Minicourse - Ricci curvature and stochastic analysis II

Robert Haslhofer (University of Toronto)

Title 2: Minicourse - Ricci curvature and stochastic analysis II

Abstract 2: I'll describe a new link between geometry and probability. First, I'll give a brief introduction to Ricci curvature, the Einstein equations and Hamilton's Ricci flow. Next, I'll give a quick introduction to Brownian motion in Euclidean space and on manifolds, and integration by parts on path space. Finally, I’ll explain joint work with Aaron Naber where we discovered an infinite-dimensional Bochner formula for martingales on path space, which vastly generalizes the classical Bochner formula for the heat flow on manifolds. Using these ideas, we can make sense of solutions of the Einstein equations and the Ricci flow in the setting of singular spaces.