We examine the correspondence between the conformal field theory of boundary operators and two-dimensional hyperbolic geometry. by consideration of domain boundaries in two-dimensional critical systems, and the invariance of the hyperbolic length, we motivate a reformulation of the basic equation of conformal covariance. The scale factors gain a new, physical interpretation. We exhibit a fully ...

I work in geometric group theory, which is the study of groups via the metric spaces on which they act. I use combinatorial, geometric, and topological tools to study the coarse geometry of infinite discrete groups. Coarse geometry is the natural setting for studying discrete groups, since their metric geometry is only well-defined up to bounded distortion. Gromov [65] revolutionized the field ...