题目: Gibbs measures and Gibbs dynamics for nonlinear dispersive partial differential equations

报告人：王玉昭 (University of Birmingham, UK)

时间: 6月28日下午4:30-5:30

地点：五教5406

摘要: In recent years, there has been significant progress on constructing Gibbs measure and understanding their associated dynamics for dispersive partial differential equations.

I will review how this subject has evolved to its current shape since the seminal work of Bourgain in the 1990s. Bourgain's introduction of the Fourier restriction norm method, rigorous construction of the focusing Gibbs measure, and the invention of the invariant measure argument to globalise local dynamics have been foundational. Recent advancements have been built upon these pillars, with Barashkov and Gubinelli's variational argument, the concept of para-controlled distributions, and Deng-Nahmod-Yue's random average operator and random tensor arguments, further expanding the boundaries of our understanding in this field.