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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.