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There will be a SOAR meeting in Glasgow on Friday 9th of February 2018. The schedule and abstracts for the talks are below.

Schedule:

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".

17:30: Dinner.

Abstracts:

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
Gabor Elek
I will give a gentle introduction to almost finiteness via algorithm theory.

Page last modified on Tuesday, 6 February 2018 14:04:08 GMT