##### Department of Mathematics,

University of California San Diego

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### Department Colloquium

## Dr. Yi Lai

#### Stanford

## Ricci flow and Hamilton's flying wing Conjecture

##### Abstract:

##### Ricci flow is an important tool in geometric analysis. There have been remarkable topological applications of Ricci flow on closed manifolds, such as the Poincaré Conjecture resolved by Perelman, and the recent Generalized Smale Conjecture resolved by Bamler-Kleiner. In contrast, much less is known about the Ricci flow on open manifolds. Solitons produce self-similar Ricci flows, which often arise as singularity models. Collapsed singularities and solitons create additional difficulties for open manifolds. In this talk, I will survey some recent developments in Ricci flow on open manifolds. In particular, I will talk about the resolution of Hamilton's flying wing Conjecture, and the resulting collapsed steady solitons.

Host: Luca Spolaor

### November 16, 2023

### 4:00 PM

APM 6402 and Zoom https://ucsd.zoom.us/j/92959890235
Meeting ID: 929 5989 0235

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