Discrete Groups in Complex Hyperbolic Geometry

Overview: The proposed research is a continued investigation of discrete groups of complex hyperbolic isometries, building upon the PI and his collaborators' recent success in constructing previously unknown nonarithmetic lattices in PU(2; 1). More specically, we propose to study lattices generated by reflections in PU(n; 1) for n > 2, geometric aspects of arithmetic lattices, and deformations of hyperbolic 3-manifold groups into PU(3; 1)