Universality in probability and mathematical physics

Random geometry and random matrix theory have driven major breakthroughs across mathematics and mathematical physics, including universality results for random matrices, scaling limits of random planar maps, Liouville quantum gravity, Schramm-Loewner evolutions and probabilistic approaches to conformal field theory. These developments link probability with analysis, geometry, algebra and physics: random matrices capture universal spectral features of quantum systems, Coulomb gases connect probability to potential theory and geometric function theory, random conformal geometry joins stochastic analysis, Gaussian fields and Loewner theory, and random tilings and determinantal processes carry rich algebraic and geometric structure. The meeting aims to bring these communities together to survey recent progress and explore new directions.