Entropy and Fisher Information in Kinetic Theory
数学专题报告
报告题目(Title)：Entropy and Fisher Information in Kinetic Theory
报告人(Speaker)：Dowan Koo（牛津大学）
地点(Place)：后主楼1124
时间(Time)：2026年7月16日(周四)9:30-11:00；7月17日(周五)10:00-11:30
邀请人(Inviter)：袁迪凡
报告摘要
This short minicourse explores the role of entropy and Fisher information in kinetic theory, ranging from convergence to equilibrium to recent developments in regularity theory. We begin with entropy dissipation and logarithmic Sobolev inequalities, continue with the framework of hypocoercivity and hydrodynamic limits, and conclude with recent advances that exploit Fisher information as a tool for compactness and regularity.
Lecture 1. Entropy: Hypocoercivity and Hydrodynamic limits
(1) Entropy and Dissipation
(2) Logarithmic Sobolev inequalities
(3) Hypocoercivity: large-time behaviour
(4) Hydrodynamic limits: convergence to the compressible Euler equations
Lecture 2. Fisher Information: Compactness and Regularity
(1) Compactness via Fisher information
(2) Monotonicity of Fisher information
(3) Recent developments (Guillen-Silvestre and related works)
(4) Perspectives and open problems
