TeeSeminar der AG KramerZeit und Ort: ZOOM

Inhalt:
Mitglieder der Arbeitsgruppe und Gäste tragen über ihre laufenden Forschungsarbeiten vor, oder über Themen, die uns interessieren.
Vorträge:
 13.04.2021 Giles Gardam (Münster) Kaplansky's conjectures
 20.04.2021 Linus Kramer (Münster) Proper actions and buildings
 27.04.2021 Jason Behrstock (CUNY) Hierarchically hyperbolic groups: an introduction
 04.05.2021 Rafael Dahmen (KIT) Direct limits of topological groups
 11.05.2021 Olga Varghese (Magdeburg) Automatic continuity for groups whose torsion subgroups are small
 18.05.2021 Jonas Beyrer (IHES) Aspects of higher rank Teichmüller theory
Abstract: Three conjectures on group rings of torsionfree groups are commonly attributed to Kaplansky, namely the unit, zero divisor and idempotent conjectures. For example, the zero divisor conjecture predicts that if K is a field and G is a torsionfree group, then the group ring K[G] has no zero divisors. I will survey what is known about the conjectures, including their relationships to each other and to other conjectures and group properties, and finish with my recent counterexample to the unit conjecture.
Abstract: I will discuss some useful facts about proper actions on proper metric spaces. One application is that proper, Weyltransitive actions on locally finite buildings are linetransitive.
Abstract: Hierarchically hyperbolic spaces provide a uniform framework for working with many important examples, including mapping class groups, right angled Artin groups, Teichmüller space, most cubulated groups, and others. In this talk I'll provide an introduction to studying groups and spaces from this point of view, both describing new tools to use to study these groups and applications of those results. This talk will include joint work with Mark Hagen and Alessandro Sisto.
Abstract: Given a directed system of topological groups, one can consider the direct limit (colimit) in the category of topological spaces. Unfortunately, sometimes this topology may fail to be a group topology due to discontinuity of the multiplication map. In these cases the topology underlying the colimit in the category of topological groups is different from the colimit in the category of topological spaces. In this talk, I want to present some wellknown results on when this pathology occurs in the case of countable directed systems  as well as some newer results on certain uncountable systems (called "long directed systems") which behave very differently than countable ones. This will be illustrated by some (hopefully) motivating examples. This is joint work with Gábor Lukács.
Abstract: In the category of locally compact Hausdorff groups LCG one has to distinguish between algebraic morphisms and algebraic and continuous morphisms. Let Epi(L,G) be the set of surjective group homomorphisms and cEpi(L,G) the subset consisting of continuous surjective group homomorphisms. The question we address is the following: Under which conditions on the discrete group G does the equality Epi(LCG,G)=cEpi(LCG,G) hold?
Abstract: 'Classical' Teichmüller space is the space of hyperbolic structures on a closed surface S. If H is the fundamental group of S, Teichmüller space can also be identified with a connected component of Hom(H,PSL(2,R))/PSL(2,R) that consists entirely of discrete and faithful representations. Surprisingly there are other Lie groups G (of higher rank) such that there exist also connected components of Hom(H,G)/G consisting entirely of discrete and faithful representations  those components are called 'Higher rank Teichmüller spaces'. In the last two decades there has been a lot of research studying those spaces, in particular the similarities (and differences) to classical Teichmüller space. In this talk I try to give a short introduction and overview of Higher rank Teichmüller theory and then discuss joint work with B. Pozzetti on this topic.