Universality: Random Matrices, Random Geometry and SPDEs

Abstract

The postulate that large random systems can be described by limiting objects whose characteristic do not depend on the exact details of the models one started from is central in probability theory, under the name of universality. This workshop was aimed at uncovering the latest developments of this concept in the various topics where it is relevant, namely statistical physics, stochastic partial differential equations, random geometries and random matrices. It was in particular the occasion to feature some important recently introduced universal objects like the stochastic quantization of the Yang-Mills measure in dimensions 2 and 3, the KPZ fixed point, Liouville quantum gravity metrics and other objects connected to the Gaussian free field.