The Thurston-Perelman geometrization theorem is possibly the most important result for geometry and topology in dimension 3. Indeed, the truthiness of the Poincare conjecture follows easily from this theorem. How does one prove this amazing result? Very carefully and with a PDE called the Ricci flow. In this talk we will introduce some Riemannian geometry necessary to understand the statement of the Ricci flow and then present some basic results to help us understand the nature of its solutions. If time permits we will discuss how Ricci flow is used to prove a special case of the geometrization theorem.
(Going With the) Ricci Flow