Past Seminars › Seminar Series

Junior Geometric Group Theory Seminar (past)

Wed, 10/10/2012
16:00 		Henry Bradford (University of Oxford) Junior Geometric Group Theory Seminar Add to calendar SR2
A Voyage into Outer Space (what I did on my holidays)
The study of free groups and their automorphisms has a long pedigree, going back to the work of Nielsen and Dehn in the early 20th century, but in many ways the subject only truly reached maturity with the introduction of Outer Space by Culler and Vogtmann in the “Big Bang” of 1986. In this (non-expert) talk, I will walk us through the construction of Outer Space and some related complexes, and survey some group-theoretic applications.
Wed, 26/09/2012
16:00 		Anitha Thillaisundaram Junior Geometric Group Theory Seminar Add to calendar SR2
The concept of p-deficiency and its applications
We use Schlage-Puchta's concept of p-deficiency and Lackenby's property of p-largeness to show that a group having a finite presentation with p-deficiency greater than 1 is large. What about when p-deficiency is exactly one? We also generalise a result of Grigorchuk on Coxeter groups to odd primes.
Wed, 25/04/2012
16:00 		Moritz Rodenhausen Junior Geometric Group Theory Seminar Add to calendar SR2
Stabilisers of conjugacy classes in free groups under the action of automorphisms

A construction by McCool gives rise to a finite presentation for the stabiliser of a finite set of conjugacy classes in a free group under the action of Aut(F_n) or Out(F_n). An important concept of my talk are rigid elements, which will allow to simplify these huge presentations. Finally I will sketch applications to centralisers in Aut(F_n).
Wed, 07/03/2012
16:00 		John MacKay Junior Geometric Group Theory Seminar Add to calendar SR2
To Be Announced
Wed, 22/02/2012
16:00 		Martin Palmer Junior Geometric Group Theory Seminar Add to calendar SR2
Homological instability
Wed, 15/02/2012
16:00 		Stefan Witzel Junior Geometric Group Theory Seminar Add to calendar SR2
Groups with prescribed finiteness properties

The first group known to be finitely presented but having infinitely generated 3rd homology was constructed by Stallings. Bieri extended this to a series of groups G_n such that G_n is of type F_{n-1} but not of type F_n. Finally, Bestvina and Brady turned it into a machine that realizes prescribed finiteness properties. We will discuss some of these examples.
Wed, 25/01/2012
16:00 		Andrew Sale Junior Geometric Group Theory Seminar Add to calendar SR2
Horocyclic Products, the Geometry of Some Metabelian Groups and Short Conjugators
The lamplighter groups, solvable Baumslag-Solitar groups and lattices in SOL all share a nice kind of geometry. We'll see how the Cayley graph of a lamplighter group is a Diestel-Leader graph, that is a horocyclic product of two trees. The geometry of the solvable Baumslag-Solitar groups has been studied by Farb and Mosher and they showed that these groups are quasi-isometric to spaces which are essentially the horocyclic product of a tree and the hyperbolic plane. Finally, lattices in the Lie groups SOL can be seen to act on the horocyclic product of two hyperbolic planes. We use these spaces to measure the length of short conjugators in each type of group.
Wed, 18/01/2012
15:45 		Owen Cotton-Barratt Junior Geometric Group Theory Seminar Add to calendar SR2
TBC
Wed, 30/11/2011
16:00 		David Hume Junior Geometric Group Theory Seminar Add to calendar SR2
Classical and Cubical Small Cancellation Theory

Building on the previous talk, we continue the exploration of techniques required to understand Wise's results. We present an overview of classical small cancellation theory running in parallel with the newer one for cubical complexes.
Wed, 23/11/2011
16:00 		David Hume Junior Geometric Group Theory Seminar Add to calendar SR2
Cube Complexes and Quasi-Convex Hierarchies

We present recent results of Dani Wise which tie together many of the themes of this term's jGGT meetings: hyperbolic and relatively hyperbolic groups, (in particular limit groups), graphs of spaces, 3-manifolds and right-angled Artin groups.
Following this, we make an attempt at explaining some of the methods, beginning with special non-positively curved cube complexes.
Wed, 16/11/2011
16:00 		Ric Wade Junior Geometric Group Theory Seminar Add to calendar DH 3rd floor SR
Automorphisms of 2 dimensional RAAGs
Wed, 22/06/2011
16:00 		Moritz Rodenhausen (Rheinische Friedrich-Wilhelms-Universität Bonn) Junior Geometric Group Theory Seminar Add to calendar SR1
Parallelogram Law for Isometries of CAT(0)-spaces
In euclidean space there is a well-known parallelogram law relating the length of vectors a, b, a+b and a-b. In the talk I give a similar formula for translation lengths of isometries of CAT(0)-spaces. Given an action of the automorphism group of a free product on a CAT(0)-space, I show that certain elements can only act by zero translation length. In comparison to other well-known actions this leads to restrictions about homomorphisms of these groups to other groups, e.g. mapping class groups.

For any corrections/updates to these listings, please contact seminars [-at-] maths [dot] ox [dot] ac [dot] uk.

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