## Aberdeen-Glasgow Operator Algebras Day## University of Aberdeen, Monday, May 13, 2013 |

A schedule can be found here.

Abstract: Consider a C*-dynamical system where the group of real numbers acts on a C*-algebra by automorphisms. When the system models time evolution in a physical system, it makes sense to talk about equilibrium states of the system. The mathematical formulation of equilibrium states is known as the KMS condition after Kubo, Martin and Schwinger. For a finite directed graph, we can view the gauge actions on the Cuntz-Krieger and Toeplitz-Cuntz-Krieger algebras as actions of the real numbers. I will discuss the KMS states of these two systems when the graph is strongly connected. I'll start by explaining what the Cuntz-Krieger and Toeplitz-Cuntz-Krieger algebras are. This is joint work with Marcelo Laca, Iain Raeburn and Aidan Sims.

Abstract: We survey the recent quest to extend key C*-algebra tools, perspectives, and results to general algebras of operators on a Hilbert space. A particular role is played by a new `positive cone' we have introduced and studied with Charles Read and Matthew Neal. This gives a device/strategy to generalize results hitherto available only for C*-algebras, results relying on positivity, and in particular on the existence of a positive cai. Much of this is intimately related to a variant of Akemann's noncommutative topology for such algebras.

Abstract: By considering the six-term exact sequence in K-homology, we propose a construction of spectral triples arising from unital extensions of C*-algebras by stable ideals. We analyse these spectral triples from the perspective of Connes' metric on the state space. We apply this construction to the equatorial Podle's spheres and the quantum SU2 group.

Abstract: In the theory of discrete quantum groups there are certain standard procedures to obtain new examples from well-understood old ones, and in many cases these procedures are invertible in a suitable sense. This includes so-called cocycle twistings and, more generally, (co-)monoidal equivalences. In this talk we describe a different notion of equivalence for discrete quantum groups which is motivated from coarse geometry. We indicate how this can be used to study operator algebraic properties of discrete quantum groups.

Rob Archbold (University of Aberdeen)

David Blecher (University of Houston)

Jorge Castillejos Lopez (University of Glasgow)

Liam Dickson (University of Glasgow)

Andrew Hawkins (University of Glasgow)

Martin Mathieu (Queen's University Belfast)

David McConnell (Trinity College Dublin)

Aaron Tikuisis (University of Aberdeen)

Richard Timoney (Trinity College Dublin)

Gabriele Tornetta (University of Glasgow)

Christian Voigt (University of Glasgow)

Stuart White (University of Glasgow)

John Wright (University of Aberdeen)

Joachim Zacharias (University of Glasgow)