Systems of points with Coulomb interactions

Abstract: Large ensembles of points with Coulomb interactions arise in various settings of condensed matter physics, classical and quantum mechanics, statistical mechanics, random matrices and even approximation theory, and they give rise to a variety of questions pertaining to analysis, Partial Differential Equations and probability.

We will first review these motivations, then present the ”mean-field” derivation of effective models and equations describing the system at the macroscopic scale. We then explain how to analyze the next order behavior, giving information on the configurations at the microscopic level and connecting with crystallization questions, and finish with the description of the effect of temperature.

mathematical physicsanalysis of PDEsclassical analysis and ODEscomplex variablesfunctional analysisspectral theory

Audience: researchers in the topic

Harmonic Analysis, Approximation Theory and related topics

Series comments: The talks run on Google Meet. To get the link, please register on the following form sites.google.com/view/athabrazil/updates?authuser=0