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Giulio Tiozzo (University of Toronto, Canada)
May 14 @ 5:00 pm - 6:00 pm CEST
Speaker: Giulio Tiozzo (University of Toronto, Canada)
Title: Central limit theorems for counting measures in coarse negative curvature
Abstract: We establish general central limit theorems for an action of a group on a hyperbolic space with respect to counting for the word length in the group.
In 2013, Chas, Li, and Maskit produced numerical experiments on random closed geodesics on a hyperbolic pair of pants. Namely, they drew uniformly at random conjugacy classes of a given word length, and considered the hyperbolic length of the corresponding closed geodesic on the pair of pants. Their experiments lead to the conjecture that the length of these closed geodesics satisfies a central limit theorem, and we proved this conjecture in 2018.
In our new work, we remove the assumptions of properness and smoothness of the space, or cocompactness of the action, thus proving a general central limit theorem for group actions on hyperbolic spaces.
We will see how our techniques replace the classical thermodynamic formalism and allow us to provide new applications, including to lengths of geodesics in geometrically finite manifolds and to intersection numbers with submanifolds.
Joint work with I. Gekhtman and S. Taylor.
NOTE: The seminar will be streamed live on our YouTube channel then saved there. If you ask questions, with your video feed on or off, you agree to the use of your image/spoken words for said purpose.