Seminar Event Detail

Complex Analysis, Dynamics and Geometry

Date:  Monday, February 07, 2022
Location: Virtual (4:00 PM to 5:00 PM)

Title:  The sublinearly Morse boundary as a Model for the Poisson boundary

Abstract:   In algology with the Gromov boundary of a Gromov hyperbolic space, we define a notion of boundary that identifies the hyperbolic directions in a proper geodesic mantric space X. It turns out many arguments in the setting of Gromov hyperbolic spaces can be carried out with sub-linear error terms instead of uniform ones. For example, the notion of Morse geodesics can be replaces with \kappa-Morse geodesics for a given a sublinear function \kappa. We define the \kappa-boundary of X to be the space of all \kappa-Morse quasi-geodesics rays. We show that this boundary, equipped with the corse visual topology, is QI-invariant, metrizable and large. Namely, for a large class of groups, the generic direction is represented by a \kappa-Morse geodesic and the \kappa-boundary can be used as a topological model for the Poisson boundary of random walk in the group. The talk is based on several joint projects with Ilya Gekhtman, Yulan Qing and Giulio Tiozzo.


Speaker:  Kasra Rafi
Institution:  University of Toronto

Event Organizer:   Alex Wright   


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