Wed, 12 Mar 2014

16:00 - 17:00
C6

Property (T) for SL<sub>n</sub>(&#8484;)

Henry Bradford
(Oxford)
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.
Mon, 03 Mar 2014
14:00
C6

Generalised metrisable spaces and the normal Moore space conjecture

Robert Leek
(Oxford)
Abstract

We will introduce a few class of generalised metrisable

properties; that is, properties that hold of all metrisable spaces that

can be used to generalise results and are in some sense 'close' to

metrisability. In particular, we will discuss Moore spaces and the

independence of the normal Moore space conjecture - Is every normal

Moore space metrisable?

Thu, 06 Mar 2014

10:00 - 11:00
C6

A survey of derivator K-theory

George Raptis
(Osnabrueck and Regensburg)
Abstract

 The theory of derivators is an approach to homotopical algebra
that focuses on the existence of homotopy Kan extensions. Homotopy
theories (e.g. model categories) typically give rise to derivators by
considering the homotopy categories of all diagrams categories
simultaneously. A general problem is to understand how faithfully the
derivator actually represents the homotopy theory. In this talk, I will
discuss this problem in connection with algebraic K-theory, and give a
survey of the results around the problem of recovering the K-theory of a
good Waldhausen category from the structure of the associated derivator.

Fri, 02 May 2014

12:00 - 13:00
C6

Using multiple frequencies to satisfy local constraints in PDE and applications to hybrid inverse problems

Giovanni Alberti
(University of Oxford)
Abstract

In this talk I will describe a multiple frequency approach to the boundary control of Helmholtz and Maxwell equations. We give boundary conditions and a finite number of frequencies such that the corresponding solutions satisfy certain non-zero constraints inside the domain. The suitable boundary conditions and frequencies are explicitly constructed and do not depend on the coefficients, in contrast to the illuminations given as traces of complex geometric optics solutions. This theory finds applications in several hybrid imaging modalities. Some examples will be discussed.

Wed, 26 Feb 2014

16:00 - 17:00
C6

Volumes of representations of 3-manifold groups.

Claudio Llosa Isenrich
(Oxford)
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.

Mon, 24 Feb 2014
14:00
C6

Elementary submodels in topology

Richard Lupton
(Oxford)
Abstract

We explore the technique of elementary submodels to prove 
results in topology and set theory. We will in particular prove the 
delta system lemma, and Arhangelskii's result that a first countable 
Lindelof space has cardinality not exceeding continuum.

Wed, 19 Feb 2014

16:00 - 17:00
C6

Embedding symplectic manifolds in comlpex projective space

Manuel Araújo
(Oxford)
Abstract

I will explain why one can symplectically embed closed symplectic manifolds (with integral symplectic form) into CPn and compute the weak homotopy type of the space of all symplectic embeddings of such a symplectic manifold into CP.

Mon, 17 Feb 2014
14:00
C6

D-spaces (4): Topological games

Robert Leek
Abstract

 We will introduce 2 types of topological games (Menger and
> Telgársky) and show how the existence or non-existence of winning
> strategies implies certain properties of the underlying topological
> space. We will then show how these, and related properties, interact
> D-spaces.

Tue, 18 Feb 2014
02:45
C6

Cancelled

Jon Toledo
(The Perimeter Institute)
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