Marston Morse Lectures

Singularity Models in 3D Ricci Flow

The Ricci flow is a natural evolution equation for Riemannian metrics on a given manifold. From the point of view of PDE, the Ricci flow is a system of linear parabolic equations, which can be viewed as the heat equation analogue of the Einstein equations in general relativity. The central problem is to understand singularity formation. In other words, what does the geometry look like at points where the curvature is large? In his spectacular 2002 breakthrough, Perelman achieved a qualitative understanding of singularity formation in dimension 3; this is sufficient for topological conclusions. In this lecture, we will discuss more recent developments which have led to a complete classification of singularity models in dimension 3.

Date & Time

February 28, 2024 | 2:00pm – 3:00pm

Location

Simonyi 101 and Remote Access

Speakers

Simon Brendle, Columbia University

Event Series

Notes

Meeting ID: 876 5496 0483

Passcode: 3267

Video link: https://www.ias.edu/video/singularity-models-3d-ricci-flow