Vladimir Pestov (University of Ottawa)

will speak

Interactions between concentration, topological transformation groups, and Ramsey theory: an introduction

Abstract:

Theory of actions of `infinite-dimensional' groups on compact spaces is in some respects very different from that of locally compact groups, for instance, some infinite-dimensional groups possess the so-called fixed point on compacta property, an extremely strong form of amenability that locally compact groups cannot have by Veech's theorem. This extreme amenability is closely linked to concentration of measure on increasing chains of subgroups (or other objects) in `infinite-dimensional' groups, as well as to Ramsey-type theorems for various highly homogeneous structures. In its turn, extreme amenability can be used as a tool to compute universal minimal flows of some groups that are not extremely amenable. In this introductory lecture we will present, with proofs, a selection of the basic concepts and results of the emerging theory, which counts among its contributors V. Milman, M. Gromov, H. Furstenberg, B. Weiss, E. Glasner....

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Last update on 20/10/02.