# Geometric Analysis and Topology Seminar

#### Uniqueness of Weak Solutions to Ricci Flow, and Perelman's Convergence Conjecture

**Speaker:**
Bruce Kleiner, NYU

**Location:**
Warren Weaver Hall 1314

**Date:**
Wednesday, September 21, 2016, 11 a.m.

**Synopsis:**

In his proof of Thurston's geometrization conjecture, Perelman proved the existence of a Ricci flow with surgery starting from any given compact smooth Riemannian 3-manifold. In the same papers, he conjectured that when the surgery parameters are sent to zero, the flow with surgery converges to a limiting "flow through singularities", yielding a canonical generalized Ricci flow. The lecture will briefly cover some background on uniqueness questions for weak solutions to geometric evolution equations (Ricci flow, mean curvature flow and harmonic map heat flow), and then discuss recent joint work of Richard Bamler and myself, giving a proof of Perelman's convergence conjecture.