报告题目：Nonlinear Schrödinger equations and Gibbs measures - I: finite-dimensional approximation
报 告 人：王玉昭 教授 英国伯明翰大学
报告时间：2024年11月16日，19：00-20：30
报告链接：Join Zoom Meeting ID: 869 1846 3254
https://bham-ac-uk.zoom.us/j/86918463254?pwd=y1zgd9MchFtGVo3qvI2mpPjruWJhkL.1
校内联系人：段犇 bduan@jlu.edu.cn
报告摘要：This lecture will consider the nonlinear Schrödinger equation (NLS) and its invariant measures. We will begin by reviewing some basic facts about NLS, such as scaling symmetry, conservation laws, and Galilean invariance. Next, we will demonstrate that it possesses a Hamiltonian structure. To understand this Hamiltonian structure, we will project the NLS into finite-dimensional spaces by truncating its Fourier series. We will provide a detailed construction of the corresponding Gibbs measure and their invariance along the dynamics for the truncated NLS. Finally, we will illustrate how to take the limit as the frequency truncation is removed and discuss the main difficulties in justifying the limits of both measures and dynamics. We will also cover recent developments in the related construction of quantum field theory and the dynamics of random (stochastic) heat, wave, and Schrödinger equations.
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。
