"Geometry and Analysis on Groups" Research Seminar
Time: 2016.01.26, 15:00–17:00
Location: Seminarraum 8, Oskar-Morgenstern-Platz 1, 2.Stock
Title: "Amenability as an affine fixed-point property in Hilbert spaces."
(École Polytechnique Fédérale de Lausanne)
Day proved in the early sixties a nice geometric fixed-point property characterising amenability. We show that such a characterisation already holds in the Hilbert world. This seemingly innocuous result will be a pretext to introduce a variant of the induction of representations that allows, to some extent, to induce representations from a group when it can be considered as a "measure-theoretical subgroup" of another group. This applies notably to non-amenable groups, which contain free groups in this measure-theoretical sense thanks to a result of Gaboriau and Lyons.
The first part of the talk will be an introduction to fixed-point properties of amenable groups. The second one will explain how measure-theoretical tools can be used to prove results about non-amenable groups starting from results about free groups.
Joint work with Nicolas Monod.