I will present an integral — requiring no character twists — converse theorem for recognizing when is a Dirichlet series with algebraic integer coefficients equal to the L-function of a modular form. This refines the unbounded denominators conjecture of Atkin and Swinnerton-Dyer. Analogies with basic function field arithmetic then suggest a quantitative refinement which precludes a pair of GL(2) automorphic L-functions […]
Estella 2099, Pomona College
610 N. College Ave., Claremont, CA, United States
We especially welcome all undergraduates and graduate students to attend topology seminar! Speaker: Reginald Anderson (Claremont McKenna College) Title: Kontsevich's Recursive Formula for Rational Plane Curves Abstract: Gromov-Witten theory was developed in the 1990s as a curve-counting theory by integrating cohomology classes against a virtual fundamental class for a moduli space of stable maps. One […]
Argue Auditorium, Pomona College
610 N. College Ave., Claremont, CA, United States
Speaker: Yimin Xiao, Professor of Statistics and Probability, Michigan State University Title: Brownian Motion, Random Fractals, and Beyond Abstract: Brownian motion is not only a fascinating object in mathematics but also a powerful stochastic model that has been applied in many scientific fields, from physics to finance, to biological sciences. The sample function of Brownian […]
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 […]
Estella 2099, Pomona College
610 N. College Ave., Claremont, CA, United States
We especially welcome all undergraduates and graduate students to attend topology seminar! Speaker: Scott Taylor (Colby College) Title: Genus 1 Bridge Number of Satellite Knots in Lens Spaces Abstract: In the mid-1950s, Horst Schubert introduced two ideas which turned out to have lasting impact in knot theory: satellite knots and bridge number. A Satellite knot […]
Argue Auditorium, Pomona College
610 N. College Ave., Claremont, CA, United States
Speaker: Scott Taylor, Professor of Mathematics, Colby College, Maine Title: Sums and Symmetries Abstract: Adding is one of the fundamental mathematical operations and we like it so much, we can't […]
Shanahan 1480, Harvey Mudd College
301 Platt Blvd., Claremont, CA, United States
This GEMS session will be facilitated by Professor Bahar Acu from Pitzer College. Title: The Hole Truth: When is a Coffee Mug a Donut? Abstract: In mathematics, topology is the study of properties of shapes that remain unchanged when shapes are bent, stretched, or deformed—so long as they aren’t torn or punctured. To a mathematician studying topology, a […]
Emmy Noether Room, Estella 1021, Pomona College,
610 N. College Ave., Claremont, CA, United States
Title: Randomly pivoted Cholesky: Fast, accurate matrix approximation for scientific machine learning Abstract: Low-rank approximation of positive semidefinite matrices is a basic problem in computational mathematics, with many applications to machine learning and scientific computing. Existing approaches for this problem largely fall into two categories: simple, fast, but sometimes inaccurate methods and sophisticated, slower methods […]
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 […]
Fall 2025 Course Preview Session Moderator: Lenny Fukshansky, Professor of Mathematics, Claremont McKenna College, CA Slide Link: https://docs.google.com/presentation/d/142NF1vUazpGNLF0pfLKc0qhkv4VoMQstSvZ0yKtMfNE/edit?usp=sharing
Emmy Noether Room, Estella 1021, Pomona College,
610 N. College Ave., Claremont, CA, United States
Title: Erlang-Distributed SEIR Epidemical Models Abstract: We examine the effects of different dynamics in epidemiological models, focusing on two key approaches. The first model incorporates reaction-diffusion dynamics, where susceptible individuals avoid areas with high concentrations of infected individuals. The second model divides exposed and infectious individuals into symptomatic and asymptomatic subclasses. Our findings emphasize the […]
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 […]
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