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.)