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Junior Geometric Group Theory Seminar (past)

Wed, 15/06/2011
16:00 		Martin Palmer (University of Oxford) Junior Geometric Group Theory Seminar Add to calendar SR1
Cutting and pasting...
... for Torelli groups of surfaces.
Wed, 08/06/2011
16:00 		Dawid Kielak (University of Oxford) Junior Geometric Group Theory Seminar Add to calendar SR1
Fusion, graphs and $ \mathrm{Out}(F_n) $.
We will attempt to introduce fusion systems in a way comprehensible to a Geometric Group Theorist. We will show how Bass–Serre thoery allows us to realise fusion systems inside infinite groups. If time allows we will discuss a link between the above and $ \mathrm{Out}(F_n) $.
Wed, 25/05/2011
16:00 		Maria Buzano (University of Oxford) Junior Geometric Group Theory Seminar Add to calendar SR1
Homogeneous Einstein metrics and the graph theorem.
First of all, we are going to recall some basic facts and definitions about homogeneous Riemannian manifolds. Then we are going to talk about existence and non-existence of invariant Einstein metrics on compact homogeneous manifolds. In this context, we have that it is possible to associate to every homogeneous space a graph. Then, the graph theorem of Bohm, Wang and Ziller gives an existence result of invariant Einstein metrics on a compact homogeneous space, based on properties of its graph. We are going to discuss this theorem and sketch its proof.
Wed, 18/05/2011
16:00 		David Hume (University of Oxford) Junior Geometric Group Theory Seminar Add to calendar SR1
Optimal embeddings of groups into Hilbert spaces
We begin by showing the underlying ideas Bourgain used to prove that the Cayley graph of the free group of finite rank can be embedded into a Hilbert space with logarithmic distortion. Equipped with these ideas we then tackle the same problem for other metric spaces. Time permitting these will be: amalgamated products and HNN extensions over finite groups, uniformly discrete hyperbolic spaces with bounded geometry and Cayley graphs of cyclic extensions of small cancellation groups.
Wed, 11/05/2011
16:00 		Alessandro Sisto (University of Oxford) Junior Geometric Group Theory Seminar Add to calendar SR1
3-manifolds and their fundamental groups
We'll discuss 2 ways to decompose a 3-manifold, namely the Heegaard splitting and the celebrated geometric decomposition. We'll then see that being hyperbolic, and more in general having (relatively) hyperbolic fundamental group, is a very common feature for a 3-manifold.
Wed, 04/05/2011
16:00 		Moritz Rodenhausen (University of Bonn) Junior Geometric Group Theory Seminar Add to calendar SR2
Normal Forms, Factorability and Cohomology of HV-groups
A factorability structure on a group G is a specification of normal forms of group elements as words over a fixed generating set. There is a chain complex computing the (co)homology of G. In contrast to the well-known bar resolution, there are much less generators in each dimension of the chain complex. Although it is often difficult to understand the differential, there are examples where the differential is particularly simple, allowing computations by hand. This leads to the cohomology ring of hv-groups, which I define at the end of the talk in terms of so called "horizontal" and "vertical" generators.
Wed, 02/03/2011
16:00 		John Mackay (Oxford University) Junior Geometric Group Theory Seminar Add to calendar SR2
Analysis on boundaries of hyperbolic groups
We'll survey some of the ways that hyperbolic groups have been studied using analysis on their boundaries at infinity.
Wed, 23/02/2011
16:00 		Hemanth Saratchandran (Oxford University) Junior Geometric Group Theory Seminar Add to calendar SR2
A brief introduction to the Steenrod squares and their applications
I will give a brief introduction to the Steenrod squares and move on to show some applications of them in Topology and Geometry.
Wed, 16/02/2011
16:00 		Lars Scheele (University Muenster) Junior Geometric Group Theory Seminar Add to calendar SR2
Slow Ultrafilters and asymptotic cones of proper metric spaces
The construction of the asymptotic cone of a metric space which allows one to capture the "large scale geometry" of that space has been introduced by Gromov and refined by van den Dries and Wilkie in the 1980's. Since then asymptotic cones have mainly been used as important invariants for finitely generated groups, regarded as metric spaces using the word metric. However since the construction of the cone requires non-principal ultrafilters, in many cases the cone itself is very hard to compute and seemingly basic questions about this construction have been open quite some time and only relatively recently been answered. In this talk I want to review the definition of the cone as well as considering iterated cones of metric spaces. I will show that every proper metric space can arise as asymptotic cone of some other proper space and I will answer a question of Drutu and Sapir regarding slow ultrafilters.
Wed, 09/02/2011
16:00 		Alessandro Sisto (Oxford University) Junior Geometric Group Theory Seminar Add to calendar SR2
Nonstandard methods in geometry: asymptotic cones
After a quick-and-dirty introduction to nonstandard analysis, we will define the asymptotic cones of a metric space and we will play around with nonstandard tools to show some results about them. For example, we will hopefully prove that any separable asymptotic cone is proper and we will classify real trees appearing as asymptotic cones of groups.
Wed, 02/02/2011
16:00 		Nicholas Touikan (Oxford University) Junior Geometric Group Theory Seminar Add to calendar SR2
Rips' Machine
Wed, 26/01/2011
16:00 		Nicholas Touikan (Oxford University) Junior Geometric Group Theory Seminar Add to calendar SR2
Rips' Machine
Wed, 19/01/2011
16:00 		Andrew Sale (Oxford University) Junior Geometric Group Theory Seminar Add to calendar SR2
Conjugacy problem and conjugator length
A brief survey of the above.
Tue, 30/11/2010
16:00 		Alexandra Pettet (Oxford University) Junior Geometric Group Theory Seminar Add to calendar DH 3rd floor SR
Spines and cohomological dimension
Tue, 23/11/2010
16:00 		Ric Wade (Oxford University) Junior Geometric Group Theory Seminar Add to calendar DH 3rd floor SR
Pushing and Pulling of Presentations of Groups
Tue, 16/11/2010
16:00 		Martin Palmer (Oxford University) Junior Geometric Group Theory Seminar Add to calendar DH 3rd floor SR
Introduction to homology-stability
Tue, 09/11/2010
16:00 		Dawid Kielak (Oxford University) Junior Geometric Group Theory Seminar Add to calendar DH 3rd floor SR
The Tarski Monster and other stories
Tue, 02/11/2010
16:00 		Benno Kuckuck (Oxford University) Junior Geometric Group Theory Seminar Add to calendar DH 3rd floor SR
Geoghegan stacks and finiteness properties of groups
Geoghegan's stack construction is a tool for analysing groups that act on simply connected CW complexes, by providing a topological description in terms of cell stabilisers and the quotient complex, similar to what Bass-Serre theory does for group actions on trees. We will introduce this construction and see how it can be used to give results on finiteness properties of groups.
Tue, 26/10/2010
16:00 		Jessica Banks (Oxford University) Junior Geometric Group Theory Seminar Add to calendar DH 3rd floor SR
Locally infinite Kakimizu complexes

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

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