Nuclear dimension and Z-stability of simple C*-algebras

Abstract: Much recent work in C*-algebra theory has focused on regularity properties. This is a response to examples of "irregular" simple nuclear C*-algebras by Villadsen (algebras with perforation in their ordered K-theory), Rordam (algebras with both finite and infinite projections), and Toms (algebras that cannot be distinguished by ordered K-theory and traces). I will describe two regularity properties: finite nuclear dimension and Z-stability (aka Jiang-Su-stability). In joint work with Castillejos, Evington, White, and Winter, we showed that these properties coincide for simple separable nuclear unital C*-algebras, verifying a conjecture of Toms and Winter. I will discuss this result and its implications.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( 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.