## Geometry Seminar - Abstracts

### Talk

Wednesday 22 February 2017, 16:00 - 17:00 in HG03.085

**Irakli Patchkoria** (Universität Bonn)

*Proper G-spectra, geometric group theory and TC*

### Abstract

We will start by discussing some classical dimension invariants
from geometric group theory and their relations with homotopy theory. This
will lead to the notion of a proper G-spectrum for any infinite discrete
group G. We will discuss basic properties or proper G-spectra and indicate
how one develops proper equivariant stable homotopy theory with them. This
is a part of a joint project with Degrijse, Hausmann, Lück and Schwede. As
the first application we will provide a geometric characterization of the
virtual cohomological dimension of a virtually torsion free group. We will
see what this gives on an explicit example of a certain Coxeter group.
This is a part of a joint work with Barcenas and Degrijse. As the second
application of the theory of proper G-spectra, we will present the
connection between proper Q_p/Z_p-spectra and topological cyclic homology.
In particular, we will see how proper Q_p/Z_p-spectra avoid p-completions.

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