Manisha Garg
University of Illinois, Urbana Champaign (UIUC)
Title
Geometry of groups through their boundaries
Abstract
Geometric group theory studies groups through their large-scale geometry. Boundaries at infinity capture the asymptotic behavior of geodesics and reveals important geometric and algebraic properties of groups. In this talk, I will ask which features of a hyperbolic group’s large-scale geometry remain detectable when we change the metric on its boundary. I will then move beyond hyperbolicity to sublinear Morse boundaries and introduce a sublinear metric based on the fellow-traveling behavior of geodesics (ongoing joint work with Sagnik Jana and Yulan Qing). Returning to the hyperbolic setting, I will discuss its geometric properties, its relationship with polynomial Floyd metrics, and questions about recovering the large-scale geometry of groups from their boundaries.
