报告题目：A selection principle for weak KAM Solutions via the Freidlin-Wentzell large deviation principle of invariant measures
报 告 人：Prof. Jianguo Liu (刘建国) (Duke University)
会议时间：2023年12月13日 15:30-17:30
报告地点：包玉书 9号楼113报告厅
报告摘要：Many ideas in weak KAM theory, rooted in Freidlin-Wentzell's variational construction of the rate function of the large deviation principle for invariant measures, are revisited in this seminar. We reinterpret Freidlin-Wentzell's theory from a weak KAM perspective. We will use one-dimensional irreversible diffusion processes on a torus to illustrate essential concepts in weak KAM theory, such as the Peierls barrier, the projected Mather/Aubry/Mane sets, and the variational formulas for both self-consistent boundary data at each local attractor and the rate function. The weak KAM representation of Freidlin-Wentzell's variational construction of the rate function is proved, based on the global adjustment for the boundary data and the local trimming from the lifted Peierls barriers. This rate function provides the maximally Lipschitz-continuous viscosity solution to the corresponding stationary Hamilton-Jacobi equation, satisfying the selected boundary data on the projected Aubry set. The rate function, the selected unique weak KAM solution, serves as the global energy landscape of the original stochastic process. Additionally, a probability interpretation of this global energy landscape from the weak KAM perspective will also be discussed.
报告人简介：1982年获复旦大学数学学士学位，1985年获复旦大学数学硕士学位，1990年获加州大学洛杉矶分校(UCLA)数学博士学位。1990-1991年在伯克利数学研究所做博士后，1991-1993年任纽约大学数学研究所讲师，1993-1997年任坦普大学数学系助理教授，1997-2001年任马里兰大学(UMCP)数学系副教授，2001-2009年任马里兰大学数学系教授，2009年转入杜克大学数学系任教授。现在美国数学会的Fellow。 在数值分析、偏微分方程和计算流体力学方面做了许多出色的工作。
