Past 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
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

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