##### Department of Mathematics,

University of California San Diego

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### Seminar on Cheeger-Colding theory, Ricci flow, Einstein metrics, and Related Topics

## Simon Brendle

#### Columbia University

## Ancient solutions to the Ricci flow, part 1

##### Abstract:

A solution to a geometric flow is called ancient if it has a backhistory going back infinitely far in time. Ancient solutions of parabolic PDE are analogous to entire solutions of elliptic PDE. In particular, they play a fundamental role in understanding singularity formation. \\ \\ Perelman studied ancient solutions to the Ricci flow in dimension 3 which are kappa-noncollapsed, and proved a crucial structure theorem for these ancient kappa-solutions. Moreover, Perelman conjectured that, up to scaling, every noncompact ancient kappa-solution in dimension 3 is isometric to either the Bryant soliton or the standard cylinder (or a quotient thereof). In these lectures, I will discuss the proof of this conjecture.

Host: Bennett Chow

### November 9, 2020

### 4:00 PM

### Email bechow@ucsd.edu for Zoom link

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