Yifan Jing
The Ohio State University
Title
A nonabelian Brunn-Minkowski theory
Abstract
The classical Brunn–Minkowski inequality gives a sharp lower bound for the volume of sumsets in Euclidean space. In 1953, Henstock and Macbeath asked whether an analogous inequality holds for arbitrary locally compact groups. In this talk, I will present the sharp nonabelian Brunn–Minkowski theorem, whose exponent is governed by the noncompact Lie dimension: for connected Lie groups, the dimension of the group minus that of a maximal compact subgroup. I will discuss applications to product growth and isoperimetric inequalities on symmetric spaces of noncompact type, and outline the key ideas of the proof. The talk is based on a series of joint works with Chieu-Minh Tran and Ruixiang Zhang.
