报告题目：Gibbs dynamics for NLS II - Probabilistic Cauchy theory and random tensor argument
报 告 人：王玉昭 教授 英国伯明翰大学
报告时间：2025年1月16日，19：00-20：30
报告链接：Join Zoom Meeting ID: 856 3669 3919
https://bham-ac-uk.zoom.us/j/85636693919?pwd=KWBEyFBSGw13jndDvXFMG3aQTsaLJc.1
校内联系人：段犇 bduan@jlu.edu.cn
报告摘要：
In this lecture, we will discuss random tensor/matrix arguments and their applications in constructing Gibbs dynamics, a field first developed by Deng, Nahmod, and Yue in their seminal 2022 paper in Inventiones Mathematicae, based on Bourgain’s pioneering work from 1996. Random tensor theory has since become a cornerstone of modern probabilistic Cauchy theory for dispersive partial differential equations (PDEs).
Using the two-dimensional cubic nonlinear Schrodinger equation as an example, we will demonstrate how random matrix theory, particularly the noncommutative Khintchine inequality, enables us to manage random operators arising from analyzing the Cauchy problem with random data. Key topics will include renormalization, Bourgain’s trick, random tensor estimates, and essential lattice counting estimates.
This lecture is based on the following papers:
Bourgain (1996) in Communications in Mathematical Physics
Deng, Nahmod, and Yue (2022) in Inventiones Mathematicae
Bringmann, Deng, Nahmod, and Yue (2024) in Inventiones Mathematicae
Liang and Wang (2024) in Communications in Mathematical Physics
报告人简介：王玉昭，英国伯明翰大学教授，博士生导师。 2005年获吉林大学数学与应用数学学士学位，2010年获北京大学数学博士学位。自2017年8月起在英国伯明翰大学任助理教授，副教授。王玉昭教授主要从事于无穷维动力系统，随机偏微分方程，调和分析的研究 —— 集中于无穷维动力系统的不变测度，随机波动方程的整体适定性相关问题。
