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）

Automorphic period and sum of L-values

Abstract: The relative Langlands duality posed by Ben-Zvi-Sakellaridis-Venkatesh predicts that periods of automorphic form can sometimes equal to sum of several special values of automorphic L-functions rather than a single one. In this talk, I will present explicit evidence for this phenomenon. I will discuss families of automorphic periods on general linear groups and classical groups that ar...

报告人：Weixiao Lu (Aix-Marseille Université)

Quantification of ergodicity for Hamilton–Jacobi equations in a dynamic random environment

Abstract: Motivated by the tensionless KPZ equation (a model of stochastic growth), we consider quantitative large-time averages for Hamilton–Jacobi equations in a dynamic random environment that is stationary ergodic and has finite-range dependence in time. In this talk, we establish, up to slowly varying factors, convergence rates with exponent 1/2 for the large-time averages of both the sol...

报告人：Prof. GUO Xiaoqin (郭小钦), University of Cincinnati

Toward Convergent Adam-Type Methods

Abstract:Adam is one of the most widely used optimizers in modern machine learning, but its convergence theory remains incomplete, even in relatively simple convex settings. A central difficulty is that Adam tightly couples momentum and adaptive preconditioning, which hides the dissipative structure needed for a Lyapunov analysis.In this talk, I will describe a Lyapunov-guided approach to Adam-...

报告人：Long Chen (University of California, Irvine)

Advancing Large Language Model Privacy and Efficiency in Federated Learning: Empirical Improvements

Organizer：何俊材Abstract: Federated learning (FL) enables fine-tuning of large language models (LLMs) on decentralized data, but faces two critical challenges: high communication costs and privacy risks. This talk presents two novel methods to address these issues. First, we introduce CG-FedLLM, a communication-efficient FL framework that compresses gradients via a client-side encoder and serv...

报告人：Huiwen Wu (Beihang University, Hangzhou International Innovation Research Institute)