Title: Bounding marginals of product measures

 Abstract:

 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.