Means and powers of convex bodies

Analysis Seminar
Wednesday, March 15, 2017 - 14:05
1 hour (actually 50 minutes)
Skiles 005
University of Minnesota
In this talk we will discuss several ways to construct new convex bodies out of old ones. We will start by defining various methods of "averaging" convex bodies, both old and new. We will explain the relationships between the various definitions and their connections to basic conjectures in convex geometry. We will then discuss the power operation, and explain for example why every convex body has a square root, but not every convex body has a square. If time permits, we will briefly discuss more complicated constructions such as logarithms. The talk is based on joint work with Vitali Milman.