Simon Machado

Brunn—Minkowski in compact Lie groups

Given a subset A of a locally compact group, the doubling constant is the ratio of the measure m(A^2) of the set A^2 of products of two elements of A to the measure m(A) of A. This constant appears naturally in the study of random walks on homogeneous spaces.

In Euclidean spaces, doubling is now particularly well understood. Beyond that, the situation is far more mysterious. A conjecture of Breuillard and Green predicts that in a compact Lie group this constant must be at least 2 to the power of the minimal co-dimension of a proper subgroup. In this talk, I will discuss the proof of this conjecture. I'll also explain how the tools employed open the door to other results, such as a Brunn-Minkowski inequality or a stability result.