Past Junior Topology and Group Theory Seminar

18 June 2014
16:00
Simon Gritschacher
Abstract

Waldhausen defined higher K-groups for categories with certain extra structure. In this talk I will define categories with cofibrations and weak equivalences, outline Waldhausen's construction of the associated K-Theory space, mention a few important theorems and give some examples. If time permits I will discuss the infinite loop space structure on the K-Theory space.

  • Junior Topology and Group Theory Seminar
28 May 2014
16:00
Thomas Wasserman
Abstract
A one hour introduction to topological K-theory, that nifty generalised cohomology theory that is built starting from the semi-ring of vector bundles over a space. As I'll need it on Thursday I'll also explain a model for K-theory in terms of difference bundles, and, if time permits, its connection with Clifford algebras.
  • Junior Topology and Group Theory Seminar
21 May 2014
16:00
Sam Brown
Abstract

Subgroup separability is a group-theoretic property that has important implications for geometry and topology, because it allows us to lift immersions to embeddings in a finite sheeted covering space. I will describe how this works in the case of graphs, and go on to motivate the construction of special cube complexes as an attempt to generalise the technique to higher dimensions.

  • Junior Topology and Group Theory Seminar
14 May 2014
16:00
Mark Penney
Abstract

As the title says, in this talk I will be giving a casual introduction to higher categories. I will begin by introducing strict n-categories and look closely at the resulting structure for n=2. After discussing why this turns out to be an unsatisfying definition I will discuss in what ways it can be weakened. Broadly there are two main classes of models for weak n-categories: algebraic and geometric. The differences between these two classes will be demonstrated by looking at bicategories on the algebraic side and quasicategories on the geometric.

  • 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

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