##### Department of Mathematics,

University of California San Diego

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### Differential Geometry

## Nolan Wallach

#### UCSD

## The effect of the Ricci flow on homogeneous metrics of positive curvature on flag varieties.

##### Abstract:

This talk will be an exposition of joint work with Man Wai (Mandy) Cheung on the effect of the Ricci flow on homogeneous metrics of positive sectional curvature on flag varieties over the complex, quaternions and octonians. The speakerâ€™s 1972 paper shows that these metrics exist only in the case of the variety of flags in the two dimension projective space over these fields. Here are some of the results: All cases can flow from strictly positive curvature to some negative sectional curvature. All cases can flow from positive definite Ricci curvature to indefinite Ricci curvature The quaternionic and octonianic cases can flow from strictly positive sectional curvature to indefinite Ricci curvature (in the case of the quaternions this is a result of Boehm and Wilking). In the complex case the flow keeps the metrics of strictly positive curvature in the metrics with positive definite Ricci curvature.

### November 15, 2012

### 9:00 AM

### AP&M 7218

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