UBC Probability Seminar: Aukash Jagannath (Online)

Historically, mean field spin glass models come from the study of statistical physics and have served as prototypical examples of complex energy landscapes. To tackle these questions statistical physicists developed a new class of tools, such as the cavity method and the replica symmetry breaking. Since their introduction, these methods have been applied to a wide variety of problems from statistical physics, to combinatorics, to data science. This course will serve as a high-level introduction to the basics of mean field spin glasses and is intended to introduce the audience to the basic notions that will arise in other courses during the ensuing program. In this first lecture we plan to cover the random energy model, the ultrametric decomposition of Gibbs measures in p-spin glass models and the connection to Poisson-Dirichlet statistics.