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Tee-Seminar der AG KramerZeit und Ort:
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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 quasi-isometry 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 Ballmann-Brin, Caprace-Sageev and others.
19.11.13 The rigidity of the topology of a group acting on a Bruhat-Tits tree (Rupert McCallum, Uni Muenster)
Abstract: We shall show how to prove that there is just one locally compact sigma-compact Hausdorff topology on the full automorphism group of a Bruhat-Tits 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 full-automorphism group which acts 2-transitively 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 Bruhat-Tits 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 large-scale 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, Springer-Verlag, 1980.
17.12.13 The Margulis lemma and the
Kazhdan-Margulis 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 14H-15H, Raum M5 Actions of Burnside-groups on affine buildings (Daniel Skodlerack, Uni Muenster)
11.03.14 10H30-11H30 Raum M6
Rigidity of the group topology for closed Weyl transitive groups of automorphisms of a Bruhat-Tits 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 Bruhat-Tits tree that act 2-transitively 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 Kac-Moody groups over finite fields.