Speaker: 陈鸿宾，上海纽约大学

Title: Hamilton--Jacobi equations from mean-field spin glasses

Language: Chinese

Time & Venue: 2026.01.08 16:00-17:00 南楼N613

Abstract: This talk focuses on the PDE side of the story. We begin by recalling the heuristics for deriving the Hamilton--Jacobi equation in the simple Curie--Weiss model, as well as the basics of viscosity solutions. We then move on to the discussion of such equations in the context of spin glasses. In this setting, the equation’s spatial variable is a monotone path, and thus the domain is a convex cone. We equip it with an $L^2$ topology, which is convenient for calculus but results in a domain with empty interior. We then explain, from the perspective of characteristics, why no boundary condition is needed on the domain, which simplifies the analysis. Finally, we discuss the well-posedness of the equation and variational representations of its solutions.