Title of Invited Talk: Curvature Flows and the Proof of the Poincaré Conjecture
Abstract: One of the most exciting developments in mathematics in the past 10 years has been the solution of the Poincaré conjecture, which was formulated over 100 years ago by the great scientist and mathematician Henri Poincaré. The conjecture involves the classification of 3-dimensional spaces, and its solution is a beautiful interplay between topology, geometry, and differential equations. In this talk we will give an introduction to the conjecture, and to the “curvature flow” equation on which its solution is based called the Ricci flow. We will present basic techniques for studying the equation, and outline some of the main ideas used in the proof of the conjecture.