Seminario Teoría de Grupos UAM-ICMAT 

Fecha: Jueves 4 de Abril, 2019
Hora: 11:30
Lugar: Aula 520 UAM

Speaker: Fabian Hanneke (Bonn)

Title: Variants of the Atiyah conjecture and their relation to K-theory

Abstract: L^{^2}-Betti numbers serve as an equivariant analogue of Betti numbers, allowing one to assign meaningful numerical invariants to arbitrary G-spaces for discrete groups G. Compared to their classical counterparts, L^{^2}-Betti numbers enjoy the curious feature of taking arbitrary non-negative real numbers as values, no longer just integers. A famous question first asked by Atiyah is whether these numbers are rational at least for universal coverings of finite CW-complexes. The original question has since been answered in the negative, but a number of "Atiyah conjectures" have emerged in its stead and are still open.
In this talk, I will discuss the full range of these conjectures and their relation to the questions about the K-theory of group rings and von Neumann regular rings.