報告題目：Measure theory, invariant measures, and Gibbs measures for Hamiltonian systems
報 告 人：王玉昭 教授 英國伯明翰大學
報告時間：2024年11月2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：In this lecture, we will cover measure theory, with a particular focus on the Gaussian measure on infinite-dimensional Hilbert spaces, such as $H^s$. We will then proceed to discuss invariant measures. Following this, we will explore the Hamiltonian system and its associated Gibbs measures. The lecture will conclude with examples of linear and nonlinear finite-dimensional systems (both deterministic and stochastic) that preserve the Gibbs measure, offering valuable insights into the behaviour of their infinite-dimensional counterparts. In particular, these examples serve as prototypes for nonlinear Schrödinger equations, wave equations, and stochastic partial differential equations.
報告人簡介：王玉昭，博士，英國伯明翰大學副教授, 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
