Academic Report of School of Mathematical Sciences [2026] No. 008

(Series Report for High-Level University Construction No. 1267)

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

Speaker：Professor Yuzhao Wang (University of Birmingham, Dalian University of Technology)

Time：11:10-12:10, Jan. 17, 2026

Location：Huixing Building 514

Abstract：In this talk, I will discuss recent progress on constructing Gibbs measures and their associated dynamics for nonlinear partial differential equations. In particular, 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 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 advancing the understanding of this field.

Speaker Profile：Professor Yuzhao Wang earned his Ph.D. from Peking University and has long been engaged in theoretical research on partial differential equations. His research findings have been published in leading international journals including Advances in Mathematics, Communications in Mathematical Physics, Proceedings of the London Mathematical Society, Journal of Functional Analysis, Communications in Partial Differential Equations (CPDE), and SIAM Journal on Mathematical Analysis.

Faculty and students are welcome to attend!

Invited by: Hailong Ye

School of Mathematical Sciences

January 16, 2026