@inproceedings{78746975a918497a8bf8260203ae330f,

title = "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 give rise to a variety of questions pertaining to calculus of variations, Partial Differential Equations and probability. We will review these as well as “the mean-field limit” results that allow to derive effective models and equations describing the system at the macroscopic scale. We then explain how to analyze the next order beyond the mean-field limit, giving information on the system at the microscopic level. In the setting of statistical mechanics, this allows for instance to observe the effect of the temperature and to connect with crystallization questions.",

keywords = "Coulomb gases, Crystallization, Gaussian Free Field, Jellium, Large deviations, Log gases, Mean field limits, Point processes",

author = "Sylvia Serfaty",

note = "Funding Information: I am very grateful to Mitia Duerinckx, Thomas Lebl?, Mathieu Lewin and Nicolas Rougerie for their helpful comments and suggestions on the first version of this text. I also thank Catherine Goldstein for the historical references and Alon Nishry for the pictures of Figure 4.; 2018 International Congress of Mathematicians, ICM 2018 ; Conference date: 01-08-2018 Through 09-08-2018",

year = "2018",

language = "English (US)",

series = "Proceedings of the International Congress of Mathematicians, ICM 2018",

publisher = "World Scientific Publishing Co. Pte Ltd",

pages = "935--978",

editor = "Boyan Sirakov and {de Souza}, {Paulo Ney} and Marcelo Viana",

booktitle = "Invited Lectures",

}