Past Junior Topology and Group Theory Seminar

12 March 2014
16:00
Henry Bradford
Abstract
Kazhdan's Property (T) is a powerful property of groups, with many useful consequences. Probably the best known examples of groups with (T) are higher rank lattices. In this talk I will provide a proof that for n ≥ 3, SLn(ℤ) has (T). A nice feature of the approach I will follow is that it works entirely within the world of discrete groups: this is in contrast to the classical method, which relies on being able to embed a group as a lattice in an ambient Lie group.
  • Junior Topology and Group Theory Seminar
26 February 2014
16:00
Claudio Llosa Isenrich
Abstract
In some of their recent work Derbez and Wang studied volumes of representations of 3-manifold groups into the Lie groups $$Iso_e \widetilde{SL_2(\mathbb{R})} \mbox{ and }PSL(2,\mathbb{C}).$$ They computed the set of all volumes of representations for a fixed prime closed oriented 3-manifold with $$\widetilde{SL_2(\mathbb{R})}\mbox{-geometry}$$ and used this result to compute some volumes of Graph manifolds after passing to finite coverings. In the talk I will give a brief introduction to the theory of volumes of representations and state some of Derbez' and Wang's results. Then I will prove an additivity formula for volumes of representations into $$Iso_e \widetilde{SL_2(\mathbb{R})}$$ which enables us to improve some of the results of Derbez and Wang.
  • Junior Topology and Group Theory Seminar
12 February 2014
16:00
Giles Gardam
Abstract

The notion of automatic groups emerged from conversations between Bill Thurston and Jim Cannon on the nice algorithmic properties of Kleinian groups. In this introductory talk we will define automatic groups and then discuss why they are interesting. This centres on how automatic groups subsume many other classes of groups (e.g. hyperbolic groups, finitely generated Coxeter groups, and braid groups) and have good properties (e.g. finite presentability, fast solution to the word problem, and type FP).

  • Junior Topology and Group Theory Seminar
22 January 2014
16:00
Robert Kropholler
Abstract
<p>Many interesting properties of groups are inherited by their subgroups examples of such are finiteness, residual finiteness and being free. People have asked whether hyperbolicity is inherited by subgroups, there are a few counterexamples in this area. I will be detailing the proof of some of these including a construction due to Rips of a finitely generated not finitely presented subgroup of a hyperbolic group and an example of a finitely presented subgroup which is not hyperbolic.</p>
  • 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

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