# Past Junior Topology and Group Theory Seminar

15 June 2011
16:00
Martin Palmer
Abstract
... for Torelli groups of surfaces.
• Junior Topology and Group Theory Seminar
8 June 2011
16:00
Dawid Kielak
Abstract
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 $\mathrm{Out}(F_n)$.
• Junior Topology and Group Theory Seminar
1 June 2011
16:00
Abstract
• Junior Topology and Group Theory Seminar
25 May 2011
16:00
Maria Buzano
Abstract
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.
• Junior Topology and Group Theory Seminar
18 May 2011
16:00
Abstract
<p>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.</p>
• Junior Topology and Group Theory Seminar
11 May 2011
16:00
Alessandro Sisto
Abstract
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.
• Junior Topology and Group Theory Seminar
4 May 2011
16:00
Moritz Rodenhausen
Abstract
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.
• Junior Topology and Group Theory Seminar
2 March 2011
16:00
John Mackay
Abstract
We'll survey some of the ways that hyperbolic groups have been studied using analysis on their boundaries at infinity.
• Junior Topology and Group Theory Seminar
23 February 2011
16:00
Hemanth Saratchandran
Abstract
I will give a brief introduction to the Steenrod squares and move on to show some applications of them in Topology and Geometry.
• Junior Topology and Group Theory Seminar
16 February 2011
16:00
Lars Scheele
Abstract
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.
• Junior Topology and Group Theory Seminar