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Seminar

GFA Young Researchers Seminar: Sampling on the Sphere by Random Subspaces October 11, 2017 (11:15 AM PDT - 12:30 PM PDT)
Parent Program:
Location: MSRI: Baker Board Room
Speaker(s) Uri Grupel (Weizmann Institute of Science)
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Abstract/Media

Let A be a subset of the n-dimensional sphere, and let H be a random subspace of dimension k. How well does the (k dimensional) surface area of the intersection of A and H approximate the (n dimensional) surface area of A?

We will discuss three theorems related to this question. The first by Klartag and Regev for the case k=n-1 and by repetitive applications up to k=n/2. The second for the case k=n/2 that considers both H and it's orthogonal complement simultaneously (under additional assumptions). The third is for small values of k (we will focus on the case k=2).

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