Forthcoming Seminars › Seminar Series

Junior Geometric Group Theory Seminar

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, 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, 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, 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, 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, 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.

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

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