Georgia Institute of Technology College of Sciences

It was shown by Keith Ball that the maximal section of an n-dimensional cube is \sqrt{2}. We show the analogous sharp bound for a maximal marginal of a product measure with bounded density. We also show an optimal bound for all k-codimensional marginals in this setting, conjectured by Rudelson and Vershynin. This talk is based on the joint work with G. Paouris and P. Pivovarov.

The loops on a topological space up to an equivalence relation called homotopy form a group called the fundamental group. We'll define the fundamental group and talk about two riddles whose solutions use this idea.