Ricci flow after Perelman

In a remarkable achievement, Perelman used Ricci flow to prove Thurston’s Geometrization Conjecture, a central conjecture in 3-manifold topology which includes the Poincare Conjecture as a special case. This breakthrough inspired twenty years of rapid progress in many directions, leading to the resolution of long-standing conjectures in geometry and topology, and opening new vistas in geometric analysis. Beginning with a recap of Perelman’s work, the lecture will survey these developments, and conclude with a discussion of some central open questions.