Mudumbai Seshachalu Narasimhan (7 June 1932 – 15 May 2021) was an Indian

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

. His focus areas included

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

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 In differential geometry, algebraic geometry, and gauge theory, the Kobayashi–Hitchin correspondence (or Donaldson–Uhlenbeck–Yau theorem) relates stable vector bundles over a complex manifold to Einstein–Hermitian vector bundles. The corres ...

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 bundle In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X (for example X could be a topological space, a manifold, or an algebraic variety): to every po ...

s 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 In mathematics, the Narasimhan–Seshadri theorem, proved by , says that a holomorphic vector bundle over a Riemann surface is stable if and only if it comes from an irreducible projective unitary representation of the fundamental group. The main c ...

which proved the necessary conditions for stable vector bundles on a

Riemann surface In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed vers ...

. 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 The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...

, London. He was also the recipient of

Shanti Swarup Bhatnagar Prize The Shanti Swarup Bhatnagar Prize for Science and Technology (SSB) is a science award in India given annually by the Council of Scientific and Industrial Research (CSIR) for notable and outstanding research, Applied science, applied or Fundamenta ...

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 Élie Joseph Cartan (; 9 April 1869 – 6 May 1951) was an influential French mathematician who did fundamental work in the theory of Lie groups, differential systems (coordinate-free geometric formulation of PDEs), and differential geometry. ...

. He joined the Tata Institute of Fundamental Research (TIFR),

Bombay Mumbai (, ; also known as Bombay — the official name until 1995) is the capital city of the Indian state of Maharashtra and the ''de facto'' financial centre of India. According to the United Nations, as of 2018, Mumbai is the second- ...

, for his graduate studies in 1953. He obtained his Ph.D. from the

University of Mumbai The University of Mumbai is a collegiate university, collegiate, State university (India), state-owned, Public university, public research university in Mumbai. The University of Mumbai is one of the largest universities in the world. , the un ...

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 operator In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation that accepts a function and retur ...

s 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 Laurent-Moïse Schwartz (; 5 March 1915 – 4 July 2002) was a French mathematician. He pioneered the theory of distributions, which gives a well-defined meaning to objects such as the Dirac delta function. He was awarded the Fields Medal in 19 ...

and was exposed to the works of other French mathematicians including Jean-Pierre Serre,

Claude Chevalley Claude Chevalley (; 11 February 1909 – 28 June 1984) was a French mathematician who made important contributions to number theory, algebraic geometry, class field theory, finite group theory and the theory of algebraic groups. He was a foundin ...

, 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 Trotskyism is the political ideology and branch of Marxism developed by Ukrainian-Russian revolutionary Leon Trotsky and some other members of the Left Opposition and Fourth International. Trotsky self-identified as an orthodox Marxist, a rev ...

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

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

s. The theorem made a connection between two areas of modern geometry viz.

and

. Both Seshadri and Narasimhan were elected

Fellows of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural knowledge, including mathemati ...

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

s. 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

that links

and

s 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 The Abdus Salam International Centre for Theoretical Physics (ICTP) is an international research institute for physical and mathematical sciences that operates under a tripartite agreement between the Italian Government, United Nations Education ...

Trieste Trieste ( , ; sl, Trst ; german: Triest ) is a city and seaport in northeastern Italy. It is the capital city, and largest city, of the autonomous region of Friuli Venezia Giulia, one of two autonomous regions which are not subdivided into provi ...

. He had also served as a visiting scholar at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

, in

Princeton, New Jersey Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of whi ...

in 1968. After retiring from ICTP, he settled in

Bangalore Bangalore (), officially Bengaluru (), is the capital and largest city of the Indian state of Karnataka. It has a population of more than and a metropolitan population of around , making it the third most populous city and fifth most ...

. He was a

Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...

, 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

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 ''Notices of the American Mathematical Society'' is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue. The first volume appeared in 1953. Each issue of the magazine since ...

, 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 The Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR) is a multidisciplinary research institute located at Jakkur, Bangalore, India. It was established by the Department of Science and Technology of the Government of India, to ...

, 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 Tamil literature has a rich and long literary tradition spanning more than two thousand years. The oldest extant works show signs of maturity indicating an even longer period of evolution. Contributors to the Tamil literature are mainly from T ...

. Narasimhan died on 15 May 2021, in

at the age of 88. He had been undergoing treatment for

cancer Cancer is a group of diseases involving abnormal cell growth with the potential to invade or spread to other parts of the body. These contrast with benign tumors, which do not spread. Possible signs and symptoms include a lump, abnormal b ...

for the previous year.

Selected publications

* *

References

External links

*
Artless innocents and ivory-tower sophisticates: Some personalities on the Indian mathematical scene
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M. S. Raghunathan Madabusi Santanam Raghunathan FRS is an Indian mathematician. He is currently Head of the National Centre for Mathematics, Indian Institute of Technology, Mumbai. Formerly Professor of eminence at TIFR in Homi Bhabha Chair. Raghunathan receiv ...

* {{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