Orbit correspondence and groupoid C*-algebras

Abstract: In those NC C*-algebras arising as quantization of a Poisson manifold one can try to establish a relation between the symplectic foliation of the manifold and the unitary dual of its quantization. This relation is what goes under the name of orbit correspondence. In the best behaved cases this correspondence is an homeomorphism. We will review some results on specific examples, stressing the use of "groupoid quantization" as a tool to better understand features of this correspondence.

Mathematics

Audience: researchers in the topic

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.