Workshop on C*-Algebras and their Classification

The structure theory of nuclear C*-algebras has seen dramatic advances in recent years. Most notably, tight links have been discovered between topological and algebraic regularity properties of C*-algebras. These results have spurred new and very broad classification theorems, with particularly satisfying applications to transformation group C*-algebras. They have also opened connections to other areas such as graph algebras or coarse geometry; these connections are waiting to be further explored.The area is extremely vivid, as reflected by the large number of well-synced recent and upcoming events (in Oberwolfach, Banff, Toronto, Copenhagen, Mnster, Barcelona, Palo Alto, to name but a few). It is particularly attractive for early career researchers, as the theory is well-developed yet highly active, with many open questions which are interesting yet accessible (even at postgraduate level). So far the UK has been somewhat underrepresented in this development. The LMS will devote their 2010 Midlands regional meeting to C*-algebras; this will be followed by a four day workshop. The LMS meeting aims to spur some important new developments in C*-algebras to a wider mathematical public; we will explore these results and potential further developments in more detail during the workshop. We plan to emphasize the structure theory and classification of nuclear C*-algebras during these events, with particular attention paid to applications such as dynamical systems or graph algebras.

As is typical for an activity rooted at the foundations of pure mathematics, the impact will become most apparent within the mathematical community. The LMS meeting aims at disseminating important recent developments to a wider mathematical public, and hence will raise the awareness of these results at a broad level. This will be most beneficial for mathematicians with a general interest in functional analysis and its applications. The workshop seeks to make progress on open cutting edge research problems, as such we expect it to be beneficial for researchers in C*-algebras worldwide. We hope both the LMS meeting and the workshop will be of particular benefit for current and prospective PhD students and PostDocs, as we will emphasize current and future developments many of which are accessible at postgraduate level. In this respect, the meeting will serve as an entry point for talented students and junior researchers into a rapidly developing and highly attractive area in modern mathematics. It will thus contribute to generating highly skilled researchers in the UK, expose them to cutting edge research problems and let them make contact with the leading experts in the field. The meeting will be part of our strategy to establish the UK as a leading centre in the classification of C*-algebras; it will raise the standing of the UK in this internationally highly active and rapidly developing research area.