Amenability and concentration
by
Vladimir Pestov
Victoria University of Wellington

There seems to be a close connection between the phenomenon of concentration of measure on high-dimensional structures and amenability (understood in a broad variety of contexts, e.g. amenability of groups, actions, unitary representations, and C ^* -algebras). A general principle seems to be that whenever the former appears in a dynamical setting, it always leads to amenability, and vice versa. Our talk will offer a mini-survey of the results in this direction, featuring work by Gromov and V. Milman, Eli Glasner, Furstenberg and Benji Weiss, and the speaker (some of it jointly with Thierry Giordano).

Date received: October 4, 2000