Mudumbai Seshachalu Narasimhan (7 June 1932 – 15 May 2021) was an Indian mathematician. His focus areas included number theory,

algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

, representation theory, and

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be sol ...

s. He was a pioneer in the study of

moduli space In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects. Such spac ...

s of holomorphic vector bundles on projective varieties. His work is considered the foundation for Kobayashi–Hitchin correspondence that links

differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...

and algebraic geometry of vector bundles over

complex manifold In differential geometry and complex geometry, a complex manifold is a manifold with an atlas of charts to the open unit disc in \mathbb^n, such that the transition maps are holomorphic. The term complex manifold is variously used to mean a com ...

s. He was also known for his collaboration with mathematician C. S. Seshadri, for their proof of the Narasimhan–Seshadri theorem which proved the necessary conditions for stable vector bundles on a Riemann surface. He was a recipient of the Padma Bhushan, India's third highest civilian honor, in 1990, and the Ordre national du Mérite from France in 1989. He was an elected Fellow of the Royal Society, London. He was also the recipient of Shanti Swarup Bhatnagar Prize in 1975 and was the only Indian to receive the King Faisal International Prize in the field of science.

Early life

Narasimhan was born on 7 June 1932 into a rural family in Tandarai in present day Tamil Nadu, as the eldest among five children. His family hailed from the North Arcot district. After his early education in rural part of the country, he joined Loyola College in Madras for his undergraduate education. Here he studied under Father Charles Racine, a French Jesuit professor, who in turn had studied under the French mathematician and geometer Élie Cartan. He joined the Tata Institute of Fundamental Research (TIFR), Bombay, for his graduate studies in 1953. He obtained his Ph.D. from the University of Mumbai in 1960 where his advisor was the mathematician

K. S. Chandrasekharan Komaravolu Chandrasekharan (21 November 1920 – 13 April 2017) was a professor at ETH Zurich and a founding faculty member of School of Mathematics, Tata Institute of Fundamental Research (TIFR). He is known for his work in number theory an ...

, who was known for his work on number theory.

Career

Narasimhan started his career in 1960 when he joined the faculty of the Tata Institute of Fundamental Research (TIFR); he later went on to become an honorary fellow. His areas of focus while at TIFR included studying partial differential operators and

elliptic operator In the theory of partial differential equations, elliptic operators are differential operators that generalize the Laplace operator. They are defined by the condition that the coefficients of the highest-order derivatives be positive, which i ...

s. During this time, he visited France under the invitation of Laurent Schwartz and was exposed to the works of other French mathematicians including Jean-Pierre Serre, Claude Chevalley, Élie Cartan, and Jean Leray. He contracted pleurisy during his time in France and was hospitalized. He would later recount the incident as exposing him to the "real France" and further strengthening his

leftist Left-wing politics describes the range of political ideologies that support and seek to achieve social equality and egalitarianism, often in opposition to social hierarchy. Left-wing politics typically involve a concern for those in soci ...

sympathies which were already triggered by his interactions with the Trotskyist Schwartz. During his time in France he also collaborated with Japanese mathematician Takeshi Kotake working on the analyticity theorems for determining specific types of

s that satisfied Cauchy–Schwarz inequalities. His work with Kotake was known as the Kotake–Narasimhan theorem for elliptic operators in the setting of ultradifferentiable functions. He collaborated with Indian mathematician C. S. Seshadri for the ground-breaking Narasimhan–Seshadri theorem which has been at the core of algebraic geometry and number theory for over half a century. The theorem derived the relation between the purely algebraic notion of stable vector bundles on Riemann surfaces. The theorem made a connection between two areas of modern geometry viz.

and

. Both Seshadri and Narasimhan were elected Fellows of the Royal Society for their work on this topic. He also collaborated with mathematician R. R. Simha on proving the existence of moduli of general type complex structures on a real analytic manifold. These measures were called Simha–Narasimhan measures on Riemann surfaces. For his work, Narasimhan was considered a pioneer in the study of

s of holomorphic vector bundles on projective varieties. His work is considered the foundation for Kobayashi–Hitchin correspondence that links

and

of vector bundles over

s. When the National Board of Higher Mathematics was established in India, Narasimhan was the first chairman of the board. In 1992, Narasimhan retired from TIFR, and became the head of the research group in Mathematics at the International Centre for Theoretical Physics in Trieste. He had also served as a visiting scholar at the Institute for Advanced Study, in Princeton, New Jersey in 1968. After retiring from ICTP, he settled in Bangalore. He was a Fellow of the Royal Society, London as well as recipient of French National Order of Merit in 1989. He was awarded the Padma Bhushan, India's third highest civilian honor, in 1990. He was also the recipient of the Shanti Swarup Bhatnagar Prize in 1975, Third World Academy of Sciences Prize for Mathematics in 1987, and the Srinivasa Ramanujan Medal in 1988. He was also the recipient of the

King Faisal International Prize for Science The King Faisal Foundation ( ar, مؤسسة الملك فيصل الخيرية; ''KFF''), is an international philanthropic organization established in 1976 with the intent of preserving and perpetuating King Faisal bin Abdulaziz's legacy. The fo ...

in 2006, and award that he won jointly with mathematician Simon Donaldson, Imperial College.Donaldson and Narasimhan Receive 2006 King Faisal Prize
- Notices of the American Mathematical Society, March 2006, Volume 53, Number 3. As of 2021, he was the only Indian to have won the King Faisal International Prize for Science.

Personal life

Narasimhan was married to

Sakuntala Narasimhan Sakuntala Narasimhan (born 30 December 1939) is an Indian journalist, consumer rights activist, and classical vocalist from the Rampur-Sahaswan gharana of Hindustani classical music. She was a disciple of Hafeez Ahmed Khan and is the only vocal ...

, a classical musician, journalist and a consumer rights activist. The couple had a daughter,

Shobhana Narasimhan Shobhana Narasimhan is an Indian academic who is Professor of Theoretical Sciences at the Jawaharlal Nehru Centre for Advanced Scientific Research in Bangalore, India. Her main area of interest is computational nanoscience. Her research examines ...

, a scientist and professor at Jawaharlal Nehru Centre for Advanced Scientific Research, and a son. Narasimhan was interested in

Indian classical music Indian classical music is the classical music of the Indian subcontinent. It has two major traditions: the North Indian classical music known as '' Hindustani'' and the South Indian expression known as '' Carnatic''. These traditions were not ...

, contemporary art and painting, as well as Tamil literature. Narasimhan died on 15 May 2021, in Bangalore at the age of 88. He had been undergoing treatment for cancer for the previous year.

Selected publications

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References

External links

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Artless innocents and ivory-tower sophisticates: Some personalities on the Indian mathematical scene
�� M. S. Raghunathan * {{DEFAULTSORT:Narasimhan, M. S. 1932 births 2021 deaths 20th-century Indian mathematicians Algebraic geometers Differential geometers Fellows of the Royal Society Institute for Advanced Study visiting scholars Narasimhan family People from Kanchipuram district Recipients of the Padma Bhushan in science & engineering Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science Scientists from Tamil Nadu Tamil scholars Tata Institute of Fundamental Research alumni TWAS laureates University of Madras alumni