Seminar
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| Location: | SLMath: Baker Board Room |
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
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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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