d2d6acf79a4e0ed36d76bae2fcf1240705c4ea", "withdrawn": "", "abstract": "", "id": "Paper/71989", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/71989"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/18113"], "source_sha256": "f76e03866c0e0742f81c2311de179adb5f04879028a9ae64a996ea6c0b240df8", "withdrawn": "", "abstract": "", "id": "Paper/72008", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72008"}, {"title": "Discussion", "webprogram_exclude": "0", "session_ids": ["Session/18113"], "source_sha256": "6b980a6234b7ddcdefd9ceef56e3e088835e7be8d1c4c83ad4357e37982daa0b", "withdrawn": "", "abstract": "", "id": "Paper/72009", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72009"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/18246"], "source_sha256": "7b3872ef3077a20cdedcbc9dae51364c7f906b924e4d9d0366f1348de518b1ae", "withdrawn": "", "abstract": "", "id": "Paper/72010", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72010"}, {"title": "Discussion", "webprogram_exclude": "0", "session_ids": ["Session/18246"], "source_sha256": "0edf22040289b910d898a96b9e0e7f6a8987cbc1066ec81e70fe6a3ce2e9451a", "withdrawn": "", "abstract": "", "id": "Paper/72011", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72011"}, {"title": "Discussion", "webprogram_exclude": "0", "session_ids": ["Session/18304"], "source_sha256": "0e36cd68acb74de59462d33254a33f19179a83cd90e1adc50a2e02e66c9dc6fe", "withdrawn": "", "abstract": "", "id": "Paper/72014", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72014"}, {"title": " A pair of Diophantine Equations and Fibonacci numbers ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "91972881d77f601376b17344fdbeca17349e84ce6e76aa4bfc07806fcff12a66", "withdrawn": "", "abstract": "For coprime integers $a$ and $b$, it is known that exactly one of the two Diophantine equations\n$$\nax+by\\ =\\ \\frac{(a-1)(b-1)}{2}\n\\qquad\\text{and}\\qquad\n1+ax+by\\ =\\ \\frac{(a-1)(b-1)}{2}\n$$\nadmits a nonnegative integer solution, and that this solution is unique. We first generalize this result by replacing the right-hand side with an arbitrary integer $m$ and its complement $ab-a-b-m$. This framework enables us to study the existence and uniqueness of nonnegative integer solutions to\n$$\nax+by\\ =\\ \\frac{(a-1)(b-1)}{k}\n\\qquad\\text{and}\\qquad\n1+ax+by\\ =\\ \\frac{(a-1)(b-1)}{k},\n$$\nwhere $k$ is a fixed positive integer. We then obtain explicit results when $a$ and $b$ are consecutive Fibonacci numbers. Finally, we examine the original pair of equations in several particular settings, including when $b\\equiv \\pm1\\mod a$, when $b$ is replaced by a higher power, and when the parameters are squared.", "id": "Paper/72031", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72031"}, {"title": " The Prime Wavelet Tree: Compressing Carmichael Numbers ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "34d9e8946dd6878aae98f34d84dfbd71b9750cb616f2655415e1d64f8dbbc7ba", "withdrawn": "", "abstract": "The recently completed tabulation of all $308{,}279{,}939$ Carmichael numbers less than $10^{24}$ occupies $18.4$ gigabytes as text.\nWe present two number-theoretic compression techniques.\nThe first is \\textit{local}, and compresses individual numbers.\nThe second is \\textit{global}, and compresses the entire set of numbers using a \\textit{prime wavelet tree}.\nWhen used in conjunction with other standard techniques in data compression, the resulting file is $739.9$ megabytes which is $24.8$ times smaller than the raw encoding.\nThe initial $80$-bit numbers now use about $19.2$ bits per number.", "id": "Paper/72037", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72037"}, {"title": " Competition Exclusion in Two-Strain Epidemiological Models ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "f062752ea463e58e91a7e5f6fdda465aade8e758750ffa2087d10fdc256eed2e", "withdrawn": "", "abstract": "Compartmental epidemiological modeling uses disease state compartments and systems of ODEs to track the movement of a population between stages of infection. The best-known such model is the Susceptible-Infectious-Recovered, or SIR model. A well-studied variation of this basic framework is the SEIR, which adds an Exposed category to account for the incubation time of a disease.  Here, we analyze a Susceptible-Low Density-High Density-Recovered or SLHR model. This model has the same structure as an SEIR model, but tracks the dynamics of bacterial populations within a host rather than symptomatic disease progression.\n\n\nWe further consider the context of multi-strain infections.  A single disease may have multiple different strains or variations infecting the population at one time; examples include COVID-19 and flu.  We propose a model of multi-strain bacterial infection here that accounts for the unique properties of bacterial communication and their effects on disease progression.  In particular, we estimate both progression rates and superinfection dynamics using experimentally determined quorum sensing signal molecule concentrations.\n\nWe hypothesize that if two strains reach endemic equilibrium when individually modeled, that they will reach a coexistence endemic equilibrium when coupled.  We then attempt to solve for this equilibrium point for multiple different SLHR multi-strain model configurations using Groebner basis methods on the dynamical system and excluding biologically infeasible solutions.  We conclude that no such coexistence equilibrium exists.  Instead, we see clear competitive exclusion behavior between bacterial serotypes, supported by mouse models of quorum sensing strain competition.  We then discuss the ramifications of this conclusion and address ways to reconcile apparently stable multi-strain case data with our coupled SLHR model that suggests that multi-strain coexistence is not possible in the long term.", "id": "Paper/72039", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72039"}, {"title": " Line Redundancy in Typical Kakeya-type Sets ", "webprogram_exclude": "0", "session_ids": ["Session/18242"], "source_sha256": "dbe1604eeaf768830c3087016afd34f96d7bf50a9de79340b3dfd7d82ace530f", "withdrawn": "", "abstract": "A Besicovitch set is a compact subset of \\(\\mathbb{R}^n\\) with a unit line segment in every direction. The Kakeya conjecture states that every Besicovitch set in \\(n\\)-dimensional space has Hausdorff dimension \\(n\\). We study Kakeya-type sets by coding them in a product space of sets with full projection using point-line duality. We then use the Baire category theorem to prove a variety of novel results concerning typical Kakeya-type sets and code sets. These results may one day contribute to a proof of the Kakeya conjecture as typical Besicovitch sets have minimal Hausdorff dimension. In this talk, I will present several results discovered in collaboration with Tamas Keleti and Josef Bell. These include showing that typical Besicovitch sets \\(A \\subset \\mathbb{R}^n\\) have no more than \\(n\\) lines in each direction and that the set of directions of a Besicovitch set which are \\(j\\)-times redundant typically has Hausdorff dimension \\(n-j\\). I will also show that typical Besicovitch sets are not sticky and that typical Besicovitch sets have Hausdorff dimension zero intersection with any fixed horizontal hyperplane. I will also give a few results concerning typical code sets, including that they are totally disconnected, purely unrectifiable, and that they are graphs of Peano-type curves.", "id": "Paper/72040", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72040"}, {"title": " Cross-Platform Fidelity Benchmarking: Mapping Lindblad Dynamics to Real Quantum Hardware ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "ff2b43f8cf7abcf54a3199f11c39218a9432804bc700345a932ca9a5c97c4f27", "withdrawn": "", "abstract": "This work develops a cross-platform framework for benchmarking quantum hardware by mapping experimentally observed device behavior to open-system dynamics described by the Lindblad master equation. We compare Lindblad-based simulations with executions on different quantum-computing platforms using metrics such as state fidelity, measurement distributions, and observable expectation values. The study examines how relaxation, dephasing, circuit depth, and gate composition affect agreement between theoretical noise models and real hardware. The resulting methodology provides a common, hardware-agnostic framework for comparing devices across different qubit technologies and evaluating the accuracy of simplified noise models.", "id": "Paper/72041", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72041"}, {"title": " Simulating Single Transferable Voting for the Colorado House of Representatives ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "73bc0829f8b1d31bf2568fa3ec00457cf8caa1d75f47a72fd5586c375b790315", "withdrawn": "", "abstract": "Social choice theory research demonstrates that single transferable voting (STV) results in more proportionally representative legislative bodies. We aim to understand how using multi-member districts and ranked ballots with STV would affect the representation of political parties in the Colorado House of Representatives. We investigated this objective by producing 10,000 multi-member districting plans of Colorado, generating ranked ballots for each of these plans using returns from the 2022 Colorado attorney general race, and simulating STV using these ballots. Our simulated STV elections for the Colorado House of Representatives gave more proportional representation for Democrats and Republicans than the current first-past-the-post system.", "id": "Paper/72044", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72044"}, {"title": " Data-Driven Discovery and Rigorous Certification of Periodic Solutions in Infinite Dimensional Dynamical Systems ", "webprogram_exclude": "0", "session_ids": ["Session/19351"], "source_sha256": "be495af71e40cac752aa10c75da63565d520ec2637fe147f2b0c3b3b4f87e392", "withdrawn": "", "abstract": "Predictive accuracy alone does not establish whether a surrogate model reproduces the dynamical structures of its source system. We present a framework for testing explicit surrogate ordinary differential equations through held-out prediction, long-time integration, and comparisons of stability, Lyapunov growth, attractor geometry, and invariant structures. An especially strong test is whether periodic-orbit candidates found in a surrogate can be transferred to the original equations and validated by computer-assisted proof.\nWe demonstrate this framework using dense polynomial surrogates fitted in delay or spatial coordinates without a learned latent transformation. For the Mackey–Glass delay equation and periodic-domain Kuramoto–Sivashinsky equation, the resulting surrogates tracked held-out trajectories over finite prediction horizons. A six-dimensional cubic Mackey–Glass surrogate remained bounded and showed numerical evidence of chaos in three independent integrations of 20,000 time units each. For Kuramoto–Sivashinsky with Neumann potential conditions, quadratic surrogates trained using exact spectral derivatives supported refinement through 60 spatial modes.\nIn both systems, surrogate-discovered periodic-orbit candidates were validated in the original equations without Newton corrections. Computer-assisted proofs established true periodic orbits within distances of 6.00 × 10⁻⁴ and 1.00 × 10⁻⁵, respectively, in the Fourier norms and scalings of the individual proofs. This step rigorously certifies the existence of nearby periodic orbits in the source systems. Together, the examples demonstrate a method for assessing surrogate models beyond forecasting and testing whether their invariant structures correspond to solutions of the original equations.", "id": "Paper/72047", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72047"}, {"title": " Underclosed Posets ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "1e2261012c28234afd495113f2f023c5144dacfdb9fda2f21476dac6b04af887", "withdrawn": "", "abstract": "Interval graphs are well-studied graphs in which data are represented as individual points with edges drawn between related or conflicting points. They are therefore widely applicable for analyzing how phenomena interact, often used in optimizing scheduling, mapping DNA, or concurrency. However, interval graphs are limited to visualizing only straightforward, pairwise conflicts. Meanwhile, their higher-dimensional analogues, simplicial complexes, are capable of capturing more complex interactions between multiple pieces of data simultaneously. We build on previous work by Goeckner, Dochtermann, and Pavelka by studying underclosed simplicial complexes, originally introduced by Benedetti, Seccia, and Varbaro. Our research represents underclosed simplicial complexes with partially ordered sets through their order ideals, which we refer to as underclosed posets. In particular, we focus on specific underclosed posets generated by what we define as “one-gap” element, which act as our posets’ maximal elements. We prove our conjecture by using a bijective, dual function that can be applied to such underclosed posets, and imply that their order ideals are self-dual and rank-symmetric. We further represent these relationships between elements within the same partially ordered set algebraically with integer partitions corresponding to their dual structures and their respective maximal element. Ultimately, our results reveal restrictions derived by underclosed simplicial complexes can induce other symmetries and structure.", "id": "Paper/72048", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72048"}, {"title": "Discussion", "webprogram_exclude": "0", "session_ids": ["Session/18024"], "source_sha256": "9c004432260a68384e83ab33b059877476d45152b5f85bfdd1333d6855e8080f", "withdrawn": "", "abstract": "", "id": "Paper/72052", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72052"}, {"title": "Discussion", "webprogram_exclude": "0", "session_ids": ["Session/18323"], "source_sha256": "076e92ef57ecec6738b5190eba5f97bfa8d3e6d21b267906ae2a67ca216edefe", "withdrawn": "", "abstract": "", "id": "Paper/72056", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72056"}, {"title": " Non-Euclidean Planimeters ", "webprogram_exclude": "0", "session_ids": ["Session/18242"], "source_sha256": "c0dc0d2ba101b67bf89cc0f5b5ada9844332f08c799f8aca2f70a9b5e51d4084", "withdrawn": "", "abstract": "A planimeter is a drafting tool that measures the area of irregular planar regions by tracing the boundary. In the Euclidean plane, Green's Theorem provides the rationale for how a planimeter operates. We generalize the mathematical model of the planimeter to Riemannian surfaces and show that it successfully computes area on the sphere and the hyperbolic plane. Additionally, we provide an example of a surface on which the planimeter fails to compute area.", "id": "Paper/72061", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72061"}, {"title": " From ReLU Neural Networks to Clocks: A Combinatorial Journey ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "7ad538dfcd33dba408f1906e251ed3afb7052d9077dea15a5f75a83f7ddd7d2f", "withdrawn": "", "abstract": "A ReLU fan associated with a bias-free feedforward ReLU neural network partitions the input space into linear regions, each labeled by an activation pattern recording which neurons are active. We study the combinatorics of these patterns for shallow networks of architecture $(2,n,n_1)$ whose hidden layer hyperplanes are $n$ distinct lines through the origin, cutting $\\mathbb{R}^2$ into $2n$ linear regions. Two parameters are considered equivalent when their sets of activation patterns are the same up to a global permutation of the entries, and we ask how many equivalence classes arise.\n\nWe encode each oriented arrangement as a \\emph{clock}: a regular $2n$-gon whose vertices correspond to the rays of the arrangement and carry signs $\\pm$ recording the active side of each line, with antipodal vertices carrying opposite signs. There are $2^n$ such clocks. Using an adjacency lemma (two regions are neighbors exactly when their patterns differ in one coordinate), we prove that two clocks yield equivalent pattern sets if and only if they lie in the same orbit of the dihedral group $D_{2n}$ of order $4n$. Thus, the classification of activation-pattern sets reduces to counting dihedral orbits of clocks. Applying Burnside's Lemma, we obtain\n$$N(n)=\\frac{1}{|D_{2n}|}\\sum_{g\\in D_{2n}}|X^g|=\\frac{1}{4n}\\left(\\sum_{k=0}^{2n-1}\\begin{cases}2^{\\gcd(2n,k)/2}, & \\gcd(2n,k)\\nmid n,\\\\ 0, & \\gcd(2n,k)\\mid n,\\end{cases}\\;+\\;n\\,2^{\\lceil n/2\\rceil}\\right).$$\nThis gives $N(n)=1,1,2,2,4,5,9,12,\\ldots$ for $n=1,2,3,\\ldots$.", "id": "Paper/72062", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72062"}, {"title": " Extreme Instances of the Committee Size Paradox ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "ef4305fa63296f5a94c7b4f01c114b78f24cd3d3081465936fba30da67240660", "withdrawn": "", "abstract": "Imagine that several candidates are running for three available seats on a city council. A committee size paradox occurs if a candidate elected when three seats are available would fail to be elected if the number of seats were increased. The research investigates how extreme such paradoxes can be under the single transferable vote (STV), a widely used voting method for multi-winner elections. We show that for an arbitrary number of candidates, there exist elections in which the unique winner in a single-seat contest is excluded from the winning set as the number of seats increases to two, three, and so on, up to one fewer than the total number of candidates. More generally, we demonstrate that STV can exhibit highly counterintuitive non-monotonic behavior with respect to committee size, while also identifying limits on the severity of these paradoxes.", "id": "Paper/72063", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72063"}, {"title": " The Effects of an Allee Effect and Predator Competition on the Paradox of Enrichment ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "c30ce491bd676e5493179620b78463995dacaed6aa7d71cb87b04460976a6c90", "withdrawn": "", "abstract": "This project investigates the Paradox of Enrichment in predator-prey systems. In classical predator-prey models, increasing the prey's carrying capacity can increase the amplitude of population oscillations, causing predator or prey populations to reach very low population densities and become vulnerable to extinction. To study whether this effect can be reduced, the model is extended to include a strong Allee effect in the prey population and predator-specific competition. Equilibrium points and their local stability will be analyzed using linearization, Jacobian matrices, and eigenvalues. Numerical simulations will also be conducted using MATLAB. The goal is to determine whether these additional ecological mechanisms can prevent population oscillations from approaching zero and therefore reduce the effects of the Paradox of Enrichment.", "id": "Paper/72064", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72064"}, {"title": " <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"92.041ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 39628.5 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbf {\\text {Computational Modeling of Amyloid Formation Dynamics in Coacervate Phases}}</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAINB-43\" d=\"M64 343Q64 502 174 599T468 697Q502 697 533 691T586 674T623 655T647 639T657 632L694 663Q703 670 711 677T723 687T730 692T735 695T740 696T746 697Q759 697 762 692T766 668V627V489V449Q766 428 762 424T742 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xlink:href=\"#E1-MJMAINB-61\" x=\"37632\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAINB-73\" x=\"38192\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAINB-65\" x=\"38646\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAINB-73\" x=\"39174\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18238"], "source_sha256": "74c4a3e85cfdeadd201a147d13dc6fdefd2c04812fb41dd980f85249f1eb82e2", "withdrawn": "", "abstract": "Coacervates concentrate reactants and limit diffusive loss, enabling the study of amyloid aggregation relevant to neurodegenerative disease and bionanomaterials research. We present computational analyses of two such systems using a Nile Red fluorescence assay to track aggregation. In System 1, a fixed dimer concentration was tested across varying concentrations of THPP, a model compound for GSH, an antioxidant released by cancer cells. An initial decrease in signal was followed by a sigmoidal overshoot, which was interpreted as dimer decay into monomers followed by autocatalytic aggregation into a third species. In System 2, varying monomer concentrations produced near-sigmoidal growth with a transient pre-equilibrium peak, consistent with autocatalytic aggregation into multiple interacting species.\n\nSystem 1 data were baseline-corrected and scaled to the initial signal. System 2 data excluded unsaturated replicate groups and initial points affected by mixing artifacts. We developed chemical reaction networks (CRNs) capturing decay, nucleation, and aggregation, then derived ordinary differential equation (ODE) models to infer relative species concentrations and fluorescence coefficients from the combined signal. Dynamical-systems and inverse-problem analyses constrained CRN structures and model parameters, guiding model fitting and mechanistic interpretation.\n\nParameters were iteratively optimized and evaluated using residual, sensitivity, identifiability, and visual analyses. To avoid numerical instability and spurious convergence, we left the data unscaled, fitted the highest-signal trials first, and initialized subsequent fits using the closest optimized solution. Models were evaluated using goodness-of-fit metrics, uncertainty quantification, and solver-convergence tests. Preliminary results identify best-fit models for both systems and suggest that aggregation consistently outpaces nucleation. This framework integrates CRN-based ODE modeling, mathematical analyses, and experimental parameterization to relate observed kinetics to the mechanisms of amyloid formation in multiphasic condensates.", "id": "Paper/72065", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72065"}, {"title": " Efficient Path Continuation for PDE-Constrained Inverse Problems ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "d9ddaa937cfb7a6206ae0d2db0281cec6d6f3c3aa6f63b5ff02a70b96b179075", "withdrawn": "", "abstract": "Inverse problems work backwards: given a mathematical model and state data, we aim to reconstruct structure in the model that is not directly observable. We consider physical systems constrained by partial differential equations (PDEs) that include uncertain {\\em auxiliary parameters}. The standard approach involves solving the inverse problem independently at each perturbation of the auxiliary parameters. However, this strategy is computationally expensive since it ignores previous computations, and it becomes prohibitively so in the case of multiple perturbations due to the increasing number of required PDE solves. We develop efficient methods for solving inverse problems under multiple perturbations of the auxiliary parameters. We employ a predictor--corrector framework with pseudo-time continuation, which uses sensitivity information to continuously track the solution across the auxiliary parameter space. We combine pseudo-time continuation with a minimum spanning tree (MST) over the sample of perturbations. Numerical experiments indicate that this method reduces the number of PDE solves by up to a factor of three compared to the standard approach.", "id": "Paper/72067", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72067"}, {"title": " Higher-Order Singularities In Vec-Varieties ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "1bd60addec08e92319dbf825a0c51e25cf913767bbb878fc42fb5ccb8156c0fd", "withdrawn": "", "abstract": "A $\\mathbf{Vec}$-variety is a functor from the category of finite-dimensional vector spaces over a field $K$ to the category of affine algebraic $K$-varieties. Many varieties arising in the geometry of tensors, such as those of 2-tensors of rank at most $d$ as well as secants of Segre-Veronese varieties, naturally fit into this framework. In 2024, Chiu, Danelon, and Draisma showed that the singular locus of a $\\mathbf{Vec}$-variety behaves as a closed $\\mathbf{Vec}$-subvariety. We build on this work to study higher-order singularities for $\\mathbf{Vec}$-varieties in the case where $K$ is an algebraically closed field of characteristic 0. We show that, for every $m \\geq 1$, the closure of the locus of points of embedding codimension at least $m$ can be described by a closed $\\mathbf{Vec}$-subvariety. We use these loci to characterize the core of an irreducible $\\mathbf{Vec}$-variety--an important notion in the study of singularities for $\\mathbf{GL}$-varieties recently introduced by Chiu, Danelon, and Snowden--and further give a sufficient condition under which the core coincides with the singular locus. Finally, we initiate the study of higher-order singularity loci, defined by the vanishing of higher-order derivatives, and prove that these loci likewise behave uniformly as closed $\\mathbf{Vec}$-subvarieties.", "id": "Paper/72071", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72071"}, {"title": " A new method for enumerating metered parking functions ", "webprogram_exclude": "0", "session_ids": ["Session/18159"], "source_sha256": "8a4fcb83bc644dcee6562c9114ce80348932f88fb1d616134f1c86361509ef0d", "withdrawn": "", "abstract": "Parking Functions have been an active area of combinatorics research since the 1990’s. Daughtery, Harris, Klein, and McClinton introduced a variant called Metered Parking Function. Imagine a car on a one way street that is looking to park. That car has a preferred spot which it will park in if available, and if that spot is unavailable then it will\nlook at the spots after its preferred spot and park in the next available spot. The spot has a meter and after a given time, defined as t, the car leaves that spot. So, a tuple of preferences is a t-metered parking function if all cars are able to park. We will introduce a new way to\ncount metered parking functions.", "id": "Paper/72074", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72074"}, {"title": " Weakly Decreasing Metered Parking Functions and the Fibonacci Numbers ", "webprogram_exclude": "0", "session_ids": ["Session/18242"], "source_sha256": "4d26f2afa208367e71a5f64878071d5e6f5b9b91a71157e2b04d57dc3d4f47ea", "withdrawn": "", "abstract": "Parking functions have been a topic of much debate in the world of combinatorics for the past 30 years. Recently in 2024 Daughery, Harris, Klein and McClinton, introduced a variation on the classical Parking Function by adding a ``meter\" to each spot. Similar to real life, this only allows a car to park for a designated amount of time. In this talk we demonstrate that a particular subset of weakly decreasing metered parking functions are counted by the Fibonacci numbers. We do this by showing they are in bijection with weakly increasing unit Fubini rankings.", "id": "Paper/72076", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72076"}, {"title": " Permutation Invariant Metered Parking Functions ", "webprogram_exclude": "0", "session_ids": ["Session/18242"], "source_sha256": "e93a4ea9ac1412ee2838dd72bbf15121cc4354a63a3e7902541f4020618ef770", "withdrawn": "", "abstract": "Classical parking functions have been a robust area of combinatorial interest for\nthe last 30 years. In classical parking functions cars check the street for their preferred\nparking spot and, if it is occupied, continue to the next available spot. If all m cars are able\nto park in n spots, the tuple of their preferences is a valid m-n parking function. Recently,\nSpencer Daugherty, Pamela E. Harris, Ian Klein, and Matt McClinton introduced metered\nparking functions. For metered parking functions the cars stay parked for a set amount\nof time before leaving. This permits multiple cars to be able to park in the same spot,\nand allows more tuples to qualify as valid meter parking functions. In this talk we will\ndiscuss the subset of metered parking functions that are permutation invariant, and their\nconnections to classical parking functions.", "id": "Paper/72077", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72077"}, {"title": " Finite products in shrinking targets ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "882ff9e5ae4e42698c22b8f0559b9acdbe54b2a4cd3eccbce78ccc52fe0fcbd4", "withdrawn": "", "abstract": "Motivated by work of Byszewski and Konieczny on sparse generalized-polynomial sets, we study whether polynomial shrinking-target sets can contain highly structured multiplicative configurations. Let $\\mathcal A=(a_k)_{k\\geq1}$ be a sequence of pairwise-coprime integers, and let\n\\[\n\\operatorname{FP}(\\mathcal A)\n=\n\\left\\{\\prod_{i\\in I}a_i:\n\\varnothing\\ne I\\subset\\mathbb N,\\ |I|<\\infty\\right\\}\n\\]\ndenote its finite-product set. We prove that, for every $c>0$, if\n\\[\n\\log a_{k+1}=o\\!\\left(\\log(a_1\\cdots a_k)\\right),\n\\]\nthen $\\operatorname{FP}(\\mathcal A)$ is not contained in\n\\[\n\\{n\\geq1:0<\\|Q(n)\\|<n^{-c}\\}\r\n\\]\r\nfor any real polynomial $Q$ with an irrational coefficient. The proof begins with monomial phases. Assuming that every finite product lies in the shrinking target, we compare products obtained by omitting one generator at a time. Pairwise coprimality then forces strong divisibility in the resulting integer approximations, producing rational approximations to the irrational coefficient that are too close to be distinct. A dilation argument reduces the general polynomial case to the monomial case. We also obtain consequences for simultaneous monomial targets and sparse generalized-polynomial targets, and construct a superlacunary example showing that some growth restriction is necessary.", "id": "Paper/72081", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72081"}, {"title": " Closed Alternating Braid Links and <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"4.626ex\" height=\"2.843ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -934.9 1991.9 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbb {Q}B^4</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJAMS-51\" d=\"M480 -10Q480 -13 486 -24T507 -50T541 -80T588 -104T648 -114Q666 -114 688 -110T714 -106Q724 -106 728 -114T729 -130Q723 -145 663 -163T548 -181Q503 -181 463 -169T395 -139T343 -97T307 -56T284 -19L280 -3L262 1Q188 24 131 81Q57 155 37 275Q34 292 34 342T37 410Q58 528 131 601Q179 652 248 676T388 701Q485 701 562 661Q698 595 731 448Q742 410 742 341T731 235Q707 141 646 81Q616 50 575 27T493 -5L480 -10ZM568 342Q568 613 437 659L395 666Q329 666 286 626Q232 570 213 439Q210 408 210 342T213 246Q231 113 286 57Q309 37 342 23Q357 19 389 19Q420 19 437 23Q469 38 491 57Q568 134 568 342ZM174 341V354Q174 393 175 419T183 484T205 561T246 635L249 639Q246 639 224 627T193 608Q189 606 183 601T169 589T155 577Q69 491 69 344Q69 133 231 52Q247 42 247 46Q247 46 246 48Q231 69 222 85T200 141T177 239Q174 269 174 341ZM708 341Q708 410 689 467T640 556T588 606T546 630Q532 638 531 638Q530 638 531 635Q563 590 577 543Q602 472 602 341V316Q602 264 599 230T580 144T531 48Q529 44 532 45T546 52Q575 68 596 84T642 128T683 200T706 299Q708 327 708 341ZM391 -17H333Q329 -15 326 -15Q324 -15 324 -17Q324 -21 362 -68Q424 -130 506 -143Q518 -144 544 -144Q569 -144 577 -143L589 -141L575 -139Q544 -127 509 -101T453 -37L442 -19L391 -17Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-42\" d=\"M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJAMS-51\" x=\"0\" y=\"0\"></use>\n<g transform=\"translate(778,0)\">\n <use xlink:href=\"#E1-MJMATHI-42\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-34\" x=\"1074\" y=\"513\"></use>\n</g>\n</g>\n</svg>s ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "0493c64ed1d0759cbb658b2648d1b3725a25945b554d7c0dd3670ce80d4981ca", "withdrawn": "", "abstract": "A well-known problem in low-dimensional topology is deciding which rational homology 3-spheres (\\( \\mathbb{Q}S^3 \\)) bound rational homology 4-balls (\\( \\mathbb{Q}B^4 \\)).\nBecause every 3-manifold can be realized as a double cover of $S^3$ branched along a link $L\\subset S^3$, and every link can be realized as the closure of a braid, we can reformulate the question as: which braid closures admit double branched covers bounding $\\mathbb{Q}B^4s$?\n\nThis question has been completely resolved for alternating 3-braid closures, but not for general \\(m\\)-stranded families. We tackle the specific problem of classifying which of the \\(L_{m,n}\\) family of weaving links admit double branched covers bounding \\(\\mathbb{Q}B^4\\)s, using both obstructive linear algebraic methods and constructions via involutions on Dehn surgery diagrams.", "id": "Paper/72082", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72082"}, {"title": " Polynomial Surrogate Modeling for Computer-Assisted Proofs of Periodic Dynamics in Delay and Partial Differential Equations ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "d131b9c346afa638f0bfb9af06e5588235addb9bfa88d6fe75e9d9611e2df2f7", "withdrawn": "", "abstract": "Data-driven surrogate models can reproduce short-term trajectories of complex dynamical systems without necessarily preserving their invariant structures. We investigate whether periodic solutions discovered from finite-dimensional polynomial surrogates can instead be transferred to and rigorously certified in the original infinite-dimensional equations. Our approach uses explicit polynomial models fitted directly in prescribed delay or spatial coordinates, avoiding learned latent transformations, and combines numerical surrogate analysis with computer-assisted proofs.\nWe study the Mackey–Glass delay equation and the Kuramoto–Sivashinsky equation as representative infinite-dimensional systems. For Mackey–Glass, a six-dimensional cubic surrogate provides useful finite-time predictions and remains within prescribed numerical bounds during three independent 20,000-time-unit integrations. Separate polynomial fits are used to construct a periodic-orbit candidate. For Kuramoto–Sivashinsky, quadratic surrogates trained using exact spectral derivatives support periodic-orbit construction and refinement through 60 spatial modes.\nThe resulting periodic-orbit candidates are transferred unchanged to the source equations and validated without Newton corrections. Computer-assisted proofs, including control of the omitted modes, establish nearby nonstationary periodic solutions within radii of $6.00\\times10^{-4}$ for Mackey–Glass and $1.00\\times10^{-5}$ for Kuramoto–Sivashinsky in the respective norms and scalings. These results demonstrate that finite-dimensional polynomial surrogates can serve not only as predictive models but also as computational tools for locating invariant structures that can subsequently be rigorously certified in their infinite-dimensional source systems.", "id": "Paper/72084", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72084"}, {"title": " Mathematically Modeling the Impact of Phenotypic Plasticity On Pacific Treefrog Population Resilience Under Drought Stress ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "1e0c8da5080088ed24ec10c909cfd33bcf176b79337bb8b6791f3c6712fdd48a", "withdrawn": "", "abstract": "Amphibian populations around the world are declining due to drought and other stressors; however, Pacific treefrogs remain common in the Santa Monica Mountains. We aim to understand whether phenotypic plasticity in Pacific treefrogs enables their population to be resilient under drought stress. We develop a discrete stage-structured mathematical model of the treefrog life cycle. We model drought stress by reducing survivorship and decreasing breeding space, and we model plasticity by increasing the tadpole transition probability and varying body size (which alters fecundity). Numerical simulations suggest that treefrog populations are not at major risk of extinction in simulated drought conditions with or without plasticity. We predict that plasticity enables treefrog population persistence under conditions that cause extinction in the model without plasticity. Plasticity in developmental speed is most beneficial when stream drying threatens aquatic stages. However, plasticity has drawbacks; our model predicts that if plasticity delays maturation or reduces overall fecundity, population extinction may occur. By simulating the impact of features like phenotypic plasticity on population resilience, we learn when species are at greatest risk of decline and need protection.", "id": "Paper/72090", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72090"}, {"title": " When Initiative Changes Hands: A State Analysis of Priority Conversion and Recovery in Elite Sabre ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "e9b3e232130d048d4acdf55bef3588bf74e31f4c010030eeb493e5aaf48bff1f", "withdrawn": "", "abstract": "This preliminary report develops an empirical finite-state model of how tactical initiative is converted, lost, and recovered in elite sabre. We analyzed 111 touches from five elite direct-elimination bouts. Each scored touch with known initial priority was represented as a sequence tracking whether priority belonged to the initial holder or the opponent, ending in an absorbing scoring state. Of 106 eligible touches, the initial priority holder scored 76 (71.7\\%; Wilson 95\\% CI 62.5\\%-79.4\\%). Seventy touches converted before any recorded priority loss (66.0\\%; 56.6\\%-74.4\\%), accounting for 70 of the 76 initial-holder wins. Once priority was lost, the initial holder ultimately scored in only 6 of 26 touches (23.1\\%; 11.0\\%-42.1\\%). Conversion was also lower while trailing (31/50, 62.0\\%) than while tied or ahead (39/56, 69.6\\%); the 7.6-point difference remained negative in every leave-one-bout-out analysis but was uncertain (bout-stratified touch bootstrap 95\\% interval -25.7 to 10.4). This state-transition framework distinguishes direct conversion from recovery and turns tactical initiative into measurable sequence outcomes. A larger stratified sample can test whether score pressure changes transition probabilities.", "id": "Paper/72091", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72091"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/18219"], "source_sha256": "267c91b8f8e5000969a71de02038f28b67528eda824a5aa147d80aaa31d973ce", "withdrawn": "", "abstract": "", "id": "Paper/72094", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72094"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/17996"], "source_sha256": "0ccc4b43805e43e0bccf57384e65a0a5eb68212ca51962f7ee49e1c8d2299a93", "withdrawn": "", "abstract": "", "id": "Paper/72095", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72095"}, {"title": " Material Symmetry Detection in Experimental Elasticity Tensors with Correlated Noise \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/18242"], "source_sha256": "7e82ed8b47ce3a7f28fc79c04f9c6a187b1de971e04c9e7a21f288b144aea3a6", "withdrawn": "", "abstract": "Determining the symmetry class of an elasticity tensor is important for understanding material properties. However, reliable classification remains difficult due to random measurement error, which can cause an experimentally measured tensor to deviate from an ideal tensor possessing exact material symmetries. In this research, using only fundamental linear algebra and tensor analysis, we developed a hypothesis test framework for assessing whether an experimentally measured elasticity tensor belongs to or is near a specified symmetry class. Our approach generalizes previous models by accommodating correlated random measurement errors, offering a broader and more realistic noise structure. The framework was validated through numerical simulations based on realistic elasticity tensors. Our simulations and statistical power analysis demonstrate that the accompanying hypothesis test algorithm can accurately identify the correct symmetry class across multiple noise levels. Additionally, our results suggest that under realistic noise conditions, $80\\%$ power can often be achieved with a sample size of three or fewer measurements.", "id": "Paper/72097", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72097"}, {"title": " A multiple variabled elliptic system with cooperation terms ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "b794b49a7a36f7c9bb0b19291488b0fe9bf9da694e85ada8b95d51b5daa66147", "withdrawn": "", "abstract": "Multiple species of animals may reside together through cooperation in the same environment. Under what conditions can they coexist peacefully? Or under what conditions does either one of the two species become extinct, that is, either one of the two species excluded by the other? It is natural to say that they can coexist peacefully if their reproduction rates and self-limitation rates are relatively larger than those of competition rates with each other. In other words, they can survive if they interact strongly among themselves and weakly with other species. We investigate this phenomenon through a mathematical point of view by modeling a system of Partial Differential Equations.", "id": "Paper/72098", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72098"}, {"title": " Counting 8-Arcs in 3D Projective Space ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "fcd7759b5256014ddac036ef9abd4e588dec10a9daf4ae59de0257ac112c92f3", "withdrawn": "", "abstract": "An $n$-arc in projective space $\\mathrm{PG}(k,q)$ over the finite field\n$\\mathbb{F}_q$ is a set of $n$ points such that no $k+1$ points lie on a common hyperplane. These are equivalent to MDS codes in coding theory. Counting $n$-arcs by brute force means checking every $n$-subset of points against every hyperplane; for $n = 7$, this means checking 34 billion cases.\n\nIn 1988, David Glynn produced an algorithm that reduces the problem of\ncounting $n$-arcs in $\\mathrm{PG}(2,q)$ ($n$ points, no 3 collinear) to\ncounting the number of strong realizations of superfigurations,\n$A_s(3,q)$, which are highly connected, irreducible linear spaces. A\nstrong realization of a superfiguration is an injective mapping of its\npoints into $\\mathrm{PG}(2,q)$ so that all incidence relations are\nexactly preserved. Finding $A_s(3,q)$ is often not a polynomial in $q$,\nthus making these counts intricate.\n\nIn 2022, Kelly Isham generalized this algorithm to work in\n$\\mathrm{PG}(3,q)$, where we now consider hyperfigurations (the 3D\nanalogue of superfigurations)---highly connected irreducible planar\nspaces. This leaves us with the formula\n$C_{n,4}(q) = p(q) + \\sum_{h} p_h(q) A_h(4,q),$\nwhich expresses the count of $n$-arcs, $C_{n,4}(q)$, as a polynomial\n$p(q)$ plus the sum of terms contributed by each hyperfiguration's\nstrong realization count $A_h(4,q)$ multiplied by a coefficient of\ninfluence $p_h(q)$. Her paper gives counts for $n$-arcs up to $n = 7$.\n\nIn our project, we extend this work to $n=8$, where we run into a combinatorial explosion leaving us with 235 hyperfigurations, compared to just 6 for $n=7$, each needing its own strong realization count. We developed two methods using Sage to computationally make these counts feasible while cross-referencing our results to ensure accuracy. Many of these counts proved to be algebraically intricate, including many quasipolynomial formulas depending on q divisible by 2 or 3. Combining these terms with the Glynn-Isham algorithm produces the formula for $C_{8,4}(q)$, and thus also for MDS codes of the same dimensions.", "id": "Paper/72102", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72102"}, {"title": " Fourier regression and clustering of migratory patterns of humpback whales sighted off Guatemala ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "68dd16b5b807da1295ffde855ae047431a539222c44c2baea3b7a0d79218c729", "withdrawn": "", "abstract": "Northern Pacific humpback whales (\\textit{Megaptera novaeangliae}) embark on annual migrations between northern feeding grounds (California through Alaska) during the summer season to southern breeding areas (Central America) during the winter season. Our knowledge of their migratory patterns is limited by the sporadic and opportunistic nature of individual whale observations. We analyzed the migratory dynamics of whales sighted off the coast of Guatemala, using a dataset that spans 39 years and includes 5117 observations of 229 individual whales. We modeled the trajectories of individual whales using Fourier regression, and grouped these trajectories into clusters using Ward’s algorithm. Our analysis identifies three primary clusters of migratory patterns, distinguished by the locations of their feeding and breeding grounds and by the timing of migration between them. Analysis of residuals between observed versus modeled locations reveals anomalies in migratory patterns during the 2014-2016 Pacific Marine Heatwave. This research may help address conservation efforts, including the identification of critical habitats and the assessment of the impact of climate change on migratory populations.", "id": "Paper/72104", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72104"}, {"title": "Discussion: Considering the Value and Impact of SoTL in Promotion, Tenure and Faculty Evaluations", "webprogram_exclude": "0", "session_ids": ["Session/18341"], "source_sha256": "cad36842f31f688851328e44670ccb570f21a6633dd7d20e210aed949bf20b75", "withdrawn": "", "abstract": "", "id": "Paper/72106", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72106"}, {"title": " Adaptive Model Reduction for Defect Modes in Mass-Spring Lattices ", "webprogram_exclude": "0", "session_ids": ["Session/18242"], "source_sha256": "225733d84be3225d28ceec22c690c4554e3663b624089e25e4dfab306921d9f6", "withdrawn": "", "abstract": "We study reduced models of a mass-spring lattice that is periodic except for a local stiffness defect. Its vibration modes satisfy a generalized eigenvalue problem that depends on the defect stiffness. Using Rayleigh-Ritz projection, we compare a basis constructed at predetermined defect strengths with a basis constructed at strengths determined adaptively using residual indicators. We analyze whether these models reproduce defect-mode frequencies and spatial localization as the defect eigenvalue approaches neighboring eigenvalues. Spectral perturbation estimates are used to assess how eigenvalue separation affects the indicators’ reliability. We evaluate both methods against the full model at defect strengths excluded from basis construction, measuring frequency errors, reconstructed mode shape accuracy, and localization near the defect measured by the fraction of modal kinetic energy within a fixed distance of the defect. At a fixed reduced dimension, adaptive construction reproduces defect-mode localization with a smaller error than predetermined construction. The greatest improvement occurs when the defect eigenvalue and the neighboring eigenvalues are close to each other.", "id": "Paper/72108", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72108"}, {"title": "Discussion", "webprogram_exclude": "0", "session_ids": ["Session/17853"], "source_sha256": "0df7c299049e40fbc8da52780a2464587d3aeaceed1c5415eabf8ff8b8f77b8b", "withdrawn": "", "abstract": "", "id": "Paper/72111", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72111"}, {"title": " Modeling the Effects of Pathological Tau on Neuronal Voltage Dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "3660047c2033370db1522291bc0b19f7a93d083e99884077ce9d78facaac1703", "withdrawn": "", "abstract": "The progression of neuro-degenerative diseases is linked to the concentration of tau protein in the brain. In high concentrations, tau can mutate to form clusters called oligomeric tau(oTau). This oTau is thought to be toxic to neurons, and studies have shown that varying amounts of oTau injected into neurons alters action potential dynamics and sub-threshold electrophysiological properties. To understand possible mechanisms for these changes, we use an extended Hodgkin-Huxley single compartment model to replicate action potentials of CA1 pyramidal neurons in the absence and presence of oTau. Through both hand-tuning of parameters and parameter estimation programs, for this model we found that most documented changes from oTau exposure are best linked to a significant decrease in sodium reversal potential, a moderate increase in potassium equilibrium potential, and a moderate decrease in the conductance of the calcium and voltage dependent potassium channel. At the same time, these parameter changes led to a decrease in input resistance in the diseased case, contrary to the experimentally reported increase.", "id": "Paper/72117", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72117"}, {"title": " Graph-Based Clustering and Dimensionality Reduction for Environmental Data Analysis ", "webprogram_exclude": "0", "session_ids": ["Session/18238"], "source_sha256": "865e7b25d03d2415690c2d18db86f52e1d7acaa6c7ba0421f29d3c7d4b228492", "withdrawn": "", "abstract": "Environmental datasets often contain complex relationships that are difficult to identify from high-dimensional measurements. In this project, we applied graph-based and spectral methods to microbial community data from the Macatawa Watershed, using Bray–Curtis dissimilarity to construct weighted graphs and spectral clustering and dimensionality-reduction techniques to identify patterns in the data. Our analysis revealed clustering patterns associated with seasonal variation and differences among watershed sites, demonstrating how graph-based and linear algebraic methods can uncover structure in complex environmental data.", "id": "Paper/72118", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72118"}, {"title": " On the classification of regular graphs with positive Lin-Lu-Yau curvature ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "03ca31fd3650c55285d0769dc927130a17076ec5eb65bfeb38088403b9388cb9", "withdrawn": "", "abstract": "We prove several new structural and classification results about $d$-regular graphs with positive Lin--Lu--Yau (LLY) curvature. We show that any positively curved $d$-regular graph has diameter at most $2d-2$, which improves the previously best known diameter bound obtained from the Bonnet-Myers-type theorem for positively curved graphs. We further show that every positively curved $d$-regular graph is $3$-connected. We classify all positively curved $3$-regular graphs, as well as all positively curved regular planar graphs.", "id": "Paper/72119", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72119"}, {"title": " The persistent homology of torus grids in homological dimensions 0, 1, and 2 ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "919c5b3b2bb56b4e586390147e0ecd9c14c8b132d4ebb9b414fcbb9f3a4e9abb", "withdrawn": "", "abstract": "We consider the persistent homology of the Vietoris--Rips filtration of torus grids equipped with the sum metric. We compute the barcodes of these filtrations in homological dimensions 0, 1, and 2. We also conjecture a formula for the barcode of an arbitrary rectangular torus grid in dimension 2.", "id": "Paper/72120", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72120"}, {"title": " Exploring the Mapper Algorithm: An Undergraduate Research Perspective ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "9175183d453208772b47d33875caabbbfc2612320f0f4aaf8fae23a888801e17", "withdrawn": "", "abstract": "High-dimensional vector embeddings represent text as point clouds in a metric space, allowing semantic relationships to be studied geometrically. This project investigates whether Topological Data Analysis (TDA), particularly the Mapper algorithm, can use the structure of these point clouds to improve the segmentation of unstructured text.\n\nGiven a point cloud $X$, Mapper applies a filter function $f:X\\to\\mathbb{R}^k$, covers the image of $f$ by overlapping sets, clusters points within the corresponding preimages, and constructs a graph whose vertices represent clusters and whose edges represent nonempty intersections. In this study, multilingual embeddings of Spanish-language documents are analyzed using Mapper, and the resulting graph is used to identify topologically coherent regions that define candidate text segments.\n\nThese topology-based segments are compared with conventional fixed-length chunking, which divides text by character or token count without regard to the geometry of the embedding space. We evaluate whether Mapper-based segmentation produces greater internal semantic coherence and improved retrieval performance.\n\nMore broadly, this work explores how topological and combinatorial structure in high-dimensional data can reveal information obscured by global statistical summaries and provides an application of algebraic topology to modern machine-learning systems.", "id": "Paper/72122", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72122"}, {"title": " (Co)Saturation of Non-Abelian Transfer Systems ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "c48951da88c4ae0e3b83099d43a871e7aca5bb0b072b8160391d4384792b6cb7", "withdrawn": "", "abstract": "Homotopical combinatorics uses tools from combinatorics to explore and understand structures in equivariant homotopy theory. One object of study in this field is a type of directed graph called a $G$-transfer system. We will define transfer systems and present the differences between transfer systems for abelian and non-abelian groups $G$. The main focus of this work is the enumeration of dihedral transfer systems with the property of (co)saturation. We present an inductive argument that counts the (co)saturated transfers systems via inclusion of subgroups.", "id": "Paper/72131", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72131"}, {"title": " Finite Groups with Exactly m Elements of Order n ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "311f039c0348eaddb59a8e4c22d8db81c52c8c755fb911c8f71b5294104092ad", "withdrawn": "", "abstract": "Finite groups with exactly n elements of order n have been determined. The goal of this\nproject was to expand this line of study and investigate finite groups with exactly m\nelements of order n, where m, n ≥ 1. We chose to classify groups with exactly m elements of order n for m ≥ 2, approaching the question for both abelian and non-Abelian groups and generalizing what was found to be true for both cases. We made significant progress in our Abelian and general sections of work during our time in the program. Although we arrived at some concrete results for the non-Abelian case, this is what would be most useful to develop further in future work.", "id": "Paper/72136", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72136"}, {"title": " Integer Programming Optimization of Academic Year Course Distributions ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "1b0da857f31cdf60171b11ae962e40597c68c3b096928e26205061afc34285b6", "withdrawn": "", "abstract": "Scheduling classes at the departmental level is a challenging and time-consuming task. The mathematical technique of linear programming has the potential to simplify this challenge by building a model of linear constraints to find the most optimal solution that satisfies all the constraints. In this project, we are implementing a linear programming model using the DOCplex library in Python. The objective function represents instructor satisfaction with different courses, and the constraints represent limitations, such as the fact that one instructor cannot teach two courses at the same time.  We will demonstrate the implementation of  preferences to assign professors a prep day with no scheduled courses. We will also present a model revised to schedule courses for two semesters simultaneously, in response to new administrative requirements about number of credits per instructor per academic year.", "id": "Paper/72137", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72137"}, {"title": " Markov Chain for Voter Engagement Dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/18242"], "source_sha256": "7cdb314156ac7bddc37e68a00d1fda0c31bf82b98ec7413c739c7a4ec7615e89", "withdrawn": "", "abstract": "Voter engagement is not a fixed behavior; individuals may move between different levels of political participation over time. This research develops a discrete-time Markov chain model to examine voter engagement dynamics using voter registration and civic participation data from Georgia counties. Engagement is represented through a finite set of states corresponding to different levels of participation, and transition probabilities describe movement between these states over time.\nUsing R and RStudio, transition matrices are constructed and analyzed to investigate how patterns of voter engagement evolve. The model considers long-term behavior, including the possibility of convergence toward a stationary distribution, and examines how differences in transition probabilities can produce different patterns of participation. County-level comparisons are also used to explore variation in engagement dynamics across communities.\nThis project demonstrates how stochastic processes can provide a mathematical framework for studying changes in civic participation. Rather than treating voter engagement as a single static measurement, the Markov chain approach emphasizes transitions between participation states and provides a quantitative method for examining both short-term movement and long-term patterns. The research illustrates a broader application of probability and mathematical modeling to questions in the social sciences.", "id": "Paper/72138", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72138"}, {"title": " Weak Spoiler Candidates in in Multi-Winner Ranked Choice Elections ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "99ace490c0942211aae8ff473d18e5e5fab5aea1d326415353730b3fc8d8d9d1", "withdrawn": "", "abstract": "We study the spoiler effect in multi-winner ranked-choice voting methods, focusing on the method of single transferable vote (STV). The spoiler effect is typically seen as most egregious if the spoiler candidate is very \"weak\" or \"fringe\" in some sense. We analyze how susceptible STV is to the spoiler effect for various notions of weakness, and compare how STV contrasts with other methods for comparison purposes. Our general finding is that STV outcomes are often not affected by the presence of weak candidates, although the worst-case outcomes can be extreme.", "id": "Paper/72142", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72142"}, {"title": " Minimal Resolving Sets in Rectangular Grid Graphs: A Complete Characterization and Enumeration ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "b3b77f7b81efe1bbebc0f2704f2df7cd30616287140176f78bb5c595cddeab34", "withdrawn": "", "abstract": "Let $m,n \\geq 3$. A set of vertices $S$ of the rectangular grid graph $P_m \\square P_n$ is resolving if the taxicab distance vectors of the vertices of $P_m \\square P_n$ with respect to $S$ are pairwise distinct. A resolving set $S$ is minimal if no proper subset of $S$ is resolving, and a minimal resolving set of cardinality $k$ is called a $k$-minimal. We extend the work of Andersen et al., who characterized $3$-minimals, established the maximum cardinality $2\\min(m,n)-2$, and posed the complete characterization and enumeration of minimal resolving sets for grids as an open problem, and Adar and Epstein, who showed that $3$ is the only possible odd cardinality and that every minimal resolving set of cardinality at least $4$ can be ordered to form a sequence corresponding to a zigzag sequence. We provide a recursive construction that generates exactly the minimal resolving sets of cardinality at least $4$ for grids. We derive from the construction closed-form formulas to enumerate the $k$-minimals for all even $4 \\leq k \\leq 2\\min(m,n) -2$. Together with the known characterizations for cardinalities $2$ and $3$ and a direct enumeration of the $3$-minimals, this yields a complete characterization and enumeration of the minimal resolving sets of rectangular grid graphs of every possible cardinality.", "id": "Paper/72143", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72143"}, {"title": " Weaving Links, Involutions, and Rational Homology <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.162ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 500.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">4</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-34\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-balls ", "webprogram_exclude": "0", "session_ids": ["Session/18243"], "source_sha256": "d7e6e8c9f81653711f250fa111c6f2dcb5a161db1a21c80497c10e082849928d", "withdrawn": "", "abstract": "A common question in low-dimensional topology---which can be viewed as a certain generalization ideas from the Poincaré conjecture---is deciding which rational homology \\(3\\)-spheres (\\(\\mathbb{Q}S^3\\)s) bound rational homology \\(4\\)-balls (\\(\\mathbb{Q}B^4\\)s). Because every 3-manifold can be realized as a double cover of $S^3$ branched along a link $L\\subset S^3$, and every link can be realized as the closure of a braid, we can reformulate the question as: which braid closures admit double branched covers bounding $\\mathbb{Q}B^4s$? \nThe answer is known for $2-$braids, which are the $T(2,n)$ torus links. Indeed, $\\Sigma(T(2,n))$ is the lens space $L(n,1)$, which bounds a $\\mathbb{Q}B^4$ if and only if $n=\\pm1, \\pm 4$.\n\nThe problem becomes much more complicated, when one cosiders double branched covers of 3-braid closures. For alternating and nearly all quasi-alternating $3-$braids, the question has been resolved. However, for nonquasi-alternating $3-$braids, only partial results are known, and for arbitrary $m$-stranded braids the question is still open.\n\nIn this talk, we'll cover the underlying machinery in this area of low-dimensional topology, including ideas in knot theory, homology theory, handlebody decomposition of manifolds, Dehn surgery, and Kirby calculus---the calculus on $4$-manifold diagrams. Then, we'll discuss our results concerning which of the $L_{m,n}$ family of weaving links admit covers bounding rational balls.", "id": "Paper/72145", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72145"}, {"title": " Topological Data Analysis of Continuous Glucose Monitoring Time Series ", "webprogram_exclude": "0", "session_ids": ["Session/18243"], "source_sha256": "7c58f0dd88e995a03e381cfbd8a0cb070057798da8bc3da1a82fe4b5b3cc2a63", "withdrawn": "", "abstract": "Many studies involving continuous glucose monitoring (CGM) investigate fulfillment of discrete \nstates (Time in Range, or TIR) or physical components of a time series (peak glucose, AUC, etc.) such as \nto extensively characterize the morphology of some CGM time series. This is the common route in generating \nfeatures for subsequent machine learning pipelines. However, less investigated are the dynamic \nproperties of the time series which seem more interesting to understand the underlying physiology \nproducing the time series: in this case, the glucose response and its geometry takes larger consideration, less so the exact values realized. For example, understanding periodicity of the time series is a prominent \ndynamical feature, with relevant studies already existing using Fast Fourier Transforms (FFT) and other \ntechniques. However, existing dynamical methods, (for example those characterizing periodicity, \ncircadian phases, ultradian phases, etc.), may assess the characteristic (periodicity, for example) by \ngeneralizing the behavior, modeling, or decomposing (FFT) it. Rather than just indicating that a behavior \nexists and its features, we aim to better characterize these dynamic tendencies of a time series by considering (on top of a basal assessment of the characteristic) features such as aperiodicity, which \ndemonstrates the characteristic itself breaking down, changing, or continuing along the time series.\nA method to quantify dynamical feature structural properties and anomalies is Topological Data Analysis \n(TDA), which will be evaluated. As a dynamical feature weakens, strengthens, emerges, etc. TDA is \nhypothesized to recognize this change in dynamic behavior such as to complement existing models or \nmorphometric descriptions of the time series. TDA should be able to distinguish not only dynamical \nstructures, but a maintenance of those structures’ integrity over the time series, to then potentially \nenhance an understanding of the physiology underlying those dynamics.", "id": "Paper/72148", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72148"}, {"title": "Discussion", "webprogram_exclude": "0", "session_ids": ["Session/17812"], "source_sha256": "73504bae014dfe9d8870b457a25b98fed0dc22b575ab48f203fdef1f069aaa46", "withdrawn": "", "abstract": "", "id": "Paper/72150", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72150"}, {"title": "Discussion", "webprogram_exclude": "0", "session_ids": ["Session/18476"], "source_sha256": "9291a21a9398363eeb5dc737560fcd3a1c759d410e0249bd06f860717c55eaf6", "withdrawn": "", "abstract": "", "id": "Paper/72152", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72152"}, {"title": "Discussion", "webprogram_exclude": "0", "session_ids": ["Session/18314"], "source_sha256": "f8b44a78261dd58fd90b35bb1dc7297914bbe1240246294339ed2d21582a70e8", "withdrawn": "", "abstract": "", "id": "Paper/72154", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72154"}, {"title": "Introductory Remarks", "webprogram_exclude": "0", "session_ids": ["Session/18314"], "source_sha256": "99ff8911fe5bc988b56130a6f09fbcd3e662aa2fdd150a4bc31d8a8a38fea43d", "withdrawn": "", "abstract": "", "id": "Paper/72157", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72157"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/18217"], "source_sha256": "00a83455c522aaa793a435db7cedad255bc5195a34891368ff18f289463c7bda", "withdrawn": "", "abstract": "", "id": "Paper/72164", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72164"}, {"title": " Generalized Bracket Rules for <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"5.897ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 2539 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">B(\\infty )</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-42\" d=\"M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-42\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"759\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-221E\" x=\"1149\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"2149\" y=\"0\"></use>\n</g>\n</svg> Crystals ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "b399748b7c55e1c7e3c55ff301bf8c68df374f112e7a13a555f0e83282e7650e", "withdrawn": "", "abstract": "Using the theory of PBW bases, one can realize the crystal $B(\\infty)$ for any semisimple Lie algebra\nusing Kostant partitions as the underlying set. In fact there are many such realizations, one for each\nreduced expression for the longest element of the Weyl group. There is an algorithm to calculate the\nactions of the crystal operators, but it can be quite complicated. It is known that, for certain reduced\nexpressions, the crystal operators can also be described by a much simpler bracketing rule. However,\noutside of type $A$, there is no single reduced expression for which the known bracketing rules describe\nboth $B(\\infty)$ and its Kashiwara involution, $B^*(\\infty)$. Here, we extend these methods by\ndeveloping new bracketing rules for $B^*(\\infty)$ from reduced expressions with known bracketing\nrules for $B(\\infty)$. In particular, we obtain explicit combinatorial descriptions of both the crystal\noperators and star crystal operators based on a single reduced expression in types $B, C$, and $D$.", "id": "Paper/72175", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72175"}, {"title": " The Arc Game – A Topological Combinatorics Game in Knot Theory ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "79cc42b4e25624f3a6962d351de2f66ac6c8906d2685447bca2609ad49e1f7b8", "withdrawn": "", "abstract": "Knot theory is the study of embeddings of one or more circles into three-dimensional space, considered up to ambient isotopy. A knot diagram is a planar projection of a knot that records which strand passes over and which passes under at each crossing. I will present my research on a topological combinatorial game that I created called the “Arc Game”. This two-player game is played on a knot diagram, where the only starting information is a board of n crossings which are not attached to any arcs, nor are they part of any knot. Game play consists of two players taking alternating turns, and on each turn, defining arcs, which have boundary points where they would pass under a different strand in a crossing. One player’s goal is to have the final diagram include a \\textbf{link}, or a group of knots containing at least 2 inexorably linked components. The other player’s goal is to have the final diagram be an \\textbf{unlink}, or a group of knots that can be fully separated out into its components. In this poster, I will present on how one can utilize a combination of knot theory and number puzzles to outline the strategies, interesting moves, and possible outcomes of this game. I will furthermore show a method to determine who will win, and how they will do so, for every one of an infinite number of possible starting boards.", "id": "Paper/72178", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72178"}, {"title": " What Do Graph Laplacian Eigenvalues Measure in Alzheimer’s Disease EEG? ", "webprogram_exclude": "0", "session_ids": ["Session/18243"], "source_sha256": "ff7e91224b5ca4f932f3f569c7e0538a651da64e309a397ec04a1c295d175ade", "withdrawn": "", "abstract": "Alzheimer's disease (AD) may disrupt coordination between brain regions. We examined whether resting-state EEG graph Laplacian spectra reflect this disruption and what their eigenvalues measure.\n\nWe analyzed 174 recordings (76 AD participants, 11 controls; eyes open and closed), filtering 19 EEG channels to 8-13 Hz. For all 171 electrode pairs, we estimated magnitude-squared coherence, weighted phase-lag index (wPLI), and Pearson correlation. We computed the second-smallest eigenvalue $\\lambda_2$ and largest eigenvalue $\\lambda_{\\max}$ of each graph's symmetric normalized Laplacian.\n\nWhole-head $\\lambda_{\\max}$ was higher in AD across all six measure-by-condition combinations (best area under the ROC curve [AUC]: 0.926, $q=0.0001$); but $\\lambda_2$ never exceeded AUC 0.64. To examine regional effects, we rebuilt graphs using seven prespecified posterior electrodes as a scalp proxy for the default mode network. Here, $\\lambda_2$ was lower in AD and reached AUC 0.918.\n\nWe explored two interpretations. First, $\\lambda_{\\max}$ correlated more strongly with edge-weight unevenness ($r\\approx0.75$) than with node-degree heterogeneity ($r\\approx0.15$ to $0.40$), suggesting it does not primarily reflect hub concentration. Second, mean edge weight matched or exceeded both eigenvalues in AUC in 8 of 12 comparisons; an eigenvalue performed better in 4, including 2 using wPLI, which reduces sensitivity to zero-lag volume-conduction effects. These results suggest that spectral measures largely reflect differences associated with overall alpha coupling, with potential additional discriminatory value in some comparisons. They do not establish that field-spread effects were eliminated. Findings are limited by 11 controls and require replication.\n\nAcknowledgments: Research supervision by Prof. A. Assadi (UW-Madison) and mentorship at Johns Hopkins School of Medicine.", "id": "Paper/72179", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72179"}, {"title": " Smoothness Characterizations and Duality of the Type II Theta Correspondence and Basic Fourier–Jacobi Models ", "webprogram_exclude": "0", "session_ids": ["Session/18243"], "source_sha256": "bf44f38115e8de169b83bb139d83ddba5e9d6b68a9bb9ccb6975b25c9847c6c3", "withdrawn": "", "abstract": "We study the smoothness of two families of Borel-orbit closures. The first consists of matrix Schubert varieties in $\\mathrm{Mat}_{n\\times m}$. The second consists of orbit closures for the diagonal action of the upper-triangular Borel subgroup $B\\subseteq\\mathrm{GL}(V)$ on $\\mathrm{FL}(V)\\times V$, where $V=\\mathbb{C}^n$. \n\nFor matrix Schubert varieties, we prove that smoothness is equivalent to the absence of a contiguous $2\\times 2$ block of equal positive entries in the southwest rank table of the indexing partial permutation matrix. The proof also shows that every smooth matrix Schubert variety is a coordinate linear subspace. We enumerate these varieties both in total and by rank; the rank-refined counts are Catalan triangle numbers.\n\nThe $B$-orbits in $\\mathrm{FL}(V)\\times V$ are indexed by colored permutations. We give a complete smoothness criterion involving two ordinary permutation patterns and two colored patterns, together with two exceptional extensions of the final colored pattern.\n\nWhen $m=n$, the Borel orbits in the two ambient spaces are naturally in bijection, and hence so are their closures. In the framework of relative Langlands duality, this is the expected correspondence between the type~II theta-correspondence model and the basic Fourier--Jacobi model. We show that the bijection does not preserve smoothness in general and characterize the failures in one direction.", "id": "Paper/72180", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72180"}, {"title": " Quantum Optimization for Military Logistics ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "43f675f240124658e41970f379404ed93be97c429fe6ee78f8f72d9f49e0b6be", "withdrawn": "", "abstract": "Military logistics operations require the timely and reliable delivery of supplies while accounting for multiple competing objectives, including travel distance, transportation time, and exposure to operational threats. These requirements create complex routing problems that become increasingly difficult to solve as operational constraints and risk considerations are introduced. Quantum optimization algorithms, particularly the Quantum Approximate Optimization Algorithm (QAOA), offer a potential approach for addressing such combinatorial optimization problems. This work formulates a risk-aware military logistics routing problem as a multi-objective optimization model and maps it to a Quadratic Unconstrained Binary Optimization (QUBO) formulation suitable for QAOA. Small problem instances are evaluated using quantum simulation and, where feasible, quantum hardware, with results compared against classical optimization methods. Performance is assessed in terms of solution quality, computational requirements, and the ability to balance travel cost, travel time, and operational risk. The study aims to evaluate the suitability of QAOA for small-scale military logistics routing and to better understand the opportunities and limitations of near-term quantum optimization for defense applications.", "id": "Paper/72181", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72181"}, {"title": "Introductory Remarks", "webprogram_exclude": "0", "session_ids": ["Session/17105"], "source_sha256": "fe0682d20059bc7e3033b8fbdd391697e6fe8c0562180bf62295c3465ba6213b", "withdrawn": "", "abstract": "", "id": "Paper/72183", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72183"}, {"title": "Discussion", "webprogram_exclude": "0", "session_ids": ["Session/18362"], "source_sha256": "9863becd3e4c305e230f8cc8079aa4df2ecbd9602b3dd0de2210919c73df2bd5", "withdrawn": "", "abstract": "", "id": "Paper/72185", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72185"}, {"title": " Modeling demographic impacts of snowmelt variability on Valeriana edulis population dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "fc2d139750718f894f4ad0ebc4be298c5322da6bdc1ddb8ddb614d6a2c34a3ba", "withdrawn": "", "abstract": "Snow melt timing is crucial for many aspects of ecosystem function; for plants it determines the onset, length, and conditions of the growing season. Climate change is causing snow to melt earlier, while also increasing the variability of snow melt timing from year-to-year. To determine the impacts of this variability on specific plant populations, demographic theory suggests this is connected to the species’ location on the fast-slow continuum. Populations with a faster life history are better able to adjust to variation, while those of slow life history have increased ability to buffer against its impact. Here, I investigated whether the fast-slow continuum applies to population-level variation across the elevation range of the plant species \\textit{Valeriana edulis}. I combined long-term census data and remotely-sensed snow melt data to build demographic vital rate and ARIMA time series models to inform an integral projection model. I used this model, through simulations, to test the impact of changing snow melt trends on longevity and population growth. Snow melt timing impacted survival and flowering probabilities: late snow melt was negative for survival and positive for flowering. The impact of snow melt variability on population growth varied idiosyncratically across sites, while longevity values saw a standard increase with an increase in variability.", "id": "Paper/72188", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72188"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/17800"], "source_sha256": "ea60370122e32676143cfcb662535cd714471b936fd2f41d9ce484ca92649bc0", "withdrawn": "", "abstract": "", "id": "Paper/72190", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72190"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/18293"], "source_sha256": "3486d8f95e7b83732be8709f83ac8262b2ca6830185d5c8a8b823b9360a6ce6a", "withdrawn": "", "abstract": "", "id": "Paper/72192", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72192"}, {"title": " Interlacing for zeros of the Serre derivative of Eisenstein series ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "d98be8001f39cca14a4acdb032eca0405c86a1aa68d663a43c6123ef87217269", "withdrawn": "", "abstract": "In 1970, Rankin and Swinnerton-Dyer showed that the non-elliptic zeros of Eisenstein series $E_k$ in the fundamental domain all lie on the lower arc $\\{ e^{i\\theta}: \\frac{\\pi}{2} < \\theta < \\frac{2\\pi}{3}\\}$. Very recently, Sugibayashi showed that the same property also holds for the Serre derivative $\\vartheta_k(E_k)$ of Eisenstein series. We first give very precise estimates for where exactly these zeros are located on the lower arc. These location estimates then allow us to prove four main results. First, we show that the zeros of $\\vartheta_\\ell(E_\\ell)$ Stieltjes interlace with the zeros of $\\vartheta_k(E_k)$ on the lower arc for all $\\ell > k$. Second, we classify precisely when the zeros of $\\vartheta_\\ell(E_\\ell)$ (standard) interlace with the zeros of $\\vartheta_k(E_k)$ on the lower arc. Third, we show that the zeros of $\\vartheta_k(E_k)$ always (standard) interlace with the zeros of $E_{k+2}$ on the lower arc. Fourth, as an application of the third main result, we show that the zeros of the cuspidal projection of $\\vartheta_k(E_k)$ all lie on the lower arc, extending a result of Xue and Zhu.", "id": "Paper/72193", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72193"}, {"title": " DG Algebra Structures on Linear Resolutions of Edge Ideals ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "eabccbe3ea08cb7f63c64f43bff865ddaeb2af371407f23545d6ab88bccdf919", "withdrawn": "", "abstract": "Our research connects the fields of graph theory and homological algebra by studying how the structure of a graph informs the properties of corresponding algebraic objects called edge ideals. When an edge ideal satisfies the linear quotients property, this gives rise to a linear resolution. Some linear resolutions admit differential graded algebra (DGA) structures; that is, we can construct an algebra on the resolution satisfying the Leibniz rule and graded commutativity. Determining which linear resolutions admit DGA structures is a question of great interest in recent years in commutative and homological algebra, and explicit constructions of such structures are quite rare. We demonstrate that the minimal free resolution of the quotient of an edge ideal of a split graph is a DGA. We give an explicit construction of DGA's on a large class of linear resolutions.  We conjecture that this result can be extended to the edge ideals of all graphs with linear quotients. This is joint work conducted with Diethorn, Wang, and Stinson-Maas.", "id": "Paper/72194", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72194"}, {"title": " Geometry of Nearest Integer Continued Fractions ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "daea54da7a6b32d9711bbc17ce78a5ba631d09561948d9278ecec30e16f0a5a2", "withdrawn": "", "abstract": "Continued fractions are fractional approximations of real numbers. These have applications in dynamics, number theory, and ergodic theory, among other fields. Noteworthy continued fractions include the simple continued fraction (SCF), and the nearest integer continued fraction (NICF). Caroline Series established a connection between the geometry of the Farey tesselation and simple continued fractions. This talk will include visualizations of the Farey tessellation and the connections between the SCF and NICF. We will explore converting between the two continued fractions corresponding geometric implications.", "id": "Paper/72195", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72195"}, {"title": " Geometry of Nearest Integer Continued Fraction ", "webprogram_exclude": "0", "session_ids": ["Session/18243"], "source_sha256": "3bb0ff9b0fd4015a717e0ac052e6e4c95ffdbdf2018cd09bfcbd4b3fe1c4d322", "withdrawn": "", "abstract": "Continued fractions are fractional approximations of real numbers. These have applications in dynamics, number theory, and ergodic theory, among other fields. Noteworthy continued fractions include the simple continued fraction (SCF), and the nearest integer continued fraction (NICF). Caroline Series established a connection between the geometry of the Farey tesselation and simple continued fractions. This talk will include visualizations of the Farey tessellation and the connections between the SCF and NICF. We will explore converting between the two continued fractions corresponding geometric implications.", "id": "Paper/72196", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72196"}, {"title": " Non-Distributive Intervals of the <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.007ex\" height=\"1.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -576.1 433.5 721.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">c</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-63\" d=\"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-63\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Cambrian Lattice in Type B ", "webprogram_exclude": "0", "session_ids": ["Session/18159"], "source_sha256": "713c58a59c97134e4ccf7e09714163fc044802ee872dce3ee1356d2c5e956ec0", "withdrawn": "", "abstract": "In $c$-Cambrian lattices of both type A and type B, it is well known that the full permutation of 3 numbers yields a non-distributive lattice in the shape of a pentagon when permutations with certain avoiding patterns are deleted. Our goal here is to determine which intervals of the type B $c$-Cambrian lattices are non-distributive by characterizing the barring $\\vec{c}$ of the numbers being permuted and introducing conditions to the left descent set $\\nu$ that defines a subinterval. It turns out that there is only one condition required for the barring $\\vec{c}$ and the left descent set $\\nu$ only needs 3 elements given this barring, allowing this construction of non-distributive lattices to apply to a wide range of type B $c$-Cambrian lattices $B_n$ where $n\\ge5$.", "id": "Paper/72197", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72197"}, {"title": " Estimating Fiber Diameter of Fluorescent and Scanning Electron Microscopy Imaging ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "d831c16f8dbfa6efeb8743ccb71fac5c893af2ae65291e2bec5d80d663a2ca54", "withdrawn": "", "abstract": "Accurate measurement of fiber diameter is critical for characterizing electrospun scaffolds, as fiber morphology directly influences properties such as porosity, mechanical performance, and biological activity. Electrospun polycaprolactone (PCL) fiber networks are widely used in applications including wound healing, bone regeneration, and cell culture, where reliable morphological characterization is essential. In this project, we will conduct a systematic literature review using Covidence software to identify and evaluate existing strategies for estimating mean fiber diameter from microscopy images. Particular emphasis will be placed on comparing and contrasting two or more image-analysis approaches and assessing their accuracy, strengths, and limitations. Using scanning electron microscopy (SEM) and fluorescence microscopy images of electrospun fiber networks, we will perform a quantitative analysis to determine which methods provide the most accurate and reliable estimates of mean fiber diameter. The findings will provide guidance for researchers seeking robust image-based approaches for characterizing electrospun scaffolds.", "id": "Paper/72198", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72198"}, {"title": " The Memory Naibbe Cipher: Reproducing Long-Range Correlation in the Voynich Manuscript ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "47df69bc53ce9433f17e7cff3fd9711a5e714ca7e7cbf1a92be79f8e2c6c6840", "withdrawn": "", "abstract": "The Voynich Manuscript is a fifteenth-century manuscript containing illustrations and text written in an unknown script. One hypothesis is that the text represents a known language that has been encrypted using a cipher. Michael Greshko’s Naibbe Cipher is a historically plausible cipher that can be performed by hand using materials available in the fifteenth century and reproduces several statistical properties of the Voynich Manuscript. However, it fails to reproduce the manuscript’s long-range correlation. We introduce a self-citation mechanism to the Naibbe Cipher, meant to mimic a scribe using memory as a shortcut while encrypting. This modification produces long-range correlation comparable to that of the Voynich B text, as measured by the Hurst exponent (0.681 versus 0.677), whereas the original Naibbe Cipher behaves approximately like an uncorrelated sequence (0.493). Importantly, the modification achieves this while maintaining the Naibbe Cipher’s Zipfian word-frequency patterns.", "id": "Paper/72199", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72199"}, {"title": " Space-Time-Local Geometry and Dynamics of Diffusively Coupled FitzHugh-Nagumo Neurons on Adaptive, Weighted Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/18243"], "source_sha256": "b987f63251c52f2b83a657d749322d4bd15370c7a0d5bfd8345d027023fe6f80", "withdrawn": "", "abstract": "Understanding how individual neuron dynamics translate into collective network behavior remains a fundamental challenge in computational neuroscience. Analytical understanding of network dynamics is therefore often limited by assumptions regarding behavior or network topology, with many studies relying largely on numerical simulation. Adaptive networks—networks with changing weights—are hence also limited by similar assumptions. We develop a topology-independent space-time-local analytical framework for studying diffusively coupled FitzHugh–Nagumo networks on general weighted undirected graphs by considering the vector field and linearization under a coordinate basis that changes with spatial position.  We derive conditions for and classifications of bifurcations and fixed points using this framework in terms of the fixed point location and Laplacian eigenvalues. We derive $\\varepsilon$ error bounds due to the $\\delta$ space-time-local approximation of our framework. Inspired by Hebbian Learning, we introduce a weight evolution to the network and further quantify the impact of this weight evolution on the $\\varepsilon$ error, possible due to the timescale separation of neuron dynamics and weight evolution. Thus far, dynamics have been interpreted on individual 2-dimensional tangent planes, which we extend to identify global manifold structure. We then identify weight evolution as time evolution of this manifold (ore specifically, its tangent planes), which can be interpreted as a flow on a sphere.", "id": "Paper/72201", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72201"}, {"title": " Diophantine Approximation and Interpolation in the Unit Disk ", "webprogram_exclude": "0", "session_ids": ["Session/18243"], "source_sha256": "19ba0d19e19d121b4ad3dc3377551337cb95a3c2811886490f7f77f637d30952", "withdrawn": "", "abstract": "Can we find a geometric picture for irrationality measure? We explore this through the lens of sequences of the form \\[a_n = (1 - \\frac{1}{n^p})e^{2\\pi i n \\alpha}, \\quad  \\alpha,p \\in \\mathbb{R}\\]  and their connections to the pseudohyperbolic metric $\\rho$ on $\\mathbb{D}$ and ultimately Carleson's Interpolation Theorem.  In particular, we study the $H^\\infty$ interpolation problem on the unit disk $\\mathbb{D}$ for $(a_n)$, and show that the necessary and sufficient condition for when this sequence interpolates is precisely the Diophantine condition on the irrationality measure of $\\alpha$ with respect to $p-1$. From standard results about irrationality measure, we observe that $(a_n)$ is interpolating for $p > 1$ and almost all $\\alpha \\in \\mathbb{R}$, including all irrational algebraic $\\alpha$.", "id": "Paper/72204", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72204"}, {"title": " Weights and Stablization of Complete Non-Ambiguous Trees ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "81804ea1c31620acc50dce305cab2c2d4be8f32215e98538f60bccaaa1bd61b5", "withdrawn": "", "abstract": "We study complete non-ambiguous trees (CNATs), a class of trees embedded in the integer lattice with restrictions on the positions of their vertices. We define weights and coweights for CNATs through their natural bijection to fully tiered trees. We prove stabilization formulas for fixed coweight and derive a counting formula for CNATs of weight 0 (see OEIS A398579). Furthermore, we relate Abelian Sandpile Models to tiered trees with near-maximal weight. Finally, we prove a recursive formula for counting fully tiered trees by coweight, relating tiered trees with $n$ tiers to those with $n−1$ tiers.", "id": "Paper/72205", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72205"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/17916"], "source_sha256": "4cb8e59c7f0dca09c93fcaef17b919b7490d07625b4c8d61ca4a1ba84e4ed282", "withdrawn": "", "abstract": "", "id": "Paper/72207", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72207"}, {"title": " Run Don’t Fight: Zombie Apocalypse ", "webprogram_exclude": "0", "session_ids": ["Session/18159"], "source_sha256": "11007805b3253bd344240b78ecda9b33c056e1cd2fb13f5c6ad6c0714def5c17", "withdrawn": "", "abstract": "This project explores optimal path planning for an undetected survivor in a zombie apocalypse who must reach a safe zone within a set deadline. We develop a path planning model in which local slope determines the survivor's speed, while terrain type and zombie density determine the cost of movement. Because the zombies diffuse randomly, their density is modeled by the 2D diffusion equation (PDE). With the solution to the PDE, we then derive a time-dependent Hamilton-Jacobi-Bellman (HJB) equation and solve it numerically backward in time. We test the model on real elevation and terrain data from Gambier, OH, using an initial zombie population inspired by Kenyon College student activity patterns. Evaluating the model under different deadlines generates distinct optimal evacuation paths. Specifically, shortening the deadline generates a path approaching the time-optimal trajectory, whereas increasing the deadline makes the solution converge to the safest path. Overall, when the deadline is long enough, we predict it is optimal to take a slower path that avoids high-density zombie regions at the expense of time.", "id": "Paper/72209", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72209"}, {"title": " Modeling Post-COVID Changes in Influenza Outbreak and Control Dynamics Using First-Passage-Time Analysis ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "3ff0430753304bb9e3fd811e14ff2a4e4fc362df5c97f5dcb201eefa2ceda98b", "withdrawn": "", "abstract": "COVID-19 infection can cause lasting respiratory impairment, which may affect an individual’s susceptibility to other respiratory infections such as influenza. This study compares the timing and accuracy of outbreak and control predictions before and after the COVID-19 pandemic. We use influenza outbreak data from the past 10 years and stochastic modeling to estimate the transmission rate of influenza, progression rate from the exposed to infectious class, recovery rate, loss of immunity rate, coefficient for stochastic diffusion, and populations of the Susceptible, Exposed, Infectious, and Recovered classes at an initial time. These estimated parameters and state variables are used to calculate the mean first passage time (MFPT) and the variance of the first passage time (FPT) for when infection levels cross critical thresholds that distinguish disease-free stability, endemic persistence, and outbreak dynamics. Differences in the MFPT and FPT variance between the pre-pandemic period, Fall 2015 through Winter 2020, and the post-pandemic period, Winter 2020 to Spring 2026, suggests that influenza preparations may need to adapt to new population needs and increased outbreak unpredictability.", "id": "Paper/72210", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72210"}, {"title": "Discussion", "webprogram_exclude": "0", "session_ids": ["Session/18122"], "source_sha256": "2d071e3d9f4868869295b35452af01d03512fe24987f047799260af126dc224c", "withdrawn": "", "abstract": "", "id": "Paper/72214", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72214"}, {"title": " Understanding Frenet-Serret frames in n-dimensional space and its applications ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "85331cf9846d147cbe6cc92f77078699986a1b01caf84d1594f4de96be2e53f5", "withdrawn": "", "abstract": "The classical problem of reconstructing a space curve from its intrinsic invariants poses significant analytical challenges in higher-dimensional spaces. In this paper, we investigate curves in four-dimensional Euclidean space $\\mathbb{E}^4$ whose principal curvature functions satisfy specific ratio constraints: the ratio of the second to the first curvature is a linear function, $\\kappa_2/\\kappa_1 = as + b$, and the ratio of the third to the first curvature is a constant, $\\kappa_3/\\kappa_1 = c$. Using the generalized 4D Frenet--Serret apparatus, we decouple the moving frame to derive a governing fourth-order ordinary differential equation with variable polynomial coefficients for the unit tangent vector field $e_1$. We solve this equation analytically via a power series expansion about $t=0$, explicitly calculating the foundational boundary coefficients $c_4, c_5,$ and $c_6$ in terms of canonical initial frame conditions and isolating the infinite recurrence relation. Term-by-term integration yields the closed-form parametric trajectory $\\alpha(t)$ in $\\mathbb{E}^4$, whose spatial geometry is visualized through orthogonal projections onto three-dimensional hyperplanes.", "id": "Paper/72216", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72216"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/17913"], "source_sha256": "d5bcb7439dab5e8a88a092d867c0005779e92c2019a2efbffda416f78e11d277", "withdrawn": "", "abstract": "", "id": "Paper/72274", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72274"}, {"title": "Concluding Remarks", "webprogram_exclude": "0", "session_ids": ["Session/18299"], "source_sha256": "2f95fa186d975dd7f795b11bc0f97dc869e74812881cbc138cf475b9ceed18f9", "withdrawn": "", "abstract": "", "id": "Paper/72317", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72317"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/17922"], "source_sha256": "84390c9947200b2f5df5563db3a5b8bf28e1fb9116610a360d3bed4cc82bed0c", "withdrawn": "", "abstract": "", "id": "Paper/72333", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72333"}, {"title": "Discussion", "webprogram_exclude": "0", "session_ids": ["Session/18322"], "source_sha256": "2768d8fc5e80e9f491db0c30ab4a085598de68b76ec82f7a19c0294294087aaa", "withdrawn": "", "abstract": "", "id": "Paper/72335", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72335"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/18213"], "source_sha256": "f825c70b9f221c8561b2c31730a38556e1cf13a238fa24244149819f5515ced3", "withdrawn": "", "abstract": "", "id": "Paper/72336", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72336"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/18074"], "source_sha256": "214bb9898f84c2cbe815da786b4a31958b8b825c422f07a979a65cd1e1da3d0c", "withdrawn": "", "abstract": "", "id": "Paper/72337", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72337"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/18190"], "source_sha256": "db252a5a872306c2f1e272417ea5e2a20283c9eb99e833c8107d471bd8b039ee", "withdrawn": "", "abstract": "", "id": "Paper/72339", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72339"}, {"title": "Panel: Mathematics and AI, what comes next", "webprogram_exclude": "0", "session_ids": ["Session/18224"], "source_sha256": "0be3a686b22b7e2cc7110772f18da33a04384cab9daac99ad817e866e11a96ab", "withdrawn": "", "abstract": "", "id": "Paper/72340", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72340"}, {"title": " Teaching Proteins to Speak: Speech-Inspired Embeddings for Biological Discovery ", "webprogram_exclude": "0", "session_ids": ["Session/18159"], "source_sha256": "ac161b671dd8533158bd05ef2bb680ab40b4b729f5ca2e967e571b8f8b246dd5", "withdrawn": "", "abstract": "Protein representation learning has largely focused on modeling amino-acid sequences as \nstatic textual data, often overlooking the temporal and functional organization of protein activ- \nity within biological systems. In this work, we propose a novel representation framework that \ntreats protein function as a symbolic temporal sequence, inspired by methodologies from speech \nrepresentation learning. Rather than modeling proteins solely as sequences of residues, we en- \ncode functional roles and pathway interactions into symbolic structures analogous to syllables \nand phrases. These representations are embedded using speech-inspired transformer encoders \nto explore latent biological patterns in an unsupervised manner. A small proof-of-concept ex- \nperiment demonstrates that the proposed encoding yields non-random clustering of biological \npathways, suggesting that speech-based embeddings may capture complementary structural information beyond conventional protein language models. This work is intended as an exploratory \nframework and does not aim to provide clinical predictions, but rather to open new directions \nfor symbolic and temporal modeling in computational biology.", "id": "Paper/72341", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72341"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/17713"], "source_sha256": "559a163159db010bd859e59f374b0bdd49be47977c6d3b4b2334dfafb41bf5f1", "withdrawn": "", "abstract": "", "id": "Paper/72369", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72369"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/18374"], "source_sha256": "694a4b3eef3b9815e8d38d4af8a1ce52dcdbd673c09a50a0bef4be897cec8e80", "withdrawn": "", "abstract": "", "id": "Paper/72371", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72371"}, {"title": " Informing Photosynthesis Modeling with Solar-Induced Fluorescence Data ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "87c586bc5ae81ff482b863fafca7c29bacafeba66a3c2c25d3748a7d22a99add", "withdrawn": "", "abstract": "In global climate models, photosynthesis is an environmental process integral to accurately modeling the water, energy, and carbon cycles on a global scale. Within ClimaLand, the Climate Modeling Alliance’s land surface model, the fitting of the free parameters of the modeled photosynthesis process is based on matching model-predicted values to a statistically reconstructed global dataset of a measured by-product of photosynthesis. This project investigates an alternative dataset, specifically Solar-Induced Chlorophyll Fluorescence (SIF) satellite data, for calibrating photosynthetic parameters within ClimaLand. SIF data are collected globally by measuring photon flux during photosynthesis as plants fluoresce, making observations more direct. With Ensemble Kalman Inversion (EKI), free photosynthetic parameters are estimated from priors informed by the nonlinear model ClimaLand and TROPOMI SIF observations, aiming to minimize the difference between observed and simulated values. Using daily TROPOMI SIF satellite data collected in 2019, we calibrated photosynthetic free parameters with EKI. Using our found parameter values, we see improvement within global photosynthesis calculations alignment, but also an nonphysical drop in parameter values.", "id": "Paper/72372", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72372"}, {"title": " Aggregating Multiple Local Large Language Models for Theorem Retrieval ", "webprogram_exclude": "0", "session_ids": ["Session/18159"], "source_sha256": "c9eda0f6c99008558e43783dfd02b1c9ef1c7552e6bd306f74478eea3f8a8b03", "withdrawn": "", "abstract": "This project develops a tool to support the expansion of formalized mathematics with local large language models (LLMs). Mathematicians are able to verify proofs down to their foundational axioms using a software tool called Lean4, which contains a repository of formalized mathematics. Previous work has introduced a retrieval method for defined formal mathematics in which a standard English query is compared to an LLM-produced English description of formal mathematical statements. This project aims to improve this search by leveraging multiple local LLMs, thus maintaining privacy, and aggregating results, rather than relying on a single expensive production-level model.  The retrieved results can then serve as a collection of existing formalized mathematics that may help mathematicians formalize new results.", "id": "Paper/72373", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72373"}, {"title": " Radial Basis Function Interpolation for Diffusion Weighted Imaging ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "2e09d580267ee979d2defe8d51ad8b051b5b5358b89bf661f182f10d4163babf", "withdrawn": "", "abstract": "Diffusion Weighted Imaging (DWI) measures the diffusion of water particles in multiple directions at multiple locations throughout the brain. The movement directions of these water particles can be used as a proxy for the neural connections, or fibers, of the brain. High water movement in a direction indicates more axon alignment in the direction, which indicates neural connectivity. We improved on a method first developed in Lee et al. (2018), where a combination of regional linear interpolation and Radial Basis Function (RBF) interpolation is used to increase the angular resolution of a given DWI signal at any location in the brain. Through the use of polynomial-augmented RBF techniques from numerical analysis, we extended the class of RBFs used by Lee et al. and tested various regularization parameters to improve interpolation conditions. This extension and optimization lowered the interpolation error relative to Lee et al. (2018) across the majority of the brain. In addition, our methods obtained more accurate estimates of underlying neural connectivity directions than both the uninterpolated data set and the Lee et al, data set in a majority of brain regions. To demonstrate these improvements over the original method, we developed new ways of visualizing the interpolation accuracy across the entire brain, rather than the region-based verification of previous methods which could mask differences in accuracy between selected regions.", "id": "Paper/72374", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72374"}, {"title": " Exploring the Impact of Adding a Numerical Moment Stabilizer for Approximating Viscosity Solutions ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "a92cd13ea82568b87b2b45aae2b9c0913bf5fe205dcf573c6eb4735bdd9df0c6", "withdrawn": "", "abstract": "We explore the impact of adding a numerical moment stabilizer to a simple finite difference method when seeking to approximate the viscosity solution of a fully nonlinear degenerate elliptic boundary value problem. In particular, our interest is in approximating the viscosity solution to the Monge-Amp\\`ere equation due to its applications in optimal mass transport and differential geometry.  Approximating a fully nonlinear problem using a simple finite difference approach can lead to the creation of false solutions that do not correspond to the physically relevant viscosity solution.  In order to better understand the role of the numerical moment in finding the viscosity solution instead of a false solution corresponding to a numerical artifact, we consider an analogous one-dimensional problem where we can better track the impact of the numerical moment on the corresponding nonlinear algebraic system of equations.  We show how the numerical moment can remove false solutions while formulating solvers that naturally exploit the numerical moment for selectivity.  We will also look at the impact of adding a numerical moment on the consistency error.", "id": "Paper/72378", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72378"}, {"title": " Machine-Learned Flux Limiters for Finite-Volume Methods Applied to the Compressible Euler Equations ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "1e9b4b3a29792029f750b18293edd1ca25f5b8b2ffdd1383f8d58869b5d14958", "withdrawn": "", "abstract": "Flux limiters are essential to high-resolution finite-volume methods for hyperbolic conservation laws, particularly near shocks. Conventional limiters rely on analytical criteria such as monotonicity and total variation diminishing properties, but on coarse meshes their slope reduction can excessively smear shocks and contact discontinuities, introducing numerical diffusion. Recent work showed that data-driven, piecewise-linear limiters have improved finite-volume accuracy for Burgers’ equation. This study asks whether that approach extends to the $1$D compressible Euler equations, specifically whether learned limiters improve coarse-grid accuracy while preserving stability and physical admissibility.\n\nHigh-resolution solutions provide the training data for a neural-network limiter in a conservative finite-volume shock-capturing method. To account for interacting Euler waves, the limiter uses local characteristic information. The limiter is tested against Minmod, Superbee, Van Leer, and Van Albada on Sod-type shock tubes, Lax-type shock tubes, and Toro’s $1$D Riemann problems. Solution error, shock resolution, spurious oscillations, conservation, and positivity of density and pressure are assessed. \n\nAt 200 cells, preliminary results show positive density and pressure in all cases, with a mean relative $L^1$ error of 0.0189 against 0.0257 for Minmod, a 26.5\\% reduction. That is comparable to Van Leer (0.0192) but less accurate than Superbee (0.0127). The method remains conservative, with a maximum conservation-accounting residual of about $1.3 \\times 10^{-13}$. Training a neural-network limiter end-to-end through the solver produces a physically admissible limiter that improves on Minmod at coarse resolution, though during preliminary testing it does not match the best analytical limiter (Superbee).", "id": "Paper/72379", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72379"}, {"title": " Counting Quads: From Billions of Layouts to 11 Classes ", "webprogram_exclude": "0", "session_ids": ["Session/18238"], "source_sha256": "6474029e90c862f43d1c3c19606293e6df1e86c305b00e7f774fb2636326c465", "withdrawn": "", "abstract": "Quads is a card game similar to the well-known game SET. Players search among face-up cards for a quad: four cards whose color, shape, and number are, for each attribute, either all the same, all different, or arranged in two pairs. \n\nA natural question that arises is how many quads are likely to be in a random subset of $k$ cards.  While the expected number of quads in the initial round of the game is straightforward to calculate, the probability of exactly zero, one, two, or more quads is harder to determine. \n\nBy representing cards as points in $\\mathbb{Z}_2^6$, we use change-of-basis techniques to find these probability distributions for initial layouts of up to eight cards. Although there are more than 4 billion eight-card subsets, they fall into just 11 equivalence classes distinguished by their affine structure.", "id": "Paper/72380", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72380"}, {"title": " Brunnian Links and Cohen Quandles ", "webprogram_exclude": "0", "session_ids": ["Session/18239"], "source_sha256": "5c813aa8759966fd3157942c8ed706c80351780054276805986a28dfa9739983", "withdrawn": "", "abstract": "Quandles are algebraic structures that were introduced independently by Joyce and Mateev to study links and knots. Their axioms encode the three Reidemeister moves and provide a powerful invariant of knots. A Brunnian link is one where removing any component yields a trivial link. We introduce Brunnian and Cohen quandles to study these links and their generalization. We investigate their properties, with an emphasis on finite quandles of these types that can be used to construct computable link invariants. We also demonstrate colorings of links with these quandles.", "id": "Paper/72382", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72382"}, {"title": " Recurrent Spiking Predictive Coding For Sparse R ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "df52943549bfdd54023afafca74d79f94313b6c0a9418829550c10b6178677f9", "withdrawn": "", "abstract": "With the continued progression of artificial intelligence research, the energy consumption of these systems has become a growing concern. As a result, the development of approaches that improve the energy efficiency of machine learning models has become an important, active area of research. In support of this effort, we introduce a neuroscience-informed artificial intelligence (NeuroAI) computational model that we call recurrent spiking predictive coding (RSPC), a biologically-inspired alternative to traditional neural networks grounded in principles of neuromorphic computing. RSPC leverages recurrent continuous dynamics and discrete pulse trains to produce sparse, energy-efficient representations inspired by neuronal structures in the brain. We deploy our model on a visual observation task, measuring both energy efficiency and biological plausibility in comparison to neuronal activity measured in macaque monkeys. Preliminary experiments demonstrate that our model’s sparse activation patterns are similar to those found in the macaque and demonstrate promising results for biologically-inspired energy efficient learning. Our model notably contributes a new brain-inspired framework for both neuroscience and machine learning applications, grounded in the free-energy principle, and serves as a promising stepping stone towards more energy efficient, NeuroAI machine learning methods.", "id": "Paper/72383", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72383"}, {"title": " Mixing of the Geodesic Flow via Unitary Representations of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"8.766ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 3774.2 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">SL(2,\\mathbb {R})</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-53\" d=\"M308 24Q367 24 416 76T466 197Q466 260 414 284Q308 311 278 321T236 341Q176 383 176 462Q176 523 208 573T273 648Q302 673 343 688T407 704H418H425Q521 704 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xlink:href=\"#E1-MJMAIN-32\" x=\"1716\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2C\" x=\"2217\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJAMS-52\" x=\"2662\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"3384\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/18243"], "source_sha256": "64fddaa04ff292e153671cf74932a92ce477522a46a1d7938d31c765f074ffed", "withdrawn": "", "abstract": "Following classical work of C. C. Moore and M. Ratner, we study exponential mixing of the geodesic flow on a compact hyperbolic surface $M$ using the representation theory of $SL(2,\\mathbb R)$. Realizing the geodesic flow as the action of a one-parameter subgroup turns decay of correlations into a question about matrix coefficients of a unitary representation on $L^2_0(T^1M)$. To analyze these coefficients, we decompose the representation into irreducible components, with the Casimir operator giving a spectral parameter for each. Classifying these components shows that slow decay can occur only when certain parameters approach $0$. To rule out this possibility, we use the key correspondence between the Casimir and Laplace--Beltrami operators: up to normalization, the relevant parameters are nonzero Laplace eigenvalues, so the spectral gap $\\lambda_1>0$ bounds them away from $0$.\n    \n    We then show how the differential equations satisfied by these matrix coefficients give quantitative decay estimates on each irreducible component. The decay rate is determined by the corresponding spectral parameter, and the lower bound makes this rate uniform across the decomposition. Combining the componentwise estimates gives exponential mixing of the geodesic flow for smooth observables.", "id": "Paper/72384", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72384"}, {"title": " An agent-based model of cell rolling in sickle cell disease ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "9ad2d8cc04cc66183cb3de8af18ab457025b86ec4691008d8ff9d7ec024005ab", "withdrawn": "", "abstract": "Sickle Cell Disease is a genetic condition in which red blood cells deform into stiff, sickle-like shapes. Painful crises called vaso-occlusive events occur when deformed cells accumulate behind slowly rolling white blood cells and obstruct blood flow. These dynamics are difficult to observe in vivo, and standard fluid simulations struggle to capture processes that unfold over hours. Mechanistic understanding could identify therapies and explain how microscale interactions produce vessel-scale obstruction. We developed an agent-based model that represents each rigid cell as a collection of point particles fixed relative to its centroid. Particles form and rupture adhesive bonds stochastically. At each timestep, bonds generate forces and torques, and a mobility matrix maps them to translational and angular velocities. The model runs in real time and produces rolling velocities consistent with experimental values. We investigate how cell geometry, adhesion, and flow influence cell arrest and vaso-occlusion.", "id": "Paper/72387", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72387"}, {"title": " The Synchronization of Two Hyperchaotic Circuits ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "8d82f661e8f92d3ff2f8916cd303655d1da6e4d076189a8c2d9e316d1f95850e", "withdrawn": "", "abstract": "Hyperchaos occurs in dynamical systems with multiple positive Lyapunov exponents, producing complex and unpredictable behavior. As memristor circuits can exhibit hyperchaotic behavior, a natural question arises: can the behavior of two identical memristor circuits be synchronized? We analyzed the synchronization of two such circuits through negative feedback coupling. Using a differential equation model, Lyapunov exponents, bifurcation diagrams, and synchronization error, we identified coupling strengths that caused the emulated circuits to synchronize. We are extending this work to investigate synchronization in a physically reproducible emulator of a memristor circuit. Additionally, we are investigating persistent homology as an alternative method for detecting and characterizing hyperchaotic behavior, in comparison with traditional methods such as Lyapunov exponents.", "id": "Paper/72388", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72388"}, {"title": " Exploring Euclidean Processes in Hyperbolic Geometry ", "webprogram_exclude": "0", "session_ids": ["Session/18159"], "source_sha256": "98df30aa6a45e0ba328bee086b2b1f681beaec320746b36e2e94cccfcede7b4f", "withdrawn": "", "abstract": "We examine a hyperbolic coordinate system that allows us to graph functions in the Poincar\\'e disc model, determine secant and tangent lines, evaluate areas of quadrilaterals, and lay the foundation of integration.", "id": "Paper/72390", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72390"}, {"title": " Combinatorial Descriptions of Kostka-Foulkes Polynomials ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "652bbd7b7f840b551d0eade7091bbd2039989b1c960aa3b0bc93926e84b45aa3", "withdrawn": "", "abstract": "Kostka-Foulkes polynomials are Lusztig's \\textit{q}-analogues of weight multiplicities for\nirreducible representations of semisimple Lie algebras. It has long been known that these\npolynomials have non-negative coefficients. A statistic on semistandard Young tableaux with\npartition content, called \\textit{charge}, was used to give a combinatorial formula exhibiting this\nfact in type $A$. Defining a charge statistic beyond Type $A$ has been a long-standing problem.\nRecent work has taken a completely new approach based on the definition of Kostka-Foulkes\npolynomials as an alternating sum over Kostant partitions, which can be thought of as formal\nsums of positive roots. It used a sign-reversing involution to obtain a positive expansion, in\nwhich the relevant statistic is simply the number of parts in the Kostant partitions. We extend\nthis work to Type $D$.", "id": "Paper/72392", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72392"}, {"title": " Activated Random Walk on the Complete Graph ", "webprogram_exclude": "0", "session_ids": ["Session/18243"], "source_sha256": "9a509c75c177587a23203d22b9312041af1edbca466b699416300bcf922bdd30", "withdrawn": "", "abstract": "Self-organized criticality is a physics theory for how systems like snow slopes and tectonic plates maintain critical-like states. The original sandpile metaphor for the theory entails a growing sandpile that eventually reaches a critical slope maintained by unpredictable avalanches. We show that aspects of this thought experiment occur in an interacting system of random walks on the complete graph.", "id": "Paper/72394", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72394"}, {"title": " An Inversion-Preserving Bijection Between Cayley Permutations and Fubini Rankings ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "305d7697d72eb19c7e04a419d228668297bc7af1dda112fe8d85ad2a16c34d78", "withdrawn": "", "abstract": "Cayley permutations, Fubini rankings, and unit interval parking functions are defined by different combinatorial rules, yet all three families are counted by the Fubini numbers. Our broader work explores their connections through explicit bijections and the characterization and enumeration of their intersections. This poster focuses on one of these connections which is an inversion-preserving bijection between Cayley permutations and Fubini rankings. The map replaces each entry of a Cayley permutation by one plus the number of smaller entries in the sequence. Its inverse relabels the distinct ranks in increasing order, starting at one. We show that these maps are well defined and mutually inverse, and that they preserve every pairwise comparison and thus the entire inversion set. Examples illustrate the construction and the structural correspondence between these two families.", "id": "Paper/72395", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72395"}, {"title": " Fair Duels after a False Start ", "webprogram_exclude": "0", "session_ids": ["Session/18242"], "source_sha256": "500f58603f1c2a4b4ac03df891a09be8f226b720939b5d00b34324fba6a8ec98", "withdrawn": "", "abstract": "In the fair dueling game, two players take turns shooting at each other, with each shot assigned to the player who is less likely to have won the duel so far. Cooper and Dutle showed that when both players have the same probability $p$ of a successful shot, the shooting sequence converges to the Thue--Morse sequence as $p \\rightarrow 0$. We study what happens when the sequence is forced to begin with an arbitrary finite prefix before returning to this fairness rule. We prove that this finite disruption fundamentally changes the long-term behavior: in the $p \\rightarrow 0$ limit, unless the initial prefix is itself a prefix of the Thue--Morse sequence or its complement, the resulting shooting sequence is eventually periodic. Moreover, if the initial prefix has length $n$, then the least period is a power of $2$ of size at most $4^{n+1}$, and its repeating block is itself a prefix of the Thue--Morse sequence.", "id": "Paper/72396", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72396"}, {"title": " Allopregnanolone-Modulated Bifurcations in a Thalamocortical Neural Mass Model of Absence Epilepsy ", "webprogram_exclude": "0", "session_ids": ["Session/18239"], "source_sha256": "c54108340418a1d640ed5d5588127e70c145de106f5fc315ad61635de04ed3be", "withdrawn": "", "abstract": "Childhood Absence Epilepsy is a form of epilepsy characterized by 2.5-5 Hz Spike Wave Discharges, or SWDs. It is reportedly under the dependence of neurosteroid modulation, allopregnanolone (ALLO), an allosteric modulator of synaptic receptors. Previous work showed, using numerical simulations of large-scale models of conductance-based spiking neural networks, how ALLO could control transitions between different regimes of behaviors. To go deeper into the mechanisms and nature of these transitions, we will propose a minimalistic model that represents the dynamics of the four most relevant neural populations involved in these circuits through firing rates. This neural mass model, of Jansen-Rit type, is central to deriving more analytical understanding of population rhythms and their control. We will investigate the dynamical repertoire and bifurcations of the system, with a particular focus on the role of the inhibitory kinetics, and, extending this to 2-parameter bifurcation diagrams, examine the role of ALLO alongside a control parameter governing cortical excitability and thalamocortical drive. The aforementioned allows us to identify parameter regions where SWDs arise according to Hopf-mediated onsets, and how they are organized by higher codimension bifurcations. This delineates regimes associated with asynchronous levels of activity from large amplitude rhythmic discharges typical of epileptiform activity, allowing us to highlight how ALLO shifts and decomposes the relationship between normal and SWD attractors. These analyses provide a map of how neurosteroid mediated changes in inhibition reshape seizure-like rhythms, opening the way to a principled classification of regime transitions relevant to CAE dynamics and pharmacological modulation.", "id": "Paper/72397", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72397"}, {"title": " Analyzing Public School Access In Chicago, Illinois Using Persistent Homology ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "861febada83d0d083c7a006b8892294c4b687ef634144e09da827add7aa27d3a", "withdrawn": "", "abstract": "How do we define access to education within our own communities? More importantly, how can we identify areas in these communities with significant gaps in educational coverage? In recent decades, unequal funding and resource allocations have caused gaps in educational coverage across the city, subsequently causing sudden public school closures. In order to analyze the impact that public school closures have on community access, we use the topological method of Persistence Homology to discover coverage gaps within the city. We treated each public school location as a node on a map and then increased a fixed distance, ε , between each node to create connecting edges and triangles between node locations. By visualizing the connectivity and “holes” in coverage of school locations, we can see that gaps in educational coverage is a prominent issue. We compare this analysis for assigned school locations as opposed to closest school locations to quantify educational access across Chicago’s neighborhoods. Death simplices, or the locations with the worst access to schools, often overlapped with lower income neighborhoods. This suggests that low income students are often the most affected by a lack in educational coverage. This work identifies vulnerable locations which could benefit from additional funding for their education system and areas where school closures would only further hurt the local community.", "id": "Paper/72399", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72399"}, {"title": " A Topological Analysis of Hospital Access in Massachusetts and Arkansas ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "f0386c62536567f0ac45669fd88c9cc7efcb9fd72b9444ef40905e65624f7f2d", "withdrawn": "", "abstract": "The standard federal designation of medically underserved areas relies on quantities such as poverty rate, infant mortality, and provider-to-population ratios to draw a conclusion. These measurements take these metrics and condense them into one scalar number that (dis)qualifies an area as underserved. However, the final information encoded retains nothing of how these underserved areas are arranged relative to one another. We use Topological Data Analysis and Persistent Homology to study hospital access based on the hospital locations. To do this, we construct a filtration over drive-time, where a filtration is defined as a growing sequence of shapes that encode the information at a given scale. \n\nUsing publicly available data and code, we identified the hospital locations, demographic information, and computed the drive-time between hospitals.  From this data, we formed two filtrations: a Vietoris-Rips filtration on the hospital metric space, and a sublevel-set filtration of the access function over a k-nearest-neighbor complex on populated centroids. \n\nWe compared hospital access in two states: Arkansas and Massachusetts. Using the topological features of these filtrations, we identified “holes” in access in both states. The holes present in Arkansas persist for over an hour of drivetime, while Massachusetts contains only short lived features.  By incorporating population data, we see that the holes in Arkansas’s map contain real populations rather than empty land, whereas Massachusetts's gaps track geographic barriers such as rivers and coastlines. Through comparing facility locations and population data, our approach is able to identify holes in access that affect large populations, thus identifying ideal locations for new healthcare facilities.", "id": "Paper/72400", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72400"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/17849"], "source_sha256": "7bc5e2f39cf79f17261f94a010bdb8dc495f94e5b5d597e7953d8e81333a3c3c", "withdrawn": "", "abstract": "", "id": "Paper/72401", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72401"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/17849"], "source_sha256": "a8dea2c412ee43546b9f7dc886a86615224541bb1513697a6371c0a9964945bc", "withdrawn": "", "abstract": "", "id": "Paper/72402", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72402"}, {"title": " A Complete Game of  Quads : Tracking a 16-Card Deck ", "webprogram_exclude": "0", "session_ids": ["Session/18238"], "source_sha256": "74394ddd2b61d6c3afdec7660fdc564fe928ee539a226131e02b69d2fe018637", "withdrawn": "", "abstract": "\\textit{\\textbf{Quads}} is a card game similar to the well-known game \\textit{\\textbf{SET}}. Players race to find quads—sets of four cards whose color, shape, and number are, for each attribute, either all the same, all different, or arranged in two pairs. The endgame has a striking feature: after fourteen disjoint quads have been removed, the remaining eight cards either form two disjoint quads or contain no quads. Gameplay suggests that a quad-free ending occurs more often than a quad-free set of eight cards chosen at random from the full deck. \n\n\\\\\n\nWe study how removing quads changes the distribution and expected number of quads among the remaining cards.  We use change-of-basis techniques to model the progression of an entire game using a 16-card deck and investigate larger decks through simulation. In Quad-16 and Quad-32, the expected number of quads increases as the game progresses.  In Quad-64, the expected number of quads in an 8-card layout drawn from the remaining deck is fairly constant even though there is an increased chance of no quads at the end of the game.", "id": "Paper/72403", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72403"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/18247"], "source_sha256": "141df89b3a1827597dfbc78d0ffda79bd042dfacfaaf94423277c0edf1355184", "withdrawn": "", "abstract": "", "id": "Paper/72404", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72404"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/18247"], "source_sha256": "14f3eb048184225166dde477c1697b0b82b757efcc9526ebb7aae299273fdc84", "withdrawn": "", "abstract": "", "id": "Paper/72405", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72405"}, {"title": " On Signature Characters and Unitary Loci for Type <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.797ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 1204.4 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">A_1</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-41\" d=\"M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-41\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-31\" x=\"1061\" y=\"-213\"></use>\n</g>\n</svg> and <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.797ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -791.3 1204.4 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">A_2</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-41\" d=\"M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-41\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-32\" x=\"1061\" y=\"-213\"></use>\n</g>\n</svg> Quantum Groups at Roots of Unity ", "webprogram_exclude": "0", "session_ids": ["Session/18243"], "source_sha256": "4dee5833c925f1d8bfe01401e90cc1c6f217b34fa20b175cb27e07f758eff136", "withdrawn": "", "abstract": "Quantum groups arise as $q$-deformations of universal enveloping algebras, playing beautiful roles in mathematical physics and integrable systems. One central problem in their representation theory is determining when a representation is unitary, which can be studied by computing signature characters that record the signature of an invariant Hermitian form on each weight space. While explicit signature character formulas for $U_q(\\mathfrak{gl}_n)$ are known in the generic case, the root-of-unity case is substantially more complicated in its quantum groups structures and remains open.\n\nIn this work, we present closed-form derivations of signature characters and unitary loci for Type $A_1$ and $A_2$ quantum groups at roots of unity. Specifically, we discuss three distinct forms of Type $A_1$: the De Concini-Kac quantum group, the small quantum group, and Lusztig's quantum group, while for Type $A_2$, we exclusively study Lusztig's quantum group. For the rank-one De Concini-Kac quantum group, we separately discuss the highest-weight modules with dimension $< \\ell$, the $\\ell$-dimensional fully-cyclic modules, and the $\\ell$-dimensional highest- and lowest-weight modules, where $\\ell$ is the order of $q^2$. For the highest- and lowest-weight modules, we also show that the density of roots of unity giving a unitary representation is zero. Finally, we present alternative proofs for the generic cases by algebraically constructing a modified Poincaré–Birkhoff–Witt basis and check that they agree with Venkateswaran's 2014 Gelfand--Tsetlin formulas.", "id": "Paper/72407", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72407"}, {"title": " Deciphering Single-Cell Dynamics using Applied Topology & Optimal Transport ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "3931b7a936262168597a0dfd5e791acdcbd7013ef1c44dd38981e8d940cfe5b9", "withdrawn": "", "abstract": "Single-cell RNA sequencing (scRNA-seq) provides insight into the gene expression profiles of individual cells. However, since cells are destroyed upon sequencing, only a static “snapshot” of a population's dynamics is recovered. We propose a topological and optimal transport (OT)-based framework (Cell Donut) to infer cell cycle dynamics and recover developmental trajectories from this static distribution of cells. Persistent homology is first used to identify the loop structure within high-dimensional scRNA-seq data, where circular coordinates are then assigned to each cell via persistent cohomology, using effective resistance as a metric. Entropically regularized OT is implemented to find an initial vector field from the stationary point cloud that serves as a prior for our dynamical OT framework; through a neural solver it learns a velocity field trained on angular alignment, stationarity, subsampling, and kinetic energy losses. Across both synthetic and real datasets, we find that the learned vector fields yield predicted trajectories that converge to a stable limit cycle and adhere to the known phase ordering of the cell cycle.", "id": "Paper/72408", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72408"}, {"title": " Enumerating Weak Order Unit Fubini Rankings ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "5ae523ce9ff624b2fa93d6492985f4b5d7b9122581cd7dd3b59d364dcb77de66", "withdrawn": "", "abstract": "We study Fubini rankings, unit interval parking functions, and their intersection, referred to as unit Fubini rankings, all of which are subsets of parking functions. We show that they can be characterized by the behavior of their weakly increasing elements. We use our characterizations to enumerate the weakly ordered sets. Previous work by Elder et al. (2025) shows that the cardinalities of the weakly increasing unit Fubini rankings satisfy a recursion relation and are enumerated by the Fibonacci numbers. We extend this result to show that the weakly increasing unit Fubini rankings, weakly decreasing unit Fubini rankings, and weakly decreasing unit interval parking functions have equal cardinality. Moreover, we provide an independent proof with a closed formula to establish their Fibonacci enumeration. For future study, we aim to enumerate the total displacement of Fubini rankings, unit interval parking functions, and unit Fubini rankings.", "id": "Paper/72414", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72414"}, {"title": " Quasilinearization and Padé Approximation for a Nonlinear ODE Model of Substrate Consumption in Biofilms ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "474d3ec93bfdaecf9c12da6bac99c41ec556ad6e0a584d23f72690982b1872f3", "withdrawn": "", "abstract": "A nonlinear reaction-diffusion model describing steady-state substrate consumption in a biofilm is considered. The model incorporates Michaelis-Menten kinetics together with a square-law dependence of microbial death and leads, in dimensionless form, to a nonlinear two-point boundary-value problem for the substrate concentration. Existing approximate analytical treatments of this problem have employed asymptotic approximations, Taylor series, Adomian decomposition, modified Adomian decomposition, and the Akbari-Ganji method. In this work, we propose a new method that is center-based quasilinearization approach. The nonlinear reaction term is linearized about the unknown concentration $", "id": "Paper/72416", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72416"}, {"title": " A Right-Edge Reformulation of Gilbreath’s Conjecture ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "cd72310fa9e62cf070691ffc8b1598db976c60016a29c2c719857f47f7f9b4c8", "withdrawn": "", "abstract": "Gilbreath's conjecture asserts that if one repeatedly takes absolute differences of consecutive primes, every row after the first begins with $1$: with $a_{1,n}=p_n$ and $a_{m,n}=|a_{m-1,n}-a_{m-1,n+1}|$, we have $a_{m,1}=1$ for all $m\\ge 2$. We reformulate this as a condition on the next prime. Let $(r_1,\\dots,r_n)=(a_{1,n},a_{2,n-1},\\dots,a_{n,1})$ be the $n$th right edge of the triangle, and let $S_{n+1}$ be the set of integers $x$ with $|\\cdots||x-r_1|-r_2|\\cdots-r_n|=1$. Then Gilbreath's condition holds in row $n+1$ exactly when $p_{n+1}\\in S_{n+1}$. We note that Gilbreath's condition in row $n+1$ implies $p_{n+1}-p_n\\le 1+r_2+\\cdots+r_n$, with equivalence if $S_{n+1}$ is a set of consecutive odd integers. We verify computationally that $S_n$ is a set of consecutive odd positive integers for all $n\\le 10^7$. Combined with the Baker–Harman–Pintz bound $p_{n+1}-p_n\\ll p_n^{0.525}$, this reduces Gilbreath's conjecture for all sufficiently large $n$ to two structural statements about the array: that each $S_n$ is a set of consecutive odd integers, and that the right-edge sums satisfy a weak lower bound such as $r_2+\\cdots+r_n\\ge n^{0.6}$. Numerically these sums grow linearly, and we conjecture, in line with heuristics of Granville, that $\\frac{1}{n}(r_2+\\cdots+r_n)\\to 1$, equivalently $|S_n|/n\\to 1$ assuming that $S_n$ is a set of consecutive odd integers.", "id": "Paper/72419", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72419"}, {"title": " NaturalPRISM: A Natural Language Premise Retrieval Task for Research-Level Intermediate Proof States ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "ea797c68130649cd691689b0bc8c242322effa569c11bfc9f7aa727bcdf41c1f", "withdrawn": "", "abstract": "As large language models become more involved in research-level mathematics, effective retrieval of relevant mathematical statements is increasingly important for supporting proof development. This project introduces NaturalPRISM, a large-scale benchmark and dataset for premise retrieval from natural-language mathematical proofs. We constructed the dataset by processing 235,314 arXiv mathematics papers, extracting theorem-like statements and proofs from LaTeX source, and using internal references to pair partial proofs with the mathematical statements. After filtering ambiguous or low-information examples, the resulting dataset contains more than 1.7 million query–answer pairs spanning all 32 arXiv mathematics categories. We then fine-tuned Qwen3 embedding models and evaluated both general and domain-specific retrieval strategies. Fine-tuning substantially improved retrieval performance, while models trained on data from the same mathematical domain consistently performed best on domain-specific evaluations. A lightweight routing approach that directs queries to specialized models achieved the strongest overall results. These findings show that large-scale natural-language training data can make smaller, specialized retrieval models highly effective, providing a practical foundation for retrieval-augmented systems that assist mathematicians during incremental proof development.", "id": "Paper/72420", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72420"}, {"title": " MINDFUL-AI: Measuring Learning, Dependence, Well-Being, and Academic Norms in the Age of Generative AI ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "6b1fd2aa00801a62f7d1322a758bab03a6100026f159b24ec4946c781a6b9ec1", "withdrawn": "", "abstract": "MINDFUL AI is a research study examining how generative artificial intelligence influences learning, dependence, confidence, workload, stress, academic norms, and institutional guidance in higher education. Using parallel surveys of students and faculty at United States universities, primarily in Florida, the study will compare patterns of artificial intelligence use and perceptions across both groups. It will investigate cognitive offloading, perceived learning quality, academic confidence, privacy concerns, social pressure, and ethical expectations. Findings will help identify the benefits and risks of generative artificial intelligence use and inform evidence-based teaching practices, institutional policies, faculty development, and future research on responsible artificial intelligence adoption.", "id": "Paper/72421", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72421"}, {"title": " FlowPro: Efficient Training of Neural Networks for Flow Matching ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "93d058dfd7a901146e5415f7ce090a9302e9cca98b3090e22d30c6ed58a4097f", "withdrawn": "", "abstract": "The efficiency of the training process for generative models has been of great interest to the machine learning community in recent years. In this paper, we introduce FlowPro, a flow matching architecture that uses the Variable\nProjection (VarPro) technique to more efficiently train the neural network used in flow matching\nby taking advantage of the linear final layer of a separable neural network. We discuss both the results of numerical experiments in various settings as well as some theoretical results relating to training error estimation and local convexity in the VarPro implementation. Overall, we find that FlowPro\neither matches or outperforms traditional flow matching in terms of both training efficiency and accuracy.", "id": "Paper/72422", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72422"}, {"title": " The Winning Threshold for the Chip-firing Game On Certain <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"7.207ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 3102.9 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">(n-2)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-6E\" x=\"389\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2212\" x=\"1212\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-32\" x=\"2212\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"2713\" y=\"0\"></use>\n</g>\n</svg>-Uniform Hypergraphs ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "9d78860b1365523148f60624171f0b0ddc71fc3bc42f3416b0636c7b6d865f6d", "withdrawn": "", "abstract": "In this paper, we consider the chip-firing dollar game on certain uniform\nhypergraphs, which we call \\emph{two less adjacent polygon cyclically directed\nhypergraphs} (TLAPCDHs) with $p$ adjacent same-direction hyperedges.  Each\nhyperedge contains $n-2$ of the $n$ vertices, and the two vertices it omits\nare adjacent on the  polygon.  Our main result is that the winning\nthreshold for this game, i.e., the minimum total number of dollars needed to\nguarantee a winning strategy, is $pn-3p-n+1$.  This extends work of\nSarah Quintanilla on the one less family (OLAPCDHs), where the corresponding\nthreshold is $pn-2p-n+1$.", "id": "Paper/72423", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72423"}, {"title": " Deforming the Defensive Block: A Spatiotemporal Model of Ball Circulation and Defending Geometry in Elite Soccer ", "webprogram_exclude": "0", "session_ids": ["Session/18243"], "source_sha256": "38aa2b38e2430fb87096f418f7a57883065912b9077ff0871fc103ad55d31a12", "withdrawn": "", "abstract": "Traditional soccer analytics heavily rely on ball-centered metrics like location, expected threat, and forward progression. However, attacking teams often generate value not by immediately advancing the ball, but by circulating it to disrupt the opponent's defensive structure. This study models the defending team as a time-varying spatial configuration to evaluate whether defensive deformation captures attacking value missed by traditional metrics. Using player- and ball-tracking data, we extract geometric features (e.g., width, depth, compactness, centroid movement) and pair them with temporal ball-circulation metrics (e.g., tempo, switches of play). We evaluate four predictive models across settled and transition phases to forecast high-value attacking events, including penalty-area entries and shots. Our results demonstrate whether integrating defensive deformation significantly improves predictive power over baseline, ball-centered models, offering a deeper framework for quantifying off-ball attacking value.", "id": "Paper/72425", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72425"}, {"title": " Exploring a Matrix Representation of Braids ", "webprogram_exclude": "0", "session_ids": ["Session/18159"], "source_sha256": "bb4883b005b57943d10a04d0261b4d65968b59a9f704c82ee301fa04f87ac8a4", "withdrawn": "", "abstract": "We define a homomorphism which maps an $n$-strand braid to an $n \\times n$ square matrix, creating a matrix representation of the braid. We explore what information this matrix representation provides about the braid and, in particular, look at the kernel of the homomorphism.", "id": "Paper/72427", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72427"}, {"title": " Beyond the Ball: Defensive Deformation as a Predictor of Attacking Development in Professional Soccer ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "fc976e035104a907002b0c7e96c2e745df6b71f56f51f73f0259e8e29c4a64b8", "withdrawn": "", "abstract": "Traditional soccer analytics evaluates attacking play primarily through ball metrics, forward progression, and final possession outcomes. However, teams frequently generate attacking value not by advancing the ball immediately, but through purposeful circulation that reshapes the opponent's defensive structure. This study investigates whether the evolving geometry of a defending team contains predictive information about attacking development that ball position and progression alone omit. Using high-resolution tracking data, we model the defense as a time-varying spatial configuration characterized by geometric features: width, depth, compactness, occupied area, centroid shifts, and inter-player spacing. These spatial structures are paired with temporal indicators of ball circulation, such as pass speed, tempo, switches of play, and possession history. We systematically evaluate predictive performance across four progressively informative models, scaling from a baseline ball-centered model up to a full framework incorporating defensive geometry and circulation tempo. Settled possessions and transition attacks are analyzed independently to assess how tactical context influences feature importance. Finally, attacking development is quantified using penalty-area entries, shot generation, and fluctuations in possession value. Our findings demonstrate whether tracking defensive deformation unlocks measurable predictive insights that conventional, ball-centered frameworks fail to capture.", "id": "Paper/72429", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72429"}, {"title": " Lehmer Codes and the Reverse-Complement Mapping from <u>32</u>1-Avoiding Permutations to 3<u>21</u>-Avoiding Permutations ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "571b84abc5605a7fcb575ce72f2a6a2843edd23eb6b21d15febc0551dca6c5a1", "withdrawn": "", "abstract": "Let $\\mathcal{S}_n(\\underline{32}1)$ and $\\mathcal{S}_n(3\\underline{21})$ denote the sets of $n$-permutations avoiding the vincular patterns $\\underline{32}1$ and $3\\underline{21}$, respectively. These patterns refine classical permutation patterns by requiring certain entries to occur in adjacent positions. We study these avoidance classes through their Lehmer codes, which record the number of smaller entries appearing to the right of each position and therefore encode the inversion number of a permutation. Using Lehmer codes, we realize these families as weighted posets $\\mathcal{L}_n(\\underline{32}1)$ and $\\mathcal{L}_n(3\\underline{21})$, where the weight of a code is the inversion number of its permutation. We focus on the maximal elements of these posets and show that both $\\mathrm{Max}\\, \\mathcal{L}_n(\\underline{32}1)$ and $\\mathrm{Max}\\,\\mathcal{L}_n(3\\underline{21})$ are enumerated by the Fibonacci numbers. We then show that the classical reverse-complement map on permutations restricts to a natural bijection between these two sets of maximal elements. This gives a simple permutation-level explanation for a symmetry between the two families and their Lehmer-code structures.", "id": "Paper/72430", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72430"}, {"title": " Tree Eigenvalues Whose Squares Are Quadratic ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "4906107de0733a03e9b521218be54794e49ed3c24e651b97ddab4c8608c0c6c2", "withdrawn": "", "abstract": "Every totally real algebraic integer is an eigenvalue of a finite tree. We study a quantitative version of this theorem: given an algebraic integer \\(\\lambda\\), how small can a tree realizing \\(\\lambda\\) be? We focus on nonzero totally real algebraic integers for which \\(y=\\lambda^2\\) has quadratic minimal polynomial\n\\[\nF(Y)=Y^2-TY+N,\n\\]\nand compare three natural families: height-two trees, caterpillars, and spiders.\n\nFor height-two trees, the eigenvalue condition becomes the exact identity\n\\[\n\\sum_k \\frac{a_k}{y-k}=1,\n\\]\nturning the search for a smallest tree into an integer optimization problem. For caterpillars, an eigenvector calculation yields a polynomial recurrence along the spine. This gives a classification for two spine vertices and enables exhaustive searches by order for longer spines. We also reduce the caterpillar calculation modulo several primes. Over a finite field, the two tree-building operations act as projective linear transformations, so candidate caterpillars correspond to paths in a finite directed graph. Because modular solutions need not lift, every candidate is verified using the exact spine recurrence. For spiders, interlacing gives a spectral obstruction, while the limiting behavior of path-leg functions restricts the center degree to at most two possible integers. For 1,222 quadratic targets with \\(T\\le 25\\), our computations certify the smallest tree among these three families in 814 cases.", "id": "Paper/72431", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72431"}, {"title": " Equivariant Combinatorics through Tambara Reciprocity for Sums ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "822faa8b8f0a7a13ea87524315f7a456566ca450c1f4a70021e6b68a364fb0cd", "withdrawn": "", "abstract": "We examine the combinatorial aspects of the Burnside ring $A(G)$ of a finite group $G$ in the context of Tambara functors, recovering an orbit-preserving strengthening of the P\\'olya enumeration theorem. We define the ring of power series $A(G)[\\![t_{1}, \\ldots, t_{k}]\\!]$ as a Tambara functor, in which the norm $\\mathrm{nm}_{H}^{G}X$ records $X$-colorings of $G/H$. This functor also gives rise to a family of power series Tambara functors via Day convolution. Additionally, we generalize a result of Hill and Mazur about the norm of a sum in a Tambara functor over a cyclic $p$-group to all finite abelian groups.", "id": "Paper/72432", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72432"}, {"title": " Low-Cost Localization of Aircraft On and Near the Ground with the Extended Kalman Filter ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "2c106d6f3d5285cb13da6c02fc272cf837b9c93e3d14f2fd0b2a1f832cd78280", "withdrawn": "", "abstract": "The GPS, radar and other specialized sensors that airports use to locate aircraft have accuracy limitations due to signal obstructions near the ground and are prohibitively expensive for smaller airports. We introduce cameras as alternative or supplementary sensors and formulate localization as a nonlinear filtering problem, and estimate the state with the Extended Kalman Filter.\n\nWe derive simulated GPS, radar and camera measurements from historical flight trajectories. For a given aircraft, we feed these measurements into the Extended Kalman Filter and show that fusing measurements with idealized models of existing airport radar and GPS measurements improves estimation accuracy.\n\nRelative to GPS and GPS-and-radar configurations, camera inclusion reduces root mean squared error by about 60\\% and 25\\%, respectively, for a nominal increase in projected cost. We see that the GPS-and-camera configuration falls within 5\\% of the GPS-and-radar configuration for a tenth of the cost.\n\nFinally, we expand our solution by simulating trajectories for several aircraft and use the Multiple Hypothesis Tracking algorithm to assign data to each aircraft. Our results show promise for reliably maintaining correct aircraft-to-track associations, even when aircraft trajectories are near or cross over.", "id": "Paper/72433", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72433"}, {"title": " A Bound on the Fractal Uncertainty Exponent for a Square Alphabet ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "c8ece8d1a019d032b268270b0b38ec4646122096a0637be366bd66e62017e2c9", "withdrawn": "", "abstract": "We prove a lower bound of $\\frac{1}{2}- \\frac{7 \\delta}{8} - \\epsilon$ ($0 < \\delta \\leq \\frac{1}{4}$) on the fractal uncertainty exponent $\\beta$ for dilated Cantor sets $C_{k}(N)$ when the alphabet $\\mathcal A$ is given by squares, thus leading to an improvement of $\\frac{\\delta}{8}$ on the general bound of $\\frac{1}{2}-\\delta$ for undilated Cantor sets. If we restrict the dilation parameter to rational numbers with big denominator, we prove a stronger lower bound of $\\frac{1}{2} - \\frac{3 \\delta}{4}-\\epsilon$ on the fractal uncertainty exponent, which gives an improvement of $\\frac{\\delta}{4}$. As an application, these improved fractal uncertainty exponents yield corresponding spectral gaps for the associated open quantum Baker's maps.", "id": "Paper/72438", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72438"}, {"title": " AXIOS: Preserving Vertical Federated Learning Model Integrity via Decentralized Training-Time Anomaly Detection ", "webprogram_exclude": "0", "session_ids": ["Session/18243"], "source_sha256": "e2bd016776a87faac6a8cf3afb7bee4eea141c7bf1754433829d2abb073f06ca", "withdrawn": "", "abstract": "As the predictive capabilities of neural networks continue to shape the ways we make sense of the world, it is crucial to maintain the integrity of the data and training that inform these systems. Vertical Federated Learning (VFL) addresses this concern by providing a mechanism for collaborative machine learning among participants whose data occupies the same sample space but partitions the feature space, all without requiring the sharing of private data. However, distributing training among participants while keeping data private increases the challenge of detecting anomalous contributions, as dissimilar contributions are expected in a VFL setting. Existing methods which maintain privacy and model robustness while implementing anomaly detection rely on trusted entities or auxiliary data. To address this tension between privacy and anomaly detection, we propose AXIOS, a framework for decentralized VFL which utilizes cross-participant anomaly detection and an on-chain consensus protocol to ensure the trustworthy training of a collaborative model, without needing access to raw intermediate data or assumptions of honest participants. Our experimental results show that AXIOS improves training-time anomaly detection through decentralization, is scalable with respect to number of participants, and improves overall model accuracy across popular image datasets.", "id": "Paper/72441", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72441"}, {"title": " Stabilization and Computational Reduction of Khovanov Homology for <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.162ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 500.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">3</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-33\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>- and <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.162ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 500.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">4</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-34\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-strand Torus Braids ", "webprogram_exclude": "0", "session_ids": ["Session/18243"], "source_sha256": "33d3f7e19e61709c8535ae7de86cc2524e1a1f7e30ca529559e724a1ffe4c7d3", "withdrawn": "", "abstract": "We investigate computational methods for reducing the complexity of the Khovanov chain complexes of $3$- and $4$-strand torus braids. We develop code to complement the theoretical algorithmic generation of Kauffman states and their associated Temperley-Lieb words. We explore the back and forth between identifying isomorphism patterns of Gaussian elimination in order to improve computation and using computation to better identify these patterns. \nWe extend the computational techniques of Lee to $4$-strand torus braids and identify a more complicated isomorphism structure for simplifying the chain complex. This talk will illustrate how Gaussian elimination transforms the original Khovanov complex, as implemented in the algorithms, and discuss the theoretical patterns that emerge from the resulting data for $3$- and $4$-strand torus braids.", "id": "Paper/72442", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72442"}, {"title": " Formalization of Sullivan’s No Wandering Domains Theorem in Lean ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "ed5f1b0a77500c7e005cc7cd867bd8ed320b804da130a8b09e91379f34647059", "withdrawn": "", "abstract": "We report on a Lean 4 formalization of Sullivan's No Wandering Domains theorem: every Fatou component of a rational self-map of the Riemann sphere of degree at least two is eventually periodic. The project formalizes the relevant background in normal families, the Montel-Carath\\'{e}odory theorem, Julia and Fatou sets, local Sobolev regularity and Wirtinger derivatives, the Cauchy and Beurling transforms, the equivalence of analytic and geometric quasiconformality, and the measurable Riemann mapping theorem. The poster will describe the translation of this mathematics into Lean, the proof architecture, the reusable components, and the autoformalization workflow.", "id": "Paper/72443", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72443"}, {"title": " A Topological Interpretation of Divisibility ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "3e4a1a932204bc88bbda3130b86ac08be0742d525bcf9e1ce7b4b97b997fe72d", "withdrawn": "i", "abstract": "We study divisibility through the strongly multiplicatively closed (SMC) topology on a commutative ring, whose open sets are precisely the subsets closed under multiplication by arbitrary ring elements. This Alexandrov topology has a basis of principal ideals and extends naturally to commutative semigroups. We characterize its closure operator and specialization preorder in terms of divisibility. Continuous maps are exactly the maps that preserve divisibility, while homeomorphism is determined by the ordered set of associate classes together with their cardinalities. We show that compact open sets are precisely finite unions of principal ideals and that a unital commutative ring is Noetherian as an SMC space if and only if it is a Cohen--Kaplansky ring. We also obtain semigroup criteria for compactness and Artinianness and characterize sobriety for monoids by antisymmetry of divisibility and the descending chain condition on principal right ideals. The compactness characterization leads to a study of finite unions of ideals and principal ideals, including criteria in polynomial rings. Finally, for cancellative commutative monoids, we characterize finite, half-factorial, and bounded factorization through finiteness, grading by factorization length, and finite height of divisor class posets, respectively. These results identify both the algebraic information retained by the SMC topology and the limits of recovering ring structure from divisibility.", "id": "Paper/72444", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72444"}, {"title": " Cubic surfaces over <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.409ex\" height=\"2.843ex\" style=\"vertical-align: -1.005ex;\" viewBox=\"0 -791.3 1037.1 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbb {F}_q</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJAMS-46\" d=\"M584 499Q569 490 566 490Q558 490 552 497T546 515Q546 535 533 559Q526 574 506 593T469 621Q415 648 326 648Q293 648 287 647T275 641Q264 630 263 617Q262 609 260 492V370L275 372Q323 376 350 392T393 441Q409 473 409 506Q409 529 427 529Q437 529 442 519Q444 511 444 362Q444 212 442 206Q436 197 426 197Q409 197 409 217Q409 265 375 299Q346 328 280 335H260V206Q260 70 262 63Q265 46 276 41T326 35Q362 35 366 28Q377 17 366 3L360 -1H24Q12 5 12 16Q12 35 51 35Q92 38 97 52Q102 60 102 341T97 632Q91 645 51 648Q12 648 12 666Q12 675 24 683H573Q576 678 584 670V499ZM137 341Q137 131 136 89T130 37Q129 36 129 35H182Q233 35 233 39Q226 54 225 92T224 346L226 623L231 635L235 648H129Q132 641 133 638T135 603T137 517T137 341ZM549 603V648H495L506 641Q531 621 533 619L549 603ZM409 317V395L400 386Q390 376 375 366L357 355L373 346Q394 331 397 328L409 317Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-71\" d=\"M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJAMS-46\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-71\" x=\"864\" y=\"-213\"></use>\n</g>\n</svg> with 27 lines over <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"3.247ex\" height=\"3.009ex\" style=\"vertical-align: -1.171ex;\" viewBox=\"0 -791.3 1398.2 1295.7\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbb {F}_{q^2}</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJAMS-46\" d=\"M584 499Q569 490 566 490Q558 490 552 497T546 515Q546 535 533 559Q526 574 506 593T469 621Q415 648 326 648Q293 648 287 647T275 641Q264 630 263 617Q262 609 260 492V370L275 372Q323 376 350 392T393 441Q409 473 409 506Q409 529 427 529Q437 529 442 519Q444 511 444 362Q444 212 442 206Q436 197 426 197Q409 197 409 217Q409 265 375 299Q346 328 280 335H260V206Q260 70 262 63Q265 46 276 41T326 35Q362 35 366 28Q377 17 366 3L360 -1H24Q12 5 12 16Q12 35 51 35Q92 38 97 52Q102 60 102 341T97 632Q91 645 51 648Q12 648 12 666Q12 675 24 683H573Q576 678 584 670V499ZM137 341Q137 131 136 89T130 37Q129 36 129 35H182Q233 35 233 39Q226 54 225 92T224 346L226 623L231 635L235 648H129Q132 641 133 638T135 603T137 517T137 341ZM549 603V648H495L506 641Q531 621 533 619L549 603ZM409 317V395L400 386Q390 376 375 366L357 355L373 346Q394 331 397 328L409 317Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-71\" d=\"M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJAMS-46\" x=\"0\" y=\"0\"></use>\n<g transform=\"translate(611,-243)\">\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-71\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.574)\" xlink:href=\"#E1-MJMAIN-32\" x=\"572\" y=\"355\"></use>\n</g>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "15fc7ce63eb4962733530d160db81d9e691982a47cb3b4e038c63fe5e253abdf", "withdrawn": "", "abstract": "We study cubic surfaces over $\\mathbb{F}_q$ that contain 27 lines defined over $\\mathbb{F}_{q^2}$. We show all such cubic surfaces have at least one real tritangent plane. We propose a procedure to construct a class of these cubic surfaces, adapting a method used by Betten and Karaoglu (2022) to compute the number of cubic surfaces over $\\mathbb{F}_q$ with 27 rational lines. We also propose a method to compute the explicit equations of the 27 lines on cubic surfaces in this class, as well as the equations of the tritangent planes over $\\mathbb{F}_q$, building on the arc-lifting algorithm developed by Betten, Hirschfeld and Karaoglu (2018).", "id": "Paper/72450", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72450"}, {"title": " A New Variation of the Cops and Robbers Game ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "4fd4aa5c93ccdbaf7905f539eb1a2dedee0210ed5440d1f17022ce93592747a9", "withdrawn": "", "abstract": "The Cops and Robbers game is played on a graph where a team of cops attempts to capture a robber by moving along the edges of the graph. We consider a variation of the game in which the robber is allowed to remove an edge after traversing it. We investigate how this new rule affects which graphs are cop-win, the cop number of graphs, and the strategies available to both the cops and the robber. Allowing the robber to remove edges can fundamentally change the outcome of the game, and we identify cases in which the robber can evade capture on graphs that are cop-win under the traditional rules.", "id": "Paper/72452", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72452"}, {"title": " Field-Programmable Gate Array (FPGA) Routing over the Min-Plus Semiring on Client GPUs ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "7d85e630897756b62bf249e4ee4fc42757166369731e0be062c527f521d067b7", "withdrawn": "", "abstract": "Field-programmable gate arrays (FPGAs) are integrated circuits that are programmable after manufacturing and deployment, making them useful across a wide range of applications. The most time-intensive stage of FPGA design is routing, in which signals are assigned paths along the physical hardware connecting the logic blocks. In the widely used FPGA routing algorithm, PathFinder, the problem of routing is simplified to iterating single-source shortest path (SSSP) calculations by penalizing paths that share resources. \nThese shortest path calculations can be reformulated algebraically over the min-plus semiring, allowing them to be expressed as sparse matrix operations. \nWe developed an SSSP kernel using the HIP/ROCm framework for client GPUs and benchmarked it against existing industry standards, with the goal of improving runtimes without compromising the critical-path wirelength metric. \nWe present results from our routing implementation and demonstrate proof-of-concept performance for accelerating shortest-path computations arising in FPGA routing on client GPUs.", "id": "Paper/72458", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72458"}, {"title": " Maximizing the discrepancy between zero forcing parameters relative to graph order ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "d571df52f9f40cf7272c79940c4f66bd17ee1af6566a8bf512aa5e65feea290d", "withdrawn": "", "abstract": "The zero forcing color change rule states that, at every iteration, a blue vertex adjacent to exactly one uncolored vertex colors its neighbor blue. A set of blue vertices that is capable of iteratively coloring each vertex in the graph is termed a zero forcing set. In our research, we maximize the discrepancy between various zero forcing parameters relative to graph order. First, we find an upper bound on the difference in cardinality between minimal zero forcing sets (sets containing no proper zero forcing subset) of maximum and minimum size, and we show that this bound is sharp for an infinite family of graphs. Furthermore, we derive an upper bound on the discrepancy between the maximum and minimum propagation times—the number of time steps to color the entire graph—of the minimum zero forcing sets of any graph. We show also that this bound is sharp for an infinite family of graphs.", "id": "Paper/72466", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72466"}, {"title": " Relative Humidity and Wind Speed for Long-Term Electric Load Forecasting ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "73420c8bd70abf106f2fd1c4ea3bd5a6c9d6a7ff56c4c329a27cef80225de890", "withdrawn": "", "abstract": "Electric load forecasting is the process of predicting future electricity demand through historical data and explanatory variables. The most widely used explanatory weather variable is temperature, but others, such as wind speed and relative humidity, have also been studied to determine their effectiveness. We recreate two high-performing linear regression models from the past decade, one with wind speed terms and the other with relative humidity terms, and compare their performance to Tao's Vanilla Benchmark Model and its extension with recency effect temperature terms. We then propose a new comprehensive model including both wind speed and relative humidity terms. These models are tested for year-ahead point forecasting and then extended to year-ahead probabilistic forecasting. The case study is performed on Boston load data from ISO New England, and weather conditions from Boston Logan International Airport. For point forecasting, the wind speed model and relative humidity model are both shown to outperform the Vanilla Benchmark and recency effect models in all cases, and the comprehensive model is shown to outperform all four prior models in all cases, demonstrating the value of including both weather variables simultaneously. The same is found for probabilistic forecasting, across all scenario generation settings explored. In particular, depending on the scenario generation method, the comprehensive model demonstrates a 1.53\\%--3.14\\% improvement in quantile score compared to the Vanilla Benchmark and a 0.63\\%--1.45\\% improvement in quantile score compared to the recency effect model. This work demonstrates the value of relative humidity and wind speed variables even in probabilistic forecasting where their exact values are unknown.", "id": "Paper/72467", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72467"}, {"title": " Generalized Ramsey Numbers for Trees ", "webprogram_exclude": "0", "session_ids": ["Session/18159"], "source_sha256": "52875ecfa214283df0c29f353c06f609bbf1b5ed08eacb64219a11477361da17", "withdrawn": "", "abstract": "Generalized Ramsey problems ask how restrictions on the colors appearing in small subgraphs constrain the total number of colors. For example, given an edge coloring of $K_n$ in which every $k$ vertices span at least $\\ell$ colors, what is the smallest number of colors the graph may have? These problems have been studied for common families of graphs, including cycles, paths, and complete bipartite graphs. Surprisingly, almost nothing was known for trees.\n\nWe obtain nearly tight bounds on the minimum number of colors in an edge-coloring of $K_n$ in which every copy of every tree on $k$ vertices has at least $\\ell$ colors. For every $d$, when $\\ell =\\lfloor k/(d+1) + d\\rfloor$, we show that the graph has $\\Omega(n^{1+1/d})$ colors. We also provide an upper bound that is close to this lower bound.", "id": "Paper/72468", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72468"}, {"title": " On the Cardinality of the Smith Set Under Impartial Culture With Many Alternatives ", "webprogram_exclude": "0", "session_ids": ["Session/18243"], "source_sha256": "936f1ac87cf7ea4d024d37fefc192e39590479cee8f16211db57c815b1626212", "withdrawn": "", "abstract": "For some integer $\\ell\\geq 2$, consider $m=2\\ell-1$ voters, each of whom has a preference ranking over $n$ alternatives.\nThe Smith set is the smallest nonempty set of alternatives that defeats every alternative outside the set in pairwise majority comparisons.\nUnder the standard benchmark \\textit{impartial culture} where each voter uniformly and independently chooses a random preference ranking over all alternatives, \nwe study the asymptotic probability that the Smith set has cardinality $s$ for fixed $\\ell$ and $n\\to \\infty$.\n\nFirst, we prove that the probability that the Smith set has constant cardinality $s$ goes to zero at a rate of $\\Theta_{\\ell,s} (n^{-s(\\ell-1)/\\ell})$. \nNext, if $\\min\\{s,n-s\\}\\to\\infty$, we show that this probability decays superpolynomially.\nFurther, when $s$ and $n-s$ are both $\\Theta(n)$, we prove that the probability decays exponentially and determine the exact exponential base. \nFinally, we prove that the probability that the Smith set contains all alternatives approaches one at a rate of $\\Theta_\\ell(n^{-(\\ell-1)/\\ell})$. These statements resolve the conjectures posed by Liu et al. under impartial culture (2026, arXiv:2503.10990v2; accepted in Annals of Statistics).", "id": "Paper/72469", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72469"}, {"title": " Evaluating In-game Win Probabilities: ESPN’s Live-game Model vs. Benchmarks and Statistical Models ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "c804d62507aa9b5dcf59403f5afeaee82c2134ecf60b577a3ce8bc754f14e354", "withdrawn": "", "abstract": "In recent years, ESPN and other sports websites have been posting charts of real-time in-game win probabilities. How reliable are these win probabilities in predicting the ultimate outcome of the game? To what extent does this reliability improve over the course of a game? Are there significant differences  between sports in terms of the reliability of their in-game win probabilities? Using metrics initially developed to evaluate accuracies of probabilistic weather forecasts, we quantify the accuracy of ESPN’s model and compare it to the accuracies of standard benchmarks as well as regression and machine learning models.", "id": "Paper/72471", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72471"}, {"title": " A Spectral Characterization of Perfect State Transfer in Non-Hermitian Tridiagonal Matrices ", "webprogram_exclude": "0", "session_ids": ["Session/18160"], "source_sha256": "a6326f43ade7c0586a4b9ae0405a9b381dc12fc6663876ca8e4f9a13d8d95676", "withdrawn": "", "abstract": "In quantum mechanics, the states of quantum particles are described using probability. Perfect state transfer (PST) occurs when a quantum state localized at one site evolves to a target site with probability one. Equivalently, PST from the first site to the $N$-th site occurs when there exist some time $t>0$ and $\\varphi\\in\\mathbb{R}$ such that\n$e^{it\\mathbf{H}}\\mathbf{e}_1=e^{i\\varphi}\\mathbf{e}_N$,\nwhere $\\mathbf{H}$ is a Hermitian tridiagonal matrix, and $\\mathbf{e}_1$ and $\\mathbf{e}_N$ are standard basis vectors corresponding to the first and $N$-th sites, respectively. A. Kay gave a spectral characterization of Hermitian tridiagonal matrices $\\mathbf{H}$ that realize PST. We extend this result to a class of non-Hermitian tridiagonal matrices that arise in models recently studied by physicists (X. Z. Zhang et al., M. Znojil). In particular, we show that these matrices achieve PST exactly when $\\mathbf{H}$ is symmetric across the antidiagonal, and the spacings between consecutive eigenvalues $\\lambda_k$ are given by $\\lambda_{k+1}-\\lambda_k=m_k\\dfrac{\\pi}{t}$ for some $m_k \\in \\mathbb{Z}$ for $k=1,2,\\ldots,N-1$. We then provide an algorithm for constructing such matrices from some sets of eigenvalues that satisfy the condition.", "id": "Paper/72473", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72473"}, {"title": " Connections Between Hypergraph and Vector Parking Functions ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "55d08a64fbaef4b006c3cc5a9fe5e11ed706e4a559f17a98e089b484442b6590", "withdrawn": "", "abstract": "Parking functions are well-studied objects in the field of combinatorics. There are many ways to generalize these objects. We work with two ways to generalize them: hypergraph parking functions and vector parking functions. Our main goal is to classify which types of hypergraphs, or more specifically multihypergraphs, have the property that their set of hypergraph parking functions are the same as the set of vector parking functions for some vector $\\vec u$. This is a generalization of a theorem of Gaydarov and Hopkins from 2016. This classification is motivated by the problem of counting superstable configurations on a hypergraph/multihypergraph which have a one-to-one correspondence with hypergraph parking functions.", "id": "Paper/72478", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72478"}, {"title": " Tipping Cascades in a Simple Numerical Model of Antarctic Ice Shelves ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "9b53632fd2d1b675819845a2c02b0e9d441b0460f322bc32adc94ebdb71acdbd", "withdrawn": "", "abstract": "Tipping cascades occur in networks of coupled dynamical systems where nodes on the network can undergo saddle-node bifurcations, and where interactions between nodes can cause system-wide cascades of tipping behavior. We consider the tipping behavior of ocean melting of ice shelves around the Antarctic Ice Sheet, which can be described by a simple mathematical model of ocean circulation and melt. Complex numerical models of Antarctic ice shelves have shown that shelf cavities generally exist in either high or low melt rate steady states. We use a network of coupled models of Antarctic ice shelf melt to explore the phase space of this dynamic network of interacting ice shelves around Antarctica. We interrogate controls on the coupled tipping behavior through analysis of the behavior of many randomly generated ice shelf systems. We discuss our results in the context of recent work on tipping cascades in networked dynamical systems.", "id": "Paper/72482", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72482"}, {"title": " Improving the Robustness of Surgical Instrument Segmentation Models via GAN-Based Data Augmentation ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "3f4026f426b7b6dd1218630008c1bdbe0dcbef1f54a37f2b9ef6aa4538a3c101", "withdrawn": "", "abstract": "In robotics-assisted surgery, accurate segmentation of surgical instruments from background pixels is crucial for the success of various downstream tasks. Currently, popular segmentation models such as the U-Net exhibit excellent performance under major surgical conditions. However, when benchmarking the segmentation models under unforeseen surgical complications such as overbleeding, concerns toward their robustness remain. In fact, due to the lack of training datasets for the surgical segmentation models under complications, these models often exhibit degraded performances and thus result in failures for conducting accurate segmentations at the pixel level. In this paper, we leverage the Generative Adversarial Network (GAN), specifically through generating realistic images that simulate the condition of overbleeding to enlarge the training datasets  — a process known as data augmentation. With more diverse training data from different scenarios, segmentation models can be trained better and reduce the risk of errors. In addition, a dataset consisting of 17 mock endoscopic video sequences with binary masks indicating ground truths was used for training/testing. With the dataset, a U-Net architecture is used to examine performance through metrics such as the Normalized Surface Distance (NSD) and Dice Similarity Coefficient (DSC). As a result, integrations with GAN-based data augmentation allow segmentation models' performances to improve 9.07\\% for NSD and 6.63\\% for DSC. From the results, our GAN-based augmentation is proven to be effective, providing a novel direction for improving models' robustness during the training procedure, paving the way for future exploration and clinical translation of the cutting-edge deep learning models into real robotics surgery.", "id": "Paper/72484", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72484"}, {"title": " The prime graph complements of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"3.731ex\" height=\"2.676ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -863.1 1606.3 1152.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathcal {A}_{11}</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJCAL-41\" d=\"M576 668Q576 688 606 708T660 728Q676 728 675 712V571Q675 409 688 252Q696 122 720 57Q722 53 723 50T728 46T732 43T737 41T743 39L754 45Q788 61 803 61Q819 61 819 47Q818 43 814 35Q799 15 755 -7T675 -30Q659 -30 648 -25T630 -8T621 11T614 34Q603 77 599 106T594 146T591 160V163H460L329 164L316 145Q241 35 196 -7T119 -50T59 -24T30 43Q30 75 46 100T74 125Q81 125 83 120T88 104T96 84Q118 57 151 57Q189 57 277 182Q432 400 542 625L559 659H567Q574 659 575 660T576 668ZM584 249Q579 333 577 386T575 473T574 520V581L563 560Q497 426 412 290L372 228L370 224H371L383 228L393 232H586L584 249Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJCAL-41\" x=\"0\" y=\"0\"></use>\n<g transform=\"translate(798,-150)\">\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-31\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-31\" x=\"500\" y=\"0\"></use>\n</g>\n</g>\n</svg>- and <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"3.731ex\" height=\"2.676ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -863.1 1606.3 1152.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathcal {A}_{13}</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJCAL-41\" d=\"M576 668Q576 688 606 708T660 728Q676 728 675 712V571Q675 409 688 252Q696 122 720 57Q722 53 723 50T728 46T732 43T737 41T743 39L754 45Q788 61 803 61Q819 61 819 47Q818 43 814 35Q799 15 755 -7T675 -30Q659 -30 648 -25T630 -8T621 11T614 34Q603 77 599 106T594 146T591 160V163H460L329 164L316 145Q241 35 196 -7T119 -50T59 -24T30 43Q30 75 46 100T74 125Q81 125 83 120T88 104T96 84Q118 57 151 57Q189 57 277 182Q432 400 542 625L559 659H567Q574 659 575 660T576 668ZM584 249Q579 333 577 386T575 473T574 520V581L563 560Q497 426 412 290L372 228L370 224H371L383 228L393 232H586L584 249Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJCAL-41\" x=\"0\" y=\"0\"></use>\n<g transform=\"translate(798,-150)\">\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-31\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-33\" x=\"500\" y=\"0\"></use>\n</g>\n</g>\n</svg>-solvable groups ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "95cffb0ad7dfe14b708f78177426487bdb71ba95c88e27f869e87a10afc3b5ca", "withdrawn": "", "abstract": "We study prime graph complements of $\\mathcal{A}_n$-solvable groups, focusing on the cases $\\mathcal{A}_{11}$ and $\\mathcal{A}_{13}$. These provide the first classifications of $T$-solvable groups for which $|\\pi(T)|>4$. We develop structural and representation-theoretic tools for analyzing the possible prime graph complements and use them to obtain complete characterizations for both $\\mathcal{A}_{11}$-solvable and $\\mathcal{A}_{13}$-solvable groups. The methods introduced also provide a framework for studying analogous classification problems for larger alternating groups.", "id": "Paper/72486", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72486"}, {"title": " Equivariant oriented matroid structures on a finite group ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "880096e5c36f765d6863b30d6449c6013472ed1468b4bd617df283f94f67e10c", "withdrawn": "", "abstract": "We investigate the following question: given a finite group G, what are the possible (oriented) matroid structures M on G for which left multiplication by every element of G induces an automorphism of M? We begin by reinterpreting the problem for ordinary matroids in graph-theoretic terms via the matroid basis graph. We then turn to the case of oriented matroids, with particular emphasis on rank 2. Finally, we discuss how these ideas extend to matroids over idylls and outline several potential directions for the study of equivariant Grassmannians over idylls.", "id": "Paper/72489", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72489"}, {"title": " Exploring the Computational Capabilities of a Class of Biologically Inspired Cellular Automata ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "81cf441e1e9181ae7171a577857f9103e8c4b9ec3f474c293020381d96c9c2ed", "withdrawn": "", "abstract": "We study a class of cellular automata, a spatial model of computation, which has been shown to be realizable using molecular (DNA-based) tiles in an experimental environment. This class, called systems of interactive molecular arrangements (SIMAs), uses two types of tiles (``black'' and ``white'') to represent an alternating local rule in which one type of tile (e.g. ``black'') updates its state based on the other (e.g., ``white,'' resp.) and vice versa. In prior work, it has been shown that any \\emph{one-dimensional} elementary cellular automaton can be simulated with a SIMA. Here, we show that two broad classes of \\emph{two-dimensional} cellular automata may be simulated with SIMAs. Our simulation strategy works by first mapping the grid of the cellular automaton onto black cells. Next, white cells ``report'' their surrounding cells, allowing black cells to ``recover'' their neighborhood and update their states. By studying the computational capabilities of SIMAs, we can understand what constraints (if any) this subclass has in comparison to the full class of cellular automata.", "id": "Paper/72492", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72492"}, {"title": " Subgroup Analysis of Persistent Lyme Disease ", "webprogram_exclude": "0", "session_ids": ["Session/18159"], "source_sha256": "c6b1350e2536e347b1e0666e8548054ab4ffca96fa40d186cd72088eb326c387", "withdrawn": "", "abstract": "Lyme disease is a bacterial infection caused by tick bites that can induce a wide variety of symptoms, from joint pain and muscle aches to head aches and memory loss . In this study, we research patients with persistent Lyme disease to observe whether groups can be identified to develop better ways to treat patients based on their differences. In previous work by Campbell et. al, patients were split into sub groups of NEURO (Neurological) and MSK (Musculoskeletal). These groups are defined based on self-reported patient symptom severity. We used statistical and machine learning methods to try to answer the following questions: Is there a difference between the 2 groups besides the symptoms they were defined by; are there further subgroups within each group; and then a further analysis on whether the groups differ when restricted to patients with a more severe symptom level. The specific statistical methods we used range from chi-squared, Mann-Whitney U test, and Spearman's Rho Correlation. Machine learning extends from Non-Negative Matrix Factorization, Principal component analysis, and further supervised methods. In our analysis, we find that while there appears to be statistically significant features that contribute to our questions, the effect sizes of all tests are of a negligible amount; pointing to a lack of difference between the Neurological and Musculoskeletal groups.", "id": "Paper/72497", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72497"}, {"title": " How Much Do Non-Imaging Features Add Over Baseline Clinical Staging? A Subject-Grouped Analysis Framework for Reliable Cognitive-Decline Prediction and a Caution on Regression-Based Labels ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "1ee376514b1a7722f929af47cf6acf4906fe0cfc85cc51ea296abc84e27f1a36", "withdrawn": "", "abstract": "Diagnosis-based cognitive outcomes are coarse, threshold-driven, and clinician-dependent. We developed a non-imaging prediction framework using OASIS-3 to assess whether routinely collected demographic, clinical, and cognitive data predict later reliable cognitive decline beyond baseline clinical staging. Adults aged 60 years or older with baseline global Clinical Dementia Rating (CDR) at most 0.5 were linked to same-participant cognitive assessments; outcomes were assessed 24--48 months after a temporally defined prediction index. A reliable-change outcome was constructed separately within each outer cross-validation fold: cognitive norms, expected-change regression, and residual scale were fitted only in clinically stable training-reference participants. Subject-grouped nested cross-validation evaluated regularized logistic regression, random forest, and gradient boosting.\n\nThe cross-fitted binary modeling set included 523 participants, 103 of whom were classified as decliners. Logistic regression achieved AUROC 0.878 (95\\% CI 0.836--0.915), AUPRC 0.715, and Brier score 0.107. However, baseline global CDR alone achieved AUROC 0.788; the full feature set added 0.090 AUROC (paired 95\\% CI 0.058--0.122). Continuous-target prediction was more modest (Spearman $\\rho=0.395$), and a stricter temporal-anchoring sensitivity reduced logistic AUROC to 0.658 in a smaller sample. An independent NACC replication reproduced both the incremental AUROC over CDR and an association between the regression-based outcome and baseline severity.\n\nThis work provides a transparent, fold-contained framework and a non-imaging reference baseline for multi-modal/MRI analyses. It is an internal research analysis rather than a clinically actionable or transportable prediction tool.", "id": "Paper/72498", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72498"}, {"title": " Examining Choking and Clutch Performance in Professional Tennis ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "02e563b77d10b819b131834530a8e99f949af57189a17f0254c1df8e80d450aa", "withdrawn": "", "abstract": "Psychological pressure is widely believed to affect athletic performance through the phenomenon of “choking under pressure.” However, prior tennis research has reported mixed findings regarding the magnitude and direction of pressure effects. This study examines associations between high-stakes score situations and point-level performance in professional tennis using 1,118,623 points from 7,282 ATP and WTA matches. Several binary outcomes were analyzed: double faults, aces, service winners, rally winners, forced errors, and unforced errors. Service-stage outcomes were evaluated on all eligible service points, while rally-stage outcomes were assessed among 970,422 points in which the serve was returned into play.\n\nPressure situations were defined as mutually exclusive score states representing high-stakes points: break points, game points, set points, and match points. To assess the effects of pressure and contextual factors, we used contingency table analyses, chi-square tests, effect-size measures, and Bernoulli-logit generalized linear mixed models (GLMMs). Models adjusted for gender, surface, decade, deuce status, and point margin, with rally length included for rally-stage outcomes. Random intercepts accounted for clustering by tournament, match, server, and returner.\n\nResults indicate that psychological pressure was associated with measurable but generally modest differences in point-level performance. Across outcomes, contextual and player-specific characteristics showed stronger and more consistent associations with performance than pressure alone. The findings suggest that pressure effects are nuanced and depend on both competitive circumstances and individual player characteristics rather than reflecting a uniform choking-under-pressure pattern. Overall, psychological pressure appears to play a limited role in explaining point-level outcomes in professional tennis. These results contribute to a more nuanced understanding of performance under pressure and highlight the importance of accounting for contextual factors and individual differences when evaluating competitive performance.", "id": "Paper/72499", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72499"}, {"title": " Diagrammatic Perturbation Technique for Truncated Posterior Probabilities in Bayesian Inference ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "235581b94af845a10cbb9c16450a8f9dc29272011c8d851192f9695b789f9134", "withdrawn": "", "abstract": "Bayesian inference is a popular method for various data-driven applications in a variety of fields due to its ability to incorporate prior knowledge and uncertainty directly into the model. However, obtaining solutions for posterior distributions $P(\\mathbf{\\Theta} \\mid D)$ and their truncated probabilities $P(\\mathbf{\\Theta} < \\mathbf{t} \\mid D)$ (where each parameter $\\theta_i$ lies below a threshold $t_i$), is challenging, often requiring either analytical approximations that may not capture the underlying distribution with fidelity, or numerical methods like Markov Chain Monte Carlo (MCMC) which are often highly expensive computationally. Such probabilities are central to Bayesian decision-making, for instance in assessing whether a parameter lies below a critical threshold, and since the cumulative distribution function fully characterizes a distribution, they also allow us to reconstruct the entire posterior. We discuss the use of a ``Diagrammatic Perturbation Theory'' inspired by Statistical Physics and Information Field Theory, which allows the computation of the truncated probability of a perturbative non-Gaussian distribution as the exponential of a sum over connected diagrams (also known as \"Feynman diagrams\"), where each diagram is a shorthand for a mathematical expression constructed out of analytically known, simpler quantities. While traditionally used to extract moments of non-Gaussian distributions, here we apply the technique to estimate truncated probabilities. To test our technique, we benchmark it against the QUADPACK numerical integration method and find that it achieves higher speed while retaining high accuracy. We aim to adapt and apply this method to real-world statistical problems in the future, and benchmark its performance against MCMC.", "id": "Paper/72502", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72502"}, {"title": " AI-Assisted PDE-Constrained Parameter Reconstruction for Vascularization Modeling in Bioprinted Skin Grafts ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "e6a115dba32a7848480b609b3f64230792bdeff405b2095aa254f4d9195cca06", "withdrawn": "", "abstract": "We present an ongoing computational study of parameter reconstruction in a multiphysics model of vascularization in bioprinted skin grafts. The model couples fluid flow, nutrient transport, and cell-density dynamics across channel and hydrogel regions, with the goal of recovering uncertain physical and biological parameters from indirect observations. Our current work focuses on developing and validating adjoint-based optimization methods that can efficiently compute parameter sensitivities for large-scale PDE-constrained inverse problems.\n\nA central component of the project is the use of AI-assisted mathematical and computational workflows to support derivation, implementation, verification, and documentation. During the fall phase, we are extending the forward solver, deriving adjoint systems for viscosity and several additional parameters, implementing gradient-based parameter reconstruction, and validating the resulting sensitivities through consistency checks such as kappa-tests. We also plan to compare reconstruction performance across selected parameter sets and investigate how AI-assisted tools can accelerate development while preserving mathematical correctness and reproducibility.\n\nThe poster will summarize the modeling framework, numerical workflow, and available validation and reconstruction results, with emphasis on the interaction between PDE-constrained optimization, biomedical modeling, and researcher-verified AI assistance.", "id": "Paper/72503", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72503"}, {"title": " Cubic Shadows, Eliahou Numbers, and Wilf’s Conjecture ", "webprogram_exclude": "0", "session_ids": ["Session/18160"], "source_sha256": "086b357ce11ed738e604ef46e4079162248eb2be1fef6fbcfcca1171731636c0", "withdrawn": "", "abstract": "Wilf's conjecture has remained open since 1978. At conductor depth four, the first depth where the Eliahou number \\(W_0(S)\\) can be negative, Eliahou and Fromentin conjectured in 2019 that\n\\[\nW_0(S)\\geq-\\binom{e_L}{3}.\n\\]\nWe prove the stronger bound\n\\[\nW_0(S)\\geq-\\binom{|X_1|+1}{3}\\geq-\\binom{e_L}{3},\n\\]\nand determine all cases of equality. Here \\(X_1\\) is the first nonzero Apery slice and \\(e_L\\) is the number of primitive elements below the conductor.\n\nWe rewrite \\(W_0\\) using Apery factorizations. The only negative cubic terms come from order-three factorizations whose three pair sums lie in the preceding slice. Counting these factorizations against their distinct pair sums gives the bound.\n\nWe also disprove Eliahou and Fromentin's second conjecture on the minimum of \\(W_0-\\rho\\), with infinitely many counterexamples for every \\(e_L\\geq3\\).", "id": "Paper/72504", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72504"}, {"title": " Spanning Trees and Log-concavity in Hypergraphs ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "75c3eecd7d60a366dcd4c7cfc60c8e80480e28ec82c1bab8a783e2fabec566aa", "withdrawn": "", "abstract": "Hypergraphs generalize ordinary graphs by allowing edges to contain more than two vertices. Spanning trees are fundamental objects to the study of graphs and digraphs, and there are several extensions to hypergraphs coming from chip-firing ($q$-rooted spanning trees), random walks on directed hypergraphs (which we call `Igor trees'), and polytope theory (hypertrees). Here we study relations among these objects. We first show a correspondence between $q$-rooted spanning trees and Igor trees for an undirected hypergraph $H$, which in turn are seen to be refinements of the set of hypertrees of $H$. The set of hypertrees of $H$ form an $M$-convex subset of the integer lattice, and we use Lorentzian polynomial theory to demonstrate log-concavity properties in the generating functions that associate Igor trees to hypertrees.", "id": "Paper/72505", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72505"}, {"title": " Modeling Cancer Resistance Evolution with Graph Neural Network Agents ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "eb92e25b3490d577766dbc5a065a0be77d8b64c396985d72401954df0f480456", "withdrawn": "", "abstract": "During treatment, cancer cells can develop resistance as intracellular signaling pathways are rewired. This process adheres to evolutionary dynamics. As treatment begins, the adaptive landscape shifts, altering the optimal response and thus fitness of individual cancer cells. These fitness values contribute to the overall response to treatment and can be modeled with graph neural network agents. This project aims to model the development of intracellular resistance and investigate its evolution under different treatment strategies. Overall, our results suggest that double-bind treatments are the most effective in limiting resistance across a range of intracellular complexities.", "id": "Paper/72506", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72506"}, {"title": " Exploring Efficient Methods of Determining Minimum Sizes of Signed Sumsets ", "webprogram_exclude": "0", "session_ids": ["Session/18239"], "source_sha256": "734d6dadfcf1fd49cd5fbbeb16a362f0b986727bfb8288fe88a79ad62ed8d26c", "withdrawn": "", "abstract": "For a finite abelian group $G$ and a positive integer $s$, the critical number $\\chi(G,[0,s])$ is defined as the smallest positive integer $m$ for which every $m$-subset $A$ of $G$ is $s$-complete, that is, all elements of $G$ can be written as the sum of at most $s$ elements of $A$.  The value of $\\chi(G,[0,s])$ has been determined by Bajnok, and is given by a function $v(n,s)$ that depends on the order $n$ of $G$ but not the structure of $G$.  Our goals is to determine the analogous value $\\chi_{\\pm}(G,[0,s])$ where signed sums are considered, which is currently unknown.  We provide partial answers when $G$ is cyclic.", "id": "Paper/72507", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72507"}, {"title": " Activated Random Walk with Shifted Driving ", "webprogram_exclude": "0", "session_ids": ["Session/18160"], "source_sha256": "a79bc8a99ac265de24cf41a816b043546359132e44285c69fcb47c1e62833e04", "withdrawn": "", "abstract": "We study activated random walk on an interval with absorbing boundaries. Particles are added one at a time, move randomly, and can fall asleep or be reactivated by other particles. We study how many particles remain in the system when particles are added away from the center and find that the limiting density is different from the “hockey stick” curve proven for central driving.", "id": "Paper/72509", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72509"}, {"title": " Characterizations of the quantum <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.776ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex; margin-left: -0.041ex;\" viewBox=\"-17.5 -791.3 1195.4 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathfrak {sl}_3</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJFRAK-73\" d=\"M272 33Q284 33 290 70T296 138Q296 181 290 198T262 230Q257 232 246 232Q231 232 218 227T156 194L108 167L101 176Q90 192 75 219L69 230V284Q69 346 70 357V377L146 427Q181 450 202 464T223 477L225 476Q227 475 229 474Q231 472 242 466T270 450T296 431Q309 418 326 418Q342 418 361 429T392 450T403 459Q406 445 406 442Q406 440 384 421T338 382L316 363Q315 362 310 362Q292 362 251 371T173 396Q156 403 155 403Q143 386 143 342Q143 305 150 278T168 244Q171 242 181 242L190 243L315 300Q330 295 357 274Q358 273 362 270T366 266T369 261T372 253T373 239T374 217T374 185Q374 157 372 133T368 98T363 71T358 50L336 40Q288 20 255 2T211 -22T198 -29L190 -22Q181 -14 168 -3T138 19T104 38T70 46Q50 46 32 37T3 20T-9 11L-18 23L-1 41Q46 89 62 99T112 110Q141 110 157 103T225 62Q268 33 272 33Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJFRAK-6C\" d=\"M221 76L267 99Q268 98 269 96T271 88T270 82L262 76Q255 69 241 57T214 34L148 -20L98 56L99 89Q107 247 107 373Q107 494 101 621Q101 653 99 659V665L106 668L113 672L118 655Q122 642 131 617L138 597Q140 597 157 611L240 670L264 685Q265 685 270 680T276 674T269 667T247 647T219 617Q197 587 186 551T173 493T171 438Q171 376 175 282T179 147V117Q184 109 201 93T221 76Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJFRAK-73\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJFRAK-6C\" x=\"443\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-33\" x=\"1023\" y=\"-213\"></use>\n</g>\n</svg> knot invariant ", "webprogram_exclude": "0", "session_ids": ["Session/18160"], "source_sha256": "d14d48d920a82f1808314dcc19c8017415b037f29e3f931bd554dca843d3390c", "withdrawn": "", "abstract": "The $\\mathfrak{sl}_3$ link polynomial is a higher rank relative of the Jones polynomial which can be studied entirely diagrammatically using Kuperberg's web calculus. The invariant is known to detect whether a link is fibered and provides an obstruction to present positive links as positive braids. Building on the work of Harper and Kalfagianni, we construct formulae for the fourth and fifth coefficients of the quantum $\\mathfrak{sl}_3$ link invariant on positive alternating links in terms of data read from the associated Seifert graph. Then, we give a characterization of the invariant on positive alternating fibered links in terms of elementary symmetric polynomials. \\\\\\\\\nAdditionally, we formulate the Garside element ($\\Delta_3 \\in B_3$) in terms of elementary webs, give a closed formula for the polynomial on positive $3$-braids, and combine these results to give a complete characterization of the $\\mathfrak{sl}_3$ polynomial on all $3$-braids.", "id": "Paper/72510", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72510"}, {"title": " Memory-Weighted Switching and Market Stability ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "545951bf7606e81fa3af96593ff994176f2416958c8ec9e89c037a6a6e57da15", "withdrawn": "", "abstract": "We study how memory-weighted strategy switching interacts with volatility-\ntargeted demand in a heterogeneous-agent financial market with trend-following and\ncontrarian traders. Strategy shares respond to cumulative relative performance, while\ntrading intensity is scaled by perceived volatility. We formulate the stochastic market\ndynamics as a Markov chain and use a frozen-state Gaussian closure to obtain a tractable\nreduced description of stationary market composition. The analysis shows that perfor-\nmance memory creates persistent feedback between past profitability and strategy shares\nand can destabilize the balanced composition even when traders respond only weakly to\nperformance differences. Numerical simulations of the full stochastic system support this\nqualitative destabilization mechanism while also revealing stronger polarization than the\nreduced map predicts. These results highlight how memory and volatility-sensitive trading can jointly amplify endogenous shifts in market composition.", "id": "Paper/72511", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72511"}, {"title": " Choices Matter: A Geometric Reinforcement Learning Approach to S-Polynomial Selection in Buchberger’s Algorithm ", "webprogram_exclude": "0", "session_ids": ["Session/18160"], "source_sha256": "15c2bd56e34b3cfb5aec1a246a6c2d55b51f9939cdd77db6a02e1fabd9b8a297", "withdrawn": "", "abstract": "Gröbner bases are generating sets of polynomial ideals used to perform variable elimination and solve the ideal membership problem (IMP), thereby characterizing its associated variety. The efficiency of Buchberger’s algorithm, the method for computing Gröbner bases, is highly sensitive to the S-polynomial selection strategy used during the reduction phase. This strategy is heavily influenced by the specific IMP, which can be intractable. Classical heuristics, like the normal degree or sugar strategies, provide improvements to Buchberger’s algorithm. Further improvements to these selection strategies were demonstrated by Peifer and Stillman (2020), who successfully applied reinforcement learning to train agents capable of outperforming classical heuristics on specific classes of ideals. We build upon this work by introducing geometric neural network architectures as the backbone of the reinforcement learning agent. While prior approaches utilized standard feature representations of the polynomial states, a geometric architecture allows the model to natively process and exploit the inherent structural properties of multivariate polynomials. By mapping the algebraic state into a geometric space, the agent is trained to recognize spatial and combinatorial relationships to prioritize S-polynomials that advance the basis computation.", "id": "Paper/72517", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72517"}, {"title": " Inputs for the Equivariant Infinite Loop Space Machine ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "1506ed508b9effc6c42b00585f48bf1f7ac7b32b3325f18b4d45ef0f65fe8dc7", "withdrawn": "", "abstract": "Symmetric monoidal categories are central in modern algebraic topology; for instance, $K$-theory constructs spectra out of certain symmetric monoidal categories. It is known that the two inputs -- pseudoalgebras over an operad $\\cP$ and what we shall call strictly special $\\F$-pseudoalgebras (where $\\F$ is the category of based finite sets) -- are equivalent descriptions of symmetric monoidal categories. In equivariant $K$-theory, analogous machinery has been established: the inputs for constructing $G$-spectra are described by pseudoalgebras over an operad $\\cP_G$ of $G$-categories and by strictly special $\\F_G$-pseudoalgebras (where $\\F_G$ is the category of based finite $G$-sets). The equivalence of the two inputs in the equivariant case is a natural question to explore, and it connects to the question ``What are symmetric monoidal $G$-categories?''. We will provide an exposition of the two inputs in the literature, key equivariant details in the construction of $\\F_G$-pseudoalgebras associated with $\\cP_G$-pseudoalgebras, and briefly discuss the problem of constructing $\\cP_G$-pseudoalgebras associated with $\\F_G$-pseudoalgebras.", "id": "Paper/72519", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72519"}, {"title": " Edge-Informed PSF Estimation ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "6bff299c5917a0ce96464548845fc5762d8ad51fa7951bfab0a14464f32c847f", "withdrawn": "", "abstract": "Imaging devices capture the real world with a blur. This blur is modeled by convolving the true image with a blurring function, also known as a point spread function (PSF). Often, PSFs are estimated by capturing an idealized diagnostic point source to see how an individual point is blurred. We instead estimate PSFs in the more realistic setting where the true image is piecewise-smooth and no diagnostic point source is available. Through the use of a convolutional edge detection kernel, each edge is transformed into a diagnostic point. We present approximation theoretic $L^2$ error bounds for estimations of Laplace and Cauchy PSFs. We also show that, for certain PSF families, the shape parameter is a generalized eigenvalue of a pair of Fourier domain Hankel matrices. We then combine these classical PSF estimation techniques with contemporary machine learning approaches for classifying unknown families of PSFs and estimating their parameters.", "id": "Paper/72520", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72520"}, {"title": " SpaCoEx: Sparse Gene Selection for Spatially Varying Co-expression in Spatial Transcriptomics ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "ecf7539c4619678b6080053f32547c2256106cc1da416f1c73331d18a808ab22", "withdrawn": "", "abstract": "Spatial transcriptomics enables gene expression to be measured while preserving tissue location, but most existing analyses focus on spatial variation in individual genes or expression-defined domains. Here, we introduce SpaCoEx, a sparse spatial representation framework that integrates gene-expression levels with spatially varying gene-gene co-expression. SpaCoEx first estimates local co-expression matrices from neighboring spatial spots, maps them into a log-Euclidean representation, and performs structured gene selection by retaining or removing the full row and column associated with each gene. The selected genes are then used to construct both expression-level features and local co-expression features, which are combined through an $\\alpha$-weighted joint representation for downstream spatial analysis. We applied SpaCoEx to human cutaneous squamous cell carcinoma and annotated human breast cancer spatial transcriptomics datasets. In the cutaneous squamous cell carcinoma dataset, SpaCoEx selected 29 of 45 keratinocyte-related genes while preserving 96.74\\% of the spatial co-expression variation. In the breast cancer dataset, SpaCoEx identified spatially varying co-expression between B2M and HLA-C, a biologically meaningful MHC class I antigen-presentation gene pair. Their local correlation was significantly higher in cancer-associated regions than in non-cancer regions (mean difference = 0.30, spatially adjusted SE = 0.045, $P<1.0\\times 10^{-10}$), whereas B2M and HLA-C expression individually did not differ significantly between cancer and non-cancer. In benchmarking against manual tissue annotations, co-expression-only SpaCoEx achieved the strongest spatial coherence (percentage of abnormal spots [PAS] = 0.076), while the joint expression/co-expression representation achieved the highest annotation agreement, with an adjusted Rand Index (ARI) of 0.584 at $\\alpha$ = 0.60 and normalized mutual information (NMI) of 0.663 at $\\alpha$ = 0.40. By integrating marginal gene-expression information with local gene–gene co-expression structure, SpaCoEx provides a sparse, low-dimensional, and interpretable representation of spatial transcriptomics data that captures complementary aspects of tissue organization beyond expression-based variation alone.", "id": "Paper/72521", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72521"}, {"title": " Frontier Evaluation for Delay-Aware Two-Link Reinforcement of Tree Networks ", "webprogram_exclude": "0", "session_ids": ["Session/18160"], "source_sha256": "7fc3c57f53bff856d35531b9cfec120dddfaa5098f47db84b0a7de0f77f9588f", "withdrawn": "", "abstract": "Tree-shaped communication networks are inexpensive to deploy but vulnerable:\nthe failure of one original cable can disconnect an entire downstream subtree\nfrom its root. We study a restricted reinforcement problem in which at most two\nbackup links may be added to a rooted tree whose devices have nonnegative\ncriticality weights. When a failed edge is covered by a backup link, affected\ndevices can reconnect through a detour, although the detour may increase\ncommunication latency. We therefore measure service loss using both weighted\ndisconnection penalties and weighted additional rerouting latency. For any\nfixed pair of backup links, we show that the worst covered failure can be\nidentified by evaluating at most ten representative tree edges. To obtain this\nbound, we partition the two protected paths into at most five regions whose\nedges are covered by the same links, split each region into at most two\nroot-directed branches, and prove that failure loss cannot decrease toward the\nroot within a branch.\nAcross $868,893$ validation comparisons, frontier and exhaustive evaluation\nagreed exactly. On networks with $n=400$ vertices, frontier evaluation reduced full failure\nevaluations by $98.7\\%$ and achieved an aggregate runtime speedup of\napproximately $19.6\\times$.", "id": "Paper/72522", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72522"}, {"title": " Computing Hilbert Measures of linear circle actions ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "e160d944940840d8df6376fa5be5507680844c351fb48651f3c94fb6b121bad7", "withdrawn": "", "abstract": "A function of several variables is \\textit{invariant} with respect to a matrix group $G$ acting on its domain if its value does not change when a matrix in the group is applied; we say it is invariant under the action of $G$. When that group is a circle, the action can be described by a weight vector, or a set of integers that multiply the angle each vector is being rotated through. When integrating invariant functions, the action of $G$ can be used to reduce the number of variables in the integral without losing information, lowering the dimension of the domain. However, in this process, there needs to be a correction in the new integral in order to keep the value of the original integral. This correction is called the \\textit{Hilbert Measure}. \n\nWe will present a computation of the Hilbert Measure for some actions of the circle group on $\\mathbb{C}^2$ and $\\mathbb{C}^3$ as well as related spaces called \\textit{symplectic quotients}.", "id": "Paper/72523", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72523"}, {"title": " Limit Laws for Coefficients of Polynomial Powers ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "60260f3f18a824b3fcd281d46fc070d7cde498aa74b73ac5738a99a7eab62fda", "withdrawn": "", "abstract": "We study the distribution of coefficients in the expansion of $P(x)^n$ as $n \\to \\infty$ for real polynomials $P(x)$. Graphing the coefficient distribution reveals various peaks of eccentric shapes and of different widths. Some peaks oscillate, with a broad range in oscillation frequencies, while other peaks are not even symmetric. Our primary goal is to understand the visual phenomena in these graphs. \n\nWhen $P(x)$ has only nonnegative coefficients, the limiting distribution is a single Gaussian peak, which can be seen as a variant of the Central Limit Theorem. For the general case, richer structure appears, and by carefully analyzing certain complex integrals over the unit circle, we identify possible limiting shapes of the peaks with a countable collection of universality classes indexed by integers $q \\geq 2$.\n\nFor $q=2$, we recover the Gaussian peak. Interestingly, for $q=3$ the limiting shape shares some features with the Tracy-Widom law famously appearing in the random matrix theory. For each $q \\geq 2$ we prove that the local peak converges to the corresponding limiting distribution when renormalized by $n^{1/q}$, generalizing the fact that fluctuations in the Central Limit Theorem are of order $n^{1/2}$.\n\nIn addition, we explain the emergence of oscillations and develop formulae for predicting oscillation frequency in certain cases. We also establish a bound on the number of peaks of each order, present the results of computer experiments, and pose a conjecture on the possible peak combinations.", "id": "Paper/72525", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72525"}, {"title": " FORCE: Fast Online Robustness Calculation Engine for Temporal Logic-based Real-Time Systems ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "348139815f3199cc04d8132d488cbded28c6728a6f32927b31a9f0592614a58d", "withdrawn": "", "abstract": "Formal verification of complex autonomous systems is difficult; runtime verification is an effective method for monitoring specified system behavior and bridging the gap between a system’s model and its real-life counterpart. Robustness in Signal Temporal Logic (STL) is one metric monitored by some runtime verification frameworks, but hasn't been used in flight certified tools. The Realializable Responsive Unobtrusive Unit (R2U2) runtime monitor is a Mission-time Linear Temporal Logic MLTL) based flight-certified framework that provides the capabilities necessary for safe online monitoring of specifications, but robustness is not supported in MLTL. We present the new semantics and proofs required for implementing robustness in R2U2. We modify robust satisfaction intervals (RoSIs) for implementation in a stream-based runtime monitor using the new Fast Online Robustness Calculation Engine (FORCE) for R2U2. Finally, we compare our results with the existing tools.", "id": "Paper/72527", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72527"}, {"title": " Results on the Ascent of the D-Property to Monoid Algebras, and a Result Relating the MCD and Pre-Schreier Properties ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "7445a209c92a0c15364ca0e94b7e96156c55102240171c61a1a8f985374f2195", "withdrawn": "", "abstract": "For a cancellative, commutative, and torsion-free monoid $M$ and an integral domain $R$, let $R[M]$ represent the monoid algebra (generalized polynomial ring) with coefficients in $R$ and exponents in $M$. When a monoid $M$ and a ring $R$ satisfy a divisibility property, it is commonly asked what conditions on $R$ and $M$ ensure the underlying multiplicative monoid of nonzero elements of $R[M]$ satisfies this property as well. We construct an MCD-finite Puiseux monoid as well as a nonreduced, torsion-free, rank-two finite-factorization monoid, both satisfying the property that the monoid algebra of the monoid over any field is not MCD-finite. We also prove that there exists a Puiseux monoid that is pre-Schreier but not 2-MCD (and so, not MCD). Finally, we categorize the D-property's ascent to monoid algebras over integral domains.", "id": "Paper/72528", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72528"}, {"title": " Higher Order Co-infection on Hypergraphs ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "154e1523838022b891dcef9e64686dce7f9fe2ab6872869e6e2f5bcf2fb16f65", "withdrawn": "", "abstract": "People encounter infections through overlapping groups, such as\nhouseholds, classrooms, and workplaces. Understanding how these\nshared contacts affect the spread of multiple pathogens is critical\nto determining what information epidemic models need to retain.\nWe introduce HyCoSIS (Higher-order Co-infection SIS Model), a\ndiscrete-time SIS model on hypergraphs with explicit reinforcement\nbetween overlapping active groups and pairwise transmission.\nWe investigate how this reinforcement affects infection dynamics\nand whether simplified representations of graphs preserve the\nresulting behavior. We derive an exact representation of overlap\nreinforcement as target-dependent four-person interactions and\ndetermine when a symmetric representation is possible. Numerical\nexperiments examine reinforcement strength, contact structure,\nand susceptibility to secondary infection, as well as calibrated\npairwise approximations. Our results demonstrate that redistributing\noverlap weights can substantially change finite-time co-infection\neven when every individual's total overlap coefficient is preserved.\nWe further derive an exact five-person calculation and demonstrate\nwhy equal mean infection pressure does not necessarily produce\nequal acquisition probabilities. These findings identify how the\nallocation of higher-order interactions can influence contagion\ndynamics beyond their aggregate strength. Beyond epidemiology,\nthis work contributes to the statistical physics of spreading\nprocesses by examining how the arrangement of many-body interactions\nshapes collective dynamics, and what information is lost when those\ninteractions are simplified.", "id": "Paper/72531", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72531"}, {"title": " Fault Detection and Accommodation of Sensor Measurements in Nonstationary Processes Using Probabilistic Autoencoders ", "webprogram_exclude": "0", "session_ids": ["Session/18238"], "source_sha256": "aefedd39706df246c731a9f2853ba040282ff55e2f709bc39025ff5b538f81f8", "withdrawn": "", "abstract": "In applied math and engineering problems, sensor measurements track state variables to monitor system health and performance. Since sensors naturally degrade over time and suddenly fail in extreme operating conditions, robust modeling requires fault detection and accommodation systems to determine when sensors fail and correct the state variable measurements. We tackle this problem in the challenging setting of high frequency real-time modeling where the physical dynamics are complicated or unknown, the state distribution is nonstationary, and multiple forms of sensor faults arise with distinct effects on the state distribution. We propose a three-layer approach consisting of a neural network autoencoder to reconstruct the entire state distribution, a statistical detection framework, and an accommodation strategy to fuse model predictions and sensor measurements. We apply this method in the context of air-breathing hypersonic vehicle engines, where pressure measurements are helpful in predicting the shock-train leading edge (STLE), an important metric of combustion performance and stability. Pressure sensors are susceptible to producing faulty readings due to the hostile environment and highly nonlinear system inside the engine. This fault detection and accommodation system accurately finds and corrects problematic faults, improving STLE prediction under uncertainty and allowing for safer and more efficient flight. Furthermore, the performance of the system highlights the utility in using statistical and machine learning techniques for fault detection and accommodation in real-world dynamical systems.", "id": "Paper/72532", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72532"}, {"title": " On the Computability of Isomorphisms Between Dimension Groups ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "7989d97cadce729d1f14e7de2aace56c9d675e226075bb20ce3191e723e9a03e", "withdrawn": "", "abstract": "We study dimension groups $G_A$ and $G_B$ defined by nonsingular integer $n \\times n$ matrices $A$ and $B,$ respectively. Such groups arise in the study of toroidal solenoids, $\\mathbb{Z}^n$-odometers, and symbolic dynamics. Previously, Sabitova established the computability of the isomorphism set $\\operatorname{Iso}(G_A, G_B)$ in the $2 \\times 2$ case and in the general $n \\times n$ irreducible case. In our work, we present progress toward establishing the computability of $\\operatorname{Iso}(G_A, G_B)$ in the $n \\times n$ reducible case and develop a general framework for constructing this set. We also discuss potential reductions for its computation.", "id": "Paper/72533", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72533"}, {"title": " Categorifying an Unfactorizable Rank-9 Fusion Ring Through Associative Zesting ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "9410a500096cafada617a3a85984500c5a0834bd3a20a5f02fe58e3ab4c694d3", "withdrawn": "", "abstract": "Fusion categories form the natural setting of categorical quantum mechanics. Thus given an arbitrary fusion ring, categorifying it, i.e. finding associators satisfying a pentagon axiom, is important as it provides more fusion categories to work with. We compute several categorifications of the rank-$9$ fusion ring $\\mathsf{FR}^{9,1,4}_5$ by taking the bicrossed product of the Ising fusion category with itself, and then modifying its fusion rules through associative zesting. We also prove that the resulting fusion category $\\mathcal{F}$ cannot be written as an exact factorization of two fusion categories, unless either one is the fusion category of vector spaces.", "id": "Paper/72534", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72534"}, {"title": " Community-Based Federated Split Learning with Gossip and Triggered Alignment ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "2a266c5fb2fb630c756f878cb06288577a48589418cb74e5387980794a897088", "withdrawn": "", "abstract": "Federated split learning distributes neural-network training between clients and a central server, but frequent exchanges of gradients and intermediate features may cause large communication costs. FSL-SAGE reduces these exchanges using auxiliary models that estimate gradients at client together with periodic server-side alignment. We propose a community-based extension that combines shared auxiliary training, inter-community gossip, and event-triggered alignment, where clients are organized into communities that are managed by a community head who maintains one shared auxiliary model. The head returns estimated gradients for client updates and updates the auxiliary model using features and labels from its community members. Communities periodically exchange and average auxiliary model parameters through gossip for better estimate while selected features and labels are uploaded to train the server-side model. During the scheduled checks after gossip, server compares the auxiliary model’s estimated cut-layer gradients with those produced by the current server model on the same uploaded features and labels. When the discrepancy exceeds a threshold, the server adjusts the auxiliary model to reduce this discrepancy and sends the corrected model back to the community; otherwise, communities continue to use their current model. Client-side models are aggregated within communities and then at the central server. Our extension presents an algorithmic framework, which aims to further reduce communication costs and unnecessary alignment while maintaining useful gradient estimates for distributed training.", "id": "Paper/72537", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72537"}, {"title": " Classification and Periodicity in Ulam Words ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "19bcb1a6837755eb8f3b5d58487f6391677658e8aad50b75d2c2a92d4198338f", "withdrawn": "", "abstract": "The set of binary Ulam words is $\\bigcup_{n\\in\\mathbb{N}}\\mathcal{U}(n)$, where $\\mathcal{U}(1)=\\{0,1\\}$, and for $n>1$, $\\mathcal{U}(n)$ consists of the words of length $n$ that can be written in exactly one way as a concatenation of two distinct shorter Ulam words. We expand upon previous work by classifying new families of binary Ulam words. First, we show that for $c=2^k$ with $k\\geq 1$, the word $0^x1^c0^y$ is Ulam if and only if $x+y\\equiv 1\\pmod{2^k}$. Second, we completely classify the words $0^x1110^y$, corresponding to $c=3$. Lastly, we study words of the form $0^x10^a10^b10^y$ and show that, when $a$ and $b$ are odd non-Zumkeller numbers, the corresponding graph indicating whether each word is Ulam is biperiodic.", "id": "Paper/72538", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72538"}, {"title": " Wild numbers for spanning trees in edge-colored graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "eb0f4d32d4104cfa886aee15a0cdb0d2f76ba03666ce7fc79b0626dcf785feb1", "withdrawn": "", "abstract": "Edge-disjoint spanning trees reveal independent pathways for reliable communication in a network. Edge-coloring represents the allocation of certain pathways to distinct operations. We call an edge ``wild'' if it belongs to all color classes of an edge-colored graph. The wild number of an edge-colored graph is the minimum number of edges that must be colored wild to have a spanning tree in every color.  We investigate this parameter for several graph families and edge colorings including proper and equitable. The wild number for cycles, complete graphs, and complete bipartite graphs is determined. Methods used to make these determinations are inspired by Ramsey and anti-Ramsey theory techniques.", "id": "Paper/72539", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72539"}, {"title": " Oriented Line Graphs and Zeta Functions ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "c01000a0d6781f8e2998839404963d1a754d56f35ad6a6f2e76d7d7ea83420a4", "withdrawn": "", "abstract": "Let $X$ be an undirected graph and $X^o$ be its oriented line graph as defined in Kotani and Sunada's 2000 paper. A 2026 paper by Lei, Muller, and Vallieres lets us interpret the special value of the multiplicative inverse of the Ihara zeta function of $X^o$ at $u=1,$ henceforth called $g_{X^o}^*(1),$ as the cardinality of a group, here called the zeta group, associated to the divisor group on $X^o$. Since $X$ and $X^o$ share Ihara zeta functions, we have $g_{X^o}^*(1)=g_X^*(1);$ by a 1990 result by Hashimoto, the latter is divisible by $\\kappa(X),$ the number of spanning trees of $X$ and the cardinality of its Jacobian group Jac$(X)$. Given this, it is reasonable to ask for a direct link between Jac$(X)$ and the zeta group of $X^o;$ we present one such connection here in the form of a concrete embedding.\n\nIn their 2026 paper, Lei, Muller, and Vallieres also give a decomposition of the zeta group into the torsion part of the Bowen-Franks group along with a second group, which we call the lower zeta group. A 2006 result by Cornelissen, Lorscheid, and Marcolli gives the structure of the torsion part of the Bowen-Franks group of $X^o$ to be a cyclic group, but the structure of the lower zeta group of $X^o$ was unknown until now, when we show it to be isomorphic to a ``dilation\" of Jac$(X).$ \n\nOf further interest to many graph theorists is the Galois theory of graphs, specifically the behavior of certain invariants such as $\\kappa(X)$ along $\\mathbb{Z}_p-$towers of graphs. These towers often behave similarly to their number-theoretic counterparts, with Iwasawa-type formulas holding for these graph invariants just as they hold for class numbers in the number field world. In our work, we also show that the oriented line graph construction preserves Galois coverings. Combined with our other results, this allows one to use the oriented line graph construction to apply results on directed $\\mathbb{Z}_p$-towers, especially those related to the zeta group, to the undirected case.", "id": "Paper/72541", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72541"}, {"title": " Equivariant Generalized Pólya Enumeration via Ghost Maps ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "1c9918b40994d21c9d7076a289f600198ccbd7693ce7ec851d2e3f2204b13c99", "withdrawn": "", "abstract": "We develop an equivariant generalization of P\\'olya enumeration for finite \\(G\\)-sets. Classical P\\'olya enumeration counts colorings of a set up to the action of a permutation group; in the equivariant setting, we preserve the \\(G\\)-set structure of the underlying objects and express the resulting enumeration in terms of transitive \\(G\\)-sets.\n\nOur approach uses the Burnside ring (A(G)), together with the ghost map, which records the number of (H)-fixed points for each conjugacy class of subgroups (H\\ \\leq \\ G). The associated table of marks and its inverse provide a method for recovering the coefficients of a (G)-set from its fixed-point data. We use this machinery to prove an equivariant generalized P\\'olya enumeration formula, expressing the (G)-set-valued enumeration polynomial in terms of these coefficients.\n\nWe illustrate the construction with examples involving cyclic group actions and show how the same framework produces equivariant analogues of binomial coefficients through the associated lambda structure. These examples demonstrate how orbit decomposition, fixed-point data, and generating functions interact in the equivariant setting.", "id": "Paper/72542", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72542"}, {"title": " Some Results on the Ascent of the D-Property to Monoid Algebras, and a Result Relating the MCD and Pre-Schreier Properties ", "webprogram_exclude": "0", "session_ids": ["Session/18160"], "source_sha256": "27383bf53e99cc33c25835507840c85f0865a1f041682b82a55df1c1fad183c0", "withdrawn": "", "abstract": "For a cancellative, commutative, and torsion-free monoid $M$ and an integral domain $R$, let $R[M]$ represent the monoid algebra (generalized polynomial ring) with coefficients in $R$ and exponents in $M$. When a monoid $M$ and a ring $R$ satisfy a divisibility property, it is commonly asked what conditions on $R$ and $M$ ensure the underlying multiplicative monoid of nonzero elements of $R[M]$ satisfies this property as well. We construct an MCD-finite Puiseux monoid as well as a nonreduced, torsion-free, rank-two finite-factorization monoid, both satisfying the property that the monoid algebra of the monoid over any field is not MCD-finite. We also prove that there exists a Puiseux monoid that is pre-Schreier but not 2-MCD (and so, not MCD). Finally, we categorize the D-property's ascent to monoid algebras over integral domains.", "id": "Paper/72543", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72543"}, {"title": " Climate-Driven Dengue Intervention: Wolbachia Release Strategy Analysis for Rio de Janeiro, Brazil ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "05c32c832897e9d03a6c6ff2262b7c6c80ba17c220f825ca6d68d17b242fcc71", "withdrawn": "", "abstract": "Dengue is a mosquito-borne disease whose transmission is strongly influenced by mosquito ecology and climate. We developed a climate-driven compartmental model of dengue transmission in Rio de Janeiro that incorporates temperature-dependent mosquito and transmission rates, rainfall-dependent aquatic habitat and flushing, and categorical El Ni\\~no-Southern Oscillation modifiers. The model was calibrated using 183 epidemiological weeks of reported dengue incidence from July 2015 through January 2019, achieving a mean absolute error of 69.98 reported cases per week and a weighted absolute percentage error of 31.67\\%. We then extended the model to include \\textit{Wolbachia}-carrying mosquitoes and compared release timing based on modeled adult abundance, rainfall-driven flushing, and temperature. The strongest tested strategy was a one-time release at flushing onset on September 11, 2015, with a 100\\% total release budget relative to the resident non-\\textit{Wolbachia} adult-female population; it reduced reported dengue by 68.46\\% over the following 52 weeks. The best strategies in the 2015 deployment cycle clustered several months before the dominant early-2016 dengue peak, whereas the best strategies in the 2016 deployment cycle occurred after that peak. Across indicators, release timing relative to mosquito abundance, flushing, seasonal temperature phase, and epidemic timing influenced intervention performance alongside nominal release percentage. A local sensitivity analysis further identified adult mosquito mortality and biting as among the strongest local associations with modeled transmission outcomes. These results support further evaluation of ecological timing indicators for guiding \\textit{Wolbachia} deployment while emphasizing the need for local entomological validation and prospective evaluation.", "id": "Paper/72544", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72544"}, {"title": " A Tiered Model Design for Social-Media Posting Dynamics: Complexity Scaled to Data Volume, with AIC-Selected Kernels and Dormancy Treatments ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "26ae5812e02318057916788c98297f65466a94e104a324a7c249d74e5a8aff30", "withdrawn": "", "abstract": "The COVID-19 lockdown produced an abrupt, population-scale disruption to daily routines, and with it, to how people used social media. We study this disruption at the level of individual Twitter users, modeling the arrival times of posts as realizations of a temporal point process rather than as aggregated, binned counts. Because individual posting activity varies enormously---from a handful of posts to thousands---we propose a tiered model-selection pipeline that bounds the maximal model complexity considered for a user by their observed event count, ranging from a homogeneous Poisson process at the sparsest tier through Gamma/Weibull renewal processes to covariate-adjusted, gated Hawkes processes with single-exponential, double-exponential, or power-law excitation kernels at the richest tiers, with kernel choice made by AIC. We introduce a multiplicative dormancy gate to accommodate extended inactive periods without resorting to time discretization, and establish stability and identifiability conditions for every model family in the pipeline. Goodness of fit is assessed via the time-rescaling theorem, using pooled Kolmogorov--Smirnov tests and Ljung--Box tests combined across users within a tier to address the limited power of individual tests on short event sequences. We further validate the framework through simulation studies and cluster users based on shared posting behavior to examine how behavioral patterns remain stable or change following lockdown. These analyses provide a population-level view of heterogeneity in individual responses to the disruption. Applied to a cohort of Raleigh, North Carolina Twitter accounts screened for mental-health-distress language, the tiered Hawkes framework substantially outperforms simpler alternatives in capturing bursty posting dynamics, and a meaningful share of users shift toward higher-activity, more self-exciting behavior following lockdown.", "id": "Paper/72548", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72548"}, {"title": " Bounding the Diagram of Geodesic Intervals via Digons and Comparing Growth Rates in C’(1/8)-Small Cancellation Groups ", "webprogram_exclude": "0", "session_ids": ["Session/18160"], "source_sha256": "443f47be63118dbc5ae6416f62d61b0645b44e18c2ec00df06b3599d3c4fa235", "withdrawn": "", "abstract": "Let $\\Gamma$ be a group characterized by a small cancellation $C'(1/8)$-presentation. We study the structure of its Cayley graph, specifically geodesic intervals and digons. We prove that all geodesic segments [x,y] of length $n$ can be covered by finitely many digons with pairwise $C'(1/8)$-short lower intersections whose lower sides lie on a common geodesic segment [x,y]. This is a generalization of a proposition of Kharlampovich-Sklinos for random groups. We then bound this resulting diagram of digons, showing that the total perimieter of its cells and its edge count is bounded by $n$, and the cycle rank is equal to the number of distinct cell contours. Thus, although there may be many different geodesics, the size of their union is bounded linearly in the distance between their endpoints. The constant is independent of the number and lengths of the defining realtors. In particular, the estimate applies to infinite presentations with unbounded relator lengths. From this we get a consequence for growth, allowing us to compare the number of geodesic words with the number of group elements of the same length.", "id": "Paper/72549", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72549"}, {"title": " Numerical Ranges in Finite Fields ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "406cdb3256992d6fd337cdefa00e2648ab0eac7907c60840fd7e12f35201dd2d", "withdrawn": "", "abstract": "Otto Toeplitz and Felix Hausdorff initially introduced the idea of numerical ranges of square matrices with complex entries in the early twentieth century, and Rudolf Kippenhahn later contributed significantly to our knowledge by classifying the geometry of all possible ranges. Yet mathematicians did not consider matrices with entries from finite fields until 2016, and so the recent direction of research has been devoted to this area. In our research, we consider the relationship between the numerical range of a matrix with entries from a finite field and its null range, a finite-field-specific generalization of the numerical range. Hence, we explore the null range of $2\\times 2$ matrices with entries in the finite field $\\mathbb{Z}_p[i]$, particularly with $p=3$. We pay special attention to the null range of matrices with hyperbolic numerical ranges, those with $\\frac{p^2-1}{2}$ points, and consider how these ranges relate to the numerical ranges of certain $3\\times 3$ matrices. As eigenvalues are always a determinative aspect in the classical numerical range, we also consider the effect on the numerical range of eigenvalues outside of our field.", "id": "Paper/72550", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72550"}, {"title": " On <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.247ex\" height=\"3.009ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -1150.1 967.5 1295.7\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\overline {\\text {SI}}</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-53\" d=\"M55 507Q55 590 112 647T243 704H257Q342 704 405 641L426 672Q431 679 436 687T446 700L449 704Q450 704 453 704T459 705H463Q466 705 472 699V462L466 456H448Q437 456 435 459T430 479Q413 605 329 646Q292 662 254 662Q201 662 168 626T135 542Q135 508 152 480T200 435Q210 431 286 412T370 389Q427 367 463 314T500 191Q500 110 448 45T301 -21Q245 -21 201 -4T140 27L122 41Q118 36 107 21T87 -7T78 -21Q76 -22 68 -22H64Q61 -22 55 -16V101Q55 220 56 222Q58 227 76 227H89Q95 221 95 214Q95 182 105 151T139 90T205 42T305 24Q352 24 386 62T420 155Q420 198 398 233T340 281Q284 295 266 300Q261 301 239 306T206 314T174 325T141 343T112 367T85 402Q55 451 55 507Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-49\" d=\"M328 0Q307 3 180 3T32 0H21V46H43Q92 46 106 49T126 60Q128 63 128 342Q128 620 126 623Q122 628 118 630T96 635T43 637H21V683H32Q53 680 180 680T328 683H339V637H317Q268 637 254 634T234 623Q232 620 232 342Q232 63 234 60Q238 55 242 53T264 48T317 46H339V0H328Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-AF\" d=\"M69 544V590H430V544H69Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n<g transform=\"translate(24,0)\">\n <use xlink:href=\"#E1-MJMAIN-53\"></use>\n <use xlink:href=\"#E1-MJMAIN-49\" x=\"556\" y=\"0\"></use>\n</g>\n<g transform=\"translate(0,522)\">\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-AF\" x=\"-70\" y=\"0\"></use>\n<g transform=\"translate(176.81931857111312,0) scale(1.5962549868656541,1)\">\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-AF\"></use>\n</g>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-AF\" x=\"867\" y=\"0\"></use>\n</g>\n</g>\n</svg> groups and subgroups of the first Grigorchuk group ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "8e47928adb8fb4453eca90290609485c98f8f92afe4ae0ab084400561b3412e9", "withdrawn": "", "abstract": "A group is considered $\\overline{SI}$ if every chief factor of that group is abelian. This property was introduced by G. Kurosh and K. Chernikov in 1947 as a weaker and more general version of solvability. Unlike solvability, this property is not hereditary. However, there are no known examples of an $\\overline{SI}$ group that has a non $\\overline{SI}$ subgroup and doesn't contain a free group on two generators.\n\n    One previously proposed candidate to be such a group was the first Grigorchuk group. The first Grigorchuk group is $\\overline{SI}$ because it is a branch group, which isn't a property that its subgroups possess. We show that all subgroups of the Grigorchuk group are still $\\overline{SI}.$ In the process we also show that the $\\overline{SI}$ property lifts from a normal subgroup to a group if the index of that subgroup is a power of 2. We also show that if every finitely generated subgroup of some group $G$ is $\\overline{SI},$ then every subgroup of $G$ is $\\overline{SI}.$", "id": "Paper/72551", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72551"}, {"title": " <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.636ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 704.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">T</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-54\" d=\"M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-54\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-equivariant modules over the ring <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"42.743ex\" height=\"3.343ex\" style=\"vertical-align: -1.005ex;\" viewBox=\"0 -1006.6 18403.2 1439.2\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">k[x_1, x_2, \\dots , x_n][y_1, y_2, \\dots , y_{n - 1}]/(x_i y_i)_{i = 1}^{n - 1}</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6B\" d=\"M121 647Q121 657 125 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"source_sha256": "359132edbd57921a3afb907890f9645c83a0a0b1fdd054ba09c8edf2ba23d128", "withdrawn": "", "abstract": "Let $k$ be an algebraically closed field of characteristic zero, $n$ a positive integer, and $R$ the ring $k[x_1, x_2, ..., x_n][y_1, y_2, ..., y_{n - 1}]/(x_iy_i)_{i = 1}^{n - 1}$, we endow this with a natural action of the ring of functions of the torus $T = \\mathbb{G}_{m}^{n}$. In this paper, we study the derived category of $T$-equivariant $R$-modules.  In particular, we work with a natural set of generating objects $\\mathcal{L}_\\alpha$ and construct an explicit $T$-equivariant projective resolution of them. The $\\mathcal{L}_{\\alpha}$ are equipped with raising and lowering operators between them, and, by taking cones, we generate a new set of objects. A table of extension groups is calculated between these different objects. We subsequently use this to examine a set of colimits given by the $\\mathcal{L}_\\alpha$ and these raising and lowering operators in the $\\mathrm{Ind}$-completion of the category, and characterize a unique colimit in this set with respect to an $\\mathrm{Ext}$-vanishing property arising from the table. Finally, we describe how these colimits correspond to certain gluing functors on the moduli stack of $\\mathrm{GL}_{2}$-bundles of the Fargues-Fontaine curve in the case of $\\mathrm{PGL}_2$, expanding on a correspondence described by Bertoloni-Meli.", "id": "Paper/72552", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72552"}, {"title": " Weak Order Units in the Ring of Continuous Bounded Functions ", "webprogram_exclude": "0", "session_ids": ["Session/18238"], "source_sha256": "162649bc904c9c821438176444b7be7876c91bfa354e2092d4b136e234b72d38", "withdrawn": "", "abstract": "We investigate weak order units in $C^*(\\mathbb{R})$, the lattice-ordered ring of bounded real-valued continuous functions on $\\mathbb{R}$. In spaces of continuous functions, weak order units are closely tied to the behavior of zero-sets. We explore how the topological structure of a function’s zero-set determines its status as a weak order unit, paying particular attention to the role of interior points. Although a function may remain a weak order unit even when its zero-set is nonempty, we establish a definitive characterization of weak order units in $C^*(\\mathbb{R})$ in terms of zero-sets with empty interior. Concrete examples are provided to illustrate this result, deepening our understanding of the interplay between algebraic weak order units and the topological properties of zero-sets.", "id": "Paper/72553", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72553"}, {"title": " Eigenweights of Fundamental Representations from the Cartan Matrix ", "webprogram_exclude": "0", "session_ids": ["Session/18160"], "source_sha256": "68e402a5f7df654fcddfd13651a7d5224de80580e924fccb263c6f45c4273da8", "withdrawn": "", "abstract": "The eigenweights \\(\\epsilon_{\\lambda,j}\\) are combinatorial invariants attached to a reductive group \\(G\\) and a dominant weight \\(\\lambda\\). They appear in the formula of Feng--Yun--Zhang for the arithmetic volume of the moduli stack of Shtukas. Eigenweights are also conjectured to govern the arithmetic volumes of Shimura varieties. Wang and Wei have described them using two bilinear forms, but for fundamental weights the resulting formulas are case-by-case and difficult to evaluate. We give a new closed formula for eigenweights \\(\\epsilon_{\\omega_r,j}\\) in Type A (\\(\\mathfrak{sl}_{n+1}\\)); our only input is the Cartan matrix, which eliminates case-by-case complexity and makes them significantly easier to compute. We also describe how these methods extend beyond type A to a general formula for eigenweights across all types.", "id": "Paper/72554", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72554"}, {"title": " Divisibility in rational monogenic semidomains ", "webprogram_exclude": "0", "session_ids": ["Session/18160"], "source_sha256": "58c5fbc138422a3e81479362d0e4280449b09574fdf8f50ef19409418f35803c", "withdrawn": "", "abstract": "For $q \\in \\mathbb{Q}_{>0}$, let $S_q=\\mathbb{N}_0[q]$ be the rational monogenic semidomain generated by $q$. The multiplicative monoids $S_q^*$ were recently studied by Deng-Gotti-Zeng from the perspective of factorization theory. In this paper, we extend this investigation by studying divisibility properties of $S_q^*$. We determine exactly when $S_q^*$ satisfies the atom-prime (AP), ACCP, GCD, and quasi-GCD properties. We also investigate the Furstenberg, atomic, MCD, MCD-finite, and quasi-ACCP properties, focusing on the difficult case where $q \\in (0,1)$ and the denominator of $q$ has at least two distinct prime factors. In this setting, we follow Deng-Gotti-Zeng in using the technical monoid $T_q$ to analyze divisibility of elements supported by prime divisors of the denominator of $q$. We construct explicit families of parameters $q$ for which $S_q^*$ satisfies or fails these properties.", "id": "Paper/72555", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72555"}, {"title": " Low-rank Nyström approximation for polynomial kernels in Gaussian mixture estimation ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "946592053a4a75590484271d99a873f6f6de657de2f94782291647def298f33e", "withdrawn": "", "abstract": "Polynomial kernels arise naturally in the context of Gaussian mixture estimation, natural language processing, and machine learning, among many other application domains that require efficient computation and storage for the corresponding Gram matrix. We focus on the polynomial kernel matrices arising from the parameter estimation problem for heteroscedastic low-rank Gaussian mixture models via the diagonally-weighted generalized method of moments approach recently introduced by Zhang, Mickelin, Xu, and Singer [arXiv:2507.20459 (2025)]. In particular, we study randomized low-rank Nystr\\\"{o}m approximation of these polynomial kernel matrices using several landmark sampling algorithms in the literature, including ridge leverage score sampling, kernel k-means++ sampling, and randomly pivoted Cholesky. Our main results include bounds on the order of error for these algorithms dependent on the singular value decay of the matrices, together with numerical results for these algorithms on data from the heteroscedastic low-rank Gaussian mixture models.", "id": "Paper/72556", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72556"}, {"title": " Mathematical Modeling against Food Insecurity in Orlando ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "925dd732194c10e85473cbd4bcc95705f190f45347770937e4b19db7ba398174", "withdrawn": "", "abstract": "In a community-engaged research project, we collaborated with United Against Poverty Orlando (UpOrlando) to improve the efficiency of its Mobile Market program, which provides reduced-price groceries to underserved communities. We used a minimum dominating set algorithm for three modes of transportation (by car, public transportation, and on foot) to identify optimal Mobile Market locations that are commutable for the communities they serve under each mode. By car, eight locations are enough to reach all 52 candidate sites, but 45 are needed by public transportation and 51 on foot, showing how difficult the program is to reach for community members without a vehicle. As a project deliverable, we developed the UpOrlando Community Center Priority Analyzer, a standalone desktop application with no recurring costs that ranks candidate sites by community need and recomputes the minimum dominating set for each mode of transportation as staff add new sites.", "id": "Paper/72557", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72557"}, {"title": " A Mathematical Model for Spinal Cord Stimulation: Predicting Mechanisms of Pain Relief ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "5d6829749374d90b0692c1029cac03167dd88ccbff5efb2873c1cb3785abbca5", "withdrawn": "", "abstract": "Chronic pain affects roughly a quarter of the adult population in the United States, significantly impairing daily life and work capacity for many. Spinal cord stimulation (SCS) is a therapeutic treatment that emits electric signals from an implanted electrode along the spine. It has been effective for many patients; however, its efficacy varies widely across individuals and stimulation parameters (such as frequency or amplitude of the signal). \n\nTo uncover the dynamical mechanisms underlying this variability, we construct a firing-rate model using coupled differential equations to track four interacting neuronal populations in the dorsal horn (DH), the primary spinal circuit for processing pain signals. We examine two stimulation pathways, surround stimulation and local afferent fiber stimulation, and propose the time constant of the inhibitory (suppression) populations as potential mechanisms for the observed interpatient variability. \n\nIn this poster, we examine the variability in efficacy of SCS input across frequency and amplitude as a function of the inhibitory population time constant. We show that under surround stimulation, a slow membrane time constant allows inhibitory activity to build up over time, providing pain relief at low SCS amplitudes. Conversely, a fast time constant enables the population to respond much more rapidly to low-amplitude inputs. Finally, by incorporating more realistic inputs through the local stimulation pathway, the model reveals a dual mechanism of inhibitory gating and relative timing, offering insight into the diverse patient responses observed across different SCS protocols.", "id": "Paper/72560", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72560"}, {"title": " Track Reconstruction in a High-Occupancy Gas TPC  with Time-Aware Object Condensation ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "d620f84554cc1377dd242f99fd5b4f3e76c794f5dcda08d068e34ce1fe1df8e3", "withdrawn": "", "abstract": "We reconstruct charged-particle trajectories in a high-occupancy gas time-projection chamber (TPC)\nas a single-stage instance-segmentation problem over a point cloud of detector hits. For every hit, a\nfour-block transformer maps the measured features to a condensation score, a latent coordinate, and\na collision time, attending only within a fixed 32-nearest-neighbour graph to keep training cost\nbounded. Particles are recovered by greedy seeding and absorption in that latent space---no need\nfor bipartite matching, predicting the number of tracks, or enforcing a fixed upper bound.\nOur contribution is the time coordinate. The time predicted for each hit is the\n\\emph{collision time} of the interaction that produced it, and the prediction is appended as a fifth\ncoordinate of the clustering metric. The readout does not measure $z$, the coordinate along the\nbeam and the direction the ionisation drifts: it follows from the drift time only once the\ncollision time is known. Recovering that time therefore recovers a separation the TPC readout alone\ncannot give. On an independent benchmark of ten complete readout frames the time-aware model\nreaches a double-majority\nreconstruction efficiency of $\\efff = 0.948$ at 50\\% completeness and\n$\\effs = 0.917$ at 75\\%\ncompleteness, against $0.930$ and $0.901$ for the same architecture without the time coordinate, a\ngain that comes almost entirely from reduced merging. A model trained on the realistic momentum\nspectrum instead reaches 0.947 and 0.884, so the improvement is in completeness rather than in the\nnumber of particles found. The graph is built in \\emph{conformal} coordinates $u = x/r^{2}$,\n$v = y/r^{2}$, in which a circle through the origin becomes a straight line; that choice is not\nablated here.", "id": "Paper/72562", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72562"}, {"title": " Partisan Responsiveness of Congressional Redistricting Plans ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "d846a587fd30bc8eaa7f1740ac7327d90364d932fababfe784a209b358625436", "withdrawn": "", "abstract": "Analysis of redistricting in the US often focuses on partisan impact or racial fairness. Representative democracies, however, require the ability of the electorate to audit and meaningfully replace their representatives. In a healthy republic, representation should ideally change with the will of the people. Instead, the practice of gerrymandering has made it so that representation primarily changes with the choice of district map. The recent unprecedented wave of mid-cycle congressional redistricting provides an opportunity to examine how newly enacted and proposed maps have altered the responsiveness of the congressional body to the electorate. We define district-level responsiveness as the likelihood that a district changes party affiliation. When computing responsiveness, plausible election outcomes are modeled based on historical voting data. Using these models, we analyze the responsiveness of congressional plans in nine of the states that have undergone mid-cycle redistricting efforts and compare them to a collection of neutrally drawn redistricting plans. In addition, the harm of a voter, which measures which voters get their preferred electoral outcome, is contrasted with district responsiveness, which measures the extent to which voters can influence their district's partisan outcome. Considering both responsiveness and harm together provides a mechanism to audit and improve democratic processes. We find that responsiveness is substantially suppressed in South Carolina, North Carolina, Texas, Alabama, and Virginia relative to neutral ensemble expectations, moderately suppressed in Florida, and broadly consistent with those expectations in Louisiana, Tennessee, and California. Moreover, many of the recent mid-cycle redistricting practices increase harm while reducing responsiveness.", "id": "Paper/72563", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72563"}, {"title": " Counting Incorrect Fubini Rankings ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "41419d94494ee74d548e0e8a4fc4dd7017cbe056e99480a478f299abae16e2fc", "withdrawn": "", "abstract": "A Fubini ranking $\\alpha=(a_1, a_2,\\ldots, a_n)$ is a tuple of length $n$ whose entries are in $\\N=\\{1,2,3,\\ldots\\}$. Fubini rankings encode the final outcome of a competition with $n$ competitors where ties are allowed. For example, $(3,1,1)$ is the Fubini ranking for a race in which competitor $1$ places third, and competitors $2$ and $3$ tie for first. We consider $\\alpha^\\uparrow=(a'_1, \\ldots, a'_n)$ to be the weakly increasing rearrangement of $\\alpha$ - it is known that $\\alpha$ is a Fubini ranking if and only if for any $a_i' \\in \\alpha^\\uparrow$, $a_i'=a_{i-1}$ or $a_i'=i$. Given a weakly increasing Fubini ranking $\\alpha$, we say that $\\beta$ is an incorrect Fubini ranking if, for at least one $i \\in [n] = \\{1,2,\\ldots,n\\}$, $b_i \\neq a_i$. We define $b_i$ to be a \\emph{happy} competitor if $b_i > a_i$ and a \\emph{sad} competitor if $b_i < a_i$; we denote their counts using $h$ and $s$ respectively. Given a specific $\\alpha$ and values for $h$ and $s$, the set of possible incorrect Fubini rankings is denoted $\\IFR{\\alpha}{h}{s}$. We give formulas for the cardinality of $\\IFR{\\alpha}{1}{0}$, $\\IFR{\\alpha}{0}{1}$, and $\\IFR{\\alpha}{2}{0}$ for any given $\\alpha$. We also give a formula for the cardinality of $\\IFR{\\alpha}{h}{0}$ for any $h \\in \\N$ where $\\alpha=(1,1, \\ldots, 1)$.", "id": "Paper/72564", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72564"}, {"title": " Analysis of Neural Networks in Estimating Perfusion Parameters using CT Images of Stroke Patients ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "85db30e3b71c5968e52069c06a33af7293957f66ffed4c7ca4e0cca1e6f1085b", "withdrawn": "", "abstract": "Acute ischemic strokes occur when blood flow to a part of the brain is cut off suddenly because of a blood clot. These medical emergencies require quick diagnosis and treatment to minimize damage to the brain and increase chances of survival. Computed Tomography Perfusion (CTP) scanning is a diagnostic tool used to determine differences between healthy tissue from irreversibly damaged cerebral tissue in stroke patients. This is accomplished through interpreting quantitative perfusion parameter maps - such as Cerebral Blood Flow (CBF), Mean Transit Time (MTT), Cerebral Blood Volume (CBV) and Time To Peak (TTP) - generated from the CTP raw image data. Neural networks have shown significant potential for automated, highly accurate analysis of medical imaging data. In this study, two models, Temporal Convolutional Network (TCN) and Convolutional Neural Network (CNN), were developed to estimate perfusion parameters. The models were trained on data from the open-access dataset UniToBrain released by the University of Turin, which is composed of CTP images for 258 patients. The results show that the TCN is more accurate in estimating the perfusion parameters than the CNN, as demonstrated by its lower Root Mean Square Error (RMSE) and final loss values. This suggests the potential for the application of TCN to aid medical professionals with diagnosis of stroke patients and improve treatment outcomes.", "id": "Paper/72565", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72565"}, {"title": " Investigating the Strength of Eisermann’s Modulo 8 and 32 Ribbon Obstructions ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "49afc1e9d7e65bb0da56e63e1f118f6579b2cd5b44a9871886712ab6b573b487", "withdrawn": "", "abstract": "Abstract: Determining if a link is ribbon is a central problem in geometric topology. While classical algebraic obstructions, such as vanishing linking numbers $\\ell k=0$, zero signature $\\sigma=0$, and the Fox-Milnor condition, are used to identify slice suspects, Eisermann recently introduced a modern necessary condition based on a modulo 32 congruence. This project investigates whether this condition is strictly stronger than the classical suite for multi-component links. We conducted a computational sweep of over 30,000 links using SnapPy and SageMath, analyzing the 14-crossing and 15-crossing datasets. We sought \"imposters\" that satisfy classical algebraic sliceness but fail the Modulo 32 test. No counterexamples were found; all 357 suspects at 15 crossings satisfied the condition and were verified as ribbon. We also developed an analytic framework for the 2-component case, providing evidence that for low-complexity links, classical criteria may be sufficient to satisfy this modern obstruction.", "id": "Paper/72566", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72566"}, {"title": " Optimal Kalman Filters for Deep Learning with Runtime and Memory Constraints ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "2b4108619c2113f2ccc5253adf7155038a0872b25c4bd43127092509ffdec912", "withdrawn": "", "abstract": "Remarkable success has been shown by frontier models in many applications such as natural language processing and image recognition. However, they are widely trained using gradient descent algorithms that require huge datasets and lack theory that supports uncertainty quantification or optimal test accuracy. The extended Kalman filter (EKF) addresses these issues by adopting the Bayesian approach to parameter estimation of a neural network. However, this algorithm relies on covariance matrices computations that scale quadratically with the number of parameters, which is prohibitive for neural networks that have millions or billions of parameters. We investigate optimal estimation algorithms with linear runtime and memory complexity constraints through two approaches: 1) characterizing and assessing assumptions under which an exact EKF can be implemented with linear complexity, and 2) projecting step-wise onto a structured family of matrices with linear storage and update time. Experiments show that the resulting filters improve test accuracy and converge with fewer measurements compared to widely used gradient-based optimizers.", "id": "Paper/72568", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72568"}, {"title": " A Control-Theoretic Approach for Resource-Aware Consensus in Multi-Agent AI Systems ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "f8d755311d4bb0597de33a18ccdc0c32f2a455744d198c135e3ef22945e92b2c", "withdrawn": "", "abstract": "Inter-agent communication drives a large language model multi-agent system (LLM-MAS) towards consensus in order to solve complex reasoning tasks. Despite rapid empirical advances in LLM-MAS, rigorous guarantees relating consensus performance to computational resources remain limited. To capture the dynamics at the intersection of consensus coordination and resource management, we present a discrete-time switched system in which communication topologies have distinct consensus-contraction rates and token costs. By augmenting the belief dynamics with the remaining computational budget, we define a consensus safe set that jointly captures agreement and resource feasibility. We derive explicit bounds on consensus time and token expenditure and construct a consensus-budget certificate region guaranteeing finite-time convergence without resource exhaustion. Adaptive topology switching achieves a tradeoff between convergence speed and communication cost relative to fixed-topology strategies. We illustrate the predicted consensus-cost trade-offs through numerical experiments and live LLM-MAS deployments, demonstrating how control-theoretic certificates can enable resource-aware coordination in AI systems.", "id": "Paper/72569", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72569"}, {"title": " Low-Rank Kalman Filters for Deep Learning ", "webprogram_exclude": "0", "session_ids": ["Session/19350"], "source_sha256": "55cef37b47eaf72d9d5fec786a8bde73e7c2104314fa20648e02180d395db3f8", "withdrawn": "", "abstract": "The extended Kalman filter (EKF) is an approximate Bayesian method for estimating the state of a nonlinear system from noisy measurements. While typically used for dynamical systems, it has shown promise in training deep neural networks, achieving higher test accuracy and converging with fewer training observations compared to standard gradient descent methods. However, storing and computing the covariance matrices required for this estimate has memory and runtime costs that scale quadratically in the number of parameters, making the EKF infeasible for neural networks with millions or more parameters. The LOFI algorithm proposed by Chang et al. resolves this issue by restricting the inverse covariance matrix--called the information matrix--at each step of the EKF to a diagonal-plus-low-rank matrix that minimizes Frobenius norm error, which reduces the runtime and memory complexity of the algorithm to linear with respect to the number of parameters. We investigate two kinds of modifications to the information-matrix compression step in the LOFI algorithm: incorporating memory of information lost at previous steps, and replacing the Frobenius norm with alternative error metrics. Both aim to improve test accuracy while preserving the algorithm's linear scaling.", "id": "Paper/72570", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72570"}, {"title": " A Study of Minkowski Reduction for Hermitian Lattices over the Gaussian Integers ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "b31c70cbf0b9ae35156b2718b3cd478b41bfdd6f6fa56536565908143b768211", "withdrawn": "", "abstract": "Abstract: Let $f=\\sum a_{ij} x_ix_j$ be a positive definite quadratic form with real coefficients $a_{ij}$, where $a_{ij}=a_{ji}$. The form $f$ is said to be Minkowski reduced if, for each $i$, one has $f(l_1, \\ldots, l_n)\\geq a_{ii}$ for every set of integers $l_1, \\ldots, l_n$ satisfying $\\mathrm{gcd}(l_i, \\ldots, l_n)=1$. Tammela proved that, for dimensions $n\\leq 6$, these infinitely many inequalities can be replaced by a finite explicit collection of inequalities. Inspired by Tammela's result, this project investigates an analogous theory of Minkowski reduction for positive definite Hermitian lattices over the Gaussian integers $\\mathbb Z[i]$.", "id": "Paper/72572", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72572"}, {"title": " Banded and Hierarchical Covariance Approximations for Fast Online Bayesian State-Estimation ", "webprogram_exclude": "0", "session_ids": ["Session/19350"], "source_sha256": "cda673af6d6f6c833b98a7839bad49d1d0bd46e297060044810ef0f5b2acc3b5", "withdrawn": "", "abstract": "The Kalman filter is a Bayesian algorithm for state estimation from noisy measurements that has demonstrated success in applications from tracking aircraft trajectories to training machine learning models. However, due to storage and computations involving a large covariance matrix, the filter has prohibitive memory and runtime costs when applied to high dimensional systems such as neural networks or partial differential equations. To reduce these costs, we consider optimal projections of the covariance matrix onto the families of banded and hierarchical off-diagonal low-rank (HODLR) matrices so that the filtering algorithm scales linearly in runtime and memory cost with respect to the state dimension. When these filters are are used to train a convolutional neural network to classify images, they achieve higher test accuracy and converge in fewer iterations than existing low-rank filters.", "id": "Paper/72573", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72573"}, {"title": " Stochastic Completeness in Terms of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.488ex\" height=\"1.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -576.1 640.5 721.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\alpha</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-3B1\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Superharmonic Functions ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "7bcbb9dad928016f7332e78249cedd7e71afa4c36cad986b2f20fbd8debefe1d", "withdrawn": "", "abstract": "Stochastic completeness is the property that a continuous-time random walk on a graph has infinite lifetime, or equivalently, that diffusion on the graph preserves total mass over time. We study stochastic completeness using $\\alpha$-superharmonic functions, i.e., solutions of $(\\Delta+\\alpha)u \\geq 0$. We show that the existence of a uniformly positive $\\alpha$-superharmonic function for $\\alpha<0$ implies stochastic incompleteness, and that this condition becomes a characterization for weakly spherically symmetric graphs. We also show that a strong version of Khasminskii’s criterion for stochastic completeness is a characterization for weakly spherically symmetric graphs. For general graphs, the converse implications do not hold.", "id": "Paper/72574", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72574"}, {"title": " Groups Generated by Admissible Froidure–Pin Rules ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "773265e94bab9c047df70a1085fe890c855d50d4be8c3c8e43f3880c5d9eaa1a", "withdrawn": "", "abstract": "Given a finite group $G$ and a generating alphabet $A$, the Froidure-Pin algorithm produces a confluent terminating rewriting system $R$ such that $G \\cong \\langle A \\mid \\mathcal R\\rangle$.  In a recently proposed fully homomorphic encryption scheme, GRAFHEN (Guillot, Hoang Duc, Koskas, and Méhats, 2025), an altered version of this algorithm is employed which records only a selected class of $\\textit{admissible rules}$.  Motivated by this construction, we investigate the impact of rule admissibility criteria on the group $\\langle A \\mid \\mathcal R\\rangle$ produced by the modified Froidure-Pin algorithm.  In particular, we study the extent to which $\\langle A \\mid \\mathcal R\\rangle$ preserves the algebraic properties of the original group $G$.  We also study the behavior of these groups in the space of marked groups, with emphasis on convergence in the Gromov-Grigorchuk metric.", "id": "Paper/72575", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72575"}, {"title": " Simulation of Airflow in Bronchial Tube with Mucus Obstruction ", "webprogram_exclude": "0", "session_ids": ["Session/18240"], "source_sha256": "05300d53a576b481602383121046a714a83c529b210494c42cf2282e3dd892bc", "withdrawn": "", "abstract": "This research will investigate how partial mucus obstruction affects airflow resistance in a bronchial tube using Navier-Stokes equations to model the flow. The study uses Direct Numerical Simulation(DNS) and FreeFEM++ to examine how the obstruction size, location, and mucus properties influence airflow resistance. The research simulates the airflow using flow past a full step, considering mucus as a solid obstruction as well as air and mucus interaction using classical fluid-fluid interaction problems.", "id": "Paper/72576", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72576"}, {"title": " Cographs and Rational Generation of Noncommutative Pseudo-Roots ", "webprogram_exclude": "0", "session_ids": ["Session/18240"], "source_sha256": "596c286a48a60e77cb18ebab276d74db6d307072252b886b048216400375325d", "withdrawn": "", "abstract": "Factorizations of a noncommutative polynomial give rise to pseudo-roots indexed by the cover edges of a Boolean lattice. Each square face gives a rational ``diamond'' relation: knowing two neighboring pseudo-roots determines the other two. This suggests a sparse recovery problem. Choose only one pseudo-root in each coordinate direction, according to the open neighborhoods of a graph $G$, and ask when these $n$ elements determine all pseudo-roots.\n\nAt the level of diamond operations, this happens exactly when $G$ is a cograph, equivalently when $G$ has no induced four-vertex path $P_4$. Thus $P_4$ is the first obstruction to local recovery. A natural question is whether arbitrary rational operations in the free skew field can recover the missing pseudo-roots anyway.\n\nThey cannot. For the $P_4$ seed, the associated rational map has identity linearization at generic scalar points and therefore a formal local inverse, so there is no Jacobian or first-order obstruction. Nevertheless, evaluation on a carefully chosen family of $2\\times2$ matrices yields an algebraic inverse branch of degree three, forcing the induced matrix map to have generic degree at least three for every size $n\\ge2$. Hence no free rational inverse can exist. The argument extends from $P_4$ to every graph containing an induced $P_4$.\n\nConsequently, the graph-defined seed rationally generates all Boolean-lattice pseudo-roots if and only if $G$ is a cograph. Thus the same simple graph-theoretic boundary governs both local diamond generation and unrestricted rational generation.", "id": "Paper/72578", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72578"}, {"title": " Kernels of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.969ex\" height=\"2.843ex\" style=\"vertical-align: -1.005ex;\" viewBox=\"0 -791.3 1278.3 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">C^*_\\varphi</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-43\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2217\" d=\"M229 286Q216 420 216 436Q216 454 240 464Q241 464 245 464T251 465Q263 464 273 456T283 436Q283 419 277 356T270 286L328 328Q384 369 389 372T399 375Q412 375 423 365T435 338Q435 325 425 315Q420 312 357 282T289 250L355 219L425 184Q434 175 434 161Q434 146 425 136T401 125Q393 125 383 131T328 171L270 213Q283 79 283 63Q283 53 276 44T250 35Q231 35 224 44T216 63Q216 80 222 143T229 213L171 171Q115 130 110 127Q106 124 100 124Q87 124 76 134T64 161Q64 166 64 169T67 175T72 181T81 188T94 195T113 204T138 215T170 230T210 250L74 315Q65 324 65 338Q65 353 74 363T98 374Q106 374 116 368T171 328L229 286Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-3C6\" d=\"M92 210Q92 176 106 149T142 108T185 85T220 72L235 70L237 71L250 112Q268 170 283 211T322 299T370 375T429 423T502 442Q547 442 582 410T618 302Q618 224 575 152T457 35T299 -10Q273 -10 273 -12L266 -48Q260 -83 252 -125T241 -179Q236 -203 215 -212Q204 -218 190 -218Q159 -215 159 -185Q159 -175 214 -2L209 0Q204 2 195 5T173 14T147 28T120 46T94 71T71 103T56 142T50 190Q50 238 76 311T149 431H162Q183 431 183 423Q183 417 175 409Q134 361 114 300T92 210ZM574 278Q574 320 550 344T486 369Q437 369 394 329T323 218Q309 184 295 109L286 64Q304 62 306 62Q423 62 498 131T574 278Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-43\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-2217\" x=\"1094\" y=\"453\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-3C6\" x=\"1011\" y=\"-211\"></use>\n</g>\n</svg>: Interpreting the Functional Equations ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "e83d08cf824d7a6448a8f594f31ebfa45de3fa882687fe0280fec7f60d2d730a", "withdrawn": "", "abstract": "Composition operators on the Hardy space $H^2(\\mathbb{D})$ are induced by analytic self-maps of the unit disk $\\varphi$ and are defined by $C_{\\varphi} f=f\\circ \\varphi$. Although the adjoints of these operators are generally difficult to describe explicitly, previous work provides a functional equation characterizing functions in $\\ker C_{\\varphi}^*$ when $\\varphi$ is a quadratic rational self-map. The associated linear fractional map, the Miller Map, $\\zeta$, which interchanges the two preimages of $\\varphi$, falls into one of five canonical types. We investigate the first three types by solving their corresponding functional equations and translating these implicit conditions into explicit descriptions of the kernel. For Type I, the kernel consists precisely of the odd functions in $H^2(\\mathbb{D})$. For Type II, the functional equation forces every nonconstant power-series coefficient to vanish and, since every element of $\\ker C_{\\varphi}^*$ vanishes at the origin, the kernel is trivial. For Type III, a translation to the fixed point of the involution reduces the functional equation to an evenness condition, yielding functions of the form\n$$f(z)=z\\sum_{j=0}^{\\infty}a_{2j}\\left(z+\\frac{A}{2}\\right)^{2j}.$$\nThis representation also produces a successive derivative condition at $-\\frac{A}{2}$, connecting the functional-equation approach to earlier derivative-based characterizations of kernels of adjoint composition operators.", "id": "Paper/72580", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72580"}, {"title": " Symmetric Tensor Products of Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "5cdcd5ec7ccf6f428a44aa0208f2b74e5a78fe76f59ebcae859a4d517e7b941b", "withdrawn": "", "abstract": "We extend the symmetric tensor power of a graph introduced by Astaiza et al. to the symmetric tensor product of several, possibly distinct, labeled weighted graphs on a common vertex set. We study structural and combinatorial properties of graphs obtained via this operation. We also develop a polynomial representation of the symmetric tensor product, investigate how graph labeling affects the product, and study how to factorize graphs with respect to the operation.", "id": "Paper/72582", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72582"}, {"title": " Modeling Two-Cylinder Hydrodynamics in Biological Flows: Comparing Stokes and Brinkman Regimes ", "webprogram_exclude": "0", "session_ids": ["Session/19343"], "source_sha256": "12efe7b282b8e9a935e638f69bd1e8dd016eef8b1cf36200e4a2f9eeb9727126", "withdrawn": "", "abstract": "Microorganisms drive fluid motion by rotating appendages and beating cilia. In an open, homogeneous fluid these low-Reynolds-number flows are well described by the Stokes equations, but many biological settings, such as mucus, biofilms, and ciliated tissues, are crowded by a porous microstructure that screens the flow and is more faithfully captured by Brinkman flow. We investigate the hydrodynamics of rotating structures in crowded environment\n\nUsing the Method of Regularized Stokeslets and its Brinkman analogue in an unbounded two-dimensional domain, we compute the induced flow and the torque on dual rotating cylinders. We validate the solver against known analytical results, including the single-cylinder torque, and investigate the effect of varying gap distances between two cylinders.", "id": "Paper/72585", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72585"}, {"title": " Automated Generation of Positivity Conjectures for Power Series Coefficients of Multivariable Rational Functions ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "02e8196c3025b6d3c7a174bea21a797660ae9eca43e68cbb4c1edd296de8f01a", "withdrawn": "", "abstract": "We explore and conjecture the maximum real value of a parameter for select multivariable rational functions such that the coefficients of the functions' Taylor expansion are nonnegative using Maple programs.", "id": "Paper/72587", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72587"}, {"title": " Noncrossing Partitions from Biaxial Configurations ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "96c28517c9ce3f7b52e05db73021e3192b8b08351f51c7005b5a7d3961330fb7", "withdrawn": "", "abstract": "For each finite configuration of points in the plane, there is an associated lattice of noncrossing partitions. When these points form the vertex set of a convex polygon, the resulting lattice is the classical poset of noncrossing partitions which was defined by Kreweras in the 1970s and has since become an important object in algebraic combinatorics and geometric group theory. In our work, we study the analogous poset for ``biaxial configurations,'' which we define to be those which lie on a pair of intersecting lines. In particular, we show that these posets are always graded, rank-symmetric, and admit an EL-labeling. We also address when these posets are supersolvable and provide some connections with the study of lattice paths.", "id": "Paper/72591", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72591"}, {"title": " Straightening identities in the universal enveloping algebras of some map algebras ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "0c8d6924bc4462a93aeaea9f0a8a21e7b4266d9987d1262cce6537f3c9be67a0", "withdrawn": "", "abstract": "The map algebra of a Lie algebra $L$ and an associative commutative algebra $\\mathcal A$ with a multiplicative identity both over the complex numbers is defined to be the vector space $L\\otimes \\mathcal A$ with Lie bracket given by bilinearly extending the bracket given by: $[b\\otimes z, a\\otimes y]=[b,a]\\otimes zy$\nfor all $b,a\\in L$ and $z,y\\in \\mathcal A$. This map algebra itself is also a Lie algebra.\n\nThe Poincar\\'e-Birkhoff-Witt (PBW) Theorem states that the elements of the non-commutative universal enveloping algebra of a Lie algebra can be rewritten as a unique linear combination of products of basis elements of the Lie algebra in any fixed order. This process of reordering elements is defined as straightening. The PBW Theorem states that straightening is possible but does not say how it can be done.\n\n\\v Snobl and Winternitz classified all real and complex Lie algebras of dimension 6 and less. We formulated and proved general lemmas that allow us to straighten products in the universal enveloping algebras of various map algebras. Using the lemmas and \\v Snobl and Winternitz's classification, we straightened products in the universal enveloping algebras of some map algebras, $L\\otimes \\mathcal A$, where $L$ has dimension four or less and $\\mathcal A$ is general.", "id": "Paper/72592", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72592"}, {"title": " A Multispecies Interacting Particle System with Pair Immigration and Annihilation ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "bac9236c27aa8510760621a918c7b34885db67f24778588ce6f282792eff6e16", "withdrawn": "", "abstract": "The asymmetric simple exclusion process (ASEP) is an interacting particle system, where \"exclusion\" means that at most one particle may occupy a site at a time, \"simple\" means that particles can make at most one jump at a time, and \"asymmetric\" means that particles have higher probability to jump in one direction than another. Additionally, particles are blocked from jumping to an occupied site. We will consider a multispecies version where \"heavier\" particles can swap places with \"lighter\" particles. We will also allow for species with pair immigration and annihilation. In pair immigration, adjacent pairs of particles may be replaced with a pair of immigrating particles of another species. In pair annihilation, if a pair of particles attempts a swap between them, the particles will be annihilated and replaced with a pair of species of \"lighter\" weight. On $4$ lattice sites with species $1$, $2$, $3$, and $4$, we introduced pair annihilation and immigration between species $2$ and $3$. We then constructed a Hasse diagram for each communicating class of the system involving at minimum two particles of species $2$ or $3$, ordered based on the number of species $3$ in each configuration. By choosing values for the rates of immigration, annihilation, left hops, and right hops, we produced reversible measures such that configurations higher on each Hasse diagram have larger reversible measures than those below them. With the advising of Dr. Jeffrey Kuan in current work in progress, we will find the complete set of values of parameters for $A$, $S$, $L$, and $R$ for which the previous results hold true for arbitrary lattice sites. We will also find a general formula for the reversible measures with generic values of $A$, $S$, $L$, and $R$.", "id": "Paper/72593", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72593"}, {"title": " Forensic Deconvolution and Spatial Reconstruction: Unifying DNA Profiling and Mathematical Modeling in Criminal Investigations ", "webprogram_exclude": "0", "session_ids": ["Session/19365"], "source_sha256": "4752200fb5ab16bd7e26fbd8f49edd5c6aa8471889dc1934d0efd28a028ccb41", "withdrawn": "", "abstract": "Justice depends not only on a sound legal framework but also on the scientific and mathematical evidence that substantiates it. Forensic science provides this evidentiary foundation by transforming physical traces into reliable conclusions. In this project, we examine two core dimensions of forensic investigation. The first is DNA-based identification. Using overlapping fingerprints as a model, we demonstrate how biological samples from multiple contributors can be separated to determine culpability. Three techniques are applied: DNA mixture interpretation, which isolates the genetic profiles of distinct individuals; DNA intelligence (phenotyping), which constructs a probable profile of an unknown suspect; and classification, which converts raw sequencing data into conclusions suitable for investigative and legal use. The second dimension concerns the reconstruction of physical events, where we investigate the geometry and linear algebra underlying bloodstain pattern analysis and bullet trajectory reconstruction; showing how mathematical modeling allows investigators to infer the positions, movements, and sequence of events at a crime scene. Together, these analyses illustrate how forensic science unites biology, mathematics, and law to produce evidence that is both scientifically grounded and legally powerful.", "id": "Paper/72594", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72594"}, {"title": " Mathematical Models of Stem Cell Lineages and Homeostasis ", "webprogram_exclude": "0", "session_ids": ["Session/18238"], "source_sha256": "4fabf460b4fa6aa7d1a9f23e1633d9d3db101a7a378a90c140663de7d35f0b1a", "withdrawn": "", "abstract": "Adult stem cells generate all other cell types in a tissue through cell division. To maintain homeostasis, they must precisely balance self-renewal and differentiation via negative feedback. However, mutations can disable these feedback mechanisms, leading to tissue extinction, uncontrolled cell growth, and diseases such as cancer.\n\nUtilizing ordinary differential equations (ODEs), we explored simplified two-component models of stem cell lineages with different combinations of negative feedback on cell division rates and the probability of stem cell self-replication versus differentiation. Depending on parameters, the solutions approach one of the following steady states: (1) tissue extinction, (2) homeostasis of stem and progenitor cells, and (3) a stem-free steady state with only terminally differentiated cells. Using linear stability analysis and numerical simulations, we determined conditions for an exchange of steady state stability (transcritical bifurcation) across different model variants. We found stability is regulated by death rates and the average number of progenitor cells produced per stem cell division ($\\gamma$). For sustained homeostasis, we require a stem cell self-renewal probability greater than 0.5, a low stem cell death rate, and the progenitor removal rate exceeding a threshold.\n\nSince stem-free steady states are unrealistic for most tissues, we also considered ways to remove them from the basic model: (1) assuming progenitor cell division either cannot take place or requires the presence of a stem cell population to proceed, (2) assuming progenitor cells can dedifferentiate when stem cell populations become low. Including dedifferentiation, we observed that the homeostasis requires different thresholds on $\\gamma$ and cell death rates.", "id": "Paper/72597", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72597"}, {"title": " Coefficients of the quantum <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.776ex\" height=\"2.509ex\" style=\"vertical-align: -0.671ex; margin-left: -0.041ex;\" viewBox=\"-17.5 -791.3 1195.4 1080.4\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathfrak {sl}_3</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJFRAK-73\" d=\"M272 33Q284 33 290 70T296 138Q296 181 290 198T262 230Q257 232 246 232Q231 232 218 227T156 194L108 167L101 176Q90 192 75 219L69 230V284Q69 346 70 357V377L146 427Q181 450 202 464T223 477L225 476Q227 475 229 474Q231 472 242 466T270 450T296 431Q309 418 326 418Q342 418 361 429T392 450T403 459Q406 445 406 442Q406 440 384 421T338 382L316 363Q315 362 310 362Q292 362 251 371T173 396Q156 403 155 403Q143 386 143 342Q143 305 150 278T168 244Q171 242 181 242L190 243L315 300Q330 295 357 274Q358 273 362 270T366 266T369 261T372 253T373 239T374 217T374 185Q374 157 372 133T368 98T363 71T358 50L336 40Q288 20 255 2T211 -22T198 -29L190 -22Q181 -14 168 -3T138 19T104 38T70 46Q50 46 32 37T3 20T-9 11L-18 23L-1 41Q46 89 62 99T112 110Q141 110 157 103T225 62Q268 33 272 33Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJFRAK-6C\" d=\"M221 76L267 99Q268 98 269 96T271 88T270 82L262 76Q255 69 241 57T214 34L148 -20L98 56L99 89Q107 247 107 373Q107 494 101 621Q101 653 99 659V665L106 668L113 672L118 655Q122 642 131 617L138 597Q140 597 157 611L240 670L264 685Q265 685 270 680T276 674T269 667T247 647T219 617Q197 587 186 551T173 493T171 438Q171 376 175 282T179 147V117Q184 109 201 93T221 76Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJFRAK-73\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJFRAK-6C\" x=\"443\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-33\" x=\"1023\" y=\"-213\"></use>\n</g>\n</svg> knot invariant ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "f458de2fe8ea9beef452aa32b7e8216c7c406e44f1b1969cbacc42d72bbb1f29", "withdrawn": "", "abstract": "The $\\mathfrak{sl}_3$ link polynomial is a higher rank relative of the Jones polynomial which can be studied entirely diagrammatically using Kuperberg's web calculus. The invariant is known to detect whether a link is fibered and provides an obstruction to present positive links as positive braids. Building on the work of Harper and Kalfagianni, we construct formulae for the fourth and fifth coefficients of the quantum $\\mathfrak{sl}_3$ link invariant on positive alternating links in terms of data read from the associated Seifert graph. We also discuss behavior of our formulae under connected sums, and applications to knot theory. Then, we give a characterization of the invariant on positive alternating fibered links in terms of elementary symmetric polynomials. Additionally, we formulate the Garside element ($\\Delta_3 \\in B_3$) in terms of elementary webs, give a closed formula for the polynomial on positive $3$-braids, and combine these results to give a complete characterization of the $\\mathfrak{sl}_3$ polynomial on all $3$-braids.", "id": "Paper/72599", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72599"}, {"title": " Eigenweights of Fundamental Representations via the Cartan Matrix ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "1a40cfcd9bc69832522ccf6464ed4abef05bb8dd22e10ac2de8cf1de1b99c142", "withdrawn": "", "abstract": "The eigenweights \\(\\epsilon_{\\lambda,j}\\) are combinatorial invariants attached to a reductive group \\(G\\) and a dominant weight \\(\\lambda\\). They appear in the formula of Feng--Yun--Zhang for the arithmetic volume of the moduli stack of Shtukas. Eigenweights are also conjectured to govern the arithmetic volumes of Shimura varieties. Wang and Wei have described them using two bilinear forms, but for fundamental weights the resulting formulas are case-by-case and difficult to evaluate. We give a new closed formula for eigenweights \\(\\epsilon_{\\omega_r,j}\\) in Type A (\\(\\mathfrak{sl}_{n+1}\\)); our only input is the Cartan matrix, which eliminates case-by-case complexity and makes computations significantly easier. We also describe how these methods extend beyond type A to a general formula for eigenweights across all types.", "id": "Paper/72604", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72604"}, {"title": " Enumeration of RNA Hairpins Structures through Motzkin Paths ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "a2e4fb61983062bf6b1036dca06006319ee7333a2b603e220f2260020324ea7d", "withdrawn": "", "abstract": "Ribonucleic acid, or RNA, is a single-stranded acid necessary for an array of key cell functions. It is characterized by secondary structures such as hairpins, loops, and duplex regions that impact the minimum free energy and shape of each unique strand. Motzkin paths are well-known combinatorial structures used in bioinformatics to enumerate different RNA secondary structures. However, the classical Motzkin path generating function is unable to enumerate specific RNA structures that contribute largely to the energetic stability of an RNA strand, such as hairpins. In this poster, we address this issue by modifying the existing Motzkin path generating function to enumerate RNA hairpins. We develop a combinatorial model using the first return decomposition method and biological compatibility to real RNA structures.", "id": "Paper/72610", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72610"}, {"title": " Directed Graph Learning via Smooth Signals and Directional Flow ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "0b0aaea35a656ff12f1ab9052c4f8215262f53dd31d9c7524307210a6aaaeac4", "withdrawn": "", "abstract": "Graph Signal Processing (GSP) offers a structured way to model and analyze complex data networks. However, a consistent challenge in real world applications is that the underlying graph topology is often unknown. While most existing graph learning methods focus on undirected graphs, specific relationships in network data, such as diffusion, weather data and social networks, sometimes necessitate a directed graph model. In this work, we propose a novel method for learning directed graph structures from observed signals by leveraging both signal smoothness and directional flow. We introduce a Dirichlet energy formulation specifically tailored to directed graphs, favoring smoothness and downwards flow of signals over the graph. We then develop the Perseus Measure to quantify how much the learned graphs obey the directional flow constraint. In addition, we present a novel random graph algorithm that builds a signal matrix alongside the graph, and we derive certain properties about the resulting Hierarchy Graphs. Experiments on both synthetic and real-world datasets show that our directed graph learning approach effectively captures directional relationships.\n\nThis work has been published in IEEE Transactions on Signal and Information Processing over Networks (Volume 12, 2026).", "id": "Paper/72611", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72611"}, {"title": " Certified Sparse Polynomial Recovery from Value Queries via Euler-Derivative Simulation ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "a0652c0ca0adb92a215694f9a7696846f48b0866d6587ff62d3ee0449577c65a", "withdrawn": "", "abstract": "Let $F(x)=\\sum_{i=1}^t c_i x^{d_i}\\in\\mathbb{Z}[x]$, with $t\\le T$, $c_i\\ne0$, and $0\\le d_1<\\cdots<d_t\\le D$, where $D\\ge1$. We study exact sparse recovery from complex value queries with arbitrarily small certified absolute error, without a supplied coefficient bound or access to derivatives or the program evaluating $F$.\r\n\r\nAt $p$th roots of unity, inverse discrete Fourier transformation recovers $F\\bmod(x^p-1)$, grouping terms whose exponents agree modulo $p$. We construct a prime set depending only on $T,D$ and guaranteed to contain a collision-free prime. Since at least one grid separates all terms, Fourier inversion shows that a common certified bound on the sampled magnitudes also bounds every $|c_i|$. This bound is obtained from coarse value queries, rather than supplied in advance. Certified Fourier inversion and integer rounding recover the cyclic images; maximizing their numbers of nonzero coefficients identifies a collision-free prime without knowing $t$.\r\n\r\nTo recover the full exponents, we simulate the Euler derivative $zF'(z)$ using\r\n$\\mathcal{D}_hF(z)=\\frac{F(ze^{\\mathrm{i}h})-F(ze^{-\\mathrm{i}h})}{2\\mathrm{i}h}$, $h>0$, $|z|=1$.\nOur analysis accounts for finite-difference bias, query error, approximate Fourier factors, and arithmetic error. At a certified collision-free prime, the inverse transform of the exact difference samples has entries $c_i\\sin(d_i h)/h$. Dividing by the recovered $c_i$ leaves $\\sin(d_i h)/h$, whose distance from $d_i$ is at most $D^3h^2/6$. Choosing $h$ of order $D^{-3/2}$ with a sufficiently small constant and controlling the total error below $1/2$ therefore recovers each exponent exactly by rounding.\n\nThe resulting deterministic method needs neither a derivative oracle nor a prior coefficient bound, and avoids polynomial root finding and coefficientwise Chinese remaindering. The sufficient angular step is independent of coefficient size, although working precision can still depend on it.", "id": "Paper/72612", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72612"}, {"title": " A New Algorithm for Reducing Exceedance in Generalized <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"6.844ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 2946.7 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">(n, kn)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-6E\" x=\"389\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2C\" x=\"990\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-6B\" x=\"1435\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-6E\" x=\"1956\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"2557\" y=\"0\"></use>\n</g>\n</svg> Catalan-Type Lattice Paths ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "952703a2c75812781cb6fe3069c6e10e5dd4019dc5416c726e2da522b6f5cc53", "withdrawn": "", "abstract": "Classical proofs of the Catalan formula use exceedance, the number of up-steps ending strictly above the diagonal $y = x$, together with a local move that lowers exceedance by exactly one. For lattice paths from $(0,0)$ to $(n,kn)$ with boundary $y = kx$, Chung-Feller-type counts are known through global methods such as the cycle lemma (Huq, 2009), but the standard local move, exchanging an adjacent $UR$ pair for $RU$, breaks down: shifting an up-step one unit right lowers it by $k$ relative to the boundary, so a single swap may remove several exceedant steps or none.\n\nWe introduce a local exceedance-reduction algorithm that works uniformly for every positive integer $k$. The algorithm locates the path's final entry into the region above $y = kx$, selects either the $k$-th or the last up-step of the run that follows, and exchanges it with the next right-step. By tracking coordinates, we prove that each application preserves the endpoint and reduces exceedance by exactly one, so repeated application transforms any path into one lying on or below $y = kx$. The construction extends the classical local exceedance-reduction argument to boundaries of arbitrary integer slope.", "id": "Paper/72613", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72613"}, {"title": " Helly and Radon theorems for convex intersections containing <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.211ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 521.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">k</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-6B\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-flats ", "webprogram_exclude": "0", "session_ids": ["Session/18238"], "source_sha256": "5a71409b83893066e467595548ea64c4f9b53296c37640e3656bace758d1147d", "withdrawn": "", "abstract": "Radon's theorem and Helly's theorem are two important results in discrete geometry about the intersections of convex sets. In this talk, we will discuss the theorems of De Santis that extend these results to intersections containing affine flats of dimension $k$, as well as new results that extend variations of Radon’s and Helly’s theorems in a similar way. We will discuss a brief outline of the proof for the generalization of the colorful Radon theorem. This is joint work with Pablo Soberón (Baruch College).", "id": "Paper/72616", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72616"}, {"title": " Whose Community Counts? Quantifying Community Preservation in Colorado Redistricting ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "fd6e8c15c13659ab053998907e7ebbfdbc0b9548c3182ac850252a1126afb69b", "withdrawn": "", "abstract": "A \\textbf{Community of Interest (COI)} is any regional contiguous or discontiguous group of individuals sharing voting interests, demographic traits, or policy concerns. While preserving COIs is a fundamental principle in redistricting for many states, it remains an ambiguous mandate in legislative redistricting. Consequently, redistricting commissions frequently divide these groups, diluting collective voting power. This paper introduces \\textbf{Total Community Preservation (TCP)}, a probability-based metric that measures the severity of community fractures by formalizing the conditional probability of an individual being in a particular district given their community membership. We conduct a case study of Colorado across its legislative chambers to benchmark TCP against existing preservation metrics. To capture varied geographic and demographic patterns, we construct eight Colorado community indicator maps across civic, economic, and administrative domains. Using the \\textit{ReCombination} Markov chain implemented in Python's \\texttt{GerryChain} package, we generate ensembles to establish a non-partisan baseline of Colorado's legislative maps under varied optimization constraints. These maps were then scored using a variety of community preservation metrics, providing mathematical insight into the splitting and preserving of Colorado communities. Crucially, our findings reveal that \\textbf{subjective COI selection can act as a partisan lever}, shifting seat shares even under seemingly neutral optimization constraints. Without operationalized measures of preservation, commissions lack a consistent basis to evaluate how community definitions impact legislative outcomes. Ultimately, evaluations against TCP demonstrate effective measuring of community preservation, offering a statistically grounded tool to safeguard against partisan manipulation while upholding community cohesion in efforts for a fairer redistricting process.", "id": "Paper/72617", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72617"}, {"title": " Multireader multicase statistical analysis for binary outcome observer studies with correlated images in MRI ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "3fc208998d3e96465c5bea5ee6cfd4d52f20747ffa389433827bba23de00f3bf", "withdrawn": "", "abstract": "In an observer study, an observer (or reader) performs a task such as localizing a tumor in a magnetic resonance (MR) image. These studies are commonly used when evaluating and comparing medical imaging systems. In these types of studies, the outcomes are correct or incorrect, generating binary results. When multiple images from a single patient are used, this allows for a larger number of available images for an observer study, but introduces correlation in the images. In this study, we generate synthetic data modeling the results of an observer study where there are correlations between the readers, images, and interactions between readers and images. The reader-averaged percent correct in these studies can be modeled using mixed-effects analysis of variance (ANOVA). We analyze the resulting data using multireader multicase (MRMC) analysis to estimate the variance of the reader-averaged percent correct using two methodologies: one assuming the images are independent, and one taking into account image correlations. Using Monte Carlo simulations, we compare both methodologies in terms of their estimates of the variance of the reader-averaged percent correct. This analysis shows the importance of including image correlations in MRMC analysis and will be validated through human observer studies in future work.", "id": "Paper/72620", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72620"}, {"title": " An Exponential-Gamma Ratio Representation of the Lomax Distribution: Limiting Behavior and Comparative Inference ", "webprogram_exclude": "0", "session_ids": ["Session/18238"], "source_sha256": "dc53502c516124978b0684e451c3d21b97b7ea4a648dae0e55dcd15336965409", "withdrawn": "", "abstract": "We introduce the Ratio Exponential--Gamma (REG) distribution, an analogue of the exponential distribution constructed as the ratio of an independent exponential random variable and a unit-mean gamma random variable. We derive the resulting probability density function in closed form using a conditional-density (Mellin-type convolution) argument and verify that it satisfies the axioms of a probability density function. We show that, as the gamma shape parameter $\\nu \\to \\infty$, the REG distribution converges in distribution to the exponential distribution, so that the exponential arises as a limiting special case governed by a single shape parameter. We derive the cumulative distribution function, the quantile function, and the first two moments, together with the condition $\\nu > 2$ under which the variance exists. We further show that the REG distribution does not belong to the exponential family, does not possess the memoryless property, and has no moment generating function for positive arguments --- three properties that sharply distinguish it from its exponential parent despite their shared limiting relationship. We establish an exact reparameterization under which the REG distribution coincides with the classical Lomax distribution, situating REG within the broader family of Pareto-type, heavy-tailed models used in reliability theory, actuarial science, and queueing. Parameter estimation is investigated by the method of moments and by Bayesian estimation using Metropolis--Hastings sampling. Simulation studies show that method-of-moments estimation is stable and low-bias when the shape parameter $\\nu$ is known, but becomes highly unstable when both parameters are estimated jointly; Bayesian estimation, by contrast, remains stable for the rate parameter $\\lambda$ in both settings, while estimation of $\\nu$ remains comparatively more variable. We conclude with a discussion of the practical implications of these findings and directions for future work, including improved estimation strategies for the shape parameter.", "id": "Paper/72621", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72621"}, {"title": " Zeckendorf Decompositions of Tribonacci Numbers and a Quadratic Bound for Riley’s Algorithm ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "83253d4986a78a4663ba27df2515b3b876a3784799a259d2619905b81272904f", "withdrawn": "", "abstract": "Every positive integer has a unique Zeckendorf decomposition as a sum of nonconsecutive Fibonacci numbers. This project investigates what happens when this representation is applied specifically to Tribonacci numbers. The study focuses on the number of Fibonacci summands needed to represent the m-th Tribonacci number and the size of the largest Fibonacci index appearing in the decomposition. Computational experiments are combined with growth-rate arguments and the nonconsecutive-index property to examine possible bounds and patterns. These ideas are also connected to Riley’s algorithm, which uses Zeckendorf decompositions to construct short words representing powers of elementary matrices in a Cayley graph. By studying the relationship among Tribonacci growth, Fibonacci indices, gap distributions, and algorithmic word length, this project explores how number-theoretic structure can help improve our understanding of navigation in Cayley graphs.", "id": "Paper/72622", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72622"}, {"title": " What If Hash Functions Aren’t as One-Way as We Thought ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "3fee327a36b858a5fe3d662d79ee5b744d10bc5c59559249dab908ecb3608578", "withdrawn": "", "abstract": "Cryptographic hash functions are designed to make recovering information about an original input computationally difficult. This research investigated whether machine-learning models could detect information associated with the first letter of a word using only its final Cayley hash matrix. A balanced dataset of 3,000 randomly generated words was created using the alphabet A–F, word lengths of 120–130 letters, six 3x3 generator matrices, and a fixed 128-bit prime modulus. Each word was converted into a final hash matrix by multiplying its generator matrices in letter order and reducing the entries modulo the prime. Six machine-learning approaches were evaluated using an 80\\% training and 20\\% testing split. The multilayer perceptron achieved the highest first-letter prediction accuracy at 45.83\\%, compared with a 16.67\\% random-guessing baseline. Random Forest and the Exact Cayley Neighborhood with Random Forest also performed above the baseline. These results suggest that the tested final hash matrices retained detectable patterns associated with the first generator. However, the models did not recover complete words or fully reverse the hash. Further research should test additional primes, word lengths, generator sets, datasets, and validation procedures.", "id": "Paper/72623", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72623"}, {"title": " Characteristic Polynomials for Ladder Tournaments ", "webprogram_exclude": "0", "session_ids": ["Session/19346"], "source_sha256": "ebdc6edbdc5396c6b2af7d93113ddca17739f1ad3ce75ef7eb110500663ac685", "withdrawn": "", "abstract": "For each integer $n \\ge 3$, we determine closed-form expressions for the characteristic polynomial of the Seidel matrix of ladder tournaments $L_n$.", "id": "Paper/72624", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72624"}, {"title": " Finding Formulas for The Gamma Orbifold Euler Characteristic when The Symmetries are Given by a Torus ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "b3a9fc296ed3157c11e7933e2c53185ea40f345c0de57795684475a3f83e83a1", "withdrawn": "", "abstract": "The $\\Gamma$-orbifold Euler characteristic is a topological invariant which generalizes the classical Euler Characteristic to spaces with the action of a matrix group $G$. The group acts on $S$, where $S$ is a $G$-invariant subset of $R^n$, by matrix multiplication. The $\\Gamma$-orbifold Euler characteristic is dependent on $G$, $S$ and the action of $G$ onto $S$. For this project we have focused on the case where the acting group is isomorphic to a torus.\nFor various spaces and $\\Gamma$ (a finite presenting groups), we will present formulas for finding this $\\Gamma$-orbifold Euler Characteristic based on the weight matrix of the acting torus. The spaces we consider in detail include spheres, vector spaces, and symplectic quotients.", "id": "Paper/72625", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72625"}, {"title": " AI-Assisted Computational Investigation of the Pólya–Szegő Conjecture ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "275754105ca41354afd7982684a8218457cc0fe86046228d3b09a7269f6b3aae", "withdrawn": "", "abstract": "The P\\'{o}lya–Szeg\\H{o} conjecture predicts that, among all fixed-area $n$-gons, the regular $n$-gon minimizes the first Dirichlet eigenvalue. More than 75 years later, the conjecture remains open for general $n$. In order to search out unexplored patterns and behaviors that could support or contradict the conjecture, we develop an AI-assisted workflow to run rapid testing and refine our hypotheses. In applying this workflow, we explore the general potential of artificial intelligence in mathematical research. As a result of our testing, we propose a conjecture on polygon behavior that would demonstrate that for all convex polygons, the P\\'{o}lya–Szeg\\H{o} conjecture holds. We describe the extent and accuracy of numerical evidence gathered and present a direction for future theoretical study.", "id": "Paper/72626", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72626"}, {"title": " Skew Zero Forcing Over Affine Geometry Suburbia ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "5900b8df3dd6fa62d32ffd86bc166a0464fb4d4bae7e7ccce1af61eb0c15ed5f", "withdrawn": "", "abstract": "Skew Zero Forcing (SZF), is an interesting algorithmic game played on graphs of edges and vertices which colors vertices depending on some initial coloring of the vertices. Occasionally, this game gives rise to a matroid; a mathematical object that generalizes dependence over some set of elements; in this case, the vertices of the graph. We call such matroids SZF-realizable. Considering the matroids generated from the affine linear independence of vectors over a finite field, we ask the question: which of these affine matroids are SZF- realizable? This presentation shows that most affine matroids are not SZF-realizable, which validates some intuition on how the complexity of a matroid relates to its SZF-realizability. Very little literature has been published on this topic, and this ongoing project seeks to provide new insight into this interaction between graph and matroid theory.", "id": "Paper/72631", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72631"}, {"title": " THE UNION OF TWO HAMILTONIAN PATHS OR CYCLES ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "df36c8b6939de7d9b9118521d61bee780546a971ac583160a4a5b22ad5ecf4e6", "withdrawn": "", "abstract": "Each permutation $\\sigma$ on $[n]$ corresponds naturally to a Hamiltonian path: connect $\\sigma(j)$ to $\\sigma(j+1)$ for each $j\\in[n-1]$. To obtain a Hamiltonian cycle, connect $\\sigma(n)$ back to $\\sigma(1)$. This paper considers graphs which result from taking the union of the Hamiltonian path or cycle for the identity permutation, and for a handful of permutations arising in number theory. We find manifold-like structure in these graphs, and formally prove topological and metric embeddings into particular manifolds.", "id": "Paper/72632", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72632"}, {"title": " Representations of Finite Groups over Matroids over Tracts ", "webprogram_exclude": "0", "session_ids": ["Session/19346"], "source_sha256": "a386fe3ce05799621f631e71d73d72e1d8d639488624809645bbd66540622a3d", "withdrawn": "", "abstract": "Our research focuses on representations of finite\ngroups over classical matroids and matroids over tracts. In particular,\nwe study the rank $r$ subrepresentations\nof the Boolean regular representation of a finite group $G$, \ndenoted $\\mathbb{B}[G]$, generalizing the classification\nof the rank 2 and rank 3 subrepresentations. We examine\nequivalence and reducibility in the more general setting\nof matroids over tracts by adopting a category-theoretic perspective,\nand study how different classes of morphisms for matroids over tracts\naffect reducibility and equivalence.", "id": "Paper/72633", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72633"}, {"title": " Chromatic Gallai-Ramsey Numbers Involving Stars ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "26d2f53417287029a03ca1ac1136cc38bed9b081e98ec7361e208feb0ad22294", "withdrawn": "", "abstract": "In his 1980 dissertation, Michael Jaccobson considered chromatic Ramsey numbers of the form $$r^3_{1,2}(K_3, K_3, K_3, K_{1,i}, K_{1,j}, K_{1,k}),$$ defined to be the least $n\\in \\mathbb{N}$ such that every $3$-coloring of $K_n$ (using red, blue, and green) contains a monochromatic $K_3$, a red/blue $K_{1,i}$, a red/green $K_{1,j}$, or a blue/green $K_{1,k}$.  In this talk, we describe the evaluation of an analogue of these chromatic Ramsey numbers for Gallai colorings (i.e., those that avoid rainbow triangles). The main tool used in our proofs is a structure theorem for Gallai colorings, which is a reinterpretation of a 1967 result of Gallai.", "id": "Paper/72637", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72637"}, {"title": " Trimming Return Words of Irrational Rotations ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "7b110e768f8818e6802568bfb9d7263efe39147ea2900d1745183f85cb7c85a0", "withdrawn": "", "abstract": "Let $T$ be an irrational rotation of the circle. Partition the circle into finitely many intervals, and designate one of them, $G$, to be the return interval. For each point on the circle, record the intervals the point lands in as it travels on its $T$-orbit. This forms an infinite word, and the letters in between visits of $G$ are called return words, all belonging to a finite set $W_{G}$. We study an operation called \\emph{trimming} on $W_{G}$ which enlarges the set by adding new words formed by deleting from one word a suffix or prefix that also lies in the $W_{G}$, along with an adjacent letter. Repeating this until nothing new is added, we get the trim closure. A recent result shows that when the empty word, $\\varepsilon$, lies in the trim closure, this gives rise to a unique continuation principle for the associated quasiperiodic Shr\\\"odinger operator. Thus, we study the conditions under which this occurs. We find a new method to show that this holds when the endpoints of the partition lie on pairwise distinct $T$-orbits. Using this method, we also show that this holds when we only require the endpoints other than that of $G$ to lie on pairwise distinct $T$-orbits. We then give examples where this fails when we drop these extra conditions.", "id": "Paper/72639", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72639"}, {"title": " Upsilon invariants of almost L-space knots ", "webprogram_exclude": "0", "session_ids": ["Session/18238"], "source_sha256": "061dfd642249bb3ab913dede4681bfe154282898f2853e110be33a6e06f2a812", "withdrawn": "", "abstract": "A rational homology 3-sphere is an L-space if its Heegaard Floer homology has the smallest rank allowed by its first homology, making it “simple” in some sense. The L-space Conjecture, proposed by Boyer, Gordon, and Watson, suggests a deep connection between the topological, algebraic, and geometric properties of irreducible rational homology spheres.  Knots with L-space surgeries, known as L-space knots, are a natural place to explore these relationships, since their knot Floer complexes are determined by their Alexander polynomial, making computation tractable.  We focus on almost L-space knots, which miss being L-space knots by the smallest possible margin but which share many properties with L-space knots. Binns has classified the knot Floer complexes for almost L-space knots.  We use the Upsilon invariant, a concordance invariant from knot Floer homology, to better understand these complexes and develop obstructions for distinguishing them from genuine L-space knots.", "id": "Paper/72640", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72640"}, {"title": " A generalization of a tile model of circuit topology for self-entangled biopolymers ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "ea6ad4ae76f539c1fcce6962403ef7b59b7bb938508a5071ee455c9c7ed8ba27", "withdrawn": "", "abstract": "Protein function is determined by its 3D structure, which includes entanglement created by bonds and other molecular forces. There is thus a need for analysis of entanglement of proteins, which was initiated in \"A tile model of circuit topology for self-entangled biopolymers\" (Flapan, E., Mashaghi, A. and Wong, H, 2023). Their work is based on circuit topology which seeks to separate out parts of the protein into smaller units that are assumed to be rigid. They develop a theory of soft contacts using a tile model. Each tile captures some entanglement held in place by molecular forces, and the model shows how they can be pieced together to form larger entangled complexes. We now aim to generalize that tile model, using the same rigid tiles. The most complicated operation to connect tiles in \"A tile model of circuit topology for self-entangled biopolymers\" is their cross operation. We generalize by allowing for the cross operation between complexes, as opposed to just tiles.", "id": "Paper/72641", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72641"}, {"title": " Polycyclic Codes Associated with Quadrinomials: Duality, Open Problems, and New Linear Codes ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "1f67f7b04490dc052401f0b68b24bd67b9fe862fe27547dace8b7e3e8e1aa40e", "withdrawn": "", "abstract": "As a generalization of cyclic and constacyclic codes, polycyclic codes offer a promising framework for constructing codes with good properties. Since the dual of a polycyclic code is not necessarily polycyclic, characterizing their dual presents theoretical challenges. In this research, we investigate polycyclic codes associated with trinomials and quadrinomials. We establish that all dual-containing polycyclic codes are, in fact, constacyclic. Furthermore, we prove several duality results for polycyclic codes associated with trinomials and quadrinomials, and present many examples of polycyclic codes with optimum or best known parameters. Finally, we resolve an open conjecture from a recent manuscript regarding binary LCD polycyclic codes associated with trinomials.", "id": "Paper/72642", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72642"}, {"title": " Discrepancy theory, Tverberg’s theorem, and regression depth ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "1b54d67a4531830d1b9fe7f1651834c8f6c1104f076e3a6e7ace407ab64e497c", "withdrawn": "", "abstract": "We prove new bounds for Tverberg's theorem with tolerance.  We show that $N = rt+\\Theta_{d,r}(t^{1/2-1/(2d)})$, where $N$ is the smallest number such that any set of $N$ points in $\\mathbb{R}^d$ has a partition into $r$ parts such that the convex hulls of the parts intersect even if we remove any $t$ of the points.\n\nWe extend Tverberg's theorem with tolerance to families of hyperplanes in $\\mathbb{R}^d$, and show that for any set of $rt + O_{d,r}(t^{1/2-1/(2d)}\\sqrt{\\log (t+1)})$ hyperplanes in $\\mathbb{R}^d$ there exists a partition of them into $r$ parts such that the regression hulls of the parts intersect even if any $t$ hyperplanes are removed.\n\nOur bounds follow from establishing a connection between Tverberg-type results and discrepancy theory.", "id": "Paper/72646", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72646"}, {"title": " Estimating Blood Alcohol Concentration Using the Widmark Model and Differential Equations ", "webprogram_exclude": "0", "session_ids": ["Session/18241"], "source_sha256": "a4faa77e853a3837f9120bec0c528d74256630eacb838f893568c997f199dd8f", "withdrawn": "", "abstract": "This study examines alcohol-consumption patterns among college students and uses mathematical modeling to estimate blood alcohol concentration (BAC). Anonymous survey data on drinks consumed, serving sizes, alcohol content, drinking duration, and food intake are used to estimate alcohol intake and develop individualized BAC curves. The Widmark equation and Widmark constant are used to account for differences in body characteristics, while differential-equation models describe alcohol absorption and elimination over time. The resulting models are used to examine peak BAC levels and alcohol dissipation and to compare how drinking patterns and beverage types affect estimated BAC.", "id": "Paper/72647", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72647"}, {"title": " Constructing Smooth Space-Filling Hypersurfaces ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "f69d3b046d2c288d950e2451cf99822f644694d8754f5491a13205ea93b7dc59", "withdrawn": "", "abstract": "Poonen proved the existence of smooth space-filling hypersurfaces over finite fields. We study explicit constructions, beginning with the smallest possible degree, \\(q+1\\). In \\(\\mathbb{P}^n\\) over \\(\\mathbb{F}_q\\), we show that smooth space-filling hypersurfaces of degree \\(q+1\\) exist when \\(n\\) is odd, whereas none exist when \\(n>1\\) is even. At degree \\(q+2\\), we describe a matrix-based construction of space-filling hypersurfaces and derive necessary conditions for smoothness. Over characteristic two, we strengthen the result and construct geometrically smooth hypersurfaces. This is joint work with Victoria Bourgeois-Conti, Han-Bom Moon, and Amelia Warren.", "id": "Paper/72650", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72650"}, {"title": " Sensitivity Analysis of Acceptance Variance in Recombination and Marked Edge Walk ", "webprogram_exclude": "0", "session_ids": ["Session/18160"], "source_sha256": "21b46acd9e81e74ea43af8a406899e304043a8b24f44788b8f2654d319e39b79", "withdrawn": "", "abstract": "Ensemble analysis is widely used to evaluate legislative districting plans by generating large collections of maps that approximate the range of outcomes produced under specified constraints. These ensembles provide a baseline for assessing proposed or enacted plans and identifying potential partisan imbalances. However, the reliability of ensemble analysis depends on how effectively sampling algorithms explore the space of valid districting plans, particularly when additional constraints are imposed. In this research project, we investigate the sensitivity and robustness of two commonly used Markov Chain Monte Carlo redistricting algorithms, Recombination (ReCom) and Marked Edge Walk (MEW), under varying acceptance criteria. We systematically vary the strength of three constraints—compactness, competitiveness, and county preservation—and examine their effects on ensemble behavior and resulting distributions. For each algorithm on our six sample states, we generate ensembles across combinations of acceptance probabilities and county surcharge values, resulting in 4,320 ensembles overall. We evaluate the resulting ensembles using measures including compactness, county splits, competitiveness, partisan bias, mean-median difference, efficiency gap, and number of minority opportunity districts. Our preliminary results indicate that increasing constraint strictness can substantially affect the behavior of both sampling algorithms. In particular, highly selective acceptance functions can slow mixing and cause chains to become temporarily trapped in limited regions of the districting-plan space, requiring substantially more steps to reach convergence. We also observe relationships between county preservation and compactness, with stronger county-preservation requirements generally producing more compact districts and fewer county splits. By examining these effects across states and sampling algorithms, this study aims to identify conditions under which ReCom and MEW become sensitive to restrictive acceptance criteria and to provide a clearer understanding of the robustness and limitations of the samplers used for ensemble-based redistricting analysis.", "id": "Paper/72651", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72651"}, {"title": " Strong Persistence for Monomial Ideals: Combinatorial Bounds and Algorithms ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "72c123d945646d4e03d71a5c51746a2582632b7d034befdb5a0733018802b7f8", "withdrawn": "", "abstract": "An ideal $I$ has the strong persistence property if\n\\[\n(I^{q+1}:I)=I^q\n\\]\nfor every $q\\ge 1$. The strong persistence index is the smallest natural number $N$ such that $(I^{q+1}:I)=I^q$ for all $q>N$. We study these equalities for monomial ideals in a polynomial ring over a field using combinatorial properties of their exponent sets. We compute the strong persistence index for a family of ideals, which we call boundary ideals. For every positive integer $N$, we give a concrete construction of a boundary ideal with strong persistence index $N$. For equigenerated monomial ideals in two variables, we characterize the levels $q$ at which $(I^{q+1}:I)\\neq I^q$ in terms of gaps in sumsets and use a theorem of Lev to obtain a finite decision algorithm. In any number of variables, we prove that, for an equigenerated monomial ideal primary to the homogeneous maximal ideal and generated in degree $d\\ge 2$, failure can occur only at levels\n\\[\nq\\le n(d^{\\,n-1}-3)+1,\n\\]\nwhere $n$ is the number of variables. The proof uses exponent vectors modulo $d$ and the pigeonhole principle. Together with a finite bound on witness exponents, these results give an algorithm that determines precisely the positive integers $q$ for which $(I^{q+1}:I)\\neq I^q$, produces explicit monomial witnesses to each failure, and hence determines the strong persistence index.", "id": "Paper/72652", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72652"}, {"title": " Isoperiodic Foliations of the Strata <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"18.053ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 7772.7 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\Omega \\mathcal {M}_1(1,t,-1-t)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-3A9\" d=\"M55 454Q55 503 75 546T127 617T197 665T272 695T337 704H352Q396 704 404 703Q527 687 596 615T666 454Q666 392 635 330T559 200T499 83V80H543Q589 81 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xlink:href=\"#E1-MJMATHI-74\" x=\"7021\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"7383\" y=\"0\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "75606de5be79d8abeae1654ebfe284510dbc26c219d4ba33f7b98aca02c746c1", "withdrawn": "", "abstract": "This work aims to describe the geometry and topology of leaves of the isoperiodic foliations of the strata $\\Omega\\mathcal{M}_1(1,t,-1-t)$. Along the way, we give a topological classification of cores possible in $\\Omega\\mathcal{M}_1(a,b,-a-b)$, discuss how distribution of cone angle affects the geometry in higher strata, and characterize the Veech groups of leaves.", "id": "Paper/72654", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72654"}, {"title": " Real-Analyticity of Analytic Capacity for Circular Perturbations ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "84cb33e6eaddbe43ae9d09527c04ff9fe4c5e08a765e868a7061de0835a4879f", "withdrawn": "", "abstract": "The analytic capacity of a set $E$ is defined as the supremum of $|f’(\\infty)|$ taken over admissible functions of $E$ in the complex plane. A function is admissible for a set $E$ if it is both bounded $(|f(z)| \\le 1)$ and analytic over the complex plane minus $E$, with the additional criterion that $f$ vanishes at infinity. Despite its abstract formalization, analytic capacity has some intuitive properties. It is rotationally invariant, scales linearly, and has closed-form solutions for geometrical sets like ellipses and polygons. My research project on analytic capacity at the AMPS REU 2026 was an open-ended exploration of results related to analytic capacity made possible through NSF funding. In particular, we proved that the analytic capacity of a family of circular perturbations with boundary $e^{it} + ae^{ikt}$, $t\\in [0,2\\pi)$, is real-analytic with respect to $a$ at $a=0$, meaning the capacity can be written as an infinite summation of powers of $a$ in a neighborhood around $a=0$. We were able to calculate the first 100 taylor coefficients for all integer values of $k$ and show that these are integers. It remains unknown, however, whether every coefficient is an integer. \nMy research experience greatly informed my perspective on a variety of topics. I experienced firsthand the benefits of collaboration, as well as what impedes working closely with other researchers. I used LLMs in my research, which are a great tool for rapidly searching through the solution space to any particular problem, but which threaten the process of inquiry when used irresponsibly. I’ll talk about how I approached LLM use, what the research was qualitatively like, and how the project goal developed as our research progressed.", "id": "Paper/72655", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72655"}, {"title": " Spectral Band Degeneracies of Photonic Crystals on a Square Lattice ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "89f917a52db9f07ec45802e8886470933b6158a6cc3c9c5839d58f809ae7465a", "withdrawn": "", "abstract": "This work is concerned with the existence of quadratic touchings at Dirac points over a square lattice of impenetrable obstacles attaining $90^\\circ$-rotation and horizontal reflection symmetry relations in a homogeneous medium. Quadratic touchings of dispersion surfaces on structures with these symmetry relations generically appear but are not guaranteed; oftentimes the existence of which is verified using numerical methods. Our model is an example for which quadratic touchings are derived analytically.\n For our model, we consider the Dirichlet eigenvalue problem and prove the existence of Dirac points at crossings of the lower band surfaces.\n%as well as higher bands\nWe demonstrate that the eigenvalues are in the neighborhood of the singular frequencies associated with the Green’s function for the square lattice. Formulating the eigenvalue problem as an infinite linear system, we analyze the characteristic values of the associated boundary integral operators in order to prove the existence of interface modes using perturbation methods. Furthermore, we perform quantitative analysis for the eigenvalues and the slopes of the two dispersion surfaces near each Dirac point using a combination of the layer potential technique and asymptotic analysis.", "id": "Paper/72657", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72657"}, {"title": " Letter Counting in Quivers ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "fc1c5b16ce7cac9acba9bfb8b311fbcaec68c4ba9cc5f2566c20e85f36720867", "withdrawn": "", "abstract": "Given a word (or a sequence of generators) in a group, a letter braiding function counts the number of occurrences of a given subsequence of generators within the word. These functions offer an interesting way to distinguish between $n$-fold commutators; specifically, order $n$ letter braiding functions vanish on the $n+1$st term of the lower central series. Our work primarily focuses on extending the notion of letter braiding to quivers, where edge labels are analogous to generators and paths analogous to words. We find that for certain types of quivers, such as trees, cycles, and Cayley graphs, certain letter braiding functions can easily determine whether a given path is a loop. However, outside of these special cases, letter braiding functions on quivers behave poorly due to the lack of analogues for group properties, such as abelianness and the lower central series.", "id": "Paper/72659", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72659"}, {"title": " Changes in Mortality in Altensteig, Germany 1660 to 1910 ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "e8f8c636a4d58dc1561535331ee0e3173211fc301373a40347e5fed0f6f09587", "withdrawn": "", "abstract": "Mortality rates provide information about how likely an individual is to die once they reach a certain age. One can also consider data on the birth and death of individuals as information for how much time an average person has left to live given their age. In this work we use information in the local family register for the city of Altensteig, Germany, from which we gather the birth and death dates for each registered individual. We first create generational mortality tables to gain a numerical understanding of mortality. We then use multiple modeling methods including the Weibull distribution and the Heligman-Pollard model to gain a graphical representation of our data that we can then use to compare mortality rates between generations.", "id": "Paper/72661", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72661"}, {"title": " Tight Probabilistic Aspects of Friends-and-strangers Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "f0d9b4d9a1a4e40b53208f3c75502d3e8c4b9bff0d0286738b8a0a13a618c9a1", "withdrawn": "", "abstract": "Friends-and-strangers graphs, introduced by Defant and Kravitz, model arrangements of people on positions. Let $X$ and $Y$ be two graphs on $n$ vertices. The vertices of $X$ represent positions with edges denoting adjacencies while the vertices of $Y$ represent people with edges denoting friendships. Their \\emph{friends-and-strangers graph} is denoted by $\\mathsf{FS}(X,Y)$. Its vertices are all one-to-one placements of people on positions, and two placements are adjacent if one can swap two friends on adjacent positions to get from one placement to the other. \n\nA very fundamental question is whether or not a friends-and-strangers graph is connected. A natural probabilistic analog is ``If $X$ and $Y$ are independently sampled Erd\\H{o}s--R\\'{e}nyi graphs with $n$ vertices and edge probability $p,$ what is the threshold probability for $\\mathsf{FS}(X,Y)$ to be connected with high probability?'' Alon, Defant, and Kravitz (2023) showed that $p = n^{-1/2+o(1)}$ is the threshold probability and conjectured that $p = \\Theta(n^{-1/2}).$ Milojevi\\'{c} (2024) disproved this by showing $p = \\Omega(n^{-1/2}\\sqrt{\\log n})$ is necessary for connectivity with high probability. In this work, we prove a matching upper bound, thus establishing that the threshold is $p = \\Theta(n^{-1/2}\\sqrt{\\log n}).$", "id": "Paper/72663", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72663"}, {"title": " REACTION-DIFFUSION PDE MODELING OF LIVESTOCK-MEDIATED BEHAVIORAL CASCADES IN PREDATOR-PREY DYNAMICS ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "83c50fa1a477e0233a0c8764885cad93327d885eb429e2eee397180e6fe68e52", "withdrawn": "", "abstract": "Traditionally, multi-trophic interactions in grassland ecosystems are quantified by slow,\nvegetation-mediated pathways. However, recent empirical work accentuates rapid, behavior-\nmediated cascades. Hence, this study formulates a spatial reaction-diffusion partial differential equation (PDE) model representing the cattle–grasshopper–swallow behavioral cascade\nreported by Zhu et al. (2024), in which livestock grazing disturbances trigger grasshopper\nescape movements that consequently increase their vulnerability to avian predators. To quantify and implement this interaction, a one-dimensional spatial predator–prey PDE system will\nbe solved in MATLAB, directly contrasting landscape dynamics under grazed (cattle present)\nand ungrazed (cattle absent) conditions. A novel feature of the model expands the avian spatial domain beyond localized study plots and incorporates livestock disturbance. Altogether,\nthis model aims to reproduce empirical field observations, investigate mechanisms behind the\nsixfold change in predator foraging visits, and evaluate resulting grazing-induced reduction in\ngrasshopper density presented by Zhu et al.", "id": "Paper/72664", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72664"}, {"title": " On Rigidity and Stability of Surfaces with Asymptotically Conical Ends ", "webprogram_exclude": "0", "session_ids": ["Session/18159"], "source_sha256": "dafd4abcb79a5a507ec0826f2b9cb11b6decec5f5807e9411347e4f390bf8204", "withdrawn": "", "abstract": "Let $(M,g)$ be a complete Riemannian manifold with nonnegative scalar curvature. The rigidity statement associated to the positive mass theorem states that if the ADM mass of an end of $M$ is zero, then $(M,g)$ must be isometric to Euclidean space. We present an analogous rigidity statement for complete Riemannian surfaces with nonnegative Gaussian curvature and an asymptotically conical end, where the ADM mass is replaced by the asymptotic cone angle. This leads naturally to the study of the stability of such surfaces in the pointed Gromov-Hausdorff sense.", "id": "Paper/72667", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72667"}, {"title": " Efficient Catalytic Algorithms for All-Pairs Shortest Paths ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "fb19d2c5c82f9bc16174c128d21709bbcef5ba4b9e805d8f4831f30f8ab34be3", "withdrawn": "", "abstract": "Catalytic space is a model of computation in which, alongside a small amount of ordinary empty space, an algorithm is able to use a large auxiliary tape, called the catalytic tape, filled with arbitrary data -- provided that it returns the filled space to its original contents by the time the algorithm halts. Recently, Cook and Pyne initiated the study of catalytic space from an algorithmic perspective, designing fast catalytic logspace algorithms for several fundamental graph problems. Continuing this research direction, in this talk we present fast catalytic logspace algorithms for the All-Pairs Shortest Paths problem, which asks to compute distances between every pair of vertices in a weighted, directed graph. Our approach yields a deterministic catalytic logspace algorithm running in time $\\widetilde{O}\\left(n^{5.895}\\right)$, and a randomized algorithm that runs in time $\\widetilde{O}\\left(n^{5.120}\\right)$. These improve upon the previously best-known bound of $\\widetilde{O}\\left(n^{5.967}\\right)$ (for either a deterministic or randomized algorithm) [Sheffield, 2025].", "id": "Paper/72671", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72671"}, {"title": " Formalizing Linear Algebra in PVS ", "webprogram_exclude": "0", "session_ids": ["Session/19344"], "source_sha256": "3570e52f171310ee85e2037d3868537cfebadac834f201ee6d4e86105148e4a5", "withdrawn": "", "abstract": "The Kaczmarz algorithm is an iterative method for solving systems of linear equations by repeatedly projecting an estimate onto hyperplanes defined by the rows of the system. In this project, we studied the convergence of the Kaczmarz algorithm and developed a machine-checked formal proof of its convergence using the Prototype Verification System (PVS), a formal verification system with a specification language and theorem prover.\nWe began by studying Kaczmarz's original 1937 proof using an English translation and reformulated the proof in terms of modern linear algebra. In particular, we expressed the proof in terms of orthogonal projections, dot products, norms, and convergence. We then encoded the reformulated proof into PVS, developing a new linear algebra library and specifying the properties needed to establish convergence. The project resulted in a complete formal proof of the Kaczmarz algorithm's convergence in PVS.\nThis work demonstrates how a classical mathematical proof can be reformulated using linear algebra and translated into a machine-checked formal proof while preserving the underlying mathematical reasoning. It also provides a foundation for verifying additional algorithms in numerical linear algebra.", "id": "Paper/72672", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72672"}, {"title": " Combinatorial Approaches to Transfer Systems ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "e51dcca668261da5068db6f5e0ac638f2c764df00a49ad51525a6b6bfac95d4e", "withdrawn": "", "abstract": "Homotopical combinatorics is an emerging field that studies transfer systems, a type of partial ordering that can encode the combinatorial data of more complex objects in equivariant homotopy theory and homological algebra. As a new field, there are many open problems that are of interest, beyond just those of enumeration. In this presentation, we focus on transfer systems associated to a finite group, introducing transfer systems as as they relate to N infinity operads. We explore some basic properties of transfer systems, such as saturation, cosaturation, and compatible pairs of transfer systems. As we explore these properties, we construct functors between transfer systems to better describe the structure of these objects.", "id": "Paper/72677", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72677"}, {"title": " Simulating Individual Movement in Agent-based Models using Cellular Automata ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "d41ed3af1ae5fc9001ab77551e8b727376d558401368d25ce8be3d3a08f44f14", "withdrawn": "", "abstract": "Agent-based models are an increasingly popular type of computational model which has been applied in several fields such as biology, medicine, ecology, and sociology to study how local dynamics affect population-level outcomes. Despite their prevalence, few methods of analysis exist for agent-based models because of their inherent complexity and the lack of an agreed-upon mathematical formalization. In our work, we investigate how a more formal but more restrictive model of computation, a cellular automaton, can simulate the individual motion found in agent-based models. We first construct a one-dimensional cellular automaton in which directional states represent the movement and collisions of individual agents or \"particles\" on a grid. We then extend these results to a two-dimensional grid which allows diagonal motion. These constructions provide a foundation for investigating the capabilities that cellular automata have to reproduce the more complex spatial behaviors found in agent-based models.", "id": "Paper/72680", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72680"}, {"title": " Tiling Enclosed Regions in Girih Circuits ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "09e1480609730ca9d0bb65b5522085f9db5c55210963e5eb702c2a92e2831f7e", "withdrawn": "", "abstract": "Girih tiles are a set of five equilateral polygons, only two of which are regular, used to create geometric patterns in Islamic art and architecture. Motivated by a conjecture of Robert E. Dewar, we study a related model in which decagons are joined by bowtie tiles to form closed circuits. We ask whether every enclosed region can be tiled using only bowties and elongated hexagons.\nUsing exact arithmetic in the ring generated by the golden ratio, we determine the required number of each tile. An exhaustive computational search verifies tilings for all 1,037 valid circuits containing at most eleven decagons, together with additional cases containing twelve decagons. These results provide computational evidence for a broader conjecture about the tileability of Girih circuits.", "id": "Paper/72681", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72681"}, {"title": " Abstract Algebra Underlying One- and Two-Dimensional Patterns (working title) ", "webprogram_exclude": "0", "session_ids": ["Session/18238"], "source_sha256": "216578d23c42ae20e80a4c4d79aacab4140ec74fdeab898e2f4c73f611305f0c", "withdrawn": "", "abstract": "This expository talk, based on a senior comprehensive project, will outline the classification of one- and two-dimensional patterns by symmetries, drawing connections to group theory. The proof that all rigid motions of the plane are isomorphic to one of the four basic rigid motions and the proof that there are only seven classes of one-dimensional patterns will be outlined. Particular attention will be paid to those seven one-dimensional patterns and their respective isomorphisms (including to $\\mathbb{Z}$ and the infinite dihedral group). The seventeen classes of two-dimensional patterns will be briefly explained, with analogy drawn between them and the one-dimensional patterns. The talk will also feature discussion of the implications of the sophisticated mathematical underpinnings of patterns for our conception of the history of higher mathematics, as well as for our understanding of what defines a mathematician. This will be accomplished by briefly examining the history of human civilizations producing and theorizing about patterns.", "id": "Paper/72682", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72682"}, {"title": " Penalized Quantile Regression for Variable Selection Across the Birthweight Distribution ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "b441d59f8715cf4a0b00fff12c8223dee5a9086fe2a0dfff71c603879caede3e", "withdrawn": "", "abstract": "Birthweight is a key indicator of neonatal health, with birthweights below 2500 grams classified as ``low\" and birthweights above 4000 grams classified as ``high\", where these extremes carry elevated risks to the baby and the mother.\nSince the factors associated with the birthweight may differ across its conditional distribution, ordinary least squares regression fails to capture this heterogeneity. Quantile regression (QR) addresses this limitation by modeling covariate effects at different points of the conditional birthweight distribution, providing a more comprehensive view of the relationship between variables. \\\\\nLeast Absolute Shrinkage and Selection Operator (LASSO) performs variable selection by shrinking irrelevant predictors to exactly zero. \nWe apply LASSO-penalized quantile regression to identify predictors of birthweight across the conditional distribution. Using a stratified sample of singleton live births from the 2024 United States Natality Data, we examine quantiles $\\tau \\in[0.05,0.95]$. We compare four data-driven tuning parameter selection criteria: cross-validation (CV), Bayesian Information Criterion (BIC), modified BIC (mBIC), and extended BIC (eBIC). Furthermore, we evaluate how the choice of criterion affects variable selection across the birthweight distribution. \\\\\nOur results demonstrate a substantial heterogeneity in the predictors selected at different quantiles. Prenatal care and third-trimester smoking are selected more consistently at lower quantiles, whereas maternal BMI and pre-gestational diabetes are selected more prominently at higher quantiles. A comparison of the four penalization criteria illustrate broad agreement on the strongest predictors, with disagreement concentrated among weaker associations. Together, these results highlight substantial heterogeneity in the factors associated with birthweight and demonstrate the value of examining the full conditional distribution rather than focusing solely on mean effects.", "id": "Paper/72684", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72684"}, {"title": " Beyond the Finish Line: Modeling Health in Senior Athletes ", "webprogram_exclude": "0", "session_ids": ["Session/19338"], "source_sha256": "5eb47a1effd9786b93dc94b0a449a1fb00de13b42704786b14644994f20aded0", "withdrawn": "", "abstract": "Aging is commonly associated with increased risks of chronic disease and functional decline, while regular physical activity is generally linked to improved health outcomes. This study investigates the health characteristics of older adult athletes participating in the Huntsman World Senior Games in St. George, Utah, and compares them with non-athletic older adults using data from NHANES, NHATS, and HRS sources. Participants are primarily between 55 and 85 years of age and are categorized into three age groups: 55–65, 66–75, and 76–85 years. The analysis considers multiple measures of physical and general health, including blood pressure, body mass index (BMI), lipid and glucose measures, grip strength, estimated VO₂ max, cognitive function assessed through the SAGE assessment, vision, hearing, oral health, spirometry, and other available health indicators. Descriptive statistics and group comparisons are used to examine differences between athletes and non-athletes and across age groups. Multivariable regression models are also used to investigate associations between athletic participation and selected health outcomes while accounting for relevant demographic and health-related factors. By combining measures of physical performance with broader indicators of health, this study provides a more comprehensive statistical examination of healthy aging among older athletes and explores whether strong physical performance is consistently associated with favorable health profiles across multiple dimensions.", "id": "Paper/72685", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72685"}, {"title": " Chaos in Piecewise Matrix Transformations ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "a90d62a779611599a80611462a28f551170ef2dfcff414fe6546c5f6979cd8ba", "withdrawn": "", "abstract": "The dynamics of one-dimensional iterated maps of the real line have been extensively studied, exhibiting periodic or chaotic behavior. We extend this study to two-dimensional iterated piecewise linear maps, investigating the possibility of chaos. We construct a particular piecewise linear function of two matrices, adjusting parameters of rotation angles and eigenvalues to produce desired periodic orbits and behaviors seen in bifurcation diagrams. Then, we analyze numerical and graphical evidence for the stability of these orbits and the presence of chaotic behavior in our two-dimensional map.", "id": "Paper/72688", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72688"}, {"title": " Multiscale Transcriptomic Architecture of the ALS Motor Cortex ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "7483688fc9c8a75bf74a88f49a8221780dbd66a38e24f4fb594aba40d03840ab", "withdrawn": "", "abstract": "Amyotrophic lateral sclerosis (ALS) exhibits clinical and molecular heterogeneity, but how this heterogeneity is organized within disease-relevant regions remains incompletely understood. Because pooled cross-region analyses may confound regional variation with subtype structure, we focused on the motor cortex, a key site of ALS pathology, to resolve its internal transcriptomic organization. Using approximately 600 postmortem motor cortex transcriptomes from the Target ALS resource, we applied gene set variation analysis to generate sample-level pathway profiles and performed consensus clustering in pathway space. We identified seven ALS motor cortex subtypes characterized by inflammatory, damage-response, metabolic, glial, and neuronal/synaptic programs. Rather than forming isolated molecular classes, these subtypes occupied a structured pathway landscape with discrete subtype-centered peaks and continuous biological gradients. Principal component analysis and representative pathway overlays defined a major axis from an upper inflammatory/damage region to a lower neuronal/metabolic/remodeling region, with a neuronal/synaptic connector within the lower landscape. Co-expression network analysis supported this multiscale organization, revealing family-level network backbones, subtype-specific modular refinements, and bridge-like rewiring. Metadata-informed analyses showed that this molecular architecture was not primarily organized by disease duration. Instead, the landscape was associated with clinical and genetic-background variables, including ALS/FTD family history and mutation-related signals. Family-history-positive and C9orf72 repeat expansion-positive samples were more represented in the lower neuronal/metabolic/remodeling region, whereas family-history-negative samples and C9orf72-negative cases were more represented in the upper inflammatory/damage region. These findings support a model in which ALS motor cortex heterogeneity is organized as a multiscale transcriptomic architecture more closely associated with genetic-background variables than with disease duration. This framework provides a basis for subtype-aware biological comparison, patient-stratification, biomarker, or therapeutic target-prioritization studies.", "id": "Paper/72689", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72689"}, {"title": " Classification of Heart Failure Phenotypes ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "17dc8ab28747cb93e6a3b59159b6b900e0c1cff7c596e70900bad3ba8a1a513e", "withdrawn": "", "abstract": "Despite considerable research and improvements in treatment, the heart failure (HF) epidemic remains a consistent public health challenge. HF with preserved ejection fraction (HFpEF), which accounts for over half of HF cases, remains difficult to diagnose due to the heterogeneity of the patient pool. Diagnostic guidelines define HFpEF patients as having a normal-appearing ejection fraction (EF) of over 50\\%, while still exhibiting the characteristic HF symptoms associated with HF with reduced EF (HFrEF). We utilize de-identified clinical data collected from patients who had right-heart catheterization (RHC), transthoracic echocardiogram (TTE) and MRI procedures within a three-month period. Using a mechanistic differential equation model of the cardiovascular system, we estimate unique parameter sets, which describe the cardiovascular state of each patient and can be used by clinicians to better phenotype HFpEF populations. Our parameter estimation is guided by local and global sensitivity analysis and subset selection, which determines which parameters are sensitive to the available data and can be uniquely identified. On these patient-specific parameter sets, we conduct unsupervised machine learning to cluster HF patients in an effort to reveal underlying mechanistic phenotypes. These methods hold promise to enhance diagnostic accuracy of HF patients and uncover differences between HFpEF phenotypes.", "id": "Paper/72690", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72690"}, {"title": " Fairer Farm Rankings: A Bayesian Approach to Benchmarking Broiler Performance ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "0da881ebdddf2367765c4dc414754d4ec2ab18441cd5b495f317385f76ba92f9", "withdrawn": "", "abstract": "Benchmarking broiler farm performance is difficult when some farms have many observations and others have very few. Simple average-based rankings fail to communicate uncertainty and unfairly penalize small farms with limited data. We develop a Bayesian Hierarchical Model (BHM) that produces fairer rankings by borrowing strength across farms through partial pooling. Using 2,429 flock records from 1,285 farms, we find that only 17.6% of performance variation reflects persistent farm quality, with the remaining 82.4% being transient flock-to-flock noise. Standard errors for single-flock farms shrink by 9.1% with just a second observation. We provide the Probability of Target Attainment (PTA)—a risk-aware metric that translates statistical uncertainty into actionable thresholds, identifying 1,096 Confident Performers, 188 Investigate farms, and 1 Underperformer. We further introduce age stratified PTA (aPTA), which reveals that 322 farms (29.4% of the Confident tier) are Structural Victims whose favorable FCR reflects harvesting young rather than genuine efficiency.", "id": "Paper/72692", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72692"}, {"title": " A Jump-Modified Wasserstein Gradient Flow for Maximum Mean Discrepancy with Energy Kernels ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "77d9765372c732089bf4f6070a9213aa3153a12e0418f37cce4d642e3a3b5671", "withdrawn": "", "abstract": "We introduce a jump-transport evolution for the maximum mean discrepancy (MMD) associated with the energy kernels \\(K(x)=-|x|^q\\), where \\(0<q<2\\) and \\(d+q-2\\ge0\\). The evolution combines Wasserstein gradient flow with nonlocal jumps toward lower energy. Under suitable integrability and moment assumptions on the initial data and target, we prove global well-posedness in the same class.    The jump dissipation rules out spurious long-time limits: any Borel probability measure which is a zero of the dissipation functional must equal the target measure. From a second-moment identity derived from the transport term, we deduce convergence in MMD without assuming uniform-in-time $L^p$ or moment bounds beyond those implied by the initial data. For the energy kernel case \\(q=1\\), we obtain an exponential energy-decay estimate in a far-field regime by establishing a far-field Polyak--\\L{}ojasiewicz (PL) inequality, valid while prescribed separation and concentration conditions persist. Finally, we construct an $N$-particle, piecewise deterministic Markov process for which we establish quantitative propagation of chaos/mean-field convergence to our modified gradient flow and long-time convergence to the target measure.", "id": "Paper/72697", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72697"}, {"title": " Delete and Retain: Efficient Unlearning for Document Classification ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "e462d06221f19a8fc42adc6dbd86ac3d8c9016186552719dd22283bc554de08e", "withdrawn": "", "abstract": "Machine unlearning seeks to remove the influence of specified training data without full retraining. While prior work has largely focused on large language models, class-level unlearning for document classification remains less explored. We study this setting and introduce Hessian Reassignment, a simple two-step method that combines a single Hessian-based update with deterministic next-top-1 reassignment of deleted-class examples. Unlike random relabeling baselines, our approach preserves the model's learned structure over retained classes while efficiently removing deleted-class influence. Across standard text benchmarks, Hessian Reassignment closely matches complete retraining on retained-class accuracy, substantially improves privacy against membership inference attacks, and achieves significantly lower runtime. These results demonstrate that structure-aware second-order updates provide an effective and practical solution for class-level unlearning in document classification.", "id": "Paper/72698", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72698"}, {"title": " Modeling the Effects of Post Infection Mortality on Malaria Dynamics ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "738eb715520e6d4b50e2e667f8d4e273609fc0fe7b5cbf03fa16f2f433ec0d04", "withdrawn": "", "abstract": "In 2025, the World Health Organization reported 282 million cases of malaria with approximately 610,000 being fatal. Of those fatalities, about 95 percent were caused by the Plasmodium falciparum strand. P. falciparum is unique such that it can cause mortality after recovery due to long-term effects of cerebral malaria and severe anemia. To study the impact of post infection mortality (PIM), we formulated a modified susceptible, exposed, infected, and removed (SEIR) disease model for P. falciparum and investigated the change in dynamics when incorporating the PIM factor. Analytic and numerical studies demonstrate the occurrence of oscillation at parameter values induced by the joint impact of reinfection and mortality of recovered individuals. This can provide insight into public health by showing how P. falciparum disease dynamics may differ from what we previously believed and show a possible need for more long-term monitoring of recovered patients.", "id": "Paper/72700", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72700"}, {"title": " Quantifying Gerrymandering: Comparative Metric Analysis of Redrawn Districts in California, Florida, Utah, and Texas ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "9639cdb797314db19176f0d7d59be701ce259ba8fd80fe3169ee8dea65991d55", "withdrawn": "", "abstract": "This research examines how recent congressional redistricting affected quantitative measures of district compactness in California, Florida, Utah, and Texas. Using 2020 and 2024 congressional district shapefiles obtained from the U.S. Census Bureau’s TIGER/Line Shapefile datasets, this study evaluates changes in district geometry through two established compactness metrics: the Reock score and the Polsby-Popper score. Geographic Information System (GIS) software, specifically QGIS, is used to analyze district boundaries and calculate the area, perimeter, and area of each district’s smallest enclosing circle. The Reock score is calculated by dividing district area by the area of its smallest enclosing circle, while the Polsby-Popper score is calculated by multiplying district area by 4π and dividing that product by the square of its perimeter. These metrics provide complementary measures of district compactness based on the geometric properties of congressional boundaries. For each of the four states, the mean Reock and Polsby-Popper scores will be calculated across all congressional districts for both 2020 and 2024. Changes in the mean scores will be compared to identify differences in district compactness between the two periods. District-level differences between the corresponding maps will also be analyzed using one-sample t-tests to determine whether the average changes in compactness are statistically significant. By focusing on geographic characteristics rather than election results, this study provides a quantitative assessment of how congressional district boundaries have changed over time. The findings will contribute to a comparative understanding of district compactness and provide a foundation for further research into the relationship between geographic districting patterns and electoral fairness.", "id": "Paper/72701", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72701"}, {"title": " A Sharp Lower Bound for Regular Orbits on the Power Set ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "ffa4dd1d295e13dccced4fc52282a5d3e62ef5174e1771f0de700f614f33dd89", "withdrawn": "", "abstract": "Let $G$ be a finite solvable primitive permutation group on a set $\\Omega$ with $|\\Omega| \\ge 10$. We prove that $G$ has at least ten regular orbits on the power set $\\mathcal{P}(\\Omega)$. The bound is best possible: the product action of $S_4 \\wr S_2$ of degree 16 has exactly ten regular orbits. This improves the previously known uniform lower bound of eight regular orbits.", "id": "Paper/72702", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72702"}, {"title": " Exploring Stability of Expressed Personalities in LLMs using Personality Trait-Specific Prompt Nudging ", "webprogram_exclude": "0", "session_ids": ["Session/18238"], "source_sha256": "bd1e78f407bea797355a0a58c0ab15665d85b4cc9cb784005f2988eff7a797e2", "withdrawn": "", "abstract": "The expressed personality profile of a Large Language Model (LLM) plays an integral role in determining model behavior. Thus, understanding personality stability is relevant to grasping LLM behavioral consistency and reliability. In order to examine this stability, models were prompted to role-play several character personas, then prompted to change their expressed personalities in specific ways, and finally to respond to a series of task-oriented questions. Between each prompt, the LLM instances filled out a survey measuring their expressed personality trait changes over time. Drifts in expressed personality across turns were examined in relation to various potentially stable personalities. A variety of differential system models were fit to the survey responses, revealing patterns in personality shift for various personas. Heterogeneous shift towards both the default expressed personality of LLMs and the expressed personalities achieved after perturbation occurred across several AI models. These results quantify the stability and susceptibility to perturbation of various personas and personality traits, providing a mathematical framework for analyzing the dynamics of personality expression in LLMs.", "id": "Paper/72704", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72704"}, {"title": " Mathematical Modeling of Cardiac Macrophages in COVID-19 ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "5f8877dec1935476f12c6e6102bdf7da13488d715c275101fad28b12b2a5a2b8", "withdrawn": "", "abstract": "Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) manifests heterogeneously among infected individuals, exhibiting a wide range of severity and symptoms. Beyond respiratory illness, it is also associated with cardiovascular complications, including myocarditis and long-term fibrotic remodeling. Despite increasing clinical evidence linking COVID-19 to cardiac dysfunction, the underlying mechanisms by which viral infection and immune response contribute to cardiac injury remain poorly understood. To bridge the knowledge gap regarding COVID-19's impact on cardiac complications, we developed a mechanistic mathematical model of viral and immune interactions in the cardiac setting, with a particular focus on macrophage dynamics. Our model incorporates factors such as viral replication, balance between pro-inflammatory (M1) and anti-inflammatory (M2) macrophages, cardiac cell death, and key regulatory cytokines like IL-6, IL-10, TGF-β, and Type 1 interferons. By utilizing parameter values derived from published literature and data fitting, we aim to accurately capture key aspects of SARS-CoV-2 infection in cardiac tissue, including cytokine dysregulation, T cell exhaustion, and neutrophil-mediated damage. This modeling approach will help investigate how immune cell dysfunction influences COVID-19-induced cardiac complications and identify potential therapeutic leverage points for restoring immune balance. \n\nKeywords: COVID-19, SARS-CoV-2, mathematical modeling, immune response, parameter estimation", "id": "Paper/72706", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72706"}, {"title": " Ford Sphere Moment Asymptotics over Imaginary Quadratic Fields ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "9196dae6c03f7c30117dccfa203777272412ea92280c49ba9dd02d16cad1a506", "withdrawn": "", "abstract": "Ford circles encode rational approximation by representing reduced fractions as tangent circles above the real line. Their three-dimensional analogues, Ford spheres, extend this geometry to complex rational approximation over rings of algebraic integers. Building on work of Alan Haynes and Kayleigh Measures on higher moments of distances between centers of consecutive Ford spheres over the Gaussian integers $\\mathbb{Z}[i]$, this project investigates corresponding asymptotic questions over the imaginary quadratic ring $\\mathbb{Z}[\\sqrt{-2}]$. The change of ring alters both the arithmetic governing neighboring spheres and the geometry of the associated configurations. This project studies how these differences affect distance moments over families of consecutive Ford spheres and uses theoretical and computational methods to analyze the resulting asymptotic behavior. This framework extends Gaussian-integer Ford sphere distance-moment methods to a new imaginary quadratic setting.", "id": "Paper/72707", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72707"}, {"title": " Automorphisms of the <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.211ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 521.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">k</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-6B\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-separating curve graph and Ivanov’s metaconjecture ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "ae944ef6942ae7e967d7597b87499462dc03ee5b5d7ae671162ee8b198b33d7d", "withdrawn": "", "abstract": "A metaconjecture of Ivanov states that any “sufficiently rich” object associated to a surface S has an automorphism group isomorphic to the mapping class group of S. Work of Brendle and Margalit shows that $\\textrm{Aut}(C_k(S)) = \\textrm{Mod}(S)$, where $C_k(S)$ is the $k$-separating curve graph, when $S$ is a closed, orientable surface of genus at least $3k + 3$. Our work reduces this bound to $2k + 2$, as well as providing similar results for punctured surfaces.", "id": "Paper/72708", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72708"}, {"title": " Matching-Theoretic Certificates for Free Attacking Targets and Screens in Soccer Corner Kicks ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "5ffd0289d4697f728d62b2f32f2ef5f125274944380ffc4fd963c07059346500", "withdrawn": "", "abstract": "**Matching-Theoretic Certificates for Free Attacking Targets and Screens in Soccer Corner Kicks**\n\nRecent approaches to soccer corner-kick analysis have used machine learning to predict tactical outcomes, infer defensive assignments, or optimize player positioning. We introduce a complementary mathematical framework based on bipartite matching that provides exact feasibility guarantees and explicit certificates under an idealized reachability model.\n\nFor a ball flight time \\(T\\), we construct a bipartite graph \\(G_T=(A\\cup D,E_T)\\), where \\(A\\) represents attacking targets, \\(D\\) represents defenders, and \\((a_i,d_j)\\in E_T\\) when defender \\(d_j\\) can reach attacker \\(a_i\\)'s target location within time \\(T\\). We define the attacking deficiency\n\\[\n\\delta(G_T)=|A|-\\nu(G_T),\n\\]\nwhere \\(\\nu(G_T)\\) is the maximum matching size. By the deficiency form of Hall's theorem,\n\\[\n\\delta(G_T)=\\max_{S\\subseteq A}\\bigl(|S|-|N(S)|\\bigr).\n\\]\nThus, a positive deficiency guarantees that some attacking targets cannot simultaneously be assigned distinct reachable defenders, while a maximizing set \\(S\\) provides an explicit certificate explaining why. We also show that \\(\\delta(G_T)\\) is nonincreasing in \\(T\\), yielding a critical ball-flight time separating configurations with and without complete defensive assignments.\n\nOur main soccer-specific construction models an idealized full screen by removing both a screening attacker \\(s\\) and a screened defender \\(d\\). If \\(\\delta\\) and \\(\\delta'\\) denote the deficiencies before and after the screen, respectively, then\n\\[\n\\delta'-\\delta\\in\\{-1,0,1\\}.\n\\]\nMoreover, the screen increases attacking deficiency by exactly one if and only if \\(s\\) is saturated by every maximum matching of \\(G\\) and \\(d\\) is saturated by every maximum matching of \\(G-s\\). Consequently, screens can be classified exactly as deficiency-increasing, deficiency-neutral, or deficiency-decreasing within the model.\n\nThis framework applies classical matching theory to a new tactical setting and produces interpretable certificates, timing thresholds, and an exact screening criterion that complement data-driven approaches to soccer analysis.", "id": "Paper/72709", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72709"}, {"title": " Area, Boundary Touches, and Pattern Avoidance in <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"5.4ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 2325.2 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">(3,n)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-33\" x=\"389\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2C\" x=\"890\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-6E\" x=\"1335\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"1935\" y=\"0\"></use>\n</g>\n</svg>-Rational Dyck Paths ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "710d1d6596286ef93237389ae2657aa8698fad74564fcf2ac15852413b717d99", "withdrawn": "", "abstract": "For coprime positive integers $m$ and $n$, an $(m,n)$-rational Dyck path is a lattice path from $(0,0)$ to $(m,n)$ using unit north and east steps that stays strictly above the line $y = \\frac{n}{m}x$. These paths are counted by the rational Catalan number $\\frac{1}{m+n}\\binom{m+n}{m}$, and by the Rational Shuffle Theorem of Carlsson and Mellit, their area generating function is encoded by the action of the nabla operator on symmetric functions. While the total area distribution is thus well understood algebraically, many finer statistics and restricted families of rational Dyck paths have received little direct attention. We investigate several such questions. Using the algebraic height $h(x,y) = my - nx$, we study statistics such as the distribution of boundary touches, the vertices at which a path comes as close as possible to the diagonal. We also consider rational Dyck paths that avoid a fixed consecutive pattern, such as $NENE$, and compare the resulting enumeration sequences across patterns and across choices of $m$ and $n$. Combining computer experimentation with bijective and generating function techniques, we present formulas, bijections, and conjectures for these statistics and restricted families, with particular attention to small values of $m$.", "id": "Paper/72711", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72711"}, {"title": " Eigen Try To Simplify: Linearized Equations with Eigenmode Solutions Give Insight to Nonlinear Dynamics in Plasma Magnetic Reconnection ", "webprogram_exclude": "0", "session_ids": ["Session/18238"], "source_sha256": "b43a8d57d2f23c18c2cc399cf14a7a1f9a179755db38fe449abe9acb23dbd4f5", "withdrawn": "", "abstract": "Magnetic reconnection, the sudden breaking and rejoining of magnetic field lines in a plasma, powers solar flares and other stellar surface events. It is governed by a system of nonlinear partial differential equations, the magnetohydrodynamic (MHD) equations. These can be directly solved numerically, but the solutions are hard to interpret. We linearize the equations about an equilibrium and solve the resulting eigenvalue problem. Each resulting eigenmode is characterized by an eigenvector, which corresponds to a physical plasma state, and an eigenvalue, which describes the oscillation and exponential growth or decay of this mode. Because the eigenvectors form a complete basis, we can write the full nonlinear solution as a dynamic linear combination of the eigenmodes, and use the amplitudes in the sum to see which modes matter most. We find two surprises. First, decaying (stable) modes play a major role in reconnection, even though intuition says the growing (unstable) modes should dominate. Second, only a handful of the thousands of computed modes contribute significantly. This suggests that a much simpler linear model could capture the essential nonlinear behavior.", "id": "Paper/72712", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72712"}, {"title": " Can We Trust AI In Statistics? ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "2afccc7cb7cc1b899b522695b69fa785ca6dadbf00d6ffad803bad5054b5908b", "withdrawn": "", "abstract": "As more students use AI in mathematics, can we trust the statistical results it produces? This study uses survey responses from 210 students across three summer sessions of Calculus III and Differential Equations at MassBay Community College (64 in 2024, 73 in 2025, 73 in 2026). Each response was coded for:\n\\begin{itemize}\n\\item \\quad awareness of AI tools\n\\item \\quad how often students use it\n\\item \\quad what they use it for\n\\item \\quad whether they find it helpful\n\\item \\quad their concerns (accuracy of information, dependence on AI tools, privacy)\n\\item \\quad overall sentiment\n\\end{itemize}\nPerceived helpfulness, and concern about accuracy are our main measures of how much students trust AI. We test whether each measure changed across the three cohorts using a one-way ANOVA at the 0.10 significance level, calculating every p-value by hand. We then give the same data to an AI tool, have it run the same analysis, and compare its results with ours to see whether it reaches the same conclusions.", "id": "Paper/72713", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72713"}, {"title": " Irreducibility in <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"5.356ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 2305.9 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbb {N}_0[x]</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJAMS-4E\" d=\"M20 664Q20 666 31 683H142Q256 683 258 681Q259 680 279 653T342 572T422 468L582 259V425Q582 451 582 490T583 541Q583 611 573 628T522 648Q500 648 493 654Q484 665 493 679L500 683H691Q702 676 702 666Q702 657 698 652Q688 648 680 648Q633 648 627 612Q624 601 624 294V-8Q616 -20 607 -20Q601 -20 596 -15Q593 -13 371 270L156 548L153 319Q153 284 153 234T152 167Q152 103 156 78T172 44T213 34Q236 34 242 28Q253 17 242 3L236 -1H36Q24 6 24 16Q24 34 56 34Q58 35 69 36T86 40T100 50T109 72Q111 83 111 345V603L96 619Q72 643 44 648Q20 648 20 664ZM413 419L240 648H120L136 628Q137 626 361 341T587 54L589 68Q589 78 589 121V192L413 419Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-5B\" d=\"M118 -250V750H255V710H158V-210H255V-250H118Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-78\" d=\"M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-5D\" d=\"M22 710V750H159V-250H22V-210H119V710H22Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJAMS-4E\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-30\" x=\"1021\" y=\"-213\"></use>\n <use xlink:href=\"#E1-MJMAIN-5B\" x=\"1176\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-78\" x=\"1454\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-5D\" x=\"2027\" y=\"0\"></use>\n</g>\n</svg>: Atomic Density and Bounded-Distance Problems ", "webprogram_exclude": "0", "session_ids": ["Session/19340"], "source_sha256": "2ad97b22815afed6462bcd089b60c631727d704f71858a840598766df72b730b", "withdrawn": "", "abstract": "We study the asymptotic and constructive behavior of irreducible polynomials in the semiring \\(\\mathbb{N}_0[x]\\) of polynomials with coefficients in the nonnegative integers. First, we strengthen the iterated-limit formulation of the atomic density of \\(\\mathbb{N}_0[x]\\) by proving a simultaneous two-parameter density result in the uniform-height model. We then study nonuniform coefficient boxes, prescribed-coefficient boxes, and related reducible-count estimates. Finally, we introduce a certification framework for irreducibility criteria in \\(\\mathbb{N}_0[x]\\), report computational coverage data, and prove several support-based and coefficient-based irreducibility criteria suggested by the residual data. We also explore Tur\\'an's problem on the distance to irreducibility, investigating a Tur\\'an-type bounded-distance problem for irreducibility in \\(\\mathbb{N}_0[x]\\).", "id": "Paper/72714", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72714"}, {"title": " Connected Components and Diameter Bounds in Commuting Graphs of Finite <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.259ex\" height=\"2.009ex\" style=\"vertical-align: -0.671ex; margin-left: -0.089ex;\" viewBox=\"-38.5 -576.1 542 865.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">p</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-70\" d=\"M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-70\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Groups ", "webprogram_exclude": "0", "session_ids": ["Session/19362"], "source_sha256": "fc9bcbd13817ce21b2b5374cf925a3bec0a2099152ed9bd58a29be5dd585ed55", "withdrawn": "", "abstract": "The commuting graph of a finite group $G$ has vertex set $G\\setminus Z(G)$, with two distinct vertices adjacent when the corresponding elements commute. Building on the work of Lewis and McCulloch, we study how the structure of a finite $p$-group influences the connectivity and diameter of its commuting graph. We prove that if $G$ contains a noncentral element $x$ with $|C_G(x)|>|G|/p^3$, then the commuting graph has at most one noncomplete connected component with diameter at most $6$. We then give several group-theoretic conditions that guarantee bounded diameter, including conditions involving the center and the upper and lower central series. In contrast, we construct families of $p$-groups showing that such bounds cannot hold in general. In particular, at the critical centralizer size corresponding to equality in our main theorem, commuting graphs can have components of arbitrarily large diameter, even among class-$2$, exponent-$p$ groups. These results demonstrate a close connection between the internal structure of a $p$-group and the global geometry of its commuting graph.", "id": "Paper/72715", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72715"}, {"title": " RSK Shapes and Bijections for Parking Functions Avoiding Patterns of Length Four ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "b4e6511cb3e4283acf843c440b38fc30f982e21136e97ecfffeaa1a4bad9614e", "withdrawn": "", "abstract": "A parking function of length $n$ is a sequence $(a_1,\\dots,a_n)$ of positive integers whose nondecreasing rearrangement $s_1 \\le \\dots \\le s_n$ satisfies $s_i \\le i$ for all $i$. There are $(n+1)^{n-1}$ such sequences, and they appear throughout algebraic combinatorics, from hyperplane arrangements to diagonal harmonics. A word avoids a pattern $\\sigma$ if it contains no subsequence in the same relative order as $\\sigma$. Pattern avoidance in parking functions has recently attracted considerable attention, including enumerations for patterns of length three, but parking functions avoiding longer patterns remain largely unexplored. We study parking functions avoiding a pattern of length four through the lens of the Robinson--Schensted--Knuth correspondence, which sends each parking function to a pair of tableaux whose common shape is an integer partition. Using computer experimentation, we compute the distribution of RSK shapes over each avoidance class and identify patterns whose classes are equinumerous or share the same shape distribution. We then use Knuth equivalence and related tableau techniques to explain these coincidences, and we present bijections, enumerative results, and conjectures for these families.", "id": "Paper/72716", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72716"}, {"title": " Exact Optimization Methods for Total Variation Compressed Sensing ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "c3afcb8931dfaeca428bc1fc2b8681a3583c50911c0619a45ac6a63fb44c91ac", "withdrawn": "", "abstract": "Total Variation Compressed Sensing (TVCS) reconstructs signals and images from incomplete measurements by minimizing the total variation subject to some measurement constraints. Recently, Langlois and Darbon developed an exact differential-inclusion algorithm (DI) for LASSO and basis pursuit problems that reaches the solution in finitely many breakpoint steps. This motivates our main research question: can the DI framework be adapted into an efficient, exact solver for TVCS? \n\nIn one dimension, TVCS can be reduced exactly to a basis-pursuit problem, allowing us to apply DI. In two dimensions, however, the discrete gradient is not surjective, so the reduction can introduce a relaxation gap. To address this, we study a lifted partial-$\\ell_1$ formulation that preserves the original TVCS problem, while allowing us to apply DI. \n\nWe also study a complementary approach based on the Chambolle-Darbon parametric max-flow method. Even though this method cannot directly enforce measurement constraints for TVCS, it solves anisotropic total-variation denoising exactly and can be used as a TV proximal subproblem within larger splitting methods. \n\nWe compare these methods against established iterative algorithms like ADMM on one-dimensional signals and two-dimensional image reconstruction problems. Our numerical experiments study how dimension, problem formulation, and structure influyence the behavior of the exact and iterative algorithms for TVCS.", "id": "Paper/72717", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72717"}, {"title": " Counting Patterns of Independence: Closed Formulas for Independent-Event Profiles in Uniform Probability Spaces ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "c23f959f2db649100f306a2fe5fa869d6c104cd53be028a0fb0f49c60fbc798a", "withdrawn": "", "abstract": "Flip four fair coins. The events \"at least one head among coins 1-2\" and \"at least one head among coins 3-4\" are independent, and their four atoms have sizes 1, 3, 3, 9. In general, if nontrivial events $A,B$ are independent in a space of $n$ equally likely outcomes, the sorted atom sizes satisfy $k_1+k_2+k_3+k_4=n$ and $k_1k_4=k_2k_3$. Sonin (2025) counted independent pairs through these profiles but noted that no compact description of them was available, calling the profiles with four distinct parts the main difficulty. The number of profiles is OEIS A340732, where only a triple-sum formula is recorded. We prove exact closed formulas for the number of profiles and for the number $D(n)$ with four distinct parts, e.g. $8D(n)=G(n)-2n+3-2s(n)-(n-2)[2\\mid n]+3[4\\mid n]$, where $G$ is Pillai's gcd-sum function and $s(n)^2$ is the largest square dividing $n$. The proof starts from the known count $G(n)-2n+1$ of labeled $2\\times2$ tables with determinant zero and passes to profiles through the eight symmetries of a square (complement either event, or swap them); the correction terms count the tables these symmetries fix. We show that four distinct parts occur exactly when $n$ is composite, not twice a prime, and not 8, 9, or 16, and we derive the average order of $D(n)$. We also identify the profile $(1,3,3,9)$ as missing from Sonin's list for $n=16$.", "id": "Paper/72718", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72718"}, {"title": " Analysis of Local Systems within the Levi-regular Orbits of the Classical Lie Algebras ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "249aff91474baf0b0fe0f957c730ad29ddce950ee6375cb821cdd4a1882e31f3", "withdrawn": "", "abstract": "Our research investigates nilpotent orbits through their classification by partitions of a positive integer n. In particular, we analyze Levi-regular orbits, subsets of the classical nilpotent orbits further delineated by additional conditions within their corresponding partitions. Our investigation began with the enumeration of these Levi-regular orbits within partitions of n, analyzing their prevalence as n increases. We derived, for the first time, generating functions that count Levi-regular orbits across the classical types Bn, Cn, and Dn, providing a way to enumerate this previously uncounted class of orbit. We also found that the proportion of Levi-regular orbits decrease exponentially as n increases. Building on these results, we are now working to extend our investigation to other connections with Lusztig’s generalized Springer correspondence, with the goal of counting the number of equivariant local systems on these Levi-regular orbits.", "id": "Paper/72719", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72719"}, {"title": " Alternative Method for Finding the Real Roots of a Cubic Polynomial in Cases with Two or more Real Roots Part ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "8c9a4d5a7b99a824e12a4ed9644eb9805115db3144055afb9773ba35e451806a", "withdrawn": "", "abstract": "We introduce here a new method to converge to the center root of a cubic function with real coefficients, specifically elaborating in this article on the prior conditions needed for such a scenario to occur. Our approach is based on generating a sine function derived from the original cubic equation that does not intersect its mother function except in the inflection and turning points but rather is strictly greater or lower than the cubic one in certain specific intervals. In general, the argument to guaranty such positions and intersections is developed through a basic cubic function that has known positions in regard to its built-up sine function. Then, the argument is extended to all cases with two or three real roots through algebraic manipulation, substitution, and proposing theorems. The further conclusions of our article showed indeed success in proving our desired positions, intersections and sine's root value and logic. Thus, we believe this argument and resolution process is suitable for understanding the position of our sine root with respect to the zero of a cubic function, showing applications in approximation theory, numerical methods and hence overall scientific and engineering innovations.", "id": "Paper/72720", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72720"}, {"title": " Characterizations of the graph short-time Fourier transform through frame tightness on discrete and fractal graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "d0fc203255a2c6b3f9ff08ec227978c33dc38642db09d69a8f4b502450451386", "withdrawn": "", "abstract": "We consider the graph short-time Fourier transform (GSTFT) formed from the eigenvalue decomposition of the graph Laplacian and a window function on the spectrum of the Laplacian. We show that for a given underlying graph with $N$ vertices, we can use the spectral decomposition of the graph Laplacian to find necessary conditions on the window function such that the corresponding Gabor system formed by the GSTFT is a tight frame for $\\mathbb{C}^N$. We also show that when the window function is the graph heat kernel, the corresponding Gabor system forms a tight frame for $\\mathbb{C}^N$ at all times $t$ if and only if the underlying graph is walk-regular. We then look at another family of regular graphs with a predictable construction: the graph approximations of the Sierpinski gasket. We find that for graphs at the second level of construction and beyond, the graph short-time Fourier transform with the heat kernel as a window function does not lead to a tight frame. We also develop a recursive evolution for the projection matrices corresponding to the spectral decomposition at each level of the gasket.", "id": "Paper/72721", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72721"}, {"title": " The Picky Passenger Problem ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "76f969040f3de4c9443058d0bbd7fe42183dc7228aa32855a1cb8abe5c35bdfe", "withdrawn": "", "abstract": "We study a variant of parking functions inspired by airplane boarding, which we call the Picky Passenger Problem. An airplane has $n$ rows and $k$ columns. Each of the $nk$ passengers has a preferred row and a preferred column, with row preference taking priority. Passengers board sequentially and go directly to their preferred seat. If it is occupied, a passenger takes the next available seat on their preferred side of that row, which is indicated by their column preference. If that side is full, they look for the seat in their preferred column on the opposite side of that same row; if that seat is taken, they sit in the next available seat. If none are available, then a wrap-around within the same side of the row is possible. If all seats in that row are full, the passenger moves on to the next row, and the process repeats. Passengers may only move forward in the aisle, so a row that has been passed can not be revisited. We ask: for which preference vectors does every passenger find a seat?", "id": "Paper/72723", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72723"}, {"title": " Diameter Bounds and Counterexample Constructions in the Commuting Graphs of Finite <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.259ex\" height=\"2.009ex\" style=\"vertical-align: -0.671ex; margin-left: -0.089ex;\" viewBox=\"-38.5 -576.1 542 865.1\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">p</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-70\" d=\"M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-70\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Groups ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "9e009946d2a21a2025a530b0c4cefbd53d9fa917470225bedbaea596e4bf42c1", "withdrawn": "", "abstract": "The commuting graph of a finite group $G$ has vertex set $G\\setminus Z(G)$, with two distinct vertices adjacent when the corresponding elements commute. We study how the structure of a finite $p$-group influences the connectivity and diameter of its commuting graph. We prove that if $G$ contains a noncentral element $x$ with $|C_G(x)|>|G|/p^3$, then the commuting graph has at most one noncomplete connected component, and that component has diameter at most $6$. We then give several group-theoretic conditions that guarantee bounded diameter, including conditions involving the center and the upper and lower central series. In contrast, we construct families of $p$-groups showing that such bounds cannot hold in general. In particular, at the critical centralizer size corresponding to equality in our main theorem, commuting graphs can have components of arbitrarily large diameter, even among class-$2$, exponent-$p$ groups. These results demonstrate a close connection between the internal structure of a $p$-group and the global geometry of its commuting graph.", "id": "Paper/72725", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72725"}, {"title": " Lyapunov Exponents for Higher-Order Random Hill Equations and Rotational Matrix Products ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "f4b920ed9c059ab24ebf369413132b0f8d87ef7b649eaeca2818c3f04683e34f", "withdrawn": "", "abstract": "We derive an asymptotic formula for the maximum Lyapunov exponent of a generalized $2n$-dimensional random Hill's equation in the highly stable regime, utilizing WKB theory. In particular, we build upon the work of a 2013 paper by Adams, Bloch, and Lagarias, whose demonstration of an underlying rank-one structure influenced our approach. We also derive formulae for a comparative model using isotropic random rotations on $SO(2n)$, and contrast the growth rates of the two regimes, similarly motivated by a geometric dichotomy displayed in the aforementioned paper, however we do so using different methods. This work is motivated by and generalizes previous analyses of $2 \\times 2$ random matrix products associated with the classical random Hill's equation, demonstrating how the choice of random similarity transformations alters system stability.", "id": "Paper/72726", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72726"}, {"title": " Deep Learning-Based Early Warning Systems for Critical Transitions ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "381e69dceb3fa21efaa1d06b12a0f16764e1054176a5fc16fa8422098629e2f5", "withdrawn": "", "abstract": "Disease systems can undergo abrupt critical transitions leading to epidemics, making timely early warning essential for effective public health intervention. Deep learning excels at many time-series tasks, but whether it can provide early warning across pathogens from sparse, noisy signals under distribution shift remains unresolved. We prove  analytically that the non-normal, multi-timescale dynamics of epidemics suppress the signature of an approaching transition in observable case data, explaining why both traditional methods and prior deep learning models fail to generalize across diseases. Motivated by this result, we developed GEN-DL, a generative deep learning framework that reproduces this weak-observability regime in synthetic outbreaks spanning a range of epidemic timescales and trained an early-warning CNN-LSTM classifier. We evaluated GEN-DL on real-world data from three epidemiologically distinct diseases (COVID-19, influenza, and mpox). We find that a single fast-timescale GEN-DL model trained solely on synthetic outbreaks with no disease-specific fine-tuning outperforms existing indicators and a benchmark deep learning method on every dataset, and remains reliable even in test cases where every baseline falls to chance level or below. This work advances early warning of epidemic transitions by mathematically analyzing the observability of critical transitions in epidemic  systems and demonstrating a timescale-parametrized deep learning model that generalizes across diseases. The framework can be extended to other complex systems with critical transitions such as climate, ecological and financial systems.", "id": "Paper/72727", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72727"}, {"title": " Computational Reduction and Stabilization of Khovanov Homology for <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.162ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 500.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">3</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-33\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>- and <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.162ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 500.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">4</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-34\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-strand Torus Braids ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "a67ef80ee0aec8ae4ac119dc4a5ce7446845be21b0f0d975ad31af8c01ee3c3b", "withdrawn": "", "abstract": "We investigate computational methods for reducing the complexity of the Khovanov chain complexes of $3$- and $4$-strand torus braids. We develop code to complement the theorized algorithmic generation of Kauffman states and their associated Temperley-Lieb words. We explore the back and forth between identifying isomorphism patterns of Gaussian elimination in order to improve computation and using computation to better identify these patterns. We extend the computational techniques of Lee to $4$-strand torus braids and identify a more complicated isomorphism structure for simplifying the chain complex. This talk will illustrate how Gaussian elimination transforms the original Khovanov complex, as implemented in the algorithms, and discuss the theoretical patterns that emerge from the resulting data for $3$- and $4$-strand torus braids.", "id": "Paper/72728", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72728"}, {"title": " A Cost-Effective Data Collection Approach for Generating Reliable Monthly Visitation Forecasts at National Parks ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "d2a9315c11c13ab4b58f6d6bf053b0dd424b3d894ec610cda47df489c440b040", "withdrawn": "", "abstract": "Visitation at national and state parks and forests continues to rise in recent years. As increased visitation at national and state parks affects the gateway communities and the surrounding environment, it is crucial for park managers to have proper methodology to track and forecast visitation. Reliable visitation forecasts may then be used to project economic benefits of these gateway communities and assess the damages to the facilities and natural environment. However, it is often challenging for park managers to collect such data on a routine basis due to the time and cost associated with data collection. Fortunately, by using monthly photo-user-days (PUD) data from Flickr, a social media platform, it is possible to generate reliable monthly park visitation forecasts while dramatically reducing the number of on-site counts (OSC) necessary. Through analyzing monthly OSC at six major national parks, June appears to be an optimal month to conduct monthly OSC data collection without sacrificing the overall forecast accuracy. Furthermore, to generate accurate monthly visitation forecasts, June OSC need to be collected only once every two years on average while collecting them once every three years on average further relaxes economic constraints without significantly losing forecast accuracy. In other words, the proposed data collection strategy allows the national and state park managers to generate accurate monthly visitation forecasts while reducing the cost of data collection.", "id": "Paper/72730", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72730"}, {"title": " Producing Partisan Gerrymanders Under the Define-Combine Procedure ", "webprogram_exclude": "0", "session_ids": ["Session/18160"], "source_sha256": "1c436f5fc4b2ef406d2d0133b89b8e5ba27de6af570c00f4859f053c4e03000e", "withdrawn": "", "abstract": "In this paper, we examine the fairness of the Define-Combine Procedure (DCP), a two-player adversarial approach to political redistricting first introduced by Palmer, Schneer, and DeLuca. The first player, the definer, draws twice as many subdistricts as necessary, and the second player, the combiner, combines pairs of neighboring subdistricts to create the necessary number of districts. Palmer, Schneer, & DeLuca state that DCP produces more fair outcomes than the Unilateral Redistricting Procedure (URP). We show that DCP and URP perform exactly the same under theoretically optimal play in a continuous model and in a limited discrete model, with the definer holding the advantage. We also produce more extreme computational results than Palmer, Schneer, & DeLuca in 12 states via a heuristic optimization using the Marked Edge Walk (MEW). Alternative games, such as n-to-one DCP and iterated DCP, fail in the same way as the original game. Our results suggest that imposing certain constraints, such as compactness constraints or quotient graph constraints, on the districting plans generated by the definer may produce fairer outcomes than DCP and URP.", "id": "Paper/72731", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72731"}, {"title": " PROPERTIES OF WILD COLORED GRAPHS ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "fc627a08bb96f58040e88a466aa892c3e06b65146dcd118342251ea466480764", "withdrawn": "", "abstract": "An edge colored graph assigns each edge a color, for example, to represent different modes of travel through a network; such as bus lanes, bike lanes, and sidewalks. In order for a graph of this kind to be fully spanning, each color must have a spanning tree. Our research explores how making an edge “wild,” essentially having it count for all colors, impacts minimum spanning trees, and what characteristics graphs of a certain wild number have. We thus build this paper around the wild number of a graph. We develop an algorithm in Python for computing a minimum wild edge set and examine when such a set has a unique solution. We give a complete characterization of when the wild number of a two-colored wheel graph is 0 or 1, and give partial characterizations for larger graphs. We also introduce the idea of partial wild edges and prove several bounds relating total partial wildness to the wild number itself. Finally, we establish deletion–contraction relationships for the wild number, and end with some questions left on topics to further explore.", "id": "Paper/72733", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72733"}, {"title": " CANCELLED HistoRange: Modeling Histology-Guided Anisotropic Diffusion and Signaling Range in Spatial Transcriptomics \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "6f0cbc6ac612cf5bc5759b7d1b31e6246c28bd576b7db9419deeaffb61d172f4", "withdrawn": "", "abstract": "Spatial cell–cell communication (CCC) is often inferred from ligand–receptor expression and proximity, yet secreted ligands travel through structured tissue before reaching receptor-expressing cells. Tissue architecture can redirect transport, and a best-fitting spatial scale may not represent a resolvable signaling range. We developed HistoRange to address both problems. Registered hematoxylin and eosin (H&E) histology defines the tissue domain, while local structure specifies a spatially varying anisotropic diffusion tensor. We solve a screened anisotropic diffusion equation across candidate ranges to propagate ligand sources and estimate receiver exposure. A covariance-aware test evaluates whether exposure predicts receptor expression, while a simulation-calibrated estimator reports a range interval, upper bound, or no range.\n\nThe transport solver agreed with analytic and independent finite-volume solutions with sub-percent error. Across six simulation models, HistoRange reduced median range error from 1.00–2.38 bits to 0.50–0.75 bits, with 100 percent held-out 95 percent coverage for short-range intervals and 96.8 percent for informative upper bounds. Synthetic H&E experiments showed improved prediction when tissue geometry and anisotropy were informative.\n\nIn lung adenocarcinoma, HistoRange identified a localized CXCL12–CXCR4 field linking source regions to CXCR4-expressing receivers. The fitted effective range was 53.8 μm with a 95 percent upper bound of ℓ < 152.2 μm. Among CXCR4-competent receivers, modeled CXCL12 exposure was concentrated in T/NK-cell and fibroblast/CAF regions and nearly absent from tumor epithelium, supporting localized stromal–immune signaling. Across additional NSCLC, IPMN, colorectal, and pancreatic datasets, supported ranges varied by ligand–receptor pair and tissue context, while HistoRange withheld ranges when data could not resolve them. Together, these results show that tissue geometry, anisotropic transport, and calibrated inference reveal heterogeneous signaling ranges in tumors.", "id": "Paper/72734", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72734"}, {"title": " On the alternating number of of a graph ", "webprogram_exclude": "0", "session_ids": ["Session/19346"], "source_sha256": "9d142d6808b7e8d60e2bb01ee626b455a81800dd9c7dd8d41a6f9a2bb9227ce9", "withdrawn": "", "abstract": "The alternating number of independent sets in a graph is the value of its independence polynomial at -1. In this paper, we introduced a new way to analyze this number. We presented the induced result on trees and graphs with disjoint cycles, as well as the alternating number of two other relevant graphs.  We also observed an interesting trend in the percentage of trees having an alternating number zero. For future investigation, one can consider the alternating number of parallel-series graphs, which also have a more complicated decycling number calculation.", "id": "Paper/72736", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72736"}, {"title": " Histology-Guided Modeling of Anisotropic Ligand Diffusion and Effective Signaling Range in Spatial Transcriptomics ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "df518445a6cc2276ad63018095f04a493e3297851d23248f5d536b0c9d6723ab", "withdrawn": "", "abstract": "Spatial cell–cell communication (CCC) is traditionally inferred from ligand–receptor expression and spatial proximity, yet secreted ligands navigate complex tissue microenvironments whose structure directly shapes the direction and boundary of molecular transport. Moreover, a single estimated spatial scale does not guarantee that the underlying data support a precise signaling range. To address these challenges, we present HistoRange, a computational framework that uses registered hematoxylin and eosin (H&E) histology to define tissue domains and implements a spatially varying, anisotropic diffusion model of ligand transport. To our knowledge, HistoRange is the first continuum spatial CCC framework to reconstruct anisotropic transport geometry directly from histology slides.\nThe framework propagates ligand sources through tissue across a set of candidate ranges. A spatial model then tests whether ligand exposure is associated with receptor expression, while a separately calibrated estimator determines whether the data support a specific range interval, an upper bound only, or no quantitative range. Against analytic and finite-volume solutions, the transport solver achieves accuracy within 1 percent error. In simulations across six generating models, the range estimator reduced median error by more than 50 percent (to 0.50–0.75 bits). Held-out calibration achieved up to 100 percent nominal coverage for short-range intervals, with zero false positives across 180 association-null tests. Synthetic experiments confirmed that incorporating matched histology significantly improves prediction when tissue anisotropy is informative. Applied to lung adenocarcinoma, HistoRange mapped a robust CXCL12–CXCR4 effective signaling range of 53.8 μm (95 percent upper bound < 152.2 μm), concentrated within T/NK-cell and fibroblast microenvironments. Across multiple tumor datasets, HistoRange consistently quantified signaling ranges only when supported by strong spatial evidence, offering a highly robust approach to mapping structural tissue communication.", "id": "Paper/72738", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72738"}, {"title": " On dynamical and parameter spaces for the Maximally Generalized McMullen family of rational maps ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "66e69ff825b90365f50ec94a66f26b4320de47486280cbb0ac13626a6e01239d", "withdrawn": "", "abstract": "We explore the maximally generalized McMullen family of rational maps f_n,d,a,c(z) = z^n + a/z^d + c, for n,d in Z, with n,d >= 3, a in C* and c in C. In the dynamical plane, we establish annular regions containing the Julia sets, and show that the geometric limits of both the Julia and filled Julia sets as n,d -> infinity are contained in the unit circle. In parameter space, for any fixed a in C*, we examine the boundedness locus in the c-plane. When n = d, we find that, as n -> infinity, the boundedness locus tends to the union of two unit circles centered at ±2√a. For arbitrary n,d, we identify a spine consisting of unit circles determined by the critical values, and prove that the boundedness locus tends to the spine as n,d -> infinity.", "id": "Paper/72739", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72739"}, {"title": " Integer Linear Programming through Logic Synthesis and Iterated SAT Queries ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "e30bedf9d400c464c28d9febe5790d7decc752325852e12092bcb9a12921cdf9", "withdrawn": "", "abstract": "Integer linear programming (ILP) optimizes a linear objective subject to linear constraints over integer variables. Nearly all current solvers use branch-and-bound guided by the linear relaxation, so their performance is governed by how tightly that relaxation bounds the integer optimum. Boolean satisfiability (SAT) solvers decide whether there exists an assignment of truth values to the Boolean variables of a propositional formula that renders the entire statement true. In optimization, SAT solvers are applied mainly to pseudo-Boolean problems but rarely to general ILP, since expressing integer arithmetic propositionally produces a formula far larger than the original model. Recent advancements in SAT solving, such as the use of field-programmable gate arrays (FPGAs) to accelerate the solving process, motivate considering the use of SAT solving for ILP.\nWe develop a method that carries the entire integer program into propositional logic and discovers its optimum. Our algorithm reduces optimization to a sequence of feasibility questions in Boolean logic, and searches over the objective value through iterated SAT queries to locate the optimum. Standard ILP techniques, including the linear relaxation and heuristic incumbents, first tighten the model, and logic synthesis then expresses each feasibility question propositionally. The construction applies to any pure integer program in standard form.\nEvaluating our algorithm against Gurobi, CP-SAT, and HiGHS, we find that performance depends on the structure of the model, and we analyze the structural features that suit each solving method. On the formulations favoring our algorithm, it proves optimality on instances that established solvers leave unsolved.", "id": "Paper/72740", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72740"}, {"title": " Differentiable GPU Multigrid for Darcy Flow and Multilevel Diffusion Inversion ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "0842e71eb2e9b8bd1639182214f16982ebb204f83b357c3e639b9513777fd1ca", "withdrawn": "", "abstract": "We develop a GPU multigrid finite element solver for Darcy flow, $-\\nabla\\cdot(e^m\\nabla u)=f$, with permeability $e^m$. Implemented in NVIDIA Warp, it uses piecewise linear elements on triangular meshes; multigrid accelerates the solve by transferring corrections across mesh levels. Manufactured-solution tests recover second-order $L^2$ and first-order $H^1$-seminorm convergence. For a smooth coefficient, we observe six or seven V-cycles across meshes from $128\\times128$ to $4096\\times4096$. At 16.8 million degrees of freedom with zero Dirichlet data, the original forward solver takes a mean of 5.72 seconds on an NVIDIA L40S GPU and 55.71 seconds with our CPU implementation, including setup for both.\n\nA differentiable variant computes sensitivities to log-permeability. A directional derivative of a scalar test loss through fixed V-cycles agrees with centred finite differences. We compare coarse operators built directly on each mesh with those derived from fine-grid operators; the former reduce measured runtime with comparable convergence in our tests.\n\nFor inverse reconstruction, two conditional generative diffusion models estimate coarse and fine log-permeability from sensor data and the known source. The coarse estimate is interpolated to condition the fine model. On 5,000 test cases with 500 observations each, reconstruction proceeds from $32\\times32$ to $128\\times128$. Selecting the candidate with the smallest observation mismatch from 20 samples yields median relative $\\ell^2$ errors of 16.9% for permeability and 4.05% for the PDE solution. Errors are largest for short correlation lengths and high log-permeability variance. Additional guidance using gradients of observation mismatch does not improve overall median accuracy under the tested settings. We also outline an extension to incompressible Navier-Stokes flow.", "id": "Paper/72741", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72741"}, {"title": " Isolated <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"6.007ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 2586.5 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathrm {SU}(2)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-53\" d=\"M55 507Q55 590 112 647T243 704H257Q342 704 405 641L426 672Q431 679 436 687T446 700L449 704Q450 704 453 704T459 705H463Q466 705 472 699V462L466 456H448Q437 456 435 459T430 479Q413 605 329 646Q292 662 254 662Q201 662 168 626T135 542Q135 508 152 480T200 435Q210 431 286 412T370 389Q427 367 463 314T500 191Q500 110 448 45T301 -21Q245 -21 201 -4T140 27L122 41Q118 36 107 21T87 -7T78 -21Q76 -22 68 -22H64Q61 -22 55 -16V101Q55 220 56 222Q58 227 76 227H89Q95 221 95 214Q95 182 105 151T139 90T205 42T305 24Q352 24 386 62T420 155Q420 198 398 233T340 281Q284 295 266 300Q261 301 239 306T206 314T174 325T141 343T112 367T85 402Q55 451 55 507Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-55\" d=\"M128 622Q121 629 117 631T101 634T58 637H25V683H36Q57 680 180 680Q315 680 324 683H335V637H302Q262 636 251 634T233 622L232 418V291Q232 189 240 145T280 67Q325 24 389 24Q454 24 506 64T571 183Q575 206 575 410V598Q569 608 565 613T541 627T489 637H472V683H481Q496 680 598 680T715 683H724V637H707Q634 633 622 598L621 399Q620 194 617 180Q617 179 615 171Q595 83 531 31T389 -22Q304 -22 226 33T130 192Q129 201 128 412V622Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMAIN-53\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-55\" x=\"556\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-28\" x=\"1307\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-32\" x=\"1696\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-29\" x=\"2197\" y=\"0\"></use>\n</g>\n</svg> Representations with Nontrivial Zariski Tangent Space ", "webprogram_exclude": "0", "session_ids": ["Session/19358"], "source_sha256": "e661966726b66ad501f1210bac9040166c74367622a4a6288ea6e88d05d9e460", "withdrawn": "", "abstract": "Problem 3.105(B) of Robion Kirby’s \\textit{Problems in Low-Dimensional Topology} asks for a closed 3-manifold admitting an isolated representation \\(\\rho:\\pi_1(M)\\to \\mathrm{SU}(2)\\) with nontrivial Zariski tangent space. Work of Herald and Kirk provides such examples using torus knot complements. We extend their methods to 2-bridge knots, producing new examples of 3-manifolds with this property. In particular, we show that the \\(9/1\\) Dehn filling of the knot \\(7_2\\) admits an isolated representation with 1-dimensional Zariski tangent space.", "id": "Paper/72743", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72743"}, {"title": " Some Inequalities Involving Square Roots Of Prime Numbers ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "ad779a00b8c659c9faff35c05c89d3bb9c7642131ee4596bf8717d65d94c1866", "withdrawn": "", "abstract": "We compare the sums of square roots of prime numbers with the square roots of sums using the prime number theorem to show that these inequalities are eventually true. We will use inequalities by Nagura and Dusart to find an upper bound for the rank starting with which the inequalities are true, and direct computation to find the exact rank; we will also present some conjectures.", "id": "Paper/72745", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72745"}, {"title": " Wavelet-Based Machine Learning for Classifying Multi-Scale Power Grid Disturbances Induced by AI Data Center Workloads ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "4d50ced16494c9689abdab6e1d1613fdd5f15d2b3fd68fc5bc2aaa34e46bcca4", "withdrawn": "", "abstract": "The rapid expansion of artificial intelligence infrastructure has significantly increased demand for large-scale data centers, introducing highly variable electrical loads that trigger rapid fluctuations and oscillatory behavior in power grids. Promptly detecting these disturbances is critical to maintaining grid stability. However, conventional time-domain and Fourier-based techniques fail to accurately capture transient events with time-varying frequency characteristics. This paper investigates the efficacy of wavelet-based machine learning for detecting and classifying multi-scale grid disturbances associated with AI data center dynamics. Voltage, frequency, and power-demand time series are decomposed via discrete wavelet transform (DWT) into localized time-frequency components. Statistical and energy-based features extracted from the resulting wavelet coefficients are then utilized to train machine learning classifiers. The proposed framework is benchmarked against models utilizing raw time-series data and Fourier-based features, evaluated across classification accuracy, computational efficiency, noise robustness, and temporal-scale discrimination. The results demonstrate that the localized, multi-resolution properties of wavelet transforms offer a distinct advantage in identifying short-duration and oscillatory disturbances caused by highly dynamic workloads. Ultimately, this research bridges mathematical multi-scale analysis and power-system monitoring to address an critical emerging challenge in AI infrastructure grid integration.", "id": "Paper/72746", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72746"}, {"title": " Graded Analogues of Papick’s i-Extensions and Local i-Domains ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "f1430dc5c18d257a02268cc631d5662fde0b439378607f1cdcc139cea29aea82", "withdrawn": "", "abstract": "Let $R$ be an integral domain. An extension $R \\subseteq S$ of integral domains is an $i$-extension if the canonical mapping $\\operatorname{Spec}(S) \\rightarrow \\operatorname{Spec}(R)$ is injective. An integral domain $R$ is an $i$-domain if $R \\subseteq S$ is an $i$-extension for every overring $S$ of $R$. Graded analogues of these notions were introduced by Merchant. In this work, we explore results that hold for graded $i$-domains and graded extensions. In particular, we prove that a graded integral domain is a gr-local gr-$i$-domain if and only if its integral closure in its homogeneous quotient field is a gr-valuation domain, and show that a graded $i$-extension need not be graded-mated or satisfy graded going-down.", "id": "Paper/72747", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72747"}, {"title": " A Hockey Rink Through Hyperbolic Space ", "webprogram_exclude": "0", "session_ids": ["Session/18159"], "source_sha256": "4b24fad11059a1434680fe87613954ec38e004a17a79f66ece53c9f900e3d383", "withdrawn": "", "abstract": "In a normal Euclidean hockey rink, the ice is flat, the lines are straight, and the angles follow the rules of Euclidean geometry. But if we put a hockey rink in hyperbolic space, things would look and work a little differently. The lines, distances, and angles would not behave the same way they do on a regular flat rink. Looking at a hockey rink in hyperbolic space is a way to see how geometry can change when the space itself is different. Comparing a typical Euclidean hockey rink to a hyperbolic rink allows us to see the differences between the two spaces and how those differences affect the dimensions of the rink.", "id": "Paper/72749", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72749"}, {"title": " A Spectral-Stochastic Neural Operator Framework for Model Predictive Control of Precision Irrigation ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "9ff95b2b2341c92b16ed19eaeb1d36b8f96956f783b3b5457395dd6b141118c7", "withdrawn": "", "abstract": "This work develops an irrigation control framework that couples a Fourier Neural Operator (FNO) surrogate of the Richards equation, $\\partial_t\\theta=\\nabla\\cdot(K(\\theta)\\nabla(\\psi(\\theta)+z))$, a learned stochastic differential equation (SDE) extension, and chance-constrained model predictive control (MPC), recasting irrigation from a reactive process into a forecasting and control problem. Trained on NASA SMAP data, the FNO approximates the soil-moisture solution operator with relative $L^2$ test error $<0.01$ at roughly 100,000 parameters. Across five model sizes, from 512 to 524,288 parameters, the error decays as a power law in the parameter count with fitted exponent $-1.34$ ($R^2=0.927$), close to the exponent $-1.5$ predicted by neural operator approximation theory. The SDE extension adds a learned, spatially correlated noise term to the Richards dynamics and propagates uncertainty by Euler-Maruyama integration over 500 Monte Carlo trajectories. The resulting distribution agrees with a numerically solved Fokker-Planck reference, with Kullback-Leibler divergence 0.047 nats, and the empirical variance lies 37 times below the bound for spatially independent noise, a gap attributed to the correlation structure of the noise. The MPC minimizes water use subject to a 95\\% probabilistic soil-moisture safety constraint over a 7-day receding horizon re-solved every 12 hours. The closed loop exhibits exponential Lyapunov decay (fitted rate 0.0375 per day, $R^2=0.982$), with no constraint violations across 18,000 safety checks spanning nominal, drought, and pump-failure scenarios. In a 60-day hardware trial on 20 tomato plants (10 per arm), the MPC used 44.7\\% less water than a threshold controller ($p<0.0001$) with no measurable difference in plant health, and across 50 simulated sites on six continents the mean water savings were 22.3\\%, positive at every site. A central stochastic extension of the framework tests a single trajectory against the 95\\% envelope of the SDE trajectory ensemble. Because the chance constraint depends directly on the uncertainty predicted by the SDE, this test connects the stochastic model to the control objective: its key aim is to determine whether the variability of an individual trajectory is consistent with the 95\\% band on which the safety guarantee rests.", "id": "Paper/72750", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72750"}, {"title": " Isospectral unfoldings and quantum walk properties ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "f0cf9c93c5670b72e2b86b9dd024a5f1d450076bfff468946fea345e67fe2c89", "withdrawn": "", "abstract": "Isospectral reductions are mathematical techniques used to shrink\na matrix, or a graph, into a smaller, dimensionally reduced form while\npreserving its spectrum. Simple graphs that share isospectral reductions also share quantum walk properties. As such we further develop the inverse process, isospectral unfoldings, to find graphs that share isospectral reductions. We first prove many conditions relating to isospectral reductions and unfoldings. Afterwards, we define two new unfolding processes: general unfolding which unfolds the graph one vertex at a time, and equitable partition unfolding which excels at larger graph unfolding. In particular, through equitable partition unfolding, we discover many graphs that share isospectral reductions with hypercubes onto their equidistance antipodal vertices and therefore have vertices that also have perfect state transfer. Moreover, these graphs are on fewer vertices and edges which may lead to a family of graphs that give better constraints on the relation between the distance between vertices that have perfect state transfer and the number of vertices or edges required.", "id": "Paper/72751", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72751"}, {"title": " N-Body Problem with Power Series Method approximation ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "9eee420d59baa8000a48b02a218e45941d73153b7a032d5a7ac9d6ff223c915f", "withdrawn": "", "abstract": "The N-body problem has no known closed-form general solution for three or more bodies, so numerical integration is essential. We explore this problem using the Power Series Method (PSM), which computes Taylor series coefficients through recurrence relations rather than higher-order derivatives. We compare PSM against the classical Taylor Series Method and the widely used Runge-Kutta 4(5) (RK45). Because PSM can adapt both its step size and its order, we test it at several orders and with fixed and adaptive stepping. In our Python implementations, PSM runs roughly ten times faster than RK45 and needs about a hundred times fewer time steps for the same error tolerance. Notably, the accuracy and efficiency of PSM also depend on the polynomial reformulation of the N-body equations we use, even though all of them are mathematically equivalent to the original system.", "id": "Paper/72752", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72752"}, {"title": " First-Derivative Chromatic Symmetric Reconstruction For Proper Trees ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "e823869c96f4a1dfafd3f330771810b28f261c7eafe65c3eb89ab3ba3a4008e0", "withdrawn": "", "abstract": "Let $T$ be a tree. Stanley asked whether the chromatic symmetric function $X_T$ determines $T$ up to isomorphism. We approach this open problem by regarding $X_T$ as a polynomial in the power-sum symmetric functions $p_1, p_2, \\dots$ and studying the invariant $\\Phi_T = \\left.\\frac{\\partial {X_T}}{\\partial p_1}\\right\\rvert_{p_1 = 0}$. We prove that $\\Phi_T$ distinguishes every proper tree whose weighted skeleton, the tree obtained from $T$ by weighted contraction of all leaf edges, has distinct weights at non-leaf vertices. We prove further an equivalent formulation of Stanley's question obtained by attaching a fixed positive number of leaves to\nevery vertex of a tree. Finally, we count spanning forests with at most $t$ edges, grouping\nthem by the sizes of their connected components. We prove that these\ncounts cannot distinguish all trees on $k\\ge4$ vertices unless\n$t\\ge\\lfloor k/2\\rfloor$.", "id": "Paper/72753", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72753"}, {"title": " Continuation of Finite-Time Collisions in the Vanishing Repulsion Limit ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "a07d3ef831da79459738a473fab8fab4196798c522b614bd6b6fe158800652e1", "withdrawn": "", "abstract": "We investigate how to continue solutions beyond a finite-time collision in two Hamiltonian systems: the Kepler and anisotropic Kepler problems. The Kepler problem is regularizable in the sense that given an $\\varepsilon$ perturbation of a collision orbit, taking $\\varepsilon \\to 0$ recovers a unique continuation beyond collision. The anisotropic Kepler problem on the other hand is not regularizable.\n\nWe explore techniques of ``regularizing\" both problems by modifying the potential. For example, the modified anisotropic Kepler potential:\n$$\n    \\ddot{\\vec{q}} = \\nabla_{\\vec{q}} \\frac{1}{(\\mu q_1^2 + q_2^2)^{1/2}} + \\kappa \\frac{\\vec{q}}{|\\vec{q}|^{\\nu+3}} \\, , \\quad \\mu \\geq 1 \\, , \\; \\nu > 0\n$$\nwith $0<|\\kappa|\\ll 1$. By matched asymptotic analysis, we discover a critical threshold $\\varepsilon \\sim \\kappa^a$ separating the behaviors -- and, in particular, whether the continuations are unique -- of the possible double limits as $\\varepsilon,\\kappa \\to 0^+$. \n\nIn particular, for $\\kappa =0$ we develop a description of near collision orbits by matching the canonical outer problem to a transformed inner problem using a change of variables due to McGehee. We show that it is sufficient to consider a parameterized zero-energy manifold in the inner problem on which the behavior has been explored by Devaney and others. We further corroborate our findings with numerical simulations.", "id": "Paper/72754", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72754"}, {"title": " Tilings of the Sphere by Regular Polygons Including Bigons (Preliminary Report) ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "3c18400ad57d66cc311975f184f2a0c1c0408e34202cda585428555a2e7c2159", "withdrawn": "", "abstract": "Tilings of the sphere by tiles that are regular spherical $n$-gons for $n \\geq 3$ have been previously determined. In this paper, we extend to allow bigon tiles and determine exactly the additional tilings that can occur.", "id": "Paper/72755", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72755"}, {"title": " Change in Kemeny’s Constant After Vertex Identification and Edge Subdivision ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "6329733ea7fc75caa27e13dfed0764caf2c660f34743d308c5935c8aba21bb4d", "withdrawn": "", "abstract": "\\begin{abstract}\nKemeny's constant is a fundamental parameter in the study of random walks on graphs, giving the expected time for a random walk to reach a target vertex chosen according to the stationary distribution. In this paper, we investigate how Kemeny's constant changes under two graph operations: vertex identification, which merges two vertices into a single vertex, and single edge subdivision. We derive closed-form expressions for Kemeny's constant of the resulting graphs, treating vertex identification separately for the cases in which the two vertices are non-adjacent and adjacent. We use these formulas to show that Kemeny's constant always decreases after vertex identification. Future work will focus on establishing tight bounds for Kemeny's constant after these operations. \n\\end{abstract}", "id": "Paper/72757", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72757"}, {"title": " Neutrino Oscillations Through the Lens of Differential Geometry ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "80327613af6011a12fbb40d647634f423e4b9a32e866e4da281ba7784b665ea4", "withdrawn": "", "abstract": "Neutrino oscillations are a more recently discovered phenomenon that have paved the way to new and exciting particle physics by demonstrating that neutrinos do have mass. This project aims to interpret the mechanisms of two-flavor oscillations through differential geometry. By treating the neutrino state and flavor as a trajectory along the curve of a manifold, we can view Hilbert space through the lens of the Bloch sphere  where the physical pure state space lies. As the quantum state evolves, so does the flavor probability. From the two-flavor Hamiltonian, we use Schrodinger's equation to obtain the evolution of state. Then, using the state space manifolds, curves, and geometric phases, the trajectory is evaluated as we pay particular attention to the mixing angle and mass-squared difference. Thus, we are using differential geometry in this project to demonstrate how the traditional matrix formulation of neutrino oscillations can develop the process to incorporate matter and gravitational effects into geometric interpretation.", "id": "Paper/72758", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72758"}, {"title": " Value Sets of Rational Functions over Finite Fields ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "5f372f565fdfad0e129d9d6ba551ccc67bfa882fa1c22e06779e12f0f049240b", "withdrawn": "", "abstract": "Can one construct two functions over a finite field that are not related by linear changes of variables, but nevertheless take exactly the same values over $\\mathbb{F}_{q^k}$ for all $k$? We approach this question through a dictionary between rational functions and finite groups: rational functions arise from fixed fields of certian groups acting on function fields, and relations between their value sets translate into conditions on the cycle structures of the corresponding coset actions. We call $(f,g)$ \\emph{isovalent} if their value multisets agree over every finite extension, and call $(f,g,h)$ \\emph{overlaid} if the value set of $f$ is contained in the union of that of $g$ and $h$ over all finite fields of the same characteristic.\n\nUsing this dictionary, we give an algorithm for constructing isovalent rational functions and overlaid triples and implement them explicitly under certain conditions. We also construct new pairs of isovalent polynomials, classify all overlaid triples under certain conditions, and reduce the conditions to group theoretic ones.", "id": "Paper/72759", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72759"}, {"title": " Digit Probability of Normal Numbers in the Nearest Integer Continued Fractions ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "01f9cfed62fcc7a110c62faae35204a3286a4add40012d70f17b1d4a8cff3b80", "withdrawn": "", "abstract": "The probability distribution for continued fractions is $\\frac{1}{ln(2)} \\frac{1}{1+x}$, found by Gauss. The probability for nearest integer continued fractions is $\\frac{1}{2Log(G)} \\left(\\frac{1}{G+|x|} + \\frac{1}{1+G-|x|} \\right)$, where G is the golden ratio $\\frac{\\sqrt{5}+1}{2}$, discovered by Nakada-Ito-Tanaka. The methods they use cannot be generally extended to more complex continued fraction mappings. We continue their work by creating a transfer operator on the Gauss Map, and use computer computation to calculate a Taylor series for the invariant measure, and search for a simple description like the ones Gauss and Nakada et. al found.", "id": "Paper/72761", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72761"}, {"title": " Mathematical Modeling Enables Characterization and Prediction of Bioadvanced Plant Growth ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "65f83aeeaa350dfe89a6fd32809d7a90216292e4b2192b477079e73db21a9af2", "withdrawn": "", "abstract": "Pennycress (\\textit{Thlaspi arvense}) is a fast-growing winter cover crop with the ability to accumulate critical minerals, such as nickel, directly from soil. This creates opportunities for sustainable mineral recovery while allowing pennycress to grow between traditional food-crop growing seasons. At Oak Ridge National Laboratory (ORNL), the Advanced Plant Phenotyping Laboratory (APPL) uses automated imaging to observe how pennycress responds to varying nickel concentrations. While these experiments provide valuable information about plant growth, they require significant time and resources. Mathematical modeling offers a way to better understand these growth patterns and potentially predict plant behavior before an experiment is complete.\n\nHowever, modeling pennycress growth is challenging because growth trajectories vary across genotypes, nickel treatments, and even individual plants. We analyzed 12 genotypes across six nickel treatments, with five plants per combination, resulting in 360 plants observed over 28 days. Plant growth was quantified using convex area obtained from automated RGB imaging. Logistic, Gompertz, and Weibull growth models were applied at both the genotype-treatment and individual-plant levels and evaluated using root mean squared error and curve similarity. Of the models tested, the Weibull model was most successful in capturing the complex growth trajectories and was further applied to bootstrap-based outlier detection and early growth prediction. Through backtesting, models fit using only the first 21 days of data closely reproduced the complete 28-day growth trajectories. These results demonstrate how mathematical modeling can characterize biological variability while providing reliable predictions approximately one week early, offering a path toward faster and more efficient plant growth experiments.", "id": "Paper/72765", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72765"}, {"title": " Graph Pseudosimilarity and the Classification of Isomorphic Graph Extensions ", "webprogram_exclude": "0", "session_ids": ["Session/19346"], "source_sha256": "58bae9af081b133a24900cb48a57e24b101cb3eab82cda1e832879b9d4570ecf", "withdrawn": "", "abstract": "An automorphism of a graph $G=(V,E)$ can be defined by a permutation of $V$ which preserves edges.  As such, one might hope that the set of isomorphism classes of one-edge extensions of $G$ is determined by the automorphism group of $G$, but this is not the case - it is possible for two one-edge extensions $G+e_1$ and $G+e_2$ to be isomorphic via a map that is not an automorphism when restricted to $G$.  In this case, $G+e_1$ and $G+e_2$ are said to be \\emph{psuedosimilar}.\n\n  This talk introduces a novel framework for studying pseudosimilarity of one-edge and multiple-edge extensions of a graph via \\emph{psuedoautomorphisms}, particular permutations of the vertices of the one edge extension $G+e$. Pseudoautomorphisms behave like automorphisms on $G$ except for distinguished edges or non-edges. In this talk, we demonstrate that isomorphisms of one-edge extensions or one-edge deletions are given exclusively by automorphisms or pseudoautomorphisms. We also give results about the behavior of psudeautomorphisms under composition, demonstrate that edge-extension and edge-deletion classification is equivalent, and generalize to classifying isomorphisms of $n$-edge extensions of a graph.}", "id": "Paper/72766", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72766"}, {"title": " Decoding Polar Affine Grassmann Codes ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "e4867d8519fa001920f66cc506e6f3cbf5a6141a8230a8e24c9dddc9674f2ac2", "withdrawn": "", "abstract": "An Affine Grassmann code is a linear code obtained by evaluating the minors of a generic $l \\times m$ matrix.\n    By imposing an orthogonality contition on elements of the Grassmannian, we obtain the Affine Polar Grassmann code as a subspace.\n    In this talk, we will investigate possible decoding algorithms and methods for determining parity check equations for the Affine Polar Grassmann code. \n    We will look at the special case of invertible symmetric $2 \\times 2$ matrices, and their behaviors under a specific action of the general linear group.", "id": "Paper/72768", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72768"}, {"title": " Triple Linking Number and <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.766ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 760.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">C</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-43\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-43\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-complexes ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "fa325d807ab1fb3a6bce2883d32bb014a9108f07197715cfde9d003f5effbb8e", "withdrawn": "", "abstract": "A C-complex is a union of Seifert surfaces for the components of a link which intersect each other in clasps. The clasp number of a link is the minimal number of clasps amongst all C-complexes it bounds. We present a new lower bound for the number of clasps of all C-complexes bounded by a given 3-component link improving results of Amundsen-Anderson-D.-Guyer. Furthermore, we construct links that achieve these bounds. \nIn order to do so, we express the triple linking numbers as the area bounded by three curves in the plane, called word curves, and then perform the geometry and discrete optimization needed to minimize the length of these curves.", "id": "Paper/72770", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72770"}, {"title": " An Oscillator Semigroup Approach to the Finite Field Howe Correspondence ", "webprogram_exclude": "0", "session_ids": ["Session/19362"], "source_sha256": "8e681dc4d34642132f6976e8ffcc3fc2a13184e60c31ba13d6111a34503c5e71", "withdrawn": "", "abstract": "Let $\\mathbb{F}_q$ be a finite field of odd characteristic, let $W$ be a finite-dimensional symplectic space, and let $(G,G')$ be a classical tensor-product reductive dual pair in $Sp(W)$. We study the centralizing oscillator semigroup $\\Gamma'=\\operatorname{Cent}_{\\operatorname{OSp}(W)}(\\omega_\\psi(G))$, which extends $G'$ by allowing noninvertible operators arising from Lagrangian relations.\n\nWe classify the irreducible complex representations of $\\Gamma'$ and determine their restrictions to $G'$ for the orthogonal--symplectic, symplectic--orthogonal, unitary--unitary, and general linear cases. The classification reduces, via finite semigroup theory (in particular Clifford–Munn–Ponizovskiĭ classification), to representations of smaller classical groups. We then turn to the study of restriction to $G'$. For the type I cases, the restriction problem is reduced to Hecke-algebra calculations attached to certain Harish-Chandra series and yields explicit branching rules, which are multiplicity-free outside a small exceptional case. For the general linear case, related combinatorial operators with Zelevinsky's classification data determine the resulting multiplicities.\n\nIn both orthogonal--symplectic directions, we prove that the oscillator-semigroup operators span the full commutant of the source-group action. Using first occurrence, this identifies the semigroup representations appearing in the Weil representation and reconstructs the finite Howe correspondence. In particular, this work tries to answer the two questions pointed out by Roger Howe in his paper \"Oscillator semigroup over finite field.\"", "id": "Paper/72771", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72771"}, {"title": " Identifying the Optimal Times To Collect Individual Patient Data for a Mathematical Model in Wound Healing ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "1ae3eafad1385d3dae15379679efb1189b0e07cafcc2104016140596c5fc729e", "withdrawn": "", "abstract": "Previously, we developed a mathematical model for wound healing using averaged patient data (Krishna, et al., 2014).  Recently, we obtained the individual patient data and modified the mathematical model.  We used a mixed-effects modeling approach to curve the model to the data.  In this work, we sought to aid clinicians in identifying the best times for collecting data of patients with diabetic foot ulcers.  We performed computational simulations by running an SE-optimal design algorithm (Karimli, 2019).  Our results will be presented and discussed during the poster session.", "id": "Paper/72773", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72773"}, {"title": " An Agent-Based Model of  C. difficile  Transmission Between Hospitals and Communities ", "webprogram_exclude": "0", "session_ids": ["Session/19353"], "source_sha256": "2f6047b9c1e2fa197e8882632d7c55b2f34d1f35e4b506873677ef9043aa9b8f", "withdrawn": "", "abstract": "\\emph{Clostridioides~difficile} (\\emph{C.~difficile}) has traditionally been viewed as a nosocomial infection, but community-associated infections have increased in recent years. We developed an agent-based model using NetLogo to investigate \\emph{C.~difficile} transmission between a hospital and its local community and identify major sources of colonization. The model represents 10,000 individuals moving among a hospital, houses, workplaces, schools, and public restrooms. Individuals can move between four disease classes: resistant, susceptible, colonized (asymptomatic), and diseased (symptomatic). To obtain baseline results, we ran 100 one-year simulations in our community. Then, we implemented various mitigation strategies to see which most decreased incidence of colonization and disease. Preliminary results show that decreasing hospital length of stay is the most effective mitigation strategy for reducing incidence of colonization and disease in both the community and the hospital. Within the hospital, contaminated environmental surfaces are the primary source of colonization, while workplace interactions are the most common cause in the community. Additionally, the mean time for \\emph{C.~difficile} to infiltrate the community from a contaminated hospital is approximately 12 times longer than the mean time for the reverse. Our model demonstrates the potential for hospital-based interventions to reduce the incidence of \\emph{C.~difficile} beyond the hospital setting and highlights the importance of effective cleaning protocols and adherence to these protocols.", "id": "Paper/72774", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72774"}, {"title": " Local Solutions of the Landau-Bose-Einstein Equation with <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.642ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 1137.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">L^p</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-4C\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-70\" d=\"M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-4C\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-70\" x=\"963\" y=\"513\"></use>\n</g>\n</svg> Data ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "7d2a4d2feb32a68c3aa072c46645ab7a645a7d7eb22484cb5a08d7c2a19166c6", "withdrawn": "", "abstract": "We show that solutions to the Landau-Bose-Einstein equation with Coulomb potential exist and are smooth for initial data in $L^p$ for $p > 3$ for a short time depending only on this norm. We thus obtain a continuation criterion: the equation blows up only if all $p > 3$ norms blow up. Our proofs are extensions of the arguments by Arsen’ev and Peskov and by Golding and Loher for the analogous results for the Landau-Coulomb equation, modified to get around various difficulties particular to the Bose-Einstein version, such as the lack of a uniform-in-time ellipticity bound.", "id": "Paper/72775", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72775"}, {"title": " Optimal Control Strategies for  C. difficile  Transmission Between the Hospital and Community ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "0b9857fb61f0954ef8e7e17e5e31ca33529d822914b9732ecdf8900c4e32f909", "withdrawn": "", "abstract": "The United States has seen a recent increase in community-acquired \\textit{Clostridioides difficile} (\\textit{C.~difficile}) infections in recent years. \\textit{C.~difficile} is a bacteria that causes infectious diarrhea and is spread through the fecal-oral route. Infection can lead to life-threatening health complications, such as colon inflammation and infectious diarrhea, particularly among individuals who have recently taken antibiotics, older adults, and immunocompromised individuals. The rise in community-acquired infections highlights the need to better understand how \\textit{C.~difficile} spreads between healthcare and community settings. The literature suggests that individuals leaving hospitals may carry \\textit{C.~difficile} spores into the community, contributing to transmission outside healthcare facilities. Building upon previous work, we developed a system of ordinary differential equations to model \\textit{C.~difficile} transmission between hospital and community settings, including interactions between pathogen-carrying individuals and contaminated surfaces. This study estimates parameters and verifies incidence rates using reported data. Optimal Control Theory is then applied to identify mitigation strategies that reduce \\textit{C.~difficile} transmission while accounting for the costs associated with implementing these interventions. Results provide insight into how interventions can be optimally allocated to reduce \\textit{C.~difficile} infections while minimizing implementation costs.", "id": "Paper/72776", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72776"}, {"title": " Investigating the relationship between APOE and TFAM in Alzheimer’s Disease using RNA sequencing. ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "22100be7910566fa08697fea8bc5c31a86760d49da468758a5d647b2f351263d", "withdrawn": "", "abstract": "Alzheimer's disease (AD) is a neurodegenerative disorder marked by amyloid-beta plaques and tau tangles, along with disrupted glucose metabolism and lipid transport. The APOE4 allele is the strongest common genetic risk factor for late-onset AD, with risk increasing with allele dose: roughly 3-fold in heterozygotes and up to 12-fold in homozygotes. APOE is the brain's main carrier of cholesterol and fats, and APOE4-related transport defects are linked to amyloid accumulation, neuronal loss, and impaired mitochondrial function.\nHow APOE4 connects to mitochondrial dysfunction remains unclear. We test whether APOE4 and TFAM, a nuclear-encoded regulator of mitochondrial DNA transcription and packaging, act through shared molecular pathways. We reprocess publicly available RNA-seq datasets through a uniform pipeline (quality trimming, alignment to the human reference genome, and gene-level quantification), then use differential expression modeling to identify transcriptional changes across studies. By comparing expression patterns associated with APOE genotype and TFAM activity, we are looking for evidence of a joint effect on AD-related gene networks. This analysis aims to clarify whether APOE4 and TFAM act together, rather than independently, in AD pathogenesis.", "id": "Paper/72778", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72778"}, {"title": " Reproducibility, Sensitivity, and Reliability of an Automated Ocean-Contrast Algorithm for SAR Imagery ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "3baa9266f385f455fe2ffc1340f9fe0418e8a5523d3a97764802f8eb8838d919", "withdrawn": "", "abstract": "Synthetic aperture radar (SAR) imagery can identify ocean-surface features, including oil films that appear as radar-dark regions. The current research examines the reproducibility, sensitivity, and reliability of an automated, histogram-based method for estimating ocean contrast from SAR imagery. Using the NASA/JPL implementation, we reproduce the computational workflow and examine how incidence-angle binning, histogram smoothing, and clean-water selection affect estimated damping ratios. We also investigate failure cases and explore diagnostic measures for identifying unreliable clean-water estimates. The study demonstrates how reproducibility and sensitivity analysis can improve understanding of the mathematical and computational assumptions underlying automated remote-sensing algorithms.", "id": "Paper/72779", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72779"}, {"title": " Comparing Mathematical Modeling Techniques to Describe Disease Transmission in Healthcare Settings ", "webprogram_exclude": "0", "session_ids": ["Session/19353"], "source_sha256": "50c7a826d9b7d30e9f336f71602fd6b351006d64681357740018b9594862e29c", "withdrawn": "", "abstract": "\\emph{Clostridioides~difficile} is a leading cause of healthcare-associated diarrhea in the United States, driven by environmentally-persistent spores and interactions between patients, healthcare workers (HCWs), and contaminated surfaces. Mathematical models are widely used to evaluate mitigation strategies; however, their conclusions may depend on structural assumptions. Our research examines whether model structure changes the most influential parameters and resulting mitigation strategies for reducing \\emph{C.~difficile} infection in hospitals. Compared with a previously-developed model that represents HCW and environmental contamination as average levels, our newly-developed compartmental model classifies these vectors as contaminated or uncontaminated. Using systems of ordinary differential equations, we compare colonization pathways across both models to assess whether influential parameters and mitigation recommendations are robust or sensitive to modeling structure.", "id": "Paper/72780", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72780"}, {"title": " Transformer-based Partial Differential Equation Solvers ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "8c90d5782cf3344cbf48583042f602488aa2197fb94bb2997ba07fa4ccc2d5a1", "withdrawn": "", "abstract": "Transformers have revolutionized fields such as natural language processing (NLP) by\nmodelling sequences of words, namely texts, with use cases like predicting the next word in the\nsequence. Transformers model sequences of vectors by implementing an attention mechanism,\nwhich provides global information to the feedforward neural network by processing each vector\nand its relevance to the rest of the sequence. Solving partial differential equations (PDEs) is\ncrucial to many STEM fields, but traditional numerical methods can be computationally\nexpensive. Traditional numerical methods to solve PDEs often rely on using local information,\nrequiring many computations to construct a solution for the PDE. Integral transformations such\nas the Fourier transform and Laplace transform are useful when solving PDEs through\neigenfunction expansions of solutions. The attention mechanism in the transformer can be\ninterpreted as a learned discretization of a continuous integral transformation. We propose\ntransformer-based PDE solvers by implementing an attention mechanism to learn an integral\ntransformation for an initial-boundary value problem. The model takes an initial condition as\ninput. The learned discretized integral transformation is used by the feedforward neural network\nto predict the state of the solution up to a specific time step. We explore this transformer-based\napproach by using training data produced by analytical solutions and\nCrank-Nicolson approximations for $n$-harmonics.", "id": "Paper/72781", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72781"}, {"title": " Modeling the Effects of Electric Cars on Air Quality Using Differential Equations ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "dd84450e53df02b2451159bfee6924ec08c48e596cce01655d56a625dd112a6e", "withdrawn": "", "abstract": "This project models the atmospheric transport of CO₂ and PM2.5 pollutants to assess how electric vehicle adoption may affect air quality in San Francisco. Using a diffusion-advection equation that incorporates wind speed, weather effects, and measured source terms, numerical solutions are obtained in MATLAB. Results show that diffusion alone is insufficient to represent pollutant movement; the advection term is essential for capturing wind-driven transport. Comparisons between 2022 and 2025 source data reveal changes in concentration patterns, supporting the need for both diffusion and advection in realistic air-quality modeling.", "id": "Paper/72783", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72783"}, {"title": " Predicting the occurrence of Braess paradox in the synchronization threshold of coupled oscillator systems ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "9d7f3a0d8f98ed077a0820f1b68fc9061bcb88954c6d3faa55d49c9bd4d2f128", "withdrawn": "", "abstract": "Braess-type paradoxes in coupled oscillator networks where the addition of an edge to the network leads to an increase in the critical coupling required for the existence of a stable phase-locked synchronized solution.  By introducing a continuous edge-weight parameter and constructing an augmented system that allows application of the Implicit Function Theorem, we derive an explicit first-order formula for the sensitivity of the critical coupling, $K'_c(0)$, to small changes in the network structure.  This formula reveals that an edge is locally Braess if the ordering of the oscillators being coupled is opposite the ordering of their components in the critical eigenvector at the saddle-node bifurcation, providing a simple criterion for Braess paradox to occur.  We then employ this local approximation as a predictor for the occurrence of Braess paradox when the edge is fully incorporated in the network.  This prediction is tested numerically in several classes of random networks, demonstrating both high predictive fidelity and the nonlinear limitations of the local approximation.  We also examine several explicit examples, highlighting possible motifs by which Braess-type paradoxes occur. Together, these results establish a predictive framework for understanding how incremental changes in network topology can produce counterintuitive synchronization outcomes.", "id": "Paper/72784", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72784"}, {"title": " The Edge-to-Edge Tilings of the <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.395ex\" height=\"1.676ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -576.1 600.5 721.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">n</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-6E\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-Branched Cover of the Sphere by Regular Polygons (Preliminary Report) ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "381ad500629aaba34c7cc531ba8f6e8bc19ab37d325589ce7770baf1a531da2d", "withdrawn": "", "abstract": "In 1967, Zalgaller completed the classification of  all convex polyhedra composed of regular polygons. Since tilings of the 2-sphere correspond to circumscribable convex polyhedra, this proved that the edge-to-edge tilings of the 2-sphere by regular polygons are the projections to the sphere of the five Platonic solids, the 13 Archimedean solids, the 25 circumscribable Johnson solids, and the infinite families of prisms and antiprisms. In this paper, we prove that any tiling of the $n$-branched cover of the 2-sphere by regular polygons is a lift of one of these 2-sphere tilings, a gyration and/or diminishing of a lifted Platonic or Archimedean tiling, or is in one of the following new families of tilings: sunflower tilings, ice cream cone tilings, chrysanthemum tilings, or the radioactive tiling.", "id": "Paper/72788", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72788"}, {"title": " The Cheeger Inequality for the Non-Backtracking Spectrum ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "e3e06e6685dd184b574a98919190053448195452274ecd303f256a0c90acd9c5", "withdrawn": "", "abstract": "In this presentation, we will show our research on the relationship between the Cheeger constant and eigenvalues derived from non-backtracking walks. Our studies largely focus on the eigenvalues from non-backtracking walk transitional probability matrices in the edge space, which has a complex spectrum. We will discuss our findings defining the Gap from unity in various ways, such as the gap from 1 by modulus, the largest real eigenvalue, the eigenvalue with the largest real part, and the distance to 1.", "id": "Paper/72789", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72789"}, {"title": " Graph Learning for Financial Time Series]Graph Learning for Financial Time Series: A Regressor-Based Approach ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "ae8dc86a627e865da6bd55b67299ee2e6f152c7d9e32bfc47bd4052b7319df6a", "withdrawn": "", "abstract": "Financial markets are shaped both by broad macroeconomic trends and asset interactions. Traditional financial-factor frameworks usually capture known drivers, and graph-based methods reveal latent relationship structures; yet most existing approaches are either static or ignore external regressors. We propose a unified framework for modeling asset log-returns by jointly estimating the regression coefficients of known economic factors and the asset-network Laplacians over time. We develop a one-lag convex learning algorithm and a higher order polynomial-lag formulation to estimate changing market graphs. Applying the framework to historical U.S. financial data, we compare connectivity and regressor dynamics during the 2008 Global Financial Crisis and the COVID-19 crisis. The 2008 crisis exhibits particularly pronounced fragmentation across sectors, with financial companies showing stress earliest. Overall, we observe that the learned graphs reveal increased connectivity and structural instability during the different financial crises. We also evaluate a regressor-free application in which the learned graph basis is used to smooth covariance estimates for minimum-variance portfolios. In a 200-week nested walk-forward study, Graph-LW reduces realized variance relative to Ledoit--Wolf by 1.5--9.5\\% across 12-, 24-, and 36-stock universes. These results suggest that regressor-aware graph learning is useful for market analysis, providing both interpretable crisis diagnostics and benefits for portfolio risk management.", "id": "Paper/72790", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72790"}, {"title": " Modeling Time-Resolved Photoluminescence in Perovskite Nanocrystals with Systems of Nonlinear Ordinary Differential Equations ", "webprogram_exclude": "0", "session_ids": ["Session/18238"], "source_sha256": "713c9a5bcb631f160335a8eac78908965b68feea50cfc19cf65e26539643f7a7", "withdrawn": "", "abstract": "Photogenerated electrons in perovskite nanocrystals can recombine radiatively and nonradiatively. Understanding these recombination processes is important for improving the efficiency of materials used in applications such as solar cells, lasers, and photodetectors. Experimentally measured time-resolved photoluminescence provides a window into electron dynamics in these nanocrystals. Mathematical modeling with nonlinear differential equations is necessary to uncover the underlying mechanisms of recombination. Here, I will present how I used ODEs to model first- and second-order recombination processes. I will show how I extracted material parameters by fitting the solutions of the ODE systems to experimentally measured data. The first-order model depends on the proportions of the populations rather than the total population, so normalizing the populations does not affect the results. However, the second-order model depends on the actual populations. Keeping the initial electron population, \\(N_e(0)\\), instead of normalizing it to 1 allows the model to retain this information and directly relate it to the experimentally measured quantum yield.", "id": "Paper/72792", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72792"}, {"title": " Planar Quadratic Vector Field Conjugacy Applied to Koopman Eigenfunction Transport ", "webprogram_exclude": "0", "session_ids": ["Session/19363"], "source_sha256": "d3052cf907c69c8d6c02422aa16cab268efdfb0aaac5680126df63f8056d3b1d", "withdrawn": "", "abstract": "Nonlinear polynomial differential equations are rarely solvable in closed form, but a conjugacy can transfer exact solutions and Koopman eigenfunctions from a well-understood system to one that has not yet been solved. We study when such conjugacies can exist between planar polynomial vector fields. Our main tool is the divergence fingerprint, an object built from the divergence of a vector field and its successive derivatives along the the vector field's flow. The amount of independent information contained in this fingerprint divides the conjugacy problem into several regimes. Depending on the regime, we can determine a unique rational conjugacy candidate, place explicit bounds on the complexity of a conjugator--resulting in a finite computational search for a conjugacy, identify exceptional cases where no universal bound is possible, or produce explicit obstructions to conjugacy. We then apply the framework to the solvable radial family studied by Morrison and Petrovic, targeting a general-coefficient quadratic family. Using Mathematica and Macaulay2, we derive coefficient conditions under which a unique invertible polynomial conjugacy between these two systems exists, construct that transformation, transport the known Koopman eigenfunctions from the radial family onto the target general-coefficient quadratic, and obtain explicit formulas for the target trajectories \\(x(t),y(t)\\). The result is a concrete family of quadratic systems whose exact dynamics can be recovered through conjugacy.", "id": "Paper/72793", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72793"}, {"title": " Propagation Time for Fault Tolerant Zero Forcing ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "00cdb9251cfca8a01235a7e36a222d9a425327340464924e1c838a84af834359", "withdrawn": "", "abstract": "Zero forcing is an iterative graph coloring process that studies propagation time through vertex networks while highlighting optimization problems on graphs. If an initial blue vertex has exactly one white vertex neighboring it, the blue vertex forces that white neighbor to turn blue. Fault tolerant zero forcing adds to this process by ensuring that complete graph coloring is achieved even if any one vertex of the initially blue vertices from the forcing set is turned white. Propagation time refers to how many iterations it takes for a zero forcing set to force a graph. In this talk, we explore how propagation time behaves across various graph structures and discuss the differences between standard and fault tolerant propagation time.", "id": "Paper/72795", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72795"}, {"title": " Fault Tolerant Forcing and Graph Operations ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "c45754245208df43d7891a9ef4515ba37556bf741c30b1b081d7ed267544e4c4", "withdrawn": "", "abstract": "Zero forcing is a graph theory coloring process in which we begin with a set of initially blue vertices on a graph. The color change rule allows a blue vertex with exactly one white neighbor to force that neighbor to become blue. Fault tolerant zero forcing is an extension of the zero forcing process that preserves the ability to color the entire graph even after the removal of any single blue vertex from the initial forcing set. In this talk, we study fault tolerant zero forcing under graph operations, including joins, vertex sums, coronas, and Cartesian products. We examine how these operations affect fault tolerant zero forcing sets and use properties of the original graphs to understand the resulting graphs.", "id": "Paper/72796", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72796"}, {"title": " Sensitivity of Stellar Structure to the Polytropic Index in the Lane–Emden Model ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "808714fcae661c362dbb0eb02fd7875d081c345f3873f3ba404cd85dd96c5aa3", "withdrawn": "", "abstract": "The Lane–Emden equation models the structure of a spherically symmetric, self-gravitating polytropic star. In the current research, we combine analytical and numerical methods to investigate how stellar structure changes with the polytropic index (n). We validate a numerical solver using known exact solutions and compute quantities including the stellar surface, dimensionless mass, moment of inertia, and central concentration. We then derive and numerically solve a sensitivity equation with respect to (n), allowing us to study how small changes in the polytropic index affect the modeled stellar radius and other global structural quantities. This approach provides a computational framework for exploring parameter sensitivity in classical stellar models.", "id": "Paper/72803", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72803"}, {"title": " Hypergeometric Solutions to Coupled Klein-Gordon Equations in Cosmology with Small Field Excursions ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "b9edae004b2b7e9780eca98183a8e915aaec53181f10eace5bdc8d674b9d2dd3", "withdrawn": "", "abstract": "The Klein-Gordon equation is a second-order differential equation that arises in the study of particle physics. In cosmology, the Klein-Gordon equation for a field can explain the physics of inflation, or the early evolution of the universe. An analytical solution to the Klein-Gordon equation in this context has been produced. The solution was produced in the small-field excursion approximation and was written in terms of the confluent hypergeometric limit function. It is often the case in particle physics and cosmology that we would like to consider multiple interacting fields. Thus, we generalize the details of this calculation such that two interacting Klein-Gordon equations may be considered. With minimal assumptions, we show that the solution of this coupled system can be written in terms of Kummer's confluent hypergeometric limit function. Numerical calculations of the solution to this coupled system are carried out to compare to our analytic results and discuss the areas where the solutions agree and where they diverge.", "id": "Paper/72808", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72808"}, {"title": " Modeling Competition Outcomes Between Species in Shared Habitats ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "352664df98b5b4c0f2819055e7725ac77195694f3ea77a9e8a559f635c4d6f0a", "withdrawn": "", "abstract": "Understanding the role of dispersal strategy in competition is of interest in population ecology - particularly in the presence of habitat fragmentation and habitat loss. Classical theory predicts that for two competing populations in a spatially heterogeneous environment, the slower disperser will competitively exclude the faster disperser. In the current work, we consider a novel model of a “faster” dispersing species, competing with a “slower” disperser, each modeled with linearized p-Laplacian diffusion. We explore this competition in the context of a two-patch system, where species disperse between two patches of differing resource availability. We show that - while the fast disperser loses in the case of linear diffusion - if both dispersers diffuse non-linearly, the result depends on various factors such as diffusion and cross diffusion rates. Several numerical simulations are conducted to confirm our analytical findings and explore parameter regimes where we observe local stability.", "id": "Paper/72809", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72809"}, {"title": " On the Feasibility of Hybrid Variational Quantum Circuits for Reducing the Energy Footprint of AI Foundation Model Training ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "fce4181f70caecc22d03e2d0ea54398599731cc6a22547eb9d6af196231cabd8", "withdrawn": "", "abstract": "The rapid expansion of artificial intelligence infrastructure has driven an unprecedented surge in computational demand. Training frontier AI models requires hyper-scale data centers that aggregate thousands of heterogeneous accelerators, a process that remains intensely energy-demanding and creates massive thermal loads that constrain future scaling. This paper evaluates the feasibility of quantum machine learning (QML) as a mechanism to mitigate the energy and time expenditures of classical training paradigms. We investigate hybrid variational quantum circuits (VQCs) integrated into benchmark Transformer-style architectures to assess their capacity for lowering energy per epoch and accelerating convergence compared to equivalent classical baselines. This study systematically maps the operational boundary conditions—quantified by problem scale, required circuit depth, and hardware error rates—under which a genuine quantum energy advantage can be realized. Furthermore, we identify critical bottlenecks where current noisy intermediate-scale quantum (NISQ) hardware limitations preclude immediate practical benefits in hyper-scale environments. Ultimately, this work provides a foundational scalability framework for decoupling AI infrastructure expansion from unsustainable grid energy consumption.", "id": "Paper/72811", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72811"}, {"title": " Classification of El Ni˜no–Southern Oscillation Phases via Euler Characteristic Curves and Machine Learning ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "1668730adca4d600db3825f234f1c89f51b2b923023514e190c37f49a87e59cb", "withdrawn": "", "abstract": "The El Niño–Southern Oscillation (ENSO) is a recurring Pacific climate pattern traditionally monitored through the Oceanic Niño Index (ONI), a single-valued summary of sea surface temperature (SST) anomalies. We propose Euler characteristic curves (ECC), a descriptor from Topological Data Analysis (TDA), as an alternative representation that retains richer structural information from SST fields. Using monthly SST data (1950--2022) from a tropical Pacific region obtained from NOAA, we computed an ECC for each monthly field and labeled it as La Niña, Neutral, or El Niño according to the ONI. The resulting curves were used as features to train and compare three classifiers (logistic regression, Support Vector Machine (SVM), and XGBoost). The SVM classifier achieved the best performance, with ROC-AUC scores of 0.87 (La Niña), 0.70 (Neutral), and 0.86 (El Niño). These results show that ECCs capture topological structure in SST fields that is informative for distinguishing ENSO phases, suggesting a promising complement to existing index-based approaches for climate monitoring.", "id": "Paper/72812", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72812"}, {"title": " A New Metric to Differentiate Polycrystalline Microstructures ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "50d9d661120e31a663027d9cdcc4592e86655ff7aaefd6dfc8d47df27c1faa7d", "withdrawn": "", "abstract": "The microstructure of a polycrystalline material is characterized by the geometry, arrangement, and orientation of its grains, features that all strongly influence a material’s physical properties. Advances in imaging technology allow us to accurately view these structures as micrographs with visually distinct grain morphologies. To enable a more quantitative analysis of the morphology of a microstructure, we view the grain boundary network as an embedded graph. Using this abstraction, we introduce the Volume Exchange Metric (VEM): a distance between micrograph windows defined by the minimum amount of area swept out to transform one grain boundary network to another. This area is motivated by the physical energy dissipated for such a transformation, to which it is proportional. We apply the VEM by building off of previous work by Miley et al. where they represent a microstructure as a probability distribution of windows sampled from a micrograph. The advantage of their method is that it enables statistical comparison of material micrographs by their local geometries. To compare microstructures, we define a distance between window distributions by employing a modified Wasserstein distance with the VEM serving as a physically informed cost function. We empirically validate this approach on a dataset of five synthetically generated microstructures with distinct grain boundary configurations. Our results show that this method can reliably distinguish microstructures even with a relatively small number of sampled windows and can be used as a standard for downstream microstructure validation procedures.", "id": "Paper/72814", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72814"}, {"title": " Autoregressive Discovery of Symbolic Ordinary Differential Equations with Iterative Refinement ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "eed94c40e5b4531a11affc9282074f1166860079c865330a269ff93f9a9c568c", "withdrawn": "", "abstract": "Differential equations are a natural language for many dynamical systems, concisely expressing symmetries, invariants, and fundamental principles. Given raw experimental data, recovering these governing laws can therefore offer greater interpretability and generalizability than traditional black-box methods. We introduce ODEqGPT: a transformer-based approach to this inverse problem. Inspired by EqGPT's approach to partial differential equations, we train a transformer to autoregressively generate symbolic equations without coefficients, which are fit separately. Generated candidates are scored on accuracy and sparsity, and a fine-tuning loop reinforces top structures. Compared to library-based sparse regression, we demonstrate that ODEqGPT's sequential generation adapts to highly coupled or noisy systems and can reach terms absent from pre-training. ODEqGPT outperforms E-SINDy in both recovering ground-truth systems and producing stably integrable outputs. We explore a warm-start strategy---seeding the initial pool with results from standard algorithms like SINDy and its variants. These provide a strong but static approximation with no direct method for subsequent revision, while ODEqGPT excels at iterative refinement but can struggle to converge from its pre-trained state. Across synthetic benchmarks, we find that seeding ODEqGPT's search with SINDy can accelerate convergence to correct terms. BODEqGPT extends this framework to allow complex biological dynamics, namely rational kinetics with nonlinear coefficient fitting, demonstrating the versatility of these generative models in adapting to specific classes of equations.", "id": "Paper/72815", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72815"}, {"title": " Graph-based Approach to Hyperspectral Unmixing ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "9d22cb05ebe93577f66d90dfd47d5144a42ce8f1fcc23e20f20768ad26b951a4", "withdrawn": "", "abstract": "Due to limited spatial resolution, hyperspectral images often contain pixels composed of multiple materials, resulting in mixed spectral signatures. Hyperspectral unmixing (HSU) aims to identify the constituent materials (endmembers) and estimate their relative proportions (fractional abundances). In this work, we propose Graph-ALMM, a framework that combines active learning and graph-based learning from Graph-Regularized Semisupervised Unmixing (GRSU) with a modified Augmented Linear Mixing Model (ALMM). Graph-ALMM jointly updates the endmembers, incorporates labeled nodes during abundance estimation, replaces ($L_1$) with ($L_{1/2}$) regularization to promote sparsity, and introduces an improved termination criterion. We evaluate Graph-ALMM on four hyperspectral datasets; Jasper Ridge, Urban4, Apex, and Samson; in terms of endmember identification and abundance estimation. Results show that Graph-ALMM outperforms ALMM while achieving performance comparable to GRSU, and demonstrates robustness to elevated noise levels.\n\nThis project was funded by NSF grant 2326840.", "id": "Paper/72816", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72816"}, {"title": " Semisimplification of Schur Algebras in Positive Characteristic ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "3ce3392294b8f8183f48d180a463104468b1e1b0bbeb310475cece2b1a28ef68", "withdrawn": "", "abstract": "We show that, by working in the symmetric tensor category $\\mathcal C = \\mathrm{Rep}\\ k[t]/(t^p)$ over an algebraically closed base field of characteristic $p > 2$ and applying the semisimplification functor to the Schur algebra $S(X,d)$ with $X = mJ_1 \\oplus nJ_{p-1}$, we obtain exactly the Schur superalgebra $S(m|n,d)$ when $d<p$, and extra generators when $d \\geq p$. Moreover, we show that these extra generators are Frobenius-twisted coordinate functions on the Jacobson radical of the centralizer of $t$ acting on $X$. Because the extra generators form a nilpotent ideal, we also deduce that the simple modules over $\\overline{S(X,d)}$ are exactly those inflated from $S(m|n,d)$. Finally, we extend these results to the coordinate ring $\\mathcal O(\\mathrm{GL}(X))$, showing that its semisimplification is obtained from that of $\\mathcal{O}(\\mathfrak{gl}(X))$ by inverting the image of the determinant.", "id": "Paper/72817", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72817"}, {"title": " Bipartite Extremal Numbers of Trees ", "webprogram_exclude": "0", "session_ids": ["Session/18159"], "source_sha256": "13b5bcc5df387d9bda81b987f957b0b27bd7011740d66fc5e16177faaaa930e8", "withdrawn": "", "abstract": "Recently, the classical Erd\\H{o}s--S\\'os problem was resolved. We study a restriction of this problem, the extremal number of trees, to the class of bipartite host graphs when the two part-sizes are fixed. In other words, the Zarankiewicz problem for trees. We give natural lower-bound constructions and formulate a clean corresponding upper-bound conjecture. We apply a simple weighted variant of $k$-minimality to prove upper bounds for a broad family of trees including brooms, trees with part-sizes obeying certain inequalities, and all trees on at most seven vertices, resolving a problem of Caro, Patk\\'os and Tuza up to additive constants.", "id": "Paper/72818", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72818"}, {"title": " Graded <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"0.802ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 345.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">i</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-69\" x=\"0\" y=\"0\"></use>\n</g>\n</svg>-domains, valuation overrings, and integral extensions. ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "7536ed90e06781c2d077f6a3053390ab5785bbb5460db49af7a21f25335d81aa", "withdrawn": "", "abstract": "An integral domain $R$ is an $i$-domain if for every overring $S$ of $R$, the map $\\operatorname{Spec}(S) \\to \\operatorname{Spec}(R)$ is injective. Ira J. Papick showed that $R$ is an $i$-domain if and only if $R \\subseteq V$ is an $i$-extension for every valuation overring $V$ of $R$ and $R \\subseteq \\overline{R}$ is an $i$-extension, where $\\overline{R}$ is the integral closure of $R$. He also showed that if $T$ is an $i$-domain integral over $R$, then $R$ is an $i$-domain whenever $T$ is local or $R$ is integrally closed. In this paper, we explore graded analogues of both results.", "id": "Paper/72821", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72821"}, {"title": " PDE Modeling of Data Center Treatment Infrastructure and Carbon Impact: A Virginia Case Study ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "91eecf5688b3c3f0107b786f18acffb1848fcf404dab3b33dfb71f3a02664b25", "withdrawn": "", "abstract": "The rapid expansion of data centers in Northern Virginia increases regional water and energy demands and associated carbon emissions. This study develops a spatial advection-diffusion model to quantify direct facility energy use and Scope 3 indirect impacts from municipal water supply and wastewater systems. By integrating facility-level water-use data with regional utility and meteorological data and EPA eGRID emission factors, the model evaluates water infrastructure, IT operations, cooling systems, and other major energy demands. Simulation analyses identify upstream utility operations and raw water intake as major contributors to indirect impacts. The framework provides a mathematical approach for assessing the environmental impacts and future infrastructure demands associated with regional data center growth.", "id": "Paper/72822", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72822"}, {"title": " Statistical Linearization for Nonlinear Absorber Tuning ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "d2dc87dbd907caa85382de2dabbf61a13f6f2a1f311de5db303c230f8fd5019b", "withdrawn": "", "abstract": "We study whether statistical linearization could help design a nonlinear mechanical vibration absorber that experiences correlated random forcing. A damped primary oscillator was coupled to a smaller mass through a damper and a spring with linear and cubic hardening stiffness. We modeled the forcing as an Ornstein–Uhlenbeck process and got a system of stochastic differential equations. Using a Gaussian approximation, we replaced the nonlinear restoring force with an effective stiffness determined by the response variance. We calculated stationary covariance predictions and compared them with a standard linear approximation and Monte Carlo simulations of the nonlinear system. Across a range of forcing strengths and correlation times, we evaluated predicted root mean square displacement and the effectiveness of selected damping values. Statistical linearization accurately predicted vibration levels and determined damping values that resulted in substantial vibration reduction within the tested parameter range.", "id": "Paper/72823", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72823"}, {"title": " Wavelet-Based Machine Learning for Detecting Power-Grid Disturbances Induced by AI Data Centers ", "webprogram_exclude": "0", "session_ids": ["Session/19345"], "source_sha256": "fab9029694718c8cc6da2be1fe496b0b43a889d0ecd71e71b4fc40810d816273", "withdrawn": "", "abstract": "The rapid growth of artificial intelligence has increased demand for large-scale data centers, introducing highly variable electrical loads that produce rapid fluctuations and oscillatory behavior in power-grid signals. Detecting these disturbances is critical for grid reliability, yet conventional time-domain and Fourier-based methods struggle to represent transient events whose frequency characteristics vary over time. This project investigates whether wavelet-based machine learning provides a more effective representation for detecting and classifying multiscale power-grid disturbances associated with AI data-center loads. Voltage, frequency, and power-demand time series will be decomposed using the discrete wavelet transform into components at different time and frequency scales. Statistical and energy-based features extracted from wavelet coefficients will serve as inputs to machine-learning classifiers. Performance will be compared against models trained on raw time-series and Fourier-based features, using classification accuracy, computational efficiency, noise robustness, and temporal-scale discrimination. The objective is to determine whether the localized, multiresolution properties of wavelet transforms offer an advantage in identifying short-duration and oscillatory disturbances caused by rapidly changing electrical loads. By combining wavelet analysis, machine learning, and power-system monitoring, this research explores a mathematical approach to an emerging challenge created by AI infrastructure integration into the electrical grid.", "id": "Paper/72825", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72825"}, {"title": " Detecting Manatees in Consumer Sonar Imagery Using Deep Learning-Based Object Detection ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "1e3bb37afdd1437f450fc232112b5409f2a0e0275aad6ad2e388749f72b7e45d", "withdrawn": "", "abstract": "Manatees commonly live in turbid or tannin-stained waters, where standard visual methods used for other animals in shallow waters become much less reliable. Previous research has shown that side-scan sonar is useful for identifying these manatees in low-visibility areas, though systems used in the past rely on manual review and expensive equipment, which limit scalability and accessibility. This project addresses these limitations by implementing a deep learning-based object detector, which identifies manatees using consumer-grade side-scan sonar imagery. The network uses a Faster R-CNN with ResNet-50 and a Feature Pyramid Network as a foundation, with the anchor box configuration resized to better fit the shape and scale of manatees. A tuned learning-rate scheduler and denoising were also implemented to improve robustness on low-resolution and noisy data. The research is ongoing, with further progress focused on expanding the data pool from 150 to over 500 images for more reliable evaluation and addressing issues from overlapping subjects and variance in scale, particularly for mother-calf pairs. This research has broad utility in monitoring and observation efforts for many species that live in turbid waters, and its goal is to provide a scalable and accessible framework for manatee identification.", "id": "Paper/72826", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72826"}, {"title": " Prescribed-Area Spherical Ramsey Theory ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "b92b24f62cc8162a2b9ca1f53cebd0d4f512ef432b7e659ed17e07c60eb3f8f5", "withdrawn": "", "abstract": "We study a prescribed-area Ramsey problem on the two-dimensional sphere. Let \\(S_r^2\\) be the sphere of radius \\(r>0\\). We prove that, for every \\(k\\in(0,\\pi r^2)\\), every 2-coloring of \\(S_r^2\\) contains a monochromatic spherical triangle of area exactly \\(k\\). This may be viewed as a spherical analogue of Graham's theorem on monochromatic triangles of prescribed area in the Euclidean plane.", "id": "Paper/72827", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72827"}, {"title": " Direct Ink Writing of Helical Structures Using Frontal Polymerization ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "4b5e3eb201ca06dc3c17f33508587954ca39c4df49a507aa625a3ea73b30c13d", "withdrawn": "", "abstract": "Additive manufacturing has become an increasingly important manufacturing approach because it enables the production of complex components while reducing material waste and improving design flexibility (Lewis, 2006; Saadi et al., 2022). Among emerging additive manufacturing technologies, the combination of Frontal Ring-Opening Metathesis Polymerization (FROMP) and Direct Ink Writing (DIW) offers a promising method for rapidly fabricating polymer structures while consuming significantly less energy than conventional manufacturing approaches (Aw et al., 2022; Robertson et al., 2018). This project will demonstrate that combining FROMP with DIW enables rapid, energy-efficient manufacturing of polymer helical springs. Manufacturing efficiency was evaluated by examining how coil diameter and pitch affected printing parameters, spring geometry, and mechanical performance. By optimizing resin rheology and printing parameters by altering the geometric properties of the coil, this research will establish an efficient manufacturing process to produce high-quality springs that serve as building blocks for woven lattice structures.", "id": "Paper/72831", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72831"}, {"title": " Optimizing Functional Similarity and Wiring Cost in Reconstructed Mouse Visual Cortex ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "f3d505b29da5f5258d17116daf912cb74fcea910288257648252ae7a357603f6", "withdrawn": "", "abstract": "Neurons in the visual cortex communicate through synapses. Could rearranging these connections link more similarly responding neurons without increasing wiring cost? We test this question using MICrONS data from the mouse visual cortex.\n\nWe formulate a capacitated transportation linear program in which each neuron keeps its observed incoming and outgoing synapse counts, synapses may only link candidate pairs, and no pair exceeds its capacity. The objective adds up the response similarity of connected neurons once per synapse, using similarities predicted by a digital twin, a computer model of the recorded neurons. Wiring cost is approximated the same way, by adding up the distance between their cell bodies once per synapse.\n\nAcross four projections with 5,370 synapses and 55,042 candidate pairs, whole-synapse optima reach 2.51 to 3.08 times the observed score at 94.2 to 99.6 percent of the observed distance cost. Using linear-programming duality, rational dual bounds match these optima exactly, proving global optimality for the stored coefficients. In each of 62 model variants we tested, an exactly verified two-synapse switch improves both objectives. Requiring each neuron to keep its layer-by-layer synapse totals shrinks the fractional optimization gap by 34 to 57 percent, but whole-synapse improvements remain. We also found improving switches in all 200 stimulus-block bootstrap resamples for each projection.\n\nEarlier work studied how wiring cost trades off against other objectives. We contribute a checkable test of a specific optimality hypothesis that pairs global bounds with explicit full synapse counterexamples. The certificates show that the tested objectives and constraints cannot make the observed wiring optimal. Broader biological conclusions will require data from more animals. We also need to test how well similarity reflects the circuit's function and how well distance reflects its anatomy.", "id": "Paper/72832", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72832"}, {"title": " Asymptotics of Hecke polynomial coefficients on the Atkin-Lehner eigenspaces ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "1ca8d8ecc74318d0e0593fe3bda577edf6f52110f448af612332032cb642801f", "withdrawn": "", "abstract": "Let $S_k^\\sigma(N)$ denote the space of cusp forms of level $N$, weight $k$, and Atkin-Lehner sign pattern $\\sigma$, and $S_k^{\\mathrm{new},\\sigma}$ denote its new subspace. In this paper, we study the asymptotic behavior of the coefficients of the $m$-th Hecke polynomial over $S_k^\\sigma(N)$ and $S_k^{\\mathrm{new},\\sigma}(N)$. In particular, we show that in certain settings, all but finitely many of these coefficients take a particular sign. We also study settings in which the coefficients do not tend to any particular sign.", "id": "Paper/72833", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72833"}, {"title": " Sub Cesaro operators ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "f389a99965ddcd133a84fbf8efbf1a9e3a52a6686017f98b465e6c5410d1bd8b", "withdrawn": "", "abstract": "Sub Cesaro operators are projections of the classical Cesaro operators on some subspaces. They were introduced in 2024 in conjunction with the problem of the boundedness of the Rhaly matrices. Except for some very simple cases the general theory of Rhaly matrices does not apply for this kind of operators. We will discuss their norms, eigenvalues, spectral properties in general, compactness, membership in Schatten ideals and other properties.", "id": "Paper/72835", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72835"}, {"title": " Graph Pseudosimilarity and the Classification of Isomorphic Graph Extensions Poster ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "17d8d77e988d40941b1dd30b4c06f709eb74586dfe0acd6d0402a751bda58607", "withdrawn": "", "abstract": "When looking to determine the isomorphism classes of all one edge-extension of a graph $G$, one may hope to use the information of the automorphism group $G$ to generate all possible maps between its one-edge extensions.  However, this is not the case; it is possible for two one-edge extensions $G+e_1$ and $G+e_2$, $e_1, e_2 \\in E^C$, to be isomorphic via a map that is not an automorphism when restricted to $G$.  In this case, $G+e_1$ and $G+e_2$ are said to be \\emph{psuedosimilar}.\n\nOur research introduces a novel framework for studying pseudosimilarity of one-edge and multiple-edge extensions of a graph via \\emph{psuedoautomorphisms}, particular permutations of the vertices of the one edge extension $G+e$. Pseudoautomorphisms behave like automorphisms on $G$ except for distinguished edges or non-edges.  In   this poster, we introduce our motivating problem for studying pseudoautomorphisms - filtrations of clique complexes - and define the requisites for pseudoautomorphism.  Further, we state a classification theorem for one-edge extension isomorphisms along with other results governing composition of pseudoautomorphisms and generalizations to n-edge graph extensions.\n\n(Note we submitted a abstract to the contributed sessions but wanted to try for a poster as well. If this is not allowed we'd rathre be considered for the PME contributed sessions talk.)", "id": "Paper/72836", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72836"}, {"title": " Mathematical Modeling of CD8 T Cell Responses to Metabolic Therapy in Cancer ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "7ef18c26cb231c6933e5a6ad3d4fc5cb72adb5e973625a1c232abd90ce7a77fa", "withdrawn": "", "abstract": "Glycolysis, the metabolic pathway by which glucose is broken down to release energy, is profoundly upregulated in many cancers, with tumor cells adopting aerobic glycolysis (the Warburg effect) to sustain rapid proliferation while generating a nutrient‑deprived, immunosuppressive microenvironment. This heightened glycolytic demand restricts the metabolic capacity of cytotoxic CD8$^+$ T cells, driving functional exhaustion and enabling tumor progression. Recent work suggests that activating pyruvate kinase M2 (PKM2) can restore T‑cell metabolic fitness, enhance effector function, and promote durable immune memory, positioning PKM2 as a promising target for metabolic immunotherapy. Motivated by these findings, we develop a mathematical framework to investigate the impact of PKM2 activation in metastatic melanoma based on published data from a syngeneic, highly metastatic murine melanoma study. Using published B16‑F10 melanoma growth data, we identify the von Bertalanffy model as the most biologically realistic tumor growth law. We then construct a system of ordinary differential equations describing tumor dynamics, CD8$^+$ T‑cell responses, IFN‑$\\gamma$–mediated immune interactions and the pharmacological activation of PKM2. The model was then extended to incorporate CD8$^+$ T cell memory subsets. To capture the mechanistic origin of PKM2's effects, we further develop a multi-scale extension that couples this population-level framework to an intracellular submodel of glucose uptake, PKM2 conformational dynamics, and ATP production within individual effector T cells, linked to glucose competition and lactate-mediated immunosuppression in the tumor microenvironment. This framework provides a tool for exploring how metabolic interventions may enhance immediate tumor control while supporting long‑term anti‑tumor immunity.", "id": "Paper/72837", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72837"}, {"title": " Weighted Combinatorial Merging ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "362994ff24e01018bdda1361b122b51ee8008342d3a7dfa9d56c6f72cba6b370", "withdrawn": "", "abstract": "This project investigates a weighted extension of a combinatorial merging problem involving vehicles choosing between two lanes. Each arrival sequence is represented by a binary string and corresponds to a lattice path determined by the lanes selected by the vehicles. The goal is to determine how assigning different weights to the possible lane choices affects the number and expected properties of merging paths. In particular, we investigate weighted counts of paths reaching a given point \\((n,m)\\) and the expected length of the right lane under different weighting schemes. This problem connects combinatorial enumeration with probability and provides a generalization of the unweighted model. The approach uses lattice-path methods, generating functions, and computer simulation to derive and analyze weighted formulas.", "id": "Paper/72838", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72838"}, {"title": " Computing the Hilbert Measure for Non-Coregular Representations of the Special Orthogonal Group ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "f865373058e36bc411fb8e410c4c9ce03c1311a4057516219e89b92787b3f1bb", "withdrawn": "", "abstract": "The elements of the Lie group $SO(m)$ rotate points in the $m$-dimensional space $\\mathbb{R}^m$. Given a collection of $k$ vectors in $\\mathbb{R}^m$, the invariant polynomials are generated by the dot products and determinants of these vectors. If we want to integrate a function of these $k$ vectors that is invariant under the $SO(m)$-action, we can take advantage of these invariants to simplify our integral. Specifically, we can change variables to these invariants to reduce the number of variables we’re integrating over. In order to do this we need a function called the Hilbert measure that connects the integral in terms of the original coordinates to the integral in terms of the invariants. We will present computations of the Hilbert measure for the cases of $k$ points in $\\mathbb{R}^m$ that have a property called non-coregularity.", "id": "Paper/72839", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72839"}, {"title": " <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.55ex\" height=\"2.176ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -791.3 667.5 936.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbb {Z}</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJAMS-5A\" d=\"M39 -1Q29 9 29 12Q29 23 60 77T219 337L410 648H364Q261 648 210 628Q168 612 142 588T109 545T97 509T88 490Q85 489 80 489Q72 489 61 503L70 588Q72 607 75 628T79 662T81 675Q84 677 88 681Q90 683 341 683H592Q604 673 604 666Q604 662 412 348L221 37Q221 35 301 35Q406 35 446 48Q504 68 543 111T597 212Q602 239 617 239Q624 239 629 234T635 223Q635 215 621 113T604 8L597 1Q595 -1 317 -1H39ZM148 637L166 648H112V632Q111 629 110 622T108 612Q108 608 110 608T116 612T129 623T148 637ZM552 646Q552 648 504 648Q452 648 450 643Q448 639 266 343T77 37Q77 35 128 35H179L366 339L552 646ZM572 35Q581 89 581 97L561 77Q542 59 526 48L508 37L539 35H572Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJAMS-5A\" x=\"0\" y=\"0\"></use>\n</g>\n</svg> Orbifold Euler Characteristics of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"6.305ex\" height=\"2.843ex\" style=\"vertical-align: -0.838ex;\" viewBox=\"0 -863.1 2714.5 1223.9\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\text {SO}(n)</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMAIN-53\" d=\"M55 507Q55 590 112 647T243 704H257Q342 704 405 641L426 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<use xlink:href=\"#E1-MJMATHI-6B\" x=\"0\" y=\"0\"></use>\n</g>\n</svg> Copies of <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.897ex\" height=\"2.343ex\" style=\"vertical-align: -0.338ex;\" viewBox=\"0 -863.1 1247.1 1008.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">\\mathbb {R}^n</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJAMS-52\" d=\"M17 665Q17 672 28 683H221Q415 681 439 677Q461 673 481 667T516 654T544 639T566 623T584 607T597 592T607 578T614 565T618 554L621 548Q626 530 626 497Q626 447 613 419Q578 348 473 326L455 321Q462 310 473 292T517 226T578 141T637 72T686 35Q705 30 705 16Q705 7 693 -1H510Q503 6 404 159L306 310H268V183Q270 67 271 59Q274 42 291 38Q295 37 319 35Q344 35 353 28Q362 17 353 3L346 -1H28Q16 5 16 16Q16 35 55 35Q96 38 101 52Q106 60 106 341T101 632Q95 645 55 648Q17 648 17 665ZM241 35Q238 42 237 45T235 78T233 163T233 337V621L237 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7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJAMS-52\" x=\"0\" y=\"0\"></use>\n <use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMATHI-6E\" x=\"1021\" y=\"581\"></use>\n</g>\n</svg> ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "18457f0a6b979e31109a2d36834f700be6ef11a2b476f9dc98ac22d2fc13d437", "withdrawn": "", "abstract": "Given a representation of a Lie group, the $\\mathbb{Z}$-orbifold Euler characteristic describes not only the shape of the underlying group, but also the orbits and isotropy groups that emerge from the group action. Our research concerns representations of $\\text{SO}(n)$ acting on $\\mathbb{R}^{kn}$ via $k$ copies of the defining representation. In particular, we provide an explicit formula in terms of $k$ for $\\text{SO}(4)$ acting on $\\mathbb{R}^{4k}$ while detailing the general method to compute the characteristic for an arbitrary choice of $n$ and $k$.", "id": "Paper/72841", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72841"}, {"title": " Adversarial Quantum Memory as an Information-Theoretic Resource in BB84 ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "f36d18abcdcf1c190cf859abd83e68a807b467552f9022048434806336ade925", "withdrawn": "", "abstract": "Quantum key distribution (QKD) is a secure communication method that implements a cryptographic protocol based on the laws of quantum mechanics; contrary to classical communication, QKD relies on quantum mechanics rather than the unproven mathematical difficulty of complex algorithms that standard classical cryptographic protocols rely on. In the standard BB84 QKD protocol, Alice sends quantum states from randomly chosen incompatible bases, and Bob later measures them. The no cloning theorem prevents an eavesdropper (Eve) from measuring incoming photons as her measurement will change the quantum state introducing errors detectable by Bob when Alice publicly reveals her measurement basis. A more powerful attack is when Eve could store Alice’s quantum information in a quantum memory device and wait for Alice to reveal her computational basis. In practice, quantum memories are subject to decoherence, limiting the amount of information that can be retained. Understanding how these physical limitations affect the usefulness of quantum memory to an adversary provides a natural connection between quantum information security and the physics of realistic quantum storage.\n\nThis project investigates the role of an imperfect eavesdropper's quantum memory in the BB84 protocol by modeling their stored quantum information as an open quantum system. The strength and duration of the storage noise are varied to model quantum memories with different coherence properties. By comparing strategies in which an eavesdropper must perform an immediate measurement with strategies in which quantum information is stored and measured only after relevant classical information becomes available. The performance of these different methods are examined by looking at the quantum bit error rate observed by Alice and Bob, the amount of information available to the eavesdropper, and the corresponding effect on the achievable secret-key rate. This allows for a systemic analysis of when delayed quantum measurement provides an appreciable advantage and when decoherence eliminates that advantage.", "id": "Paper/72843", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72843"}, {"title": " Wave Singularity and Scattering for a Damped Dispersive Equation ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "b40bf803136e82e6eaf3f6c26fe039ddc37dfc1616162aa2f934185411b2023b", "withdrawn": "", "abstract": "This project investigates a damped nonlinear Schr\\\"odinger equation with an external electromagnetic field, modeling phenomena in geometric optics and Bose-Einstein condensation. \nWe examine the critical dynamics of this non-Hamiltonian system, \nspecifically analyzing whether minimal-mass singular solutions exist. \nBy studying the wave field's analytical behavior, including blow-up, mass concentration, and energy distribution, we reveal how external fields and damping control singularity formation and scattering. \nOur approach relies on spectral analysis paired with a generalized \\(\\mathcal{A}\\)-transform associated to the external potentials.  Similar result for the nonlinear Klein-Gordon equation is also included.", "id": "Paper/72844", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72844"}, {"title": " Modeling Natural Tree Branching Using Graph Theory and Computational Methods ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "061586c47a84883e73e89f1111b3e0435fbe165d2e03501369987060a9d3561f", "withdrawn": "", "abstract": "Modeling Natural Tree Branching Using Graph Theory and Computational Methods\n\nTrees have branching patterns that can be studied using graph theory. This project looks at how the branching structure of real trees can be represented as mathematical graphs and analyzed using computer algorithms. In the graph, branch junctions are represented by vertices and the branches connecting them are represented by edges.\n\nThe project will look at properties such as the degree of each vertex, path lengths, and the overall branching structure of different trees. Computer programs will be used to create and analyze these graphs and compare the structures of different trees. The project will also examine how well a mathematical graph can represent the branching patterns found in real trees.\n\nThis project combines graph theory and computer science to study a structure found in nature. The goal is to use mathematical and computational methods to find patterns in how trees branch and to better understand how a natural tree can be represented as a mathematical tree.", "id": "Paper/72845", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72845"}, {"title": " SASI: Semantically Annotated Spans for Inference ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "28ccce27b0d2014ad7a3c5464cc93b3f3e8835d6a064604612a4d22e3512f313", "withdrawn": "", "abstract": "Can semantic annotations make language-model pretraining more efficient when the final model must process ordinary text? We study this question using paired brackets inserted around linguistically meaningful spans in a historical encyclopedia corpus of approximately 85,000 sentences. The annotations identify 94 span types, including proper nouns, adjective phrases, and possessive pronouns, amongst many others. They provide structured information during training without changing the text used for final evaluation.\n\nWe compare nanoGPT-style transformer models under the same total training-token budget. The control model is trained entirely on unannotated text. The transfer model processes annotated text for 70\\% of its token budget, then continues training on unannotated text for the remaining 30\\%, retaining its learned parameters. Both are evaluated on held-out clean text, with no annotation system needed at inference time. Because the two conditions use different tokenizers, we compare their predictive performance in bits per byte (BPB) rather than per-token loss.\n\nAcross five held-out data splits, transfer achieves lower BPB than the control on every split. Mean BPB decreases from 1.3971 for the control to 1.3481 for transfer, a 3.5\\% relative reduction. These results suggest that span annotations can serve as temporary training scaffolding: a model can benefit from structured text during pretraining while ultimately operating on raw text. Our comparison controls for the number of training tokens processed, but does not establish equal computational cost. It is limited to one small encyclopedia corpus and one model configuration; tests on other domains, model sizes, and independent training runs are needed to assess generality.", "id": "Paper/72846", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72846"}, {"title": " Analysis of Null-Bounded LFCA Reversibility Using Generalized Toeplitz Systems  ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "e8c1b2f6e03302c5d5672c0cac5d049a4e53d26aa67d6cfa6fb2640c8ccfef8b", "withdrawn": "", "abstract": "Linear finite cellular automata (LFCA) are discrete dynamical systems consisting of a finite lattice of cells, a finite alphabet of possible cell values, and a local update rule that determines each cell’s value over discrete timesteps. A state of the LFCA assigns an element of the alphabet to each cell, and the collection of states evolves under an evolution map. This evolution map acts as a group homomorphism on the set of states. Boundary conditions, including null and periodic boundaries, can significantly affect the system’s dynamics.\nWe investigate the reversibility, transient states, and periodic structures of null-bounded LFCA whose local rules depend on 2 cells (2-rule LFCA). We define the rule difference, Δ, as the difference between the indices of these cells. To study reversibility, we consider the kernel of the evolution map. The equations formed on this kernel create a linear system with a Toeplitz representation, allowing us to analyze reversibility through the parameters of the automaton.\nFor these null-bounded systems, we vary cell count, alphabet, and rule difference to analyze their dynamical behavior. Our results establish that a null-bounded LFCA is reversible when its rule depends on the target cell, while monodirectional rules depending on neighboring cells produce transient states leading into periodic cycles. For the remaining omnidirectional case, we conjecture a complete characterization under null boundary conditions: the LFCA is reversible if and only if Δ divides the cell count m, independent of the initial state. These results characterize how the parameters of null-bounded LFCA determine their reversibility and periodic structure.", "id": "Paper/72847", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72847"}, {"title": " On Support of Temperley-Lieb Immanants of Ribbon Decomposition Matrices ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "d703e00e380900c57c9a1069cda7b6888f97e3fa7f6fc19f29643766c17f4a2e", "withdrawn": "", "abstract": "A 2005 result of Rhoades and Skandera establishes that Temperley--Lieb immanants, a subset of the dual canonical basis, are Schur-positive when evaluated on Jacobi--Trudi matrices. In 2025, Nguyen and Pylyavskyy established a Littlewood--Richardson rule for Temperley--Lieb immanants of Jacobi--Trudi matrices via \\emph{shuffle tableaux}. This rule was later extended to Temperley--Lieb immanants evaluated on \\textit{ribbon decomposition matrices}, a class of matrices which subsume several classical determinantal formulas for skew Schur functions, including the Jacobi--Trudi, Giambelli, and Lascoux--Pragacz identities.\n    \n    In 2026, Yevtushenko proved that for a restricted class of shapes, the Schur supports of Temperley--Lieb immanants of the corresponding Jacobi--Trudi matrices have a maximal element with respect to the dominance order. He conjectured that the Schur support contains both maximal and minimal elements with respect to the dominance order for all shapes. We resolve and generalize Yevtushenko's conjecture by proving that the Schur supports of Temperley--Lieb immanants of all ribbon decomposition matrices contain maximal and minimal elements, each appearing with coefficient one.", "id": "Paper/72848", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72848"}, {"title": " Area Deficit and Angle Variance for Reuleaux Polygons ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "5c3858905781c2c63d6f0f8128a50e995fc7f951f0ab34e6df85be30504b0158", "withdrawn": "", "abstract": "Reuleaux polygons are planar shapes of constant width bounded by circular arcs. For odd $n$, Firey-Sallee theorem states that the regular Reuleaux $n$-gon $R_n$ uniquely maximizes area among Reuleaux polygons of the same width with at most $n$ sides. We quantify this maximality by relating area deficit to the variance of the arc angles. For every odd $n\\ge5$ and every Reuleaux $n$-gon $P$ of width $1$, we prove\n\\[\nA(R_n)-A(P)\\ge\\frac{\\pi}{24}\\mathcal V(P),\n\\qquad\n\\mathcal V(P)=\\frac1n\\sum_{i=1}^n(\\alpha_i-\\pi/n)^2,\n\\]\nwhere the $\\alpha_i$ are central arc angles in radians. The coefficient $\\pi/24$ is optimal among constants valid simultaneously for all odd $n\\ge5$. The proof utilizes a support-function identity, a strengthened Jensen inequality, and vertex-splitting constructions which establish sharpness of the uniform constant. For every fixed $n$, we give explicit bounds $L_n\\le C_n^*\\le U_n$ on the optimal global constant and show that $C_n^*\\to\\pi/24$ as $n\\to\\infty$ through odd integers. In particular, $0.1418<C_5^*<0.2042$, so $C_5=0.14$ is globally valid. There is also a complementary second-variation argument that shows rigid motions are the only null directions at the regular polygon. As nonregular pentagons approach the regular pentagon modulo rigid motions, we get\r\n\\[\r\n\\frac{A(R_5)-A(P)}{\\mathcal V(P)}\r\n\\longrightarrow\\frac12\\tan(\\pi/5)\\approx0.363.\r\n\\]\r\nThis is a local asymptotic coefficient and not a global constant. We conjecture, with numerical experiments, that $C_5^*=U_5\\approx0.2041$, the value approached by degeneration to a Reuleaux triangle. However, this equality remains unproved.", "id": "Paper/72851", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72851"}, {"title": " Implementing Fast Khovanov Homology in C ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "7e9b6553845ecdee57829e6edca9c255aeea8d2a2ba70bdc5ec9eb112c434adc", "withdrawn": "", "abstract": "Khovanov homology is a knot invariant that categorifies the Jones polynomial, but direct computation is limited by the $2^n$ states in the cube of resolutions. Bar-Natan's Fast Khovanov homology algorithm reduces this cost in practice by constructing the complex locally and repeatedly simplifying it using delooping and Gaussian elimination. We implement this scanning approach in C, based in part on the architecture of JavaKh but using concrete C representations for the smoothings, cobordisms, linear combinations, and differential matrices required by the computation. The program constructs and simplifies tangle complexes one crossing at a time, supports integral and finite-field coefficients, and accepts braid, planar-diagram, and Dowker--Thistlethwaite inputs through a common pipeline. We validate the implementation against independently tabulated Khovanov homology. The C implementation is intended to reduce memory and runtime overhead and to support computations on a larger scale, and we evaluate its performance relative to existing implementations. One target application is to extend computations to prime knots with 18--20 crossings and, where feasible, beyond, while comparing the distinguishing power of Khovanov homology with that of the Jones and HOMFLY-PT polynomials.", "id": "Paper/72853", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72853"}, {"title": " A sharp uniqueness threshold for a nonlocal Riemann–Hilbert problem and pole-free inverse scattering for the continuum Calogero–Moser equation ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "3260575768a4e6ed60357331aa304582af1f24126f2d4eac2f3bd23ff8730d1d", "withdrawn": "", "abstract": "The focusing continuum Calogero–Moser equation is an integrable nonlocal PDE whose direct scattering theory leads to a nonlocal Riemann–Hilbert inverse problem. I prove a sharp threshold for unique solvability. For continuous scattering data $\\beta$ with $|\\beta|_2^2\\le 4\\pi^2$, the normalized pole-free problem has a unique solution for every spatial point. This threshold is optimal: smooth compactly supported data with norm arbitrarily close to $4\\pi^2$ from above can produce nonuniqueness. At the critical norm uniqueness still holds for every datum, but the inverse norm can become arbitrarily large; below threshold, I obtain a universal quantitative bound depending only on the distance to criticality. For smooth compactly supported $\\beta$, the inverse reconstruction yields a rapidly decaying smooth potential $q$ with nonnegative Fourier support, satisfies the exact mass identity $|q|_2^2=(2\\pi)^{-1}|\\beta|_2^2$, recovers the prescribed reflection coefficient, and has no point spectrum. Combining this inverse theorem with the linear scattering evolution $\\beta(t,\\lambda)=e^{-i\\lambda^2 t}\\beta(0,\\lambda)$, I obtain a global pole-free inverse-scattering solution of the continuum Calogero–Moser equation. Thus $4\\pi^2$ is simultaneously a sharp uniqueness threshold and a conditioning threshold for the inverse problem.", "id": "Paper/72854", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72854"}, {"title": " How Many Directions Determine a Shape? Finite Reconstruction with the Euler Characteristic Transform ", "webprogram_exclude": "0", "session_ids": ["Session/19352"], "source_sha256": "5b740437cb253112f08f94f4a86386236dfdce25810bb691d2ca34db8d9a781d", "withdrawn": "", "abstract": "The Euler Characteristic Transform (ECT) studies a shape by sweeping it with hyperplanes in different directions and recording the Euler characteristic of each sublevel set. Although the transform is defined using every direction, results of Curry, Mukherjee, and Turner show that, under suitable geometric conditions, finitely many directions can be enough to determine a shape.\n\nIn this talk, I will introduce the ECT through directional height functions and Euler characteristic curves, explain why it can distinguish and reconstruct embedded shapes, and examine the geometric ideas that make finite directional reconstruction possible. The broader goal is to illustrate how topology can turn geometric reconstruction into a question about how much information is actually necessary to describe a shape.", "id": "Paper/72857", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72857"}, {"title": " Smooth Space-Filling Hypersurfaces of n-Dimensions ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "6dffe9b76a5e8294b3db7be3fd71cdc08157c5e9d8608411b9360d7f7428dd9e", "withdrawn": "", "abstract": "We study space-filling hypersurfaces in the projective space over a finite field $F_q$, where q is a prime power. Building on the work of the Homma-Kim paper (2013) that characterized the smoothness of all space-filling curves in the 2-dimensional projective space with linear algebra techniques, we investigated varieties of Tallini's space-filling homogeneous polynomial generators over the n-dimensional projective space ($P^n$). We develop a method of construction of a space-filling hypersurface in $P^n$ from an (n+1)\\times(n+1) square matrix, investigate its smoothness when the matrix is diagonal or companion, and show by induction the existence of smooth n-dimensional hypersurfaces for any n, using properties of finite fields, linear recursion techniques, and some abstract algebra. This is a joint work with Han-Bom Moon, Erick Perez, and Amelia Warren.", "id": "Paper/72860", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72860"}, {"title": " Recovering Cycle Pairings in Plane Cactus Graphs ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "dfd594a1b15e7bb4e6bdcc8cea4b9df095c11a835216e35273ae92e4e5390bd0", "withdrawn": "", "abstract": "We study plane cactus graphs, a class of graphs in which no edge belongs to more than one cycle. One-sided Betti curves record the cycle extrema but forget how those extrema are paired. We ask how many additional slab measurements are needed to recover that missing pairing information. There are two ways to choose the slab widths: all at once, or one at a time using the results of earlier measurements. We show that this choice matters. With $n$ cycles, an adaptive strategy needs exactly $n-1$ measurements in the worst case, while a nonadaptive strategy can require on the order of $n^2$.", "id": "Paper/72862", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72862"}, {"title": " Fixed Points in the Sukhatme Luce Model: A Quantitative Poisson Approximation ", "webprogram_exclude": "0", "session_ids": ["Session/19370"], "source_sha256": "1238b646b63bf9a4297c3b57ff212f381ce57bcb5037789be97fc8a0698d6883", "withdrawn": "", "abstract": "For a uniform random permutation, the number of fixed points converges to a Poisson distribution with mean one. We study how this changes in the highly nonuniform Sukhatme Luce model. Labels $1,\\ldots,n$ are drawn without replacement; at each step, a remaining label $i$ is chosen with probability proportional to its weight $n-i+1$. A fixed point occurs when label $i$ is drawn in position $i$.\n\nBorga, Chatterjee, and Diaconis conjectured that the fixed-point count diverges and asked whether Poisson behavior persists after suitable rescaling. We prove that its mean is $e^{-1}\\log n+O(1)$ and that its distribution is within $O(\\log\\log n/\\sqrt{\\log n})$ in total variation of a Poisson distribution with parameter $e^{-1}\\log n$. This gives a quantitative answer to their question and yields a law of large numbers and a central limit theorem: the count grows logarithmically, with asymptotically Gaussian fluctuations on the scale $\\sqrt{\\log n}$.\n\nThe proof uses independent exponential clocks to represent the random permutation. Grouping nearby clock rates into blocks reduces the problem to uniform random matchings, while concentration estimates control the resulting Poisson parameter.\n\nThese conclusions are stable under perturbations of the weights. After reversing the labels, write the perturbed weights as $r_j$. For fixed $A<\\infty$ and $0\\leq\\gamma<1/2$, the same mean asymptotics and total variation error bound hold uniformly whenever $j/2\\leq r_j\\leq2j$ and $|r_j-j|\\leq Aj^\\gamma$.", "id": "Paper/72868", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72868"}, {"title": " Optimizing Pyranim Play ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "4102fe4e027cb061896a2849cdb87ba544aa0c9d4edc6dcb1aab5fd2bbbee616", "withdrawn": "", "abstract": "For this 2-player Nim game, first studied by Curran et. al in 2022, you start with an $n$-tier pyramid of chips. Player 1 goes first, and can take any chip that does not have two chips above it. Upon doing so, it will also remove all chips supported by the removed chip. Player 2 does the same with the modified pyramid and play continues until the final chip is taken, and the last to take a chip is the winner. We will utilize methods from combinatorial game theory and graph theory centered around the study of Nim games---a class of games that are well studied under optimal play strategies and classification (Sprague-Grundy Theorem). We conjecture an optimal play strategy using ``nimbers'' associated with the aforementioned nim games. Results stem mainly from directed acyclic graphs and Dyck paths, both of which are integral to our studies of this game.", "id": "Paper/72870", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72870"}, {"title": " The Mathematics of Consciousness: Synchronization Thresholds in Cortical Networks ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "3f8554076cd2a846c84d26a011fc61fb00cadc8abaacb8dc4ed092a5907aa22d", "withdrawn": "", "abstract": "Conscious perception emerges when sensory information becomes globally available across cortical networks through widespread neural synchronization (Dehaene \\& Changeux, 2011). Yet quantitative predictions of the coupling strength required to induce global synchrony remain limited.\n\nI analyzed synchronization dynamics in cortical networks by applying the Kuramoto model for coupled phase oscillators (Ermentrout \\& Kopell, 1991). Each cortical region is treated as a gamma-band oscillator (30--80 Hz) with natural frequency $\\omega$ drawn from a distribution $g(\\omega)$, specifying the relative probability of oscillators at each frequency. I examined transitions from asynchronous to synchronous states by deriving the critical coupling threshold $K_c$, the minimum coupling strength required for global synchrony, and validated predictions using simulations of cortical networks.\n\nMathematical analysis yields $K_c = \\frac{2}{\\pi g(0)}$, where $g(0)$ is the frequency distribution at the mean. For Lorentzian-distributed frequencies with spread $\\gamma$, this simplifies to $K_c = 2\\gamma$, showing that the coupling threshold increases linearly with frequency variability. For modular networks simulating distinct cortical areas, local synchrony can occur even when inter-region coupling is weak ($K_{\\mathrm{out}} < K_c$). This corresponds to unconscious processing, where information is confined to specialized regions. Global synchronization requires strong inter-region coupling exceeding $K_c$, interpreted as conscious awareness.\n\nI applied this mathematical framework to schizophrenia, where reduced gamma-band synchrony and structural dysconnectivity suggest diminished effective interregional coupling (Uhlhaas \\& Singer, 2010). The model predicts that coupling near the critical threshold produces unstable synchronization and impaired global integration, providing a quantitative mechanism for cognitive deficits and disorganized thought. Overall, the framework links network synchronization dynamics to conscious perception and psychopathology (Tononi et al., 2016).", "id": "Paper/72871", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72871"}, {"title": " Motzkin Numbers Count 2-Stack-Sortable Permutations Ending in Their Least Entry ", "webprogram_exclude": "0", "session_ids": ["Session/17693"], "source_sha256": "891e4465b80a526a72a5126fd0645b609072f6ac5e9c6e869277ca041e8582e9", "withdrawn": "", "abstract": "We prove the following conjecture of Zhang (arXiv:2604.10779, Conjecture 6.1): for $n \\geq 0$, the number of $2$-stack-sortable permutations of $\\{0,1,\\dots,n\\}$ ending in $0$ is the $n$th Motzkin number. By Zhang's result, there is a bijection between $2$-stack-sortable permutations ending in their least element and standard composition tableaux of width at most $2$. We then show bijectively that there are an equal number of these and standard Young tableaux of width at most $3$, which are known to be counted by the Motzkin numbers.", "id": "Paper/72872", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72872"}, {"title": " Ricci Flow on Asymptotically Locally Hyperbolic Manifolds ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "1d8f1112b6f5a8d74c43f48bbe3fbcaae24f1613664cb5bcca6deb633bccc8ce", "withdrawn": "", "abstract": "We study asymptotically locally hyperbolic (ALH) manifolds under the\nnormalized Ricci flow\n$\\partial_tg=-2(\\operatorname{Ric}(g)+(n-1)g)$ in dimensions $n\\geq3$.\nFor complete flows with bounded curvature on compact time intervals,\nwe prove preservation of ALH geometry of order $n/2<\\beta<n$,\r\nwith an admissible reduction in the H\\\"older exponent, together\r\nwith preservation of weighted scalar-curvature integrability.\r\nWe derive evolution estimates for asymptotic staticity and establish\r\nan exponential evolution law for the reference-adjusted\r\nWang--Chru\\'sciel--Herzlich mass. For flows with nonnegative scalar\r\ndeficit and nonzero initial charge, this yields a terminal-mass\r\ncharacterization of finite-time singularities.\r\nWe further prove that complete expanding Ricci solitons in the\r\nfinite-end ALH class are Einstein under the prescribed decay and\r\nintegrability assumptions. Finally, we develop corrected-mass\r\ndissipation and Einstein-defect energy estimates to establish\r\nrigidity of ancient ALH flows in certain cases, showing that\r\nthese flows are stationary Einstein metrics.", "id": "Paper/72876", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72876"}, {"title": " Form uniqueness for graphs with weakly spherically symmetric ends ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "e326461bf6f7c516cfe4f899269867c9fe74fb315fd4e7307483ed8df0a1504d", "withdrawn": "", "abstract": "We give characterizations for the failure of form uniqueness on weakly spherically symmetric graphs. The first characterization is in terms of the graph structure, the second involves the capacity of a Cauchy boundary. We also discuss the stability of form uniqueness and give characterizations for graphs which, following the removal of a set, consist of a disjoint union of weakly spherically symmetric graphs.", "id": "Paper/72877", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72877"}, {"title": " Asymptotics of Hypergraph Fuss-Catalan Numbers ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "43fa65c85c6c13ed019fb2792d1b4e76d29fbdc52d9dde2155ecc01fe1840614", "withdrawn": "", "abstract": "The Catalan numbers $C_n$ admit two well-studied generalizations: the Fuss-Catalan numbers, which count plane trees of fixed arity, and the hypergraph Catalan numbers of Gunnells, which count walks on uniform hypertrees. This paper concerns their common refinement, the hypergraph Fuss-Catalan numbers $FC_n^{(r,m)}$. We give combinatorial interpretations of each of these families in terms of plane trees and walks on hypertrees. We then describe the weighted degree of a vertex by means of Euler tours, associating to each tour a transition assignment and its transition digraph; this factors the weighted degree of a uniform hypertree as a product over its degree sequence. A bijection between $FC_1^{(r,m)}$ and circular Smirnov words yields the generating function of $FC_n^{(r,m)}$ and expresses it as a sum over rooted plane hypertrees, from which we obtain an all-order asymptotic expansion of $FC_n^{(r,m)}$ for every $m\\ge 2$; at $r=1$ this extends the first-order asymptotic of Hainzl to all orders. We further define two analogs of the Narayana numbers for the Fuss-Catalan numbers and determine their closed forms.", "id": "Paper/72879", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72879"}, {"title": " A Combinatorial Perspective on the <svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.943ex\" height=\"2.343ex\" style=\"vertical-align: -0.671ex;\" viewBox=\"0 -719.6 1267.2 1008.6\" role=\"img\" focusable=\"false\" xmlns=\"http://www.w3.org/2000/svg\" aria-labelledby=\"MathJax-SVG-1-Title\">\n<title id=\"MathJax-SVG-1-Title\">q,t</title>\n<defs aria-hidden=\"true\">\n<path stroke-width=\"1\" id=\"E1-MJMATHI-71\" d=\"M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMAIN-2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"></path>\n<path stroke-width=\"1\" id=\"E1-MJMATHI-74\" d=\"M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z\"></path>\n</defs>\n<g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" aria-hidden=\"true\">\n <use xlink:href=\"#E1-MJMATHI-71\" x=\"0\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMAIN-2C\" x=\"460\" y=\"0\"></use>\n <use xlink:href=\"#E1-MJMATHI-74\" x=\"905\" y=\"0\"></use>\n</g>\n</svg>-Catalan Polynomials ", "webprogram_exclude": "0", "session_ids": ["Session/18238"], "source_sha256": "473ef7809f0be4e9c0b7c7812eb95b39dc06cb487c314907125e82e5f80e2f8a", "withdrawn": "", "abstract": "A central open problem in algebraic combinatorics is to find a direct combinatorial proof of the symmetry\n$$ C_n(q,t)=C_n(t,q). $$\nLee, Li, and Loehr proposed approaching this problem by organizing Dyck paths into global chains along which area decreases by one while dinv increases by one. Han, Lee, Li, and Loehr later developed this framework through local chains and tail constructions. Building on this framework, we construct the stable \\(m=0\\) chains by lifting complete segments from lower-deficit chains, assembling them into rooted rails, and continuing their terminal objects into second-order tails. We then extend this architecture to \\(m=1\\), including the first-stable-row corrections, and develop uniform lifting, rail, tail, and counting constructions for general \\(m\\). We conclude with recent progress toward realizing the general-\\(m\\) intrinsic construction inside a compatible global-chain decomposition.", "id": "Paper/72884", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72884"}, {"title": " Impact of Non-Ideal Data Conditions on RCBD Analysis ", "webprogram_exclude": "0", "session_ids": ["Session/17694"], "source_sha256": "c8de18824f3dd1fc48f854326c117ad3d9053574490a020249715416ff631426", "withdrawn": "", "abstract": "Mean separation testing in a randomized complete block design (RCBD) framework is an important step in many data analyses. Many types of undesirable data conditions may affect the outcome of mean separation testing, impacting the inferences drawn from the experiment. Ample research has been conducted on the need for proper data preprocessing, however very little has been recorded on the specific consequences of using data that violate modeling assumptions in different ways. Unequal variance, outliers, and missing values are examples of unwanted conditions observed in real-world experiments. Due to the high frequency of these characteristics, we use analysis of variance (ANOVA) testing to investigate differences between ideal and condition-plagued datasets. We use simulation studies to identify patterns, allowing us to provide recommendations for dealing with each condition. For example, we find mean separation testing to be robust against unequal variances under multiple data transformations. Generating outliers of multiple forms caused our models to be too conservative, potentially increasing the probability of Type II errors. As for missing data, we compare methods of imputation and their impact on mean separation results. Understanding the impact of these methods allows us to provide protocols for others on how to diagnose and combat these issues while conducting randomized complete block designs in a variety of different fields.", "id": "Paper/72888", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72888"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/18011"], "source_sha256": "02832c7acaaf26ae5183660de266d4ccd62b8b5249b59f4428cff4e988eefa70", "withdrawn": "", "abstract": "", "id": "Paper/72892", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72892"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/18315"], "source_sha256": "e8b1f1a313273974e0e02290a70f809094915ac4b55854feec8fb5b9ce2ee634", "withdrawn": "", "abstract": "", "id": "Paper/72893", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72893"}, {"title": "Discussion", "webprogram_exclude": "0", "session_ids": ["Session/18281"], "source_sha256": "d085bdddc9fa27ee65e26a9addf73511c7c92fdccf6fcd9d3eb9c9ced174e070", "withdrawn": "", "abstract": "", "id": "Paper/72895", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72895"}, {"title": "Discussion", "webprogram_exclude": "0", "session_ids": ["Session/18345"], "source_sha256": "411f3b969a2881f4cb1552ba34a5962116347dc5605bb38839ca64928ca54920", "withdrawn": "", "abstract": "", "id": "Paper/72899", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72899"}, {"title": "Discussion", "webprogram_exclude": "0", "session_ids": ["Session/18345"], "source_sha256": "1cb894f6cec9207c08eb912b34609bd9d83a5a4fff4799d2fa6fd3496ddf7f0c", "withdrawn": "", "abstract": "", "id": "Paper/72900", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72900"}, {"title": "Discussion", "webprogram_exclude": "0", "session_ids": ["Session/18345"], "source_sha256": "ba8ab2c8c306cf798bc067941f9a68659a73f8023adde0489a0e72f8ebe5794a", "withdrawn": "", "abstract": "", "id": "Paper/72901", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72901"}, {"title": "Discussion", "webprogram_exclude": "0", "session_ids": ["Session/18352"], "source_sha256": "4392d98810e6f29426c274b014c7af5c0cbe1d3f3869c77fb73c0c7f5d5f026a", "withdrawn": "", "abstract": "", "id": "Paper/72902", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72902"}, {"title": "Discussion", "webprogram_exclude": "0", "session_ids": ["Session/18314"], "source_sha256": "c9e8be55df42337f2e02bb867b8b2085077bf5d2575e8fb3a2f5be71e56f1622", "withdrawn": "", "abstract": "", "id": "Paper/72903", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72903"}, {"title": "Discussion", "webprogram_exclude": "0", "session_ids": ["Session/18443"], "source_sha256": "9f5852d9686a8806bb69c97c5c70c80fb7a2dd4419cdae298bf8205f518ffdc3", "withdrawn": "", "abstract": "", "id": "Paper/72904", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72904"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/17961"], "source_sha256": "6c5d114fe578e7b613bc9e5bae2a4e1495e835b480415ef154119116f5143631", "withdrawn": "", "abstract": "", "id": "Paper/72905", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72905"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/18211"], "source_sha256": "5fd440272f1fe73568de6e06a1daebc0a9e9849bc90176a0020145b336ff5352", "withdrawn": "", "abstract": "", "id": "Paper/72906", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72906"}, {"title": "Break", "webprogram_exclude": "0", "session_ids": ["Session/18212"], "source_sha256": "6f1f37b3ce3659be5229c688c374abc328802179e38b458af1cd2f6715fb58f7", "withdrawn": "", "abstract": "", "id": "Paper/72907", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72907"}, {"title": "Discussion", "webprogram_exclude": "0", "session_ids": ["Session/18208"], "source_sha256": "075c901468a66b5d42e4891e3d4b580691fbeb9dbb89af72acceea16e4d774bf", "withdrawn": "", "abstract": "", "id": "Paper/72908", "source_url": "https://meetings.ams.org/math/jmm2027/meetingapp.cgi/Paper/72908"}, {"title": " Oscillation Theory for Block Jacobi Matrices on Trees \r\n\r\n", "webprogram_exclude": "0", "session_ids": ["Session/17809"], "source_sha256": "3d85c2c4cee4a76fcb52b5f06c3bffed7fb12d6ddf41de705c754219ea11d94c", "withdrawn": "", "abstract": "We study oscillation theory for block Jacobi matrices on tree graphs, connecting eigenvalue counts to sign changes of a solution within a given interval. Here, the role of sign changes is played by the Duistermaat index, an integer-valued topological invariant describing the relative position of three Lagrangian planes in symplectic space. 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