  The theory of complex hyperbolic discrete groups is still in its childhood
but promises to grow into a rich subfield of geometry. In this paper I will
discuss some recent progress that has been made on complex hyperbolic
deformations of the modular group and, more generally, triangle groups. These
are some of the simplest nontrivial complex hyperbolic discrete groups. In
particular, I will talk about my recent discovery of a closed real hyperbolic
3-manifold which appears as the manifold at infinity for a complex hyperbolic
discrete group.

Differential Geometry;Group Theory