##### Department of Mathematics,

University of California San Diego

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### Math 288 - Probability & Statistics Seminar

## Karl-Theodor Sturm

#### University of Bonn

## The space of spaces: curvature bounds and gradient flows on the space of metric measure spaces

##### Abstract:

Equipped with the $L^2$-distortion distance, the space "$X$" of all metric measure spaces $(X,d,m)$ is proven to have nonnegative curvature in the sense of Alexandrov. Geodesics and tangent spaces are characterized in detail. Moreover, classes of semiconvex functionals and their gradient flows on "$X$" are presented.

Host: Bruce Driver

### June 3, 2013

### 2:00 PM

### AP&M 6402

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