Rethinking the theoretical foundation of reinforcement learning

Abstract: Given two candidate functions, can we identify which one is the true value function of a large Markov decision process (MDP), given a "benign" dataset? Trivial as it might seem, a version of the question was open for 20+ years in reinforcement learning (RL), and the core difficulties are intimately related to the training instability of modern deep RL. In this talk, I will argue that ...

报告人：Nan Jiang (University of Illinois at Urbana-Champaign)

Frobenius Identities and the Hard Lefschetz Theorem in Combinatorics

Abstract:In 2020, Papadakis and Petrotou gave a proof of the g-theorem, a characterization of the face numbers of simplicial spheres, using a surprising identity in characteristic 2. This identity implies a generic Hard Lefschetz theorem for face rings of simplicial spheres. In this talk, based on joint work with Adiprasito, Oba, Papadakis, and Petrotou, we reformulate these results in commuta...

报告人：Eric Katz (Ohio State University)

The Guo-Jacquet trace formula

Organizer: Huajie LiAbstract: In the mid-eighties, Jacquet introduced a relative trace formula to give a new proof of a famous theorem of Waldspurger on toric periods of automorphic forms on inner forms of GL(2). The so-called Guo-Jacquet trace formula is an expected generalization of Jacquet's relative trace formula, focusing on periods along maximal Levi subgroups of inner forms of GL(n). In ...

报告人：Pierre-Henri Chaudouard (Université Paris Cité)

The asymptotic Plateau problem: past, current progress and future problems

Abstract: The asymptotic Plateau problem is a set of problems in hyperbolic 3-space concerning the existence, multiplicity and applications of minimal surfaces asymptotic to a given Jordan curve on the sphere at infinity. I will address some past results, new progress, and open problems. This is based on joint work with Lowe and Seppi.Bio: Zeno Huang is currently a professor of mathematics at t...

报告人：Zeno Huang （ City University of New York）

Gårding Polynomials and Ideal Structures: Geometry, Convexity, and Applications

Abstract:In this talk, we develop a general theory of Gårding polynomials based on the positive ray test, which provides a geometric framework for studying multivariate polynomials through their positivity regions.We introduce the class of ideal Gårding polynomials, a refinement that recursively incorporates convexity through derivatives. This yields strong structural consequences, including co...

报告人：方浩（The University of Iowa）