Noncommutative geometry of arithmetic groups

Abstract: In this talk we look at constructions from noncommutative geometry which encode various number theoretic properties of arithmetic groups.

In the first part of the talk we will discuss the relation between Conway's big picture and the Connes-Marcolli Gl(2) system. This relation leads to noncommutative spaces encoding properties of groups commensurable with the modular group. In the second part of the talk we discuss Hecke operators for Bianchi groups and the action of these in K-homology via Bredon homology and the Baum-Connes conjecture.

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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