Abstract

This workshop, sponsored by AIM and the NSF, will be devoted to the study of the effects which symmetry has on the Brunn-Minkowski inequality, a corner stone of convex geometric analysis. It is well understood that many inequalities in analysis self-improve under additional symmetry assumptions, however, it is not clear how to effectively adapt some of the analytic tools to the study of the Brunn- Minkowski type inequalities to obtain meaningful geometric consequences. In recent years, a number of relevant conjectures have appeared, such as the Log-Brunn-Minkowski conjecture, the B-conjecture, the Gardner-Zvavitch dimensional Brunn-Minkowski conjecture, and others. These conjectured inequalities are intimately connected to certain Monge-Ampere type differential equations that are recent versions of the Minkowski problem. The aim of this workshop is to bring together experts working in convex and differential geometry, functional analysis, harmonic analysis and PDEs, geometric flows, complex analysis, in order to work together towards better understanding the role of symmetry in geometric inequalities.