Systems of points with Coulomb interactions. I
Monday October 30, 2023 at 16:00, Tuttleman Learning Center, room 103
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. In the first lecture, we will review these motivations and describe the main results.

Systems of points with Coulomb interactions. II
Wednesday November 1, 2023 at 11:00, Wachman 617
The goal of this lecture is to explain how to analyze the next order behavior of Coulomb gases with temperature, giving information on the configurations at the microscopic level and connecting with crystallization questions. The main results are "local laws", a Large Deviations Principle describing the local limits and Central Limit Theorem for fluctuations in the two-dimensional log case.

Systems of points with Coulomb interactions. III
Wednesday November 1, 2023 at 14:00, Wachman 617
The goal of this lecture is to present the "modulated energy" method that allows to derive the mean-field or effective PDE dynamics for evolutions of systems in Coulomb or Riesz interactions.