Welcome to the home page of J. K. Verma



Graduate School Days at Purdue: I graduated in 1987 from Purdue University. My thesis adviser was Prof. Bill Heinzer. I learnd a lot from Craig Huneke in a series of six courses and seminars that he offered at Purdue. They are my gurus of commutative algebra. My guru and a good friend during my post-doc position at Kansas was Dan Katz. From him I learnt a lot.

My thesis was about topologies defined by powers and symbolic powers of ideals. During those days of struggle, Jack Ratliff took keen interest in my work.

While I was at Purdue, I was fortunate to be a member of the commutative algebra group. There was a tremndous amount of activity during those days. I was exposed to Hilbert functions, Rees algebras, form rings and mixed multiplicities in many student seminars we used to have at Purdue every week. Some of my contemporaries were Sam Huckaba, Bernie Johnston, Tom Marley, Kishor Shah, K. N. Raghavan, Kyung Ho Oh, and Sun Sook Noh.

Research: Rees algebras and mixed multiplicities were introduced by Rees in the fifties. In 1987, I found an interesting connection between them which led to several papers identifying Cohen-Macaulay Rees algebras by computing the Hilbert function of their maximal homogenous ideal.

Besides Rees algebras and Hilbert functions, I have also worked on Zariski's theory of complete ideals, face rings of simplicial complexes, local cohomology, bounds on a-invariants, fiber cones, joint reductions and form rings and polytopes.

Jobs: I taught at the University of Kansas and Louisiana State University during 1987-1990. I am at IIT Bombay since 1990.

About my Students and colloborators I have been fortunate to get good Ph. D. students: Clare D'Cruz (1996) , A. V. Jayanthan (2003) and Mousumi Mandal (2011) at IIT Bombay. It has been a pleasure to work with them. Clare is now a professor at the Chennai Mathematics Institute, Chennai. Jayanthan is an assistant professor at IIT Madras and Mousumi Mandal is at IISc, Bangalore. Besides them, I have collaborated with Bernie Johnston, Dan Katz, Satya Mandal, K. N. Raghavan, Balwant Singh, Vijay Kodiyalam, Tony Puthenpurakal, Parangama Sarkar,N. V. Trung, Juergen Herzog and Shiro Goto.