Claudia Lückert

Wilhelm Killing Kolloquium: Prof. Dr. Jean-Christophe Mourrat (École normale supérieure de Lyon): Mean-field disordered systems and Hamilton-Jacobi equations

Thursday, 20.04.2023 14:15 im Raum M4

Mathematik und Informatik

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 alignement 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 alignement, and some for anti-alignement. 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 might bring to the topic.

Angelegt am Friday, 24.02.2023 12:48 von Claudia Lückert
Geändert am Thursday, 13.04.2023 14:10 von Claudia Lückert
[Edit | Vorlage]

Kolloquium Wilhelm Killing