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DTSTART;TZID=America/Los_Angeles:20250401T121500
DTEND;TZID=America/Los_Angeles:20250401T131000
DTSTAMP:20260612T120209
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SUMMARY:Permutation pattern avoidance\, alternating sign matrices\, and asymptotics (Justin Troyka\, Cal State LA)
DESCRIPTION:A big area in combinatorics over the last several decades has been the study of pattern-avoiding permutations\, whose enumeration is exciting and mysterious. Alternating sign matrices (ASMs) are a generalization of permutations whose study in combinatorics has also been exciting and mysterious. In this talk\, I will explain some new asymptotic results involving the number of ASMs that avoid a given permutation pattern\, from my joint work with Mathilde Bouvel\, Eric Egge\, Rebecca Smith\, and Jessica Striker. I will also show some of the highlights in the histories of both pattern-avoiding permutations and ASMs.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-justin-troyka-cal-state-la/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20250408T121500
DTEND;TZID=America/Los_Angeles:20250408T131000
DTSTAMP:20260612T120209
CREATED:20250212T050525Z
LAST-MODIFIED:20250407T150550Z
UID:3692-1744114500-1744117800@colleges.claremont.edu
SUMMARY:The ANTC of ChatGPT: On the Mathematical Foundations of Large Language Models (Gizem Karaali\, Pomona)
DESCRIPTION:Large Language Models like ChatGPT rely on surprisingly familiar mathematics. This talk will explore how ideas from (linear) algebra\, number theory and combinatorics  appear — both directly and indirectly — in the structure and behavior of these models. Along the way\, we’ll touch on themes like structure\, symmetry\, and scale\, and consider how abstract mathematical ideas can shed light on systems that process and generate human language. The talk will be self-contained\, and no background in machine learning will be assumed. (This abstract was prepared with the assistance of ChatGPT\, which seems to be remarkably self-aware of its own mathematical foundations.)
URL:https://colleges.claremont.edu/ccms/event/antc-talk-gizem-karaali-pomona-3/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20250415T121500
DTEND;TZID=America/Los_Angeles:20250415T131000
DTSTAMP:20260612T120209
CREATED:20250226T050009Z
LAST-MODIFIED:20250413T154206Z
UID:3715-1744719300-1744722600@colleges.claremont.edu
SUMMARY:Jacobians of tropical curves and finite graphs (Carrie Frizzell\, Scripps)
DESCRIPTION:A Jacobian variety is a principally polarized abelian variety (PPAV) associated with a smooth complex algebraic curve. For dimensions less than or equal to 3\, every PPAV is either a Jacobian or a product of Jacobians. The Schottky problem concerns dimensions 4 and greater: which PPAVs are Jacobians? The Schottky problem can also be posed in the tropical setting\, in which the Jacobian of a tropical curve is a real torus. We will spend most of the talk discussing tropical Jacobians and their discrete counterparts\, but we will also survey a few results related to the aforementioned Schottky problem.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-carrie-frizzell-scripps/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20250422T121500
DTEND;TZID=America/Los_Angeles:20250422T131000
DTSTAMP:20260612T120209
CREATED:20250304T000158Z
LAST-MODIFIED:20250421T175544Z
UID:3727-1745324100-1745327400@colleges.claremont.edu
SUMMARY:Algebraic properties of linguistic structure (Isabella Senturia\, Yale / Caltech)
DESCRIPTION:The recognition that theoretical models of natural language syntax have robust algebraic foundations is longstanding. Both the syntactic structures proposed (trees\, semirings\, etc.) and metrics developed to understand them (the Chomsky hierarchy\, partial orders\, and so forth) closely resemble structures and systems familiar to theoretical mathematicians (groups\, rings\, fields\, …). Despite the underlying mathematical tools\, rarely do structural properties of language get analyzed at an algebraic level. I use two complementary perspectives\, one representational and continuous (spectral graph theory) and one derivational and discrete (Hopf algebras)\, as lenses to explore mathematical properties of linguistic structure. I will also show a connection between the two approaches through a case study on the problem of learning syntactic parameters.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-isabella-senturia-yale-caltech/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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