A gentle introduction to Ricci flow

Richard Hamilton introduced the Ricci flow as a way to study the Poincaré conjecture, which says that every simply connected, compact three-manifold is homeomorphic to the three-sphere. In this talk, we will introduce the Ricci flow in a way that is accessible to anyone with basic knowledge of Riemannian geometry. We will give some examples, discuss finite time singularities, and give an application to a theorem of Hamilton which says that every compact Riemannian 3-manifold with positive Ricci curvature admits a metric of constant positive sectional curvature.