Dixmier trace formulas and negative eigenvalues of Schroedinger operators on noncommutative tori
Raphael Ponge (Sichuan University)
Abstract: In this talk, we shall first address a question raised by Alain Connes during a conference at Fudan University in Shanghai in 2017. We will also explain a link that has come to light only recently between noncommutative geometry and the work of Birman-Solomyak on semiclassical analysis of Schroedinger operators in the 70s. We will then present results obtained jointly with Ed McDonald (UNSW-Sydney) on Cwikel-type estimates on NC tori. As an application we obtain a version of Connes' integration formulas under very weak assumptions. Further applications include versions of the Cwikel-Lieb-Rozenblum and Lieb-Thirring inequalities for negative eigenvalues of Schroedinger operators on noncommutative tori. Ultimately, we get a seminclassical Weyl law for curved noncommutative tori, i.e., NC tori endowed with arbitrary Riemannian metrics.
geometric topologynumber theoryoperator algebrasrepresentation theory
Audience: researchers in the topic
( 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.
Organizers: | Alexander A. Katz, Igor V. Nikolaev* |
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