Searching for noncommutative spectrum functors

Abstract: In the classical algebra-geometry correspondences, the assignment turning an algebra into a space is a type of spectrum. Thus spectra of noncommutative algebras have been of interest for a long time in both algebra and noncommutative geometry. Because the spectrum typically provides a functor from commutative algebras to spaces, it is natural to ask whether we can extend it to a noncommutative spectrum functor. I will discuss this problem, along with negative and partial positive results toward its resolution.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper | 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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