My primary field of research is Einstein's theory of general relativity, and I specialize in numerical solution of the field equations. Some of my new and on-going projects include: understanding the nature of and gravitational wave emission from binary compact object mergers, where each member is either a black hole or neutron star; critical phenomena at the threshold of gravitational collapse; the stability and dynamics of higher dimensional black holes; the nature of singularities that generically appear in black hole and cosmological spacetimes; solutions to higher dimensional asymptotically Anti de-Sitter (AdS) Einstein gravity, where one of the anticipated applications is to understand RHIC (Relativistic Heavy Ion Collider) physics via the AdS/CFT correspondence of string theory. The non-linearity and complexity of Einstein's equations make it challenging to solve them even numerically, and some portion of my time is spent designing algorithms to efficiently solve the equations in parallel on large computer clusters, and writing software to manipulate and visualize the simulation results.