CBMS Conference: The Basic Homotopy Lemma, The Asymptotic Uniqueness Theorem, and Classification of C*-Algebras, June 1-5, 2015

This award will fund a CBMS Conference entitled 'The Basic Homotopy Lemma, The Asymptotic Uniqueness Theorem, and Classification of C*-Algebras' with principal lecturer Huaxin Lin to be held at the University of Wyoming during June of 2015. The study of operator algebras is one of the major branches of modern mathematics. It was launched by John von Neumann in 1930's with an aim of explicating quantum mechanics. The classification of at least the more well-behaved amenable C*-algebras is considered as one of the main questions at the moment in operator algebra theory. Recently this subject has been developing very rapidly, and substantial progress has been made. The main goal of this conference is to have a detailed and systematic account of this breakthrough in the classification of C*-algebras, with an emphasis on basic homotopy lemmas and asymptotic uniqueness theorems. The conference will pull together these recent results, to get a clear picture of the current status, and to chart the possible direction of future research. This grant will support the participation of graduate students and junior faculty members in the conference, and also foster the production of a monograph which will be used by the wider community.

The topic of the project is on the classification of C*-algebras, the basic homotopy lemmas, and the asymptotic uniqueness theorems. After the discovery of various exotic examples of AH-algebras, the program of the classification of amenable C*-algebras has been focused on the more well-behaved C*-algebras, or the class of C*-algebras which absorb the Jiang-Su algebra Z. With the one-parameter deformation technique introduced by Winter, the classification of Z-stable C*-algebras can be reduced to the construction of a certain homotopy between two homomorphisms of the rationalized C*-algebras. The existence of such a homotopy is ensured by Lin's very recent asymptotic uniqueness theorems and basic homotopy lemmas, which have already had an impact outside classification theory.