My area of research is hyperbolic 3-manifolds and knot theory. Thurston established the importance of hyperbolic geometry and geometric invariants in the study of 3-manifolds and knot theory. I am interested in the deformations of hyperbolic structures on 3-manifolds and interactions between hyperbolic geometry with number theory. Jones revolutionized knot theory by introducing the Jones polynomial in 1984 which led to families of diagrammatic invariants. My current research is motivated by the problem of relating geometric invariants like hyperbolic volume to diagrammatic invariants like the Jones polynomial. I am also interested in understanding knots from the point of view of graph theory.

Dr Champanerkar earned his Ph.D. at Columbia University in 2003. Before joining CSI he worked for one year at Barnard College, Columbia University as a postdoc and for four years at the University of South Alabama as an Assistant Professor.

Dr. Champanerkar is a member of a Focused Research Group (FRG) that received an NSF-FRG grant for collaborative research on topics in geometric topology. With this funding, Dr. Champanerkar has co-organized two major international conferences, with a special focus on the Volume Conjecture. Dr. Champanerkar is a co-organizer of the Geometry and Topology seminar at the CUNY Graduate Center.  For details about his research, see http://www.math.csi.cuny.edu/~abhijit/