Property (T) for SL<sub>n</sub>(ℤ)
Abstract
14:00
Generalised metrisable spaces and the normal Moore space conjecture
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?
A survey of derivator K-theory
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.
Using multiple frequencies to satisfy local constraints in PDE and applications to hybrid inverse problems
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.
Volumes of representations of 3-manifold groups.
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.
14:00
Elementary submodels in topology
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.
Embedding symplectic manifolds in comlpex projective space
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∞.
14:00
D-spaces (4): Topological games
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.