Speaker: **George Elliott** (Univ. Toronto)

Title: Recent progress in the classification of amenable C^{*}-algebras

Time/Date: 4:45-6:15, Wed. July 22, 2014

Room: 122

Abstract:
Recently Gong, Lin, and Niu (GLN) classified Jiang-Su
stable, simple, unital, separable, amenable (= nuclear),
rationally tracially approximately point--line C^{*}-algebras,
and showed that these exhausted the natural invariant for
C^{*}-algebras with all except the last property, but assumed
to be finite. (The infinite ones are already classified---
by Kirchberg-Phillips---, assuming the UCT.)
Using work of Niu, Santiago, Tikuisis, and me, Gong, Lin,
Niu, and I have shown that the class of simple, unital,
approximately subhomogeneous (ASH) C^{*}-algebras is contained
in the class classified by GLN---and therefore (since ASH
algebras also exhaust the invariant) coincides with it.
There remains the question of showing that arbitrary
stably finite, simple, unital, separable, amenable
C^{*}-algebras are ASH---interesting as the Jiang-Su stable
ones would then be classifiable. (Also, by a result of
Dadarlat, it would follow that the UCT holds for any
separable amenable C^{*}-algebra. Of course, it would still
be interesting just to assume the UCT.)