Gwion Evans, On the Cuntz-Krieger algebras of higher-rank graphs
There has been much interest in various operator algebras associated with higher-rank graphs over the last thirteen years. We will focus on the Cuntz-Krieger algebras associated with higher-rank graphs. Part of the interest in these C*-algebras stems from the fact that many properties of the C*-algebra can be characterised in terms of the underlying higher-rank graph. Indeed their classification, at least under certain constraints, seem within reach but, as we will explore, the situation seems much more difficult than for (rank 1) graph C*-algebras.
James Waldron, Lie Algebroids over Orbifolds
I will explain the noncommutative geometry approach to orbifolds - spaces which are locally of the form R^n / W for some finite group W of diffeomorphisms. The geometry of the orbifold is described by a Lie groupoid, and the convolution algebra of the groupoid plays the role of the algebra of functions on the orbifold. This algebra is generally noncommutative.
After this, I will explain what is a Lie algebroid, how one can use the above tools to describe Lie algebroids over orbifolds, and give some recent results.
Rolf Gohm, Noncommutative Markov Processes and Multi-Variable Operator Theory
This is an introductory talk about connections between these two fields. We explain the physics picture of a noncommutative Markov process as a model of repeated quantum interactions and the operator picture as a dilation of a tuple of operators. As time allows we then compare the concept of a scattering operator (in the physics picture) with the concept of a characteristic function (in the operator picture). This leads to certain generalisations of characteristic functions which we recently studied in joint work with S. Dey.