##### Department of Mathematics,

University of California San Diego

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### Differential Geometry Seminar

## Adam Jacob

#### Columbia University

## The Yang-Mills flow and the Atiyah-Bott formula on compact Kahler manifolds.

##### Abstract:

In this talk I will describe the limiting properties Yang-Mills flow on a holomorphic vector bundle E, in the case where the flow does not converge. In particular I will describe how to determine the $L^2$ limit of the curvature endomorphism along the flow. This proves a sharp lower bound for the Hermitian-Yang-Mills functional and thus the Yang-Mills functional, generalizing to arbitrary dimension a formula of Atiyah and Bott first proven on Riemann surfaces. I will then show how to use this result to identify the limiting bundle along the flow, which turns out to be independent of metric and uniquely determined by the isomorphism class of $E$.

Host: Ben Weinkove

### January 13, 2012

### 3:00 PM

### AP&M 6402

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