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Complex waist inequalities

Geometry/Topology

Speaker: Bo'az Klartag, Tel Aviv University
Location: 2112 MSB
Start time: Tue, Nov 28 2017, 1:10PM

Let Z be the zero set of a holomorphic map from C^n to C^k. Assume that Z is non-empty. We prove that for any r > 0, the Gaussian measure of the Euclidean r-neighborhood of Z is at least as large as the Gaussian measure of the Euclidean r-neighborhood of E, where E is any (n-k)-dimensional, affine, complex subspace whose distance from the origin is the same as the distance of Z from the origin. The proof is based on Eldan's stochastic localization method.