Fifteen Eighty Four

Even though I have liked mathematics ever since elementary school, I really started to enjoy mathematics in middle school, when I learned proofs in Plane Geometry. During my high school (up to grade 12), I continued to like mathematics but I was quite dissatisfied the way mathematics was taught (particularly differential and integral calculus with no emphasis on rigor). This led me to lean more towards physics during the last two years of high school. However, to my disappointment, physics was even more imprecise. Even though I studied Mathematics, Physics and Chemistry during my B.Sc. years, I was decidedly more interested in mathematics and it became clear that mathematics is what I would like to pursue as a career. During my first two years of college, I got hold of W. Rudin’s Principles of Mathematical Analysis which I found fascinating to read. It finally cleared all the imprecisions I had encountered in my calculus education – it was a very ‘liberating’ feeling. During those two years, I also studied I.N. Herstein’s Topics in Algebra. It was fun to do exercises from the book, particularly group theory.

I earned my B.Sc. degree in 1973 from a small college affiliated to Gorakhpur University (in northeastern India) and then my M.Sc. degree in mathematics from Bombay University in 1975. Immediately afterwards, I joined the Tata Institute of Fundamental Research (TIFR), Bombay, to do my Ph.D. in mathematics which I obtained in 1986.

I held two postdoctoral positions: for one year (1983-84) at the Mathematical Sciences Research Institute, Berkeley, and for another year (1984-85) at MIT (as C.L.E. Moore Instructor). Then, I returned to TIFR as Fellow and then promoted to Reader. I moved to the University of North Carolina, Chapel Hill in 1991 as a Full Professor.

I have held short and long term visiting professor/scholar positions at various institutions including the Institute for Advanced Study, Princeton; MIT; The University of British Columbia; University of P. and M. Curie, Paris; Scoula Normale Superiore, Pisa; Ecole Normale Superieure, Paris; Max Planck Institut fur Mathematik, Bonn; ICTP, Trieste; Research Institute for Mathematical Sciences, Kyoto; Erwin Schrodinger International Institute for Mathematical Physics, Wien; Issac Newton Institute for Mathematical Sciences, Cambridge; Weizmann Institute, Israel; Hausdorff Research Institute for Mathematics, Bonn; Institut Mittag-Leffler, Djursholm (Sweden); Duke University; University of Sydney.

In trying to build a theory it is very important to look at some examples and ‘test’ the questions one wants to ask. But, in the end, I am more interested in ‘general’ results. For example, I will not be satisfied to prove a result say for SL(n) (unless it is not true more generally) and I will try to prove it for general semisimple groups (which may sometimes require a different modified formulation). For me, examples are stepping stones to a general theory. In the same vein, I am completely dissatisfied with a caseby-case proof of a general result. I like collaborations as is evident from my fairly long list of collaborators (36 so far). Collaborators bring different expertise to bear on the problem at hand, which is often a great asset. But, it is important to have ‘right tuning’ with the collaborators.

It is very important to convey your results in a precise and clear way. When I am writing a paper or a book, I keep this principle in mind. I hope I have not been too unsuccessful. Some of the books by Milnor (e.g., his book with Stasheff on ‘Characteristic Classes’), Rudin and Serre are my ideals.