Scottish  operator  algebras  research  (SOAR)

Scottish Operator Algebras Research meeting

University of Glasgow, Friday 8 February, 2018

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.


Schedule

Breaks will be held in the Common Room.

Friday 8 Februrary
Talks are in Room 116 and 311 of the Mathematics Building.

13:05-14:00   David Kerr 1 (Maths-Stats Seminar Room 311)
14:00-14:30   Tea, coffee, and discussion
14:30-15:10   Evgenios Kakariadis
15:20-16:00   Gabor Elek
16:00-16:30   Tea, coffee, and discussion
16:30-17:30   David Kerr 2


The meeting is organised by Stuart White, and Michael Whittaker.

Support

Funding for this meeting is provided by the Glasgow Mathematical Journal Trust.