Student Probability Seminar

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Discrepancy theory

Speaker: Dylan Altschuler, CIMS

Location: TBA

Date: Wednesday, November 4, 2020, 1 p.m.

Synopsis:

I will talk about combinatorial discrepancy theory. Given n vectors from an n-dimensional convex set, can I sign the vectors (multiply by +1 or -1) so that their sum lies in the cube? This is a deterministic question, but it turns out the answer is "yes---and there is an efficient algorithm---if the gaussian measure of the convex set is sufficiently large". Some probabilistic tools we will use are correlation inequalities and isoperimetry. If time permits, I will discuss some of my current research on the discrepancy of random matrices.