This operator algebras meeting is one in a series of meetings in Scotland focusing on operator algebras research.
Participants are welcome from anywhere.
Please email Michael Whittaker if you plan to come to dinner.
David Kerr (Texas A&M University ) - Almost finiteness, comparison, and Z-stability
I will explain how one can develop a dynamical version of some of the theory surrounding the Toms-Winter conjecture for simple separable nuclear C*-algebras. In particular, I will formulate a notion of almost finiteness for group actions on compact spaces which can be seen as an analogue of both hyperfiniteness in the measure-preserving setting and of Z-stability in the C*-algebra setting and is related to dynamical comparison in the same way that Z-stability is related to strict comparison in the Toms-Winter context. For free minimal actions of countably infinite groups on compact metrizable spaces the property of almost finiteness implies that the crossed product is Z-stable, which leads to new examples of classifiable crossed products.
Evgenios Kakariadis (University of Newcastle) - Amalgamated free products of operator algebras
The amalgamated free product of C*-algebras has become a standard construction in the subject. It is central in studying group C*-algebras, free probability, quantum information, dynamical systems on C*-algebras, and the Connes Embedding Conjecture via its connection to Kirchberg?s conjecture and also to Tsirelson?s conjectures. Boca?s result on completely positive maps on amalgamated free products has become a useful technical tool in thise endeavour. In this talk we will show a general method of extending unital completely positive maps to amalgamated free products of C*-algebras that covers Boca's Theorem.
Several applications on the C*-envelope will be discussed. The talk is based on joint work with Davidson (Proc. R. Soc. Ed. A) and with Davidson and Fuller (Memoirs AMS).
Gabor Elek (University of Lancaster) - Cantor combinatorics and almost finiteness.I will give a gentle introduction to almost finiteness via algorithm theory.
Breaks will be held in the Common Room.
Friday 8 Februrary
Talks are in Room 116 and 311 of the Mathematics Building.
The meeting is organised by Stuart White, and Michael Whittaker.
Funding for this meeting is provided by the Glasgow Mathematical Journal Trust.