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Department of Mathematics,
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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