Antoine Dahlqvist: Yang-Mills measure and master fields on surfaces

Abstract: This talk is about a notion of state, called master field, on the group of reduced rectifiable loops on a surface. After introducing a definition and sketching its origin from Euclidean Quantum field Theory and non-abelian gauge theory, I will present a conjecture , due to I.M. Singer in the late 90’s, that relates master fields to two-dimensional Yang-Mills measures. I shall show how harmonic analysis on the unitary group was recently used to solve part of this problem and some questions that this model raises in random matrices and free probability.