# Probability and Mathematical Physics Seminar

#### Spin glasses, statistical inference, and Hamilton-Jacobi equations

**Speaker:**
Jean-Christophe Mourrat, NYU Courant Institute

**Location:**
Warren Weaver Hall 1302

**Date:**
Friday, November 1, 2019, 11:10 a.m.

**Synopsis:**

Spin glasses are models of statistical mechanics where a large number of variables interact with one another, with random interactions that can be positive or negative. It is a surprisingly difficult problem to calculate the limit free energy of these models, called the Parisi formula. For a certain class of models, this problem was resolved in a remarkable series of works by Guerra-Talagrand and Panchenko. I will describe a new way to think about this result, which recasts the Parisi formula as the solution of a Hamilton-Jacobi equation. I will then explain how to use this new point of view as a proof strategy in a simpler situation related to the problem of inferring a large rank-one matrix.