Analysis on curved noncommutative tori

Abstract: Noncommutative tori are important examples of noncommutative spaces. Following seminal work by Connes-Tretkoff, Connes-Moscovici, Fathizadeh-Khalkhali, and others a differential geometric apparatus on NC tori is currently being built. So far the main focus has been mostly on conformal deformation of the (flat) Euclidean metric or product of such metrics.

This talk will report on ongoing work to deal with general Riemannian metrics on NC tori (in the sense of Jonathan Rosenberg). Results include local and microlocal Weyl laws, Gauss-Bonnet theorems metrics, and local index formulas.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( 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 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.

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