Kolloquium: Siegfried Echterhoff (Universität Münster): „Amenable Group Actions on Spaces and Operator Algebras

Amenable Group Actions on Spaces and Operator Algebras – Vortragender: Siegfried Echterhoff, Universität Münster – Einladender: K. Li

Abstract: Motivated by the study of paradoxical decompositions (as in the Banach-Tarski paradoxon), the notion of an amenable group has been introduced by von Neumann in the 1920’s. In the 1980’s Zimmer introduced the concept of amenable group actions on measure spaces in order to study rigidity properties of lattices in Lie groups. In the meantime, various notions of amenability were introduced for actions on topological spaces and on operator algebras, where the latter can be viewed as non-commutative analogues of measure or topological spaces. They have important applications in the interplay between group theory and operator algebras. After a gentle introduction to various notions of amenable actions we want to give an overview over some exciting recent results.