|Location:||MSRI: Baker Board Room|
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).No Notes/Supplements Uploaded No Video Files Uploaded