TeeSeminar der AG KramerZeit und Ort:

Inhalt:
Mitglieder der Arbeitsgruppe tragen über ihre laufenden Forschungsarbeiten vor, oder über Themen, die uns interessieren. Vor dem Seminar (ab 10:00) gibt es in Zimmer 301b Tee.
Vorträge:
29.10.13 Uniformly finite homology and amenable groups (Matthias Blank, Uni Regensburg)
Abstract:
Uniformly finite homology is a coarse invariant for metric spaces; in particular, it is a quasiisometry invariant for finitely generated groups. We give a general introduction to uniformly finite homology and discuss its relation to homology with l^{∞}coefficients. Then, we present an overview about known applications, in particular regarding questions about amenability and rigidity of groups. Finally, we present our calculation of uniformly finite homology of many amenable groups.
The talk is based on joint work with Francesca Diana.
12.11.13 Conjectures on rank rigidity for CAT(0) spaces (Petra Schwer, Uni Muenster)
Abstract: I will present the (various versions of the) rank rigidity conjecture
for CAT(0) spaces and quickly explain and mention previous partial
results obtained by BallmannBrin, CapraceSageev and others.
19.11.13 The rigidity of the topology of a group acting on a BruhatTits tree (Rupert McCallum, Uni Muenster)
Abstract: We shall show how to prove that there is just one locally compact sigmacompact Hausdorff topology on the full automorphism group of a BruhatTits tree which is compatible with the group operations. We shall examine the question of whether this result is also true of a closed subgroup of the fullautomorphism group which acts 2transitively on the ends of the tree. This problem is currently unsolved, but we shall explore a few different approaches that we have tried so far.
3.12.13 Quotients of trees for arithmetic subgroups of GL2 over a rational function ﬁeld (Koen Struyve, Uni Ghent)
Abstract:
Let F be the rational function ﬁeld over a ﬁnite ﬁeld. A place p of this function ﬁeld of F induces a valuation on F, from which one can construct a BruhatTits tree X. If A is the subring of F consisting of the elements of F having poles only at p, then Γ := PGL2(A) is an arithmetic group which acts on X.
In order to understand the structure of the group Γ, one can try to calculate the quotient of the tree X by Γ. This is one of the questions considered in [1], where the largescale structure of the quotient is determined for arbitrary degree and the exact form for degrees up to four.
In this talk I show how to explicitly calculate these quotients for arbitrary degree.
(Joint work with Ralf Köhl and Bernhard Mühlherr.)
References:
[1] J.P. Serre, Trees, SpringerVerlag, 1980.
17.12.13 The Margulis lemma and the
KazhdanMargulis Theorem (Stefan Witzel, Uni Muenster)
07.01.14 Cubulating Small Cancellation Groups (Lukas Buggisch, Uni Muenster)
Abstract: Small Cancellation Groups are a large class of groups in the geometric group theory. D.T. Wise
used a version of Sageev's cube complex to show that certain classes
of Small Cancellation Groups act properly discontinuously and
cocompact of a locally finte CAT(0)cube complex. I will give a short overview of the methods he used and state the simpler case of B(4)T(4) or
B(6)C(7)Small Cancellation Groups.
18.02.14 14H15H, Raum M5 Actions of Burnsidegroups on affine buildings (Daniel Skodlerack, Uni Muenster)
11.03.14 10H3011H30 Raum M6
Rigidity of the group topology for closed Weyl transitive groups of automorphisms of a BruhatTits tree (Rupert McCallum, Uni Muenster)
Abstract: We´ll present a proof of a conjecture stated in a previous talk about closed groups of automorphisms of a BruhatTits tree that act 2transitively on the ends of the tree, deriving it from a slightly more general proposition about groups of automorphisms that are closed and Weyl transitive. If time permits we may also discuss how similar techniques can be applied to prove a similar proposition for maximal KacMoody groups over finite fields.