##### Department of Mathematics,

University of California San Diego

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### MATH 258 - Differential Geometry Seminar

## Brett Kotschwar

#### ASU

## Backward propagation of warped-product structures under the Ricci flow and asymptotically conical shrinkers

##### Abstract:

We establish sufficient conditions for a locally-warped product structure to propagate backward in time under the Ricci flow. As an application, we show that if a gradient shrinking soliton is asymptotic to a cone whose cross-section is a locally warped product of Einstein manifolds, the soliton must itself be a warped product over the same manifolds.

### May 19, 2022

### 11:00 AM

Zoom ID 924 6512 4982

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