The Poincare conjecture, one of the most famous unsolved problems throughout the 20th century, states that every closed, simply-connected 3-manifold is homeomorphic to the 3-sphere. Completed by Grigori Perelman in 2003, the highly geometric proof is based on Hamilton's Ricci flow.

In this talk, I will give an overview of the Ricci flow method to solve the Poincare conjecture. I will start by reviewing some relevant concepts from geometry and topology, and then introduce the Ricci flow. Next, I will state Perelman's result on the existence of Ricci flow with surgery, and show how this proves the main result. The extensive analytical details will be omitted in order to focus on the topological and geometric aspects. While Perelman's work goes much further and in fact proves Thurston's geometrization conjecture, I will focus on the special case of the Poincare conjecture. Speaker(s): Mark Greenfield (UM)