Colloquium: Curtis Kent (Courant Institute of Mathematics)

Event Details

Title: The coarse geometry of relatively hyperbolic spaces

Abstract: Coarse geometry is the study of metric spaces from a large scale point of view. Two metric spaces have the same coarse geometry if they look the same from infinitely far away. Asymptotic cones are one useful way to formalize this idea of looking at a space from infinitely far away. Originally constructed by Gromov in his proof of the Polynomial Growth Theorem, asymptotic cones provide a rich setting for the study of groups. I will discuss how asymptotic cones give rise to several classes of groups which generalize hyperbolic groups. Specifically I will discuss the asymptotic cones of relatively hyperbolic groups and present a Cartan-Hadamard type theorem for relatively hyperbolic groups.