Singularity Models in 3D Ricci Flow

Explore the intricacies of singularity formation in 3D Ricci flow during this one-hour Aisenstadt Chair lecture by Simon Brendle. Delve into the Ricci flow as a natural evolution equation for Riemannian metrics, comparing it to the heat equation analogue of Einstein's equations in general relativity. Examine the central problem of understanding singularity formation and geometric behavior at points of high curvature. Learn about Perelman's groundbreaking 2002 qualitative understanding of singularity formation in three dimensions and its topological implications. Discover recent developments leading to a comprehensive classification of singularity models in three-dimensional Ricci flow, advancing our understanding beyond Perelman's initial insights.