Oxford

Hrushovski-Martin-Rideau have proved rationality of Poincare series counting 
numbers of equivalence classes of a definable equivalence relation on the p-adic field (in connection to a problem on counting representations of groups). For this they have proved 
uniform p-adic elimination of imaginaries. Their work implies that these Poincare series are 
motivic. I will talk about their work.

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).

This is joint work with Angus Macintyre. I will discuss new developments in 
our work on the model theory of adeles concerning model theoretic 
properties of adeles and related issues on adelic geometry and number theory.

In this talk, two concepts are brought together: Algebras with triangular decomposition (as studied by Bazlov & Berenstein) and pointed Hopf algebra. The latter are Hopf algebras for which all simple comodules are one-dimensional (there has been recent progress on classifying all finite-dimensional examples of these by Andruskiewitsch & Schneider and others). Quantum groups share both of these features, and we can obtain possibly new classes of deformations as well as a characterization of them.

 We take a look at diamond and use it to build interesting 
mathematical objects.

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.

We will discuss TQFTs (at a basic level), then higher categorical extensions, and see how these lead naturally to the notion of Segal spaces.