Remembering MS Narasimhan, a versatile and fearless mathematician

MS Narasimhan, December 2010. Photo: Bocardodarapti / Wikimedia Commons, CC BY-SA 3.0

With the death of Mr. S. Narasimhan, India lost one of its most versatile mathematicians.

As someone to whom he has been a mentor, colleague, longtime collaborator and close friend, I feel particularly helpless.

Narasimhan, or MSN as his friends called it, came from a family in a small village called Thandarai, in Tiruvannamalai district, Tamil Nadu. His family had a good income from farming and was doing well, although MSN’s father died before the age of 12.

Thandarai did not have a high school and MSN remembered going to school in a nearby town on an ox cart. He did well in his studies and was able to enter the prestigious Loyola College of Madras (now Chennai), where he was fortunate to be taught by good teachers.

One of them was Father Racine, a Jesuit who came to India as a missionary from France, after receiving a doctorate under the direction of Elie Cartan, one of the great mathematicians of the twentieth century. Although Racine was no longer involved in research, he was familiar with contemporary mathematics. It was extremely rare in India at that time.

One of MSN’s classmates was another prominent researcher, CS Seshadri, who died late last year. Seshadri founded the School of Mathematics in the late 1980s, which later became the Chennai Mathematics Institute.

Father Racine had a knack for identifying good students and he encouraged the brightest to come to the brand new Tata Institute of Fundamental Research (TIFR), Bombay, which had been established with Homi J. Bhabha as director. MSN and Seshadri both joined TIFR in 1953.

One of the sections of TIFR was “The School of Mathematics,” which aspired to be in the same league as its counterpart at the Institute of Advanced Study at Princeton. The principal of this school at the time was K. Chandrasekharan, known as KC, who had returned to India after a stint at the Princeton Institute.

KC was aware that very few people in India had even a rudimentary knowledge of modern mathematics. He had the understanding, the necessary contacts and the administrative capacity to deal with this. He invited top mathematicians from various centers around the world and asked each of them to teach a course in an area of ​​mathematics, had students write the lectures, and helped publish the notes.

One of the guests was Laurent Schwartz, the Frenchman who had won the Fields Medal in 1950. MSN was Schwartz’s note writer, and Schwartz was soon impressed with the ability of MSN and other students. He encouraged many French mathematicians, young and old, to visit the TIFR and also organized the visit of TIFR students to French universities through scholarships.

As a result, MSN and Seshadri were delegated to France. While there, MSN studied under Schwartz and other accomplished mathematicians. With a Japanese mathematician named Takeshi Kotake, he wrote an important article on differential equations.

Unfortunately, he suffered from pleurisy1 during his stay and had to be hospitalized. He was never bitter about this circumstance; in fact, he felt that it allowed him to socialize with many layers of French society outside of academia and also that it made him feel comfortable with the spoken dialects of French.

I was a graduate student when he returned, and his knowledge was to me, then a struggling student, a great boon as I tried to find a problem to work on for my PhD. With a younger colleague, Mr. S. Raghunathan, who was to reach great heights later, we organized a seminar which was well received.

MS Narasimhan and S. Ramanan, at ICTP in Trieste in the 1980s. Photo: S. Ramanan

One day, while I was playing tennis, MSN was waiting backstage and asked me when I was done, “You’ve learned a lot of good math but do you have math problems to work on?” I had learned differential geometry from one of the visiting mathematicians from France, JL Koszul, and said I knew one (in the vector bundle classification space there was a homogeneous connection and I was wondering if this could be universal for connections as well).

MSN was excited about the problem and we worked day and night for ten days or so, and finally proved my guess to be correct. It turned out to be central to many subsequent developments, both in the fields of differential geometry and gauge theory.

Seshadri had also returned by this time, and he and MSN worked together on an issue that stemmed from the concept of “stable bundles”, which had just been introduced by David Mumford. This resulted in a foundational work that brought together two different concepts – one of topology and the other algebraic-geometric. This is still cited today, after 60 years; some time ago there was also a lecture called “Fifty Years of Narasimhan-Seshadri Theorem”!

Narasimhan’s influence on the TIFR school was immense. It has been a privilege and a pleasure to work with him for over 20 years. For some of our students, we were “co-mentors”. He has trained many students who, over time, have distinguished themselves as good mathematicians.

“You have to learn to work from the top,” MSN said. What he meant was that you shouldn’t get bogged down in details while researching. You have to try to think outside the box, solve the problem, and then work out the details. This attitude helped him fearlessly tackle problems in a variety of fields, including gauge theory in physics, differential equations, differential geometry, algebraic geometry, and representations of real Lie groups, to name a few. areas. It also allowed him to collaborate with mathematicians from different vintages.

Administratively, MSN became the first chairman of the National Council for Higher Mathematics, and I had the pleasure of working as secretary at that time. He insisted that bright Indian students should be retained in India. Even if they emigrated abroad, efforts would have to be made to recover them, he said. Only then can the students in India be well educated and the general scientific level of the country will increase.

His concern also extended to students from other developing and underdeveloped countries. After nearly 40 years at TIFR, he decided to accept the offer to lead the mathematics section of the International Center for Theoretical Physics in Trieste, established by Pakistani Nobel laureate Abdus Salam in 1964. Upon his return, MSN s ‘is based in Bengaluru.

Although he retired, he was still well engaged in mathematical research, and even a few months before the end he helped solve a problem that a pupil of a mutual friend, Oscar Garcia-Prada, was in the process of. taken.

Besides math, MSN was interested in books, especially in Tamil. His wife Sakuntala, an accomplished singer in the Carnatic and Hindustani traditions, once recalled that during his honeymoon, he had packed books in Tamil and also on mathematics! MSN was also an admirer of art, making the most of his stays in France. His daughter, Shobana, is a solid-state physicist who, to MSN’s delight, was recently elected to the American Academy of Arts and Sciences. His son Mohan was in the US for several years and came to India and helped MSN in his later years.

I have been fortunate to have the close company of MSN for as long as I have. Rest in peace my friend.

S. Ramanan is a mathematician and assistant professor at the Chennai Mathematical Institute.

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