|Location:||MSRI: Simons Auditorium|
We will discuss two possible ways to define the "limit" of a divergent sequence of convex bodies: the Banach limit approach and the ultrafilter approach. We will also present an application for each approach. The Banach limit will be used to construct the geometric mean of convex bodies, while the ultrafilter limit will be used to construct the power of a convex body.
The talk is (partially) based on joint work with V. Milman, and is motivated by Milman's talk on September 14th. However, the talk will be self-contained.