# Past Junior Topology and Group Theory Seminar

20 October 2011
14:00
Alessandro Sisto
Abstract
• Junior Topology and Group Theory Seminar
12 October 2011
15:45
Alessandro Sisto
Abstract
• Junior Topology and Group Theory Seminar
22 June 2011
16:00
Abstract
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.
• 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