CUNY

Divergence, thickness, and relative hyperbolicity are three geometric properties which determine aspects of the quasi-isometric geometry of a finitely generated group. We will discuss the basic properties of these notions and some of the relations between them. We will then then survey how these properties manifest in right-angled Coxeter groups and detail various ways to classify Coxeter groups using them.

This is joint work with Hagen and Sisto.

Abstract: We will explain a certain natural way to project elements of

the mapping class to simple closed curves on subsurfaces. Generalizing

a coordinate system on hyperbolic space, we will use these projections

to describe a way to characterize elements of the mapping class group

in terms of these projections. This point of view is useful in several

applications; time permitting we shall discuss how we have used this

to prove the Rapid Decay property for the mapping class group. This

talk will include joint work with Kleiner, Minksy, and Mosher.