Discrete subgroups of Lie groups

Princeton University, Princeton NJ

Investigators

Abstract

Abstract Oh The proposed project mainly deals with understanding of the structure, classification and description of semisimple Lie groups as well as their discrete subgroups. We are investigating problems arising in connection with number theory and geometry. The techniques we have used involve the theories of algebraic groups, arithmetic groups, dynamical properties of flows on homogeneous spaces and infinite dimensional unitary representations. A semisimple Lie group and its lattices are special collections of symmetries of a geometric or arithmetic object. This research aims to contribute to understanding of the symmetries whose study has proven to be one of the central themes in mathematics and physics. Some of these has found remarkable applications in such fields as computer science and quantum mechanics.