Happening @ Michigan https://events.umich.edu/group/4900/rss RSS Feed for Happening @ Michigan Events at the University of Michigan. RTG DeomTopDyn: A 0-1 law for horoball packings of coarsely hyperbolic metric spaces and applications to cusp excursion (April 10, 2024 4:00pm) https://events.umich.edu/event/120554 120554-21844900@events.umich.edu Event Begins: Wednesday, April 10, 2024 4:00pm
Location: East Hall
Organized By: RTG Seminar on Geometry, Dynamics and Topology - Department of Mathematics

On the cusp of the 100 year anniversary, Khinchin’s theorem implies a strong 0-1 law for the real line; namely, the set of real numbers within distance q^{-2-\epsilon} of infinitely many rationals p/q is Lebesgue measure 0 for \epsilon>0, and full measure for \epsilon=0. In these lectures, I will present an analogous Khinchin-type theorem for horoballs packings in Gromov hyperbolic metric spaces that arise from geometrically finite actions with controlled parabolic growth. An application is the logarithm law for cusp excursion; that is, we prove asymptotics for the depth in the horoball packing of a typical geodesic. This is joint work with Giulio Tiozzo.

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Workshop / Seminar Thu, 21 Mar 2024 14:31:19 -0400 2024-04-10T16:00:00-04:00 2024-04-10T17:20:00-04:00 East Hall RTG Seminar on Geometry, Dynamics and Topology - Department of Mathematics Workshop / Seminar East Hall