Dynamical applications of C*-classification

Abstract: By the work of many mathematicians, including Elliott, Gong, Lin and Niu, the class of infinite-dimensional, simple, separable C*-algebras that have finite nuclear dimension and satisfy the UCT can be classified by an invariant based on K-theory and traces. Insofar as the theme of classification is pervasive throughout science in general, and (noncommutative) topology in particular, this result is an extraordinary feat of mathematics. What's more, it provides powerful machinery for the analysis of the internal structure of amenable C*-algebras. In this talk, I will explain one such application: In the subclass of classifiable C*-algebras consisting of those for which the simplex of tracial states is nonempty, with extremal boundary that is compact and has the structure of a connected topological manifold, automorphisms can be shown to be generically tracially chaotic. Using similar ideas, I will show how certain stably projectionless C*-algebras can be described as crossed products.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper | slides | video )

Noncommutative Geometry in NYC

Series comments: Noncommutative Geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. Our seminar welcomes talks in Number Theory, Geometric Topology and Representation Theory linked to the context of Operator Algebras. All talks are kept at the entry-level accessible to the graduate students and non-experts in the field. To join us click sju.webex.com/meet/nikolaei (5 min in advance) and igor DOT v DOT nikolaev AT gmail DOT com to subscribe/unsubscribe for the mailing list, to propose a talk or to suggest a speaker. Pending speaker's consent, we record and publish all talks at the hyperlink "video" on speaker's profile at the "Past talks" section. The slides can be posted by providing the organizers with a link in the format "myschool.edu/~myfolder/myslides.pdf". The duration of talks is 1 hour plus or minus 10 minutes.