##### Department of Mathematics,

University of California San Diego

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### Differential Geometry Seminar

## Andrea Young

#### University of Arizona

## Ricci Yang-Mills solitons on nilpotent Lie groups

##### Abstract:

There has been much recent progress in the study of Ricci solitons on nilpotent and solvable Lie groups. In this talk, I will define the Ricci Yang-Mills flow which is related to the Ricci flow. I will also define Ricci Yang-Mills solitons, which are generalized fixed points of the Ricci Yang-Mills flow. These metrics are related to Ricci solitons; however, they are defined on principal G-bundles and are designed to detect more of the bundle structure. On nilpotent Lie groups, one can say precisely in what sense Ricci Yang-Mills solitons are related to Ricci solitons. I will provide examples of 2-step nilpotent Lie groups that admit Ricci Yang-Mills solitons but that do not admit Ricci solitons. This is joint work with Mike Jablonski.

Host: Ben Weinkove

### November 4, 2009

### 3:00 PM

### AP&M 6402

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