Christopher Kennedy (Queen’s)

PDEs & Applications Seminar

Tuesday, September 19th, 2023

Time: 9:30 a.m.  Place: Jeffery Hall, Room 319

Speaker: Christopher Kennedy (Queen’s)

Title: A Bochner Formula on Path Space for the Ricci Flow

Abstract: Aaron Naber (Northwestern) and Robert Haslhofer (Toronto) have characterized solutions of the Einstein equation in terms of both sharp gradient estimates for Brownian motion and a Bochner formula on elliptic path space. They also successfully characterized solutions of the Ricci flow in terms of an infinite-dimensional gradient estimate on parabolic path space of space-time. In this talk, we shall generalize the classical Bochner formula for the heat flow on evolving manifolds to an infinite dimensional Bochner formula for martingales, thus proving the parabolic counterpart of their results in the elliptic setting as well as characterizing solutions of the Ricci flow in terms of Bochner inequalities on parabolic path space. Time-permitting, we shall also discuss gradient and Hessian estimates for martingales on parabolic path space as well as a condensed proof of previous characterizations of the Ricci flow.