Seminar Event Detail

Complex Analysis, Dynamics and Geometry

Date:  Monday, January 31, 2022
Location: Virtual (4:00 PM to 5:00 PM)

Title:  A global shadow lemma and logarithm law in Hilbert geometry

Abstract:   The asymptotic properties of cusp excursions in hyperbolic manifolds are famously quantified by Sullivan's logarithm law, which relates the depth of excursion with the Hausdorff dimension of the limit set. In this talk, we extend this work to Hilbert geometries, proving a global shadow lemma and a logarithm law for Patterson-Sullivan measures in geometrically finite Hilbert manifolds.
We also prove a Dirichlet-type theorem for hyperbolic metric spaces which have sufficiently regular Busemann functions. Joint work with Harry Bray.


Speaker:  Giulio Tiozzo
Institution:  University of Toronto

Event Organizer:   Alexander Wright


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