Robert Kozma : Tarski's theorem - non-amenable groups are paradoxical

Posted by Alexander Furman , part of the Graduate Groups and Dynamics Seminar.

At

Oct. 2, 2018, 3 p.m.

In

1227 SEO

Abstract

The basis for the Hausdorff-Banach-Tarski "paradox" is the fact that the free group $F_2$, and therefore any group containing $F_2$, admits a paradoxical decomposition. Amenable groups have no paradoxical decompositions. While not all n-n-amenable groups contain $F_2$, Tarski proved that every non-amenable group admits a paradoxical decomposition. The talk presents a proof of this theorem.