# Past Junior Topology and Group Theory Seminar

12 June 2013
16:00
Benno Kuckuck
Abstract
<p><span><span style="color: black; font-family: Calibri; font-size: small;"><span style="font-size: 12pt;"> <div></div> <div>&nbsp;To any splitting of a group G as an HNN extension we can associate a map from G to Z. Conversely, a group that allows a non-trivial homomorphism to Z may be written as an HNN extension in an obvious way. In this talk we will consider the question when such a homomorphism G-&gt;Z is associated to a non-obvious HNN splitting of G. We will then see how this information can be collected into an invariant of the group which may be described by a simple connectivity condition on Cayley graphs.<span><span style="color: black; font-family: Calibri; font-size: small;"><span style="font-size: 12pt;"> </span></span></span></div> </span></span></span></p>
• Junior Topology and Group Theory Seminar
5 June 2013
15:30
Elisabeth Fink
Abstract
<p>I will talk about random walks on groups and define the Poisson boundary of such. Studying it gives criteria for amenability or growth. I will outline how this can be used and describe recent related results&nbsp;and still open questions.</p>
• Junior Topology and Group Theory Seminar
29 May 2013
16:00
Sven Raum
Abstract
<p>This talk consists of three parts. As a motivation, we are first going to introduce von Neumann algebras associated with discrete groups and briefly describe their interplay with measurable group theory. Next, we are going to consider group von Neumann algebras of general locally compact groups and highlight crucial differences between the discrete and the non-discrete case. Finally, we present some recent results on group von Neumann algebras associated with certain locally compact HNN-extensions.</p>
• Junior Topology and Group Theory Seminar
22 May 2013
16:00
Thomas Wasserman
Abstract
<p><span style="font-size: x-small;"><span style="font-size: 10pt;">In this talk I will describe an attempt to construct a conformal field theory with target space a symmetric product of $R^D$ (referred to by physicists as orbifold sigma model). The construction uses branched covers of $S^2$ to lift the well studied formulation of a sigma model on $S^2$, in terms of vertex operator algebras, to higher genus surfaces. I will motivate and explain this construction. </span></span></p>
• Junior Topology and Group Theory Seminar
15 May 2013
16:00
Martin Finn-Sell
Abstract
<p><span>Group actions play an important role in both topological problems and coarse geometric conjectures. I will introduce the idea of a partial action of a group on a metric space and explain, in the case of certain classes of coarsely disconnected spaces, how partial actions can be used to give a geometric proof of a result of Willett and Yu concerning the coarse Baum-Connes conjecture.</span></p>
• Junior Topology and Group Theory Seminar
8 May 2013
16:00
Abstract
<p><span style="font-size: x-small;"><span style="font-size: 10pt;">The integers (while wonderful in many others respects) do not make for fascinating Geometric Group Theory. They are, however, essentially the only infinite finitely generated group which is both hyperbolic and amenable. In the class of locally compact topological groups, the intersection of these two notions is richer, and the major aim of this talk will be to give the structure of a classification of such groups due to Caprace-de Cornulier-Monod-Tessera, beginning with Milnor's proof that any connected Lie group admitting a left-invariant negatively curved Riemannian metric is necessarily soluble.</span></span></p>
• Junior Topology and Group Theory Seminar
1 May 2013
16:00
Robert Kropholler
Abstract

To continue the day's questions of how complex groups can be I will be looking about some decision problems. I will prove that certain properties of finitely presented groups are undecidable. These properties are called Markov properties and include many nice properties one may want a group to have. I will also hopefully go into an algorithm of Whitehead on deciding if a set of n words generates F_n.

• Junior Topology and Group Theory Seminar
6 March 2013
16:00