Mathematics Colloquium

Mean-field disordered systems and Hamilton-Jacobi equations

Speaker: Jean-Christophe Mourrat, Courant Institute of Mathematical Sciences

Location: Warren Weaver Hall 1302

Date: Monday, March 2, 2020, 3:45 p.m.


The goal of statistical mechanics is to describe the large-scale behavior of collections of simple elements, often called spins, that
interact through locally simple rules and are influenced by some amount of noise. A celebrated model in this class is the Ising model, where
spins can take the values +1 and -1, and the local interaction favors the alignment of the spins.

In this talk, I will mostly focus on the situation where the interactions are themselves disordered, with some pairs having a
preference for alignment, and some for anti-alignment. These models, often called "spin glasses", are already surprisingly difficult to
analyze when all spins directly interact with each other. I will describe a fundamental result of the theory called the Parisi formula. I
will then explain how this result can be recast using suitable Hamilton-Jacobi equations, and what benefits this new point of view may
bring to the topic.