Past Junior Topology and Group Theory Seminar

4 December 2013
16:00
Alejandra Garrido
Abstract

I will introduce and motivate the concept of largeness of a group. I will then show how tools from different areas of mathematics can be applied to show that all free-by-cyclic groups are large (and try to convince you that this is a good thing).

  • Junior Topology and Group Theory Seminar
27 November 2013
16:00
Hemanth Saratchandran
Abstract
<p>I will show how to construct an infinite family of totally geodesic surfaces in the figure eight knot complement that do not remain totally geodesic under certain Dehn surgeries. If time permits, I will explain how this behaviour can be understood via the theory of quadratic forms.</p>
  • Junior Topology and Group Theory Seminar
13 November 2013
16:00
Antonio De Capua
Abstract

Last week in the Kinderseminar I talked about a rough estimate on volumes of certain hyperbolic 3-manifolds. This time I will describe a different approach for similar estimates (you will not need to remember that talk, don't worry!), which is, in some sense, complementary to that one, as it regards mapping tori. A theorem of Jeffrey Brock provides bounds for their volume in terms of how the monodromy map acts on the pants graph (a relative of the better known curve complex) of the base surface. I will describe the setting and the relevance of this result (in particular the one it has for me); hopefully, I will also tell you part of its proof.

  • Junior Topology and Group Theory Seminar
6 November 2013
16:00
Thomas Wasserman
Abstract

A bit more than ten years ago, Peter Oszváth and Zoltán Szabó defined Heegaard-Floer homology, a gauge theory inspired invariant of three-manifolds that is designed to be more computable than its cousins, the Donaldson and Seiberg-Witten invariants for four-manifolds. This invariant is defined in terms of a Heegaard splitting of the three-manifold. In this talk I will show how Heegaard-Floer homology is defined (modulo the analysis that goes into it) and explain some of the directions in which people have taken this theory, such as knot theory and fitting Heegaard-Floer homology into the scheme of topological field theories.

  • Junior Topology and Group Theory Seminar
30 October 2013
16:00
Sophie Raynor
Abstract
<p>Working together with the Blue Brain Project at the EPFL, I'm trying to develop new topological methods for neural modelling. As a mathematician, however, I'm really motivated by how these questions in neuroscience can inspire new mathematics. I will introduce new work that I am doing, together with Kathryn Hess and Ran Levi, on brain plasticity and learning processes, and discuss some of the topological and geometric features that are appearing in our investigations.</p>
  • Junior Topology and Group Theory Seminar
23 October 2013
16:00
Henry Bradford
Abstract
<p>A group is said to be quasirandom if all its unitary representations have “large” dimension. After introducing quasirandom groups and their basic properties, I shall turn to recent applications in two directions: constructions of expanders and non-existence of large product-free sets.</p>
  • Junior Topology and Group Theory Seminar
16 October 2013
16:00
Robert Kropholler
Abstract
<p>It is an open question whether a group with a finite classifying space is hyperbolic or contains a Baumslag Solitar Subgroup. An idea of Gromov was to use aperiodic tilings of the plane to try and disprove this conjecture. I will be looking at some of the attempts to find a counterexample.</p>
  • 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

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