中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
偏微分方程研讨班
Speaker: Professor Sylvia Serfaty（Sorbonne Université）
Inviter: Nguyen Quoc Hung
Language: English
Title: Statistical mechanics of Coulomb and Riesz gases:I
Time & Venue: 2026年5月27日（星期三）15：00-16：00 & Zoom ID: 373 227 3489/Passcode: AMSS2026
Abstract: Coulomb and Riesz gases are ensembles of points with pair interaction of the form |x|^{-s}, with a confining potential, which arise in classical models for matter, and random matrix theory, among others. We are focused on the range s\in [d-2,d), where d is the dimension, which includes the Coulomb case s=d-2 and the logarithmic cases s=0 in dimensions 1 and 2. In the first lecture, we will describe the mean-field behavior and the relation to the equilibrium measure. We will discuss a Large Deviations Principle which characterizes the local behavior, which connects naturally to crystallization questions of number-theoretic nature.In the second lecture, we will discuss local laws proven by a bootstrap on scales, and fluctuations around the mean-field limit by a transport method.
-------------------------------------------------------------------------
Title: Statistical mechanics of Coulomb and Riesz gases: II
Time & Venue: 2026年5月29日（星期五）15：00-16：00 & Zoom ID: 373 227 3489/Passcode: AMSS2026
Abstract: Coulomb and Riesz gases are ensembles of points with pair interaction of the form |x|^{-s}, with a confining potential, which arise in classical models for matter, and random matrix theory, among others. We are focused on the range s\in [d-2,d), where d is the dimension, which includes the Coulomb case s=d-2 and the logarithmic cases s=0 in dimensions 1 and 2. In the first lecture, we will describe the mean-field behavior and the relation to the equilibrium measure. We will discuss a Large Deviations Principle which characterizes the local behavior, which connects naturally to crystallization questions of number-theoretic nature.In the second lecture, we will discuss local laws proven by a bootstrap on scales, and fluctuations around the mean-field limit by a transport method.
附件：