A homotopical view on $K$ and $KK$-theory for $C^{*}$-algebras

Abstract: The goal of this talk is to motivate the consideration of spectrum-valued K-theory for $C^{*}$-algebras. To this end I will discuss some examples where the spectrum-valued functor helps to simplify classical statements and their justification. I will then explain how to construct a spectrum-valued $K$-theory functor using a homotopical refinement of KK-theory. Accepting the language of $\infty$-categories, the latter can be obtained in a straightforward way by forcing the desired universal properties.

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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