Remarks on the Cuntz Semigroup

Abstract: The Cuntz semigroup was introduced by J. Cuntz in the late 1970s as a refinement of K-theory for C*-algebras. Around 2000, A. Toms discovered examples of simple $C^*$-algebras that share the same Elliott invariant, given by K-theory, traces, and their pairings, but differ in their Cuntz semigroups. This showed that the Cuntz semigroup captures additional structure beyond the classical invariants and renewed interest in its study. In this talk, I will give an overview of the Cuntz semigroup, explain its basic ideas, and discuss some recent developments related to it. Topics will include the way-below relation and the notion of Cu-nuclearity.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( slides | video )

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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 meet.google.com/zjd-ehrs-wtx (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.

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