# Operator theory seminar

Title: The tight groupoid of an inverse semigroup

Speaker: Ruy Exel, Universidade Federal de Santa Catarina

Date and time:
15 Oct 2014,
3:30pm -
4:30pm

Location: Clearihue C109

Read full description

Given an inverse semigroup S, we will consider the natural action of S on the space of tight filters over the idempotent semi-lattice of S, as well as the groupoid of germs built from this action. We will then present various algebraic properties of S, each of which will be shown to imply (or to be equivalent to) a relevant property of the above mentioned groupoid of germs. When all of these properties are satisfied, the associated groupoid C*-algebra is shown to be purely infinite simple.

Title: An Introduction to Cuntz-Pimsner Algebras and their Application to Substitution Tilings

Speaker: Peter Williamson, University of Victoria

Date and time:
08 Oct 2014,
3:30pm -
4:30pm

Location: Clearihue C109

Read full description

This will be a two part talk. In the first I will introduce Hilbert Modules and all of the necessary machinery to define a generalization of the Toeplitz algebra and finally define the Cuntz-Pimsner algebra as a quotient. A few examples will be examined. In the second talk, I will discuss how this construction has been applied to a C*-dynamical system associated with a substitution tiling.

Title: Introduction to group actions and non commutative geometry

Speaker: Heath Emerson, University of Victoria

Date and time:
24 Sep 2014,
3:30pm -
4:30pm

Location: Clearihue C109

Read full description

I will give a general talk on the role of operator algebras in studying topological aspects of group actions. The talk is meant for a fairly general audience. I will start by describing the crossed-product construction, which associates a C*-algebra (or "noncommutative topological space") to a group action. I will describe some families of basic examples, which one might consider as falling into roughly the Type I, Type II and Type III classes appearing in von Neumann algebra theory. Then I will discuss the fundamental problem of computing the K-theory of crossed-products, especially for the examples given.

Title: A fractal approach to spectral triples on aperiodic tilings

Speaker: Mike Whittaker, University of Wollongong

Date and time:
10 Sep 2014,
3:30pm -
4:30pm

Location: Clearihue C109

Read full description

I will report on progress towards defining an odd spectral triple on a C*-algebra associated to an aperiodic tiling. A fractal tree can be inscribed in an aperiodic substitution tiling T satisfying mild conditions, which is invariant under the substitution. The fractal tree gives us a notion of geodesic distance between two tilings in the translational equivalence class of T. Using this data we define an odd spectral triple on a C*-algebra which is strongly Morita equivalent to the tiling C*-algebra defined by Kellendonk. This is joint work with Michael Mampusti building on work with Natalie Frank and Sam Webster.