報告題目：Nonlinear Schrödinger equations and Gibbs measures - I: finite-dimensional approximation
報 告 人：王玉昭 教授 英國伯明翰大學
報告時間：2024年11月16日，19：00-20：30
報告鍊接：Join Zoom Meeting ID: 869 1846 3254
https://bham-ac-uk.zoom.us/j/86918463254?pwd=y1zgd9MchFtGVo3qvI2mpPjruWJhkL.1
校内聯系人：段犇 bduan@jlu.edu.cn
報告摘要：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.
報告人簡介：王玉昭，英國伯明翰大學教授，博士生導師。 2005年獲吉林大學數學與應用數學學士學位，2010年獲北京大學數學博士學位。自2017年8月起在英國伯明翰大學任助理教授，副教授。王玉昭教授主要從事于無窮維動力系統，随機偏微分方程，調和分析的研究 —— 集中于無窮維動力系統的不變測度，随機波動方程的整體适定性相關問題。
