Paul Mitchener, An Introduction to Coarse Geometry
The plan in this talk is to introduce some of the main ideas behind the coarse geometry of metric spaces. Topics covered will include coarse maps and coarse invariants, including examples based on both algebraic topology and the theory of operator algebras. We conclude with by looking at the coarse Baum-Connes conjecture and some of its applications. The aim is give an introduction that is friendly for analysts!
Roger Plymen: The idea of a noncommutative quotient, with applications to representation theory
Noncommutative quotients appear in several versions, but the simplest and most useful version is the extended quotient of a space by a finite group. The extended quotient is a down-to-earth object which is quite easy to calculate. I will illustrate this with some examples. The extended quotient has applications in representation theory, especially the representation theory of p-adic groups and affine Hecke algebras. This will be a non-technical talk.
Joint work with Anne-Marie Aubert and Paul Baum.
Nick Wright: Translation algebras and theorems of Lance, Pimsner and Voiculescu
The celebrated Pimsner-Voiculescu sequence computes, amongst other things, the K-theory of C*r(F_n). Later Lance gave an alternative way of computing this and more generally of computing K-theory for certain free products. Pimsner generalised this to all free products and HNN-extensions. In this talk I will explain how the exact sequences in these proofs are special cases of an exact sequence for translation algebras. This leads to a more elementary proof of Pimsner's theorem and directions for further K-theory computations.
This is joint work with Brodzki, Putwain and Niblo.