Geometry & Topology Seminar – Yulan Qing – Boundary of Groups
Jan 12, 2023
3:30PM to 4:30PM
Date(s) - 12/01/2023
3:30 pm - 4:30 pm
Abstract” Gromov boundary provides a useful compactification for all infinite-diameter Gromov hyperbolic spaces. It consists of all geodesic rays starting at a given base-point and it is an essential tool in the study of the coarse geometry of hyperbolic groups. In this study we introduce a generalization of the Gromov boundary for all finitely generated groups. We construct the sublinearly Morse boundaries and show that it is a QI-invariant topological space and it is metrizable. We show the geometric genericity of points in this boundary using Patterson Sullivan measure on the visual boundary of CAT(0) spaces. Lastly we discuss the connection between the sublinearly Morse boundary and random walk on groups. As applications we answer open problems regarding QI-invariant models of random walk on CAT(0) groups and on mapping class groups.
Location: Hamilton Hall, Room 312