Guillaume Baverez: Integration by parts in random conformal geometry and applications

Abstract:

The Gaussian free field and Schramm-Loewner evolutions are prominent examples of stochastic processes exhibiting conformal invariance. In this talk, I will explain how these measures vary under quasiconformal transformations, and deduce some integration by parts formulas. These formulas can be neatly rephrased as representations of the Virasoro algebra on the L2-space of the measure, and I will discuss some consequences of this algebraic structure. Based on joint works with Antoine Jego.