EGGG (East German Geometric Group theory)

07.05.2026, 13:15 Uhr  –  Campus Golm, Haus 9, Raum 2.22
Workshop

Anna Cascioli, Piotr Mizerka, Waltraud Lederle

Schedule

    13:15 Talk Lederle
    14:25 Talk Cascioli
    15:25 Break
    16:00 Talk Mizerka

Webpage with registration link: https://sites.google.com/view/grouptheoryandfriends/eggg

Abstracts:

Anna Cascioli (University of Münster)

Title: Stationary boundaries on the space of amenable subgroups and C*-simplicity

Abstract: Every countable group acts on its space of subgroups, and the induced dynamics on the space of amenable subgroups encode structural features of the group. We study stationarity for this action and give a sufficient condition for the existence of a probability measure μ on G that admits a non-trivial μ-boundary modeled on the space of amenable subgroups of G. This leads to non-uniqueness of stationary measures and connects to C*-simplicity, a property that naturally arises in the study of unitary representations of a group. The criterion applies to wreath products and to Thompson’s group F. This is joint work with Martín Gilabert Vio and Eduardo Silva.

Waltraud Lederle (University of Bielefeld)

Title: Compact Invariant Random Subgroups

Abstract: An IRS is a conjugacy-invariant probability measure on the space of subgroups of a locally compact group. We are interested in those IRS that give full measure to the set of compact subgroups. This talk is about what we know about those, how it connects to the structure theory of locally compact groups, and what we would still like to figure out.
Joint with Tal Cohen, Helge Glöckner and Gil Goffer.


Piotr Mizerka (Adam Mickiewicz University in Poznań)

Title: Non-vanishing of group cohomology of SL(n,Z) in the rank

It has been recently shown by Bader and Sauer that the cohomology of SL(n,Z) with coefficients in orthogonal representations without non-trivial invariant vectors vanishes below the rank. We show that for n=3 and n=4 their result is sharp: we indicate specific representations for which SL(n,Z) possesses non-trivial cohomology in the rank. We apply the Steinberg duality which allows us to compute the group cohomologies of interest by means of a specific model of a symmetric space. The key idea is to translate such computations to calculations stemming from group rings. The latter could be accomplished with the help of computers. This is the joint work with B. Brück, S. Hughes, and D. Kielak.