The phenomenon of concentration of measure and group representations in Banach spaces
by
Todd Rangiwhetu
Victoria University of Wellington

The recently discovered phenomenon of concentration of measure in high dimensional structures manifests itself in numerous mathematical disciplines and uses techniques from a variety of areas of mathematics.

Some by now classical results such as certain isoperimetric inequalities and the Law of Large Numbers can be derived from measure concentration considerations and, more importantly, some very surprising discoveries about the nature of objects in high dimensions have been made.

It appears that our intuition, having been nurtured predominantly in 2 and 3 dimensions, tends to fail when applied to the realms of high-dimensional geometry and the structures therein.

In this talk we shall discuss some of the meanings and manifestations of measure concentration and talk about some new results concerning the concentration property of the unit sphere in Banach spaces of representations of amenable groups.

The majority of the talk will be aimed at a general audience, and any notions not in common usage shall be explained.

Date received: October 8, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caek-55.