Abstract

The generalized Hamiltonian gradient flow is a recently developed important tool for studying irreversible phenomena in Hamiltonian systems. We will focus on the optimal transport problem induced by the generalized Hamiltonian gradient flow, as well as some new developments in the Hamilton-Jacobi equations on measure spaces arising from it. In particular, we will touch upon a series of important issues related to new equilibrium measures beyond the Mather measure, along with some partial results. This work is based on collaborations with Piermarco Cannarsa, Jiahui Hong, Kaizhi Wang, Wenxue Wei, and others. We will also discuss some prospects for the stochastic setting.

Biography

Professor Wei Cheng is the Zhicheng Distinguished Professor at the School of Mathematics, Nanjing University, and serves as the Director of its Teaching Committee. His research lies at the intersection of Hamiltonian dynamical systems, Aubry--Mather theory, the viscosity solution theory of Hamilton--Jacobi equations, mean field game theory, and optimal transport. He has published numerous influential papers in leading international journals, including Publications Mathématiques de l'IHÉS, and his work has had a significant international impact. He has led several national-level research projects, including key projects funded by the National Natural Science Foundation of China (NSFC). He currently serves as an Executive Council Member of the Chinese Mathematical Society.