The Varieties of Discrete Experience, and Other Tales of Isometric Actions on Gromov Hyperbolic Metric Spaces

Abstract: We survey joint work with David Simmons and Mariusz Urbanski that explores extensions of the classical theory of Kleinian groups acting on a finite-dimensional hyperbolic space to analogous actions on hyperbolic metric spaces in the sense of Gromov, a broad class of spaces which includes infinite-dimensional rank one symmetric spaces of noncompact type and much more!

Several phenomena induced by greater degrees of freedom than in finite dimensions (e.g. the different shades of discreteness alluded to in the title) introduce new delicacies and thereby uncover fresh seams that await investigation. The talk is aimed at students and beginners who are unencumbered by the wisdom of experts and others tragically burdened by knowing too much. Being a novice, any help from the audience in generating new questions will be graciously accepted.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

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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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