Systems of points with Coulomb interactions

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.

Biography

Sylvia Serfaty is Silver Professor of Mathematics at the Courant Institute of Mathematical Sciences of New York University. She earned her PhD in 1999 from the Université Paris Sud Orsay, and has held positions at New York University and Université Pierre et Marie Curie (now Sorbonne Université). Recipient of the EMS and Henri Poincaré prizes, plenary speaker at the ICM, she is also a member of the American Academy of Sciences.