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Tuesday, September 29, 2020

The legacy of C S Seshadri, mathematician, researcher and educator

Among C S Seshadri's key contributions, the founding of Chennai Mathematical Institute and breakthrough research in algebraic geometry

Written by Kabir Firaque , Edited by Explained Desk | New Delhi | Updated: July 21, 2020 1:42:06 pm
C S Seshadri died on Saturday, aged 88.

In life, the mathematician C S Seshadri was recognised around the world with awards ranging from the Padma Bhushan and the Shanti Swarup Bhatnagar Award in India to fellowships with Royal Society fellowship and American Mathematical Society abroad. In death, he has received tributes from the Prime Minister, the President and leaders in science and mathematics.

From the huge body of his contributions to mathematical research and teaching, two stand out. He founded the Chennai Mathematical Institute, which attracts talent from around the world with its courses on mathematics, computer science and theoretical physics. The other standout is his breakthrough research in algebraic geometry; there is a theorem and a type of constant named after him.

Seshadri died on Friday, aged 88.

The Institute

In Chennai in the mid-1980s, Seshadri got an offer from the newly formed SPIC Science Foundation to form a School of Mathematics. Seshadri was then at the Institute of Mathematical Sciences, where he had launched a doctoral programme but was keen on a programme that would combine high-level research with undergraduate teaching.

“Since it seemed to offer a more realistic path towards launching an undergraduate teaching programme, Seshadri made the radical decision to move to this private setting,” his long-time friend P S Thiagarajan told The Indian Express by email from California. Thiagarajan is a theoretical computer scientist whom Seshadri had recruited at the Institute of Mathematical Sciences, and whom he took along to build the new school. “I was delighted to join him on this adventure,” he said. Others who joined them were then PhD students Vikraman Balaji (mathematics) and Madhavan Mukund (computer science), both now senior faculty members at the Chennai Mathematical Institute.

It began as a teaching programme with initial recognition from Bhoj Open University (Madhya Pradesh). The curriculum centred on mathematics but included core computer science courses. In 1998, the School of Mathematics was reorganised as the Chennai Mathematical Institute, which went on to be recognised as a deemed university by the UGC in 2006.

Today, CMI offers undergraduate education in mathematics and computer science, a research programme in these subjects as well as theoretical physics, and an MSc programme that includes data science. It plans to expand into quantum computing, cryptography, computational biology and mathematical economics, Thiagarajan said.

“Without a doubt, CMI with its present stature and potential would not exist without the vision, leadership and monumental efforts of Seshadri,” Thiagarajan said. “His personality, a delightful mix of simplicity, lack of malice, love of life and uncompromising standards of excellence, attracted the goodwill and support of all those who came into contact with him. This has contributed immeasurably to the founding and development of CMI.”

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His research

Senior school students are familiar with graphs that plot straight lines from linear equations in two variables; science stream students go on to work with higher-order equations that describe two-dimensional shapes such as a circle or 3D shapes such as cube. Seshadri’s field of study was algebraic geometry, a core discipline in modern mathematics that investigates the geometry of solution-sets of such equations.

Applications of algebraic geometry arise in statistics, control theory, robotics, coding theory, integer programming and theoretical physics. The Narasimhan-Seshadri theorem, developed in 1965 with his friend M S Narasimhan, plays a central role in conformal field theory and string theory.

Born in 1932 in Kanchipuram and educated in Chengleput (Tamil Nadu), Chennai and Mumbai (he got his PhD from Bombay University), Seshadri made his major contributions after he went to Paris in 1957. “At the time that he finished his doctoral work, the subject itself was undergoing a unique revolution,” said CMI’s Professor Balaji, one of the PhD students who had joined Seshadri in his move from the Institute of Mathematical Sciences in the 1980s.

“Seshadri went to Paris in 1957 and very quickly entered the sanctum of this new temple of algebraic geometry. This provided a distinctively unifying perspective which connected it to all branches of mathematics at some level,” Balaji said.

It was in this setting that one should view Seshadri’s collaboration with Narasimhan, Balaji said. Its roots lay in the work of the French mathematician André Weil and were closely linked to the work of Henri Poincaré. The Narasimhan-Seshadri theorem set up a correspondence between two basic classes of objects, Balaji said.

“Setting up such correspondences was somewhat like the process of identifying a Rosetta stone for the deciphering of hieroglyphics. The two classes in the Narasimhan-Seshadri theorem were analogous to two of the lines in the Rosetta stone,” Balaji said. “A third line came up much later from the work of Simon Donaldson during the mid-1980s. Once this was provided, many subtle and beautiful aspects of differential geometry, topology, mathematical physics and number theory got unravelled miraculously.”

It was from Seshadri’s work with Narasimhan that arose the concept of “Seshadri constants”.

After Paris

Seshadri returned to India in 1960 and joined Tata Institute of Fundamental Research, where he helped establish a school of algebraic geometry. In 1984, he moved to the Institute of Mathematical Sciences, where he recruited Thiagarajan who was then abroad. From there would follow the Chennai Mathematical Institute.

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