"Geometry and Analysis on Groups" Research Seminar
Time: 2016.10.18, 15:00–17:00
Location: Seminarraum 9, Oskar-Morgenstern-Platz 1, 2.Stock
Title:"Amenability for étale
groupoids, failures of Hulanicki's theorem and the weak containment
Finn-Sell (Universität Wien)
In this talk, we will discuss variants of the classical theorem of Hulanicki from 1964 that shows that amenability of a discrete group can be characterised by the property that every representation is weakly contained in the left regular representation. A version of this result has been conjectured to hold for discrete groups acting on compact Hausdorff spaces, but has recently been shown to fail by Willett for certain pathological groupoids, far from actions of groups, originally constructed by Higson, Lafforgue and Skandalis in their work on the Baum-Connes conjecture - these groupoids are non-amenable, but they have the "weak containment" property. I will present a result (that is joint with Vadim Alekseev), in which we give a new example of groupoids that are not amenable, have weak containment and are much closer to group actions.
The introductory part of this seminar will focus on weak containment of representations, amenability and the original theorem of Hulanicki, and the second half will focus on the broader question concerning groupoids - here we will understand what it means for a groupoid to be amenable, have the weak containment property and the overall scheme of the proof using representation theory of groups and homological techniques concerned with groupoid \(C^*\)–algebras.