Introduction to amenability
von 16:00 bis 17:30
|Wo||Hörsaal des Mathematischen Instituts, Arndtstraße 2, 1. Stock, Raum 111|
Abstract: The Banach-Tarski paradox says that one can decompose the 3-ball into 5 pieces and translate and rotate these 5 pieces in R^3 to obtain two isometric copies of the ball. Thus you can "double the moon".
The reason that this phenomenon occurs for the three-ball, but not the 2-ball, is that SO(3) contains a densely embedded free subgroup, and that free groups admit "paradoxical decompositions". Von Neumann initiated the study of groups without such paradoxical decompositions, which he called "messbar", and which are now called amenable. By now where exist several dozens equivalent characterizations of amenable groups, which relate amenable groups to basically
all branches of mathematics in which symmetries play a role.
In this talk I will give a gentle introduction to amenable groups and amenable actions, with a focus on Lie groups and their lattices.