Extra QLunch: Antoine Mouzard

Speaker: Antoine Mouzard (ENS Paris)

Title: Paracontrolled calculus and the Anderson Hamiltonian on compact surfaces

Abstract: The Anderson Hamiltonian is the random Schrodinger operator with potential the space white noise, a random distribution with negative Holder regularity. In this talk, I will explain the construction of this operator on a finite segment and a compact surface. In the one dimensional case, precise results were recently obtained by Dumaz and Labbe for the large volume limit. In two dimensions, the operator falls in the range of singular stochastic operator and and its construction requires a probabilistic renormalization procedure following the recent progress in singular stochastic PDEs.