Professor Kumar is a full professor at Washington University in Saint Louis. He was awarded in 1994 the Shanti Swarup Bhatnagar Prize for Science and Technology, the highest science award in India, in the mathematical sciences category. Doctor Kumar has made profound and original contributions to commutative algebra and algebraic geometry.
He is well known for his contribution settling the Eisenbud-Evans conjectures proposed by David Eisenbud.
Another work that has received much acclaim, is his paper on rational double points on rational surfaces.