Dr Parthasarathy has done significant work on the application of probability theory to locally compact groups. Working in collaboration with K Schmidt, he has derived infinitely divisible projective representations, the Levy-Khinchine-Araki formula on locally compact groups and limit theorems for uniformly infinitesimal families of positive definite Kernels. His work has had a significant impact in the area of theoretical quantum mechanics associated with names of Araki and Woods.