There will be a SOAR meeting in Glasgow on Friday 9th of February 2018. The schedule and abstracts for the talks are below.
12:30 - 12:55: Pizza lunch in the Level 3 common room.
13:00 - 14:00: Seminar room 311B. David Kerr (Texas A&M) "Almost finiteness, comparison, and Z-stability 1".
14:30 - 15:10: Room 116. Evgenios Kakariadis (Newcastle) "Amalgamated free products of operator algebras".
15:20 - 16:00: Room 116. Gabor Elek (Lancaster) "Cantor combinatorics and almost finiteness".
16:30 - 17:30: Room 116. David Kerr (Texas A&M) "Almost finiteness, comparison, and Z-stability 2".
Almost finiteness, comparison, and Z-stability
David Kerr, Texas A&M University
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.
Amalgamated free products of operator algebras
Evgenios Kakariadis, Newcastle University
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).
Cantor combinatorics and almost finiteness
I will give a gentle introduction to almost finiteness via algorithm theory.