Overview of hyperbolic and CAT(0) groups
This expository talk will give a overview of Gromov hyperbolic and CAT(0) groups. These broad classes of groups are of central interest in geometric group theory, but also have connections and applications in operator theory. After defining Gromov hyperbolic and CAT(0) metric spaces, which are coarse notions of negative or non-positive curvature, we will discuss key geometric features, look at important examples, and highlight applications of these geometric ideas to group theory and operator theory.
Particular attention will be paid to the utility of the “boundaries at infinity” that arise from these geometric conditions.