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Conjeevaram Srirangachari Seshadri

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Conjeevaram Srirangachari Seshadri

In His Own Words

Those Magic Moments

There are a number of moments I cherish.

For instance:

- Proving a particular case of a problem of Serre and then finding my solution to a question posed by Chevalley during his seminar,

- Working collaboratively with M.S. Narasimhan and my construction of the related moduli spaces,

- Working on a well-known conjecture of David Mumford,

- Having the first idea of a standard monomial theory, inspired by some work of De Concini and Procesi and then formulating the precise conjectures in collaboration with Lakshmibai.

Challenges to Come

In the context of my present interest and collaboration with Balaji, the challenge is to gain a deeper understanding of moduli problems under specialization.


In my formative years in Paris, I learned from the masters like Chevalley, Serre and Grothendieck and attended the Cartan and the Bourbaki seminars. I made friends with Verdier, Gabriel, Demazure, and Douady. Later, I collaborated with Drezet and appeared as a volume in Asterisque. The Indo-French collaboration started with Verdier and is now in the able hands of Waldschmidt.

Words for the Up & Coming

Continue the great traditions of mathematics in France!




professor Conjeevaram Srirangachari Seshadri

Presented by Sinnou David, professor of mathematics


It is an honor for me to present C.S. Seshadri today. Above all, I wish to acknowledge the scientist, for whom I can only outline his vast contribution.


At the beginning of his scientific life in the 50s, Seshadri paved the way to a solution to a Serre conjecture on projective modules over polynomial rings.


Influenced by Chevalley, his construction of Picard varieties is inspired by the work at the Chevalley seminar in Paris.


He is considered a pioneer in the development of a satisfactory theory of the moduli spaces of vector bundles on a projective curve, which was the focus of much of his subsequent work. A major step in this direction is his work with M.S. Narasimhan, another great figure of the Indian school, on the classification of stable bundles of curves. The construction of the moduli space has inspired a series of space module constructions.


A third area of his work is on quotients spaces and geometric reductivity. His rich contributions to this area led firstly to the demonstration of the Mumford conjecture for GL(2). The tools he then developed in this direction have led in particular to the Seshadri criterion for amplitude, a numerical criterion also called “Seshadri constants.” They are now widely used for both the classification of algebraic varieties and in arithmetic, for example, to show that curves have uniformly very few rational points.


One lat area I would like to discuss is that of the “theory of standard monomials,” which he initiated in 1970 and continued with V. Lakshmibai and C. Musili, which generalized Hodge theory for Grassmaniennes. The aim was to build bases for sections of line bundles on Schubert varieties, and therefore the basis for the space of irreducible representations of reductive algebraic groups. This theory reflects the intrinsic geometry of the Schubert variety and the intricate combinatorics of the Weyl group.


Recognition of his work by the international scientific community is shown by the numerous invitations he has received, and we have been lucky enough to receive C.S. Seshadri as a visiting professor at our University. He is a Fellow of the Royal Society, a member of the American Academy of Sciences, and winner of TWAS. India has honored him repeatedly, with both scientific and civil honors: he was received in the order of Padma Bushan, and given the rare distinction of “National Professor.”


C.S. Seshadri is also an organizer and an entrepreneur. In 1989, he embarked on a unique challenge: to establish a research institute in fundamental mathematics and theoretical computing that was entirely privately funded. This is now the Chennai Mathematical Institute, where students, in accordance with Seshadri’s vision, live immersed in the world of research from the moment they arrive, at the bachelor’s level. They rub shoulders daily with the experts around them.


His dream was to build a training center of excellence, inspired by the successful model of the école Normale Supérieure in France. The institute accepts young people every year who, at the bachelor’s level, already aspire to prepare a thesis. It is the center in which some of the brightest students in the country can be found.


C.S. Seshadri is one of the few mathematicians who have contributed to make the Indian School what it is today. He has had many students, including Pavaman Murthy, V. Lakshmibai Madhav Nori and Vikraman Balaji.


Finally, and this is the last thing I would like to note, C.S. Seshadri somehow personifies Franco- Indian relations.


Born in 1932, he studied at Loyola College in Madras in the heart of British India (the Madras Presidency), and he was exposed to French culture at an early age. His teacher was a French mathematician, trained by E. Cartan, known as “Father Racine”, who encouraged him to join the Tata Institute of Fundamental Research in Bombay, which was a newly created institution after India’s independence.


Seshadri spent 1957 to 1960 in Paris. During this period, he interacted with members of the French school of mathematics, such as Cartan, Chevalley, Grothendieck, and Serre Scwartz. He returned to Tata in 1960, where he remained until 1984, when he joined the Institute of Mathematical Sciences, Chennai.


In the 60s, he was one of the architects of the great success of ‘’the Tata course” which had several French scientists involved, led by Laurent Schwartz. Foreign researchers would spend at least three months and many reference books were published from the class notes. Mumford’s book on abelian varieties, whose notes were organized by Seshadri’s students, is a perfect example.


In the 80s, he led the revival of Franco-Indian scientific cooperation that had somewhat weakened in the previous decade. With J.L. Verdier on the French side, they relaunched the partnership between the two countries by signing a cooperation agreement with the CNRS. The scientific exchanges from that agreement were successful and several of them were subsequently extended through bilateral programs funded by CEFIPRA (the Franco- Indian Centre for the Promotion of Advanced Research). This revival led to the creation of the IFIM (The Indo-French Institute of Mathematics).


The institute he created, CMI, is a partner with the ENS. And every year, several ENS students spend a few months in India to learn mathematics with local researchers including Seshadri. Our young people are offered the opportunity to teach at a high level to an informed public. Some CMI students spend several months each year in Paris to follow our M2 courses. The CMI is a partner of UPMC, and our research professors regularly deliver specialized courses.


His work has been fundamental to the development of the scientific landscape in India and to its strengthening at each stage through a new generation of talent. For fifty years, he has been a driving force in relations between our two countries. He is a friend of France and a friend of UPMC. We are proud to have this prestigious researcher as Doctor Honoris Causa of our University.