Dr. Raghunathan has made advancements in the area of Lie groups, particularly discrete subgroups of Lie groups. In his earlier work he proved the rigidity of "non-uniform" arithmetic lattices connected with Selberg's conjecture. Later, he essentially solved Selberg's conjecture for non-uniform lattices before the complete solution of the conjecture by G.A. Margulis. Through his recent work he has made significant contributions to Serre's conjecture on the "Congruence Sub-group Problem" and generalisations of Quillen's solution of Serre's problem on vector bundles on the affine space.