Eli Hawkins (University of York), An Obstruction to Quantization of the Sphere
A strict deformation quantization of a manifold M involves a family of C*-algebras that begins from the algebras of functions on M and deforms the product in a way characterized by a Poisson structure on M. This family of algebras is parameterized by "Planck's constant" h. In some examples, h can be any real number; in other examples the set of allowed values is almost discrete. Why?
In the simplest example of the latter kind, M is the 2-sphere with a symplectic structure. I will show that there does not exist any well-behaved strict deformation quantization of the 2-sphere for which the set of values of h is connected.
Martin Finn-Sell (University of Southampton), Counterexamples to the coarse Baum-Connes conjecture and Schreier Quotients of Free Groups
To any uniformly discrete bounded geometry metric space it is possible to associate a groupoid that captures its coarse geometry. For certain spaces, known as expander graphs, it is known that the Baum-Connes assembly map for the associated groupoid fails to be a surjection. Recent work of Willett and Yu establishes, for expanders of large girth, that whilst the conjecture is not surjective, it is injective - that is the coarse Novikov conjecture holds. I will outline the framework in which the groupoid counterexamples live, and talk about a geometric strengthening of this result for regular large girth expanders, which is joint work with Nick Wright.
Paul Mitchener (University of Sheffield): Nonarchimidean analysis and K-theory
It this talk we introduce some of the basic notions and properties of non-archimedean analysis, such as the analysis of the p-adic numbers. We then talk about functional analysis over p-adic fields, and how we might go about defining K-theory for p-adic Banach algebras. This talk is intended to start from the basics; no prior knowledge of p-adic analysis is assumed!