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 integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mat ...

, algebraic geometry,

representation theory Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...

, and partial differential equations. He was a pioneer in the study of moduli spaces of

holomorphic vector bundle In mathematics, a holomorphic vector bundle is a complex vector bundle over a complex manifold such that the total space is a complex manifold and the projection map is holomorphic. Fundamental examples are the holomorphic tangent bundle of a ...

s on

projective varieties In algebraic geometry, a projective variety over an algebraically closed field ''k'' is a subset of some projective ''n''-space \mathbb^n over ''k'' that is the zero-locus of some finite family of homogeneous polynomials of ''n'' + 1 variables wi ...

. 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 co ...

that links differential geometry 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 p ...

s over complex manifolds. He was also known for his collaboration with mathematician

C. S. Seshadri Conjeevaram Srirangachari Seshadri (29 February 1932 – 17 July 2020) was an Indian mathematician. He was the founder and director-emeritus of the Chennai Mathematical Institute, and is known for his work in algebraic geometry. The 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 ...

which proved the necessary conditions for

stable vector bundle In mathematics, a stable vector bundle is a ( holomorphic or algebraic) vector bundle that is stable in the sense of geometric invariant theory. Any holomorphic vector bundle may be built from stable ones using Harder–Narasimhan filtration. Stable ...

s 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 ver ...

. He was a recipient of the

Padma Bhushan The Padma Bhushan is the third-highest civilian award in the Republic of India, preceded by the Bharat Ratna and the Padma Vibhushan and followed by the Padma Shri. Instituted on 2 January 1954, the award is given for "distinguished service ...

, India's third highest civilian honor, in 1990, and the

Ordre national du Mérite The Ordre national du Mérite (; en, National Order of Merit) is a French order of merit with membership awarded by the President of the French Republic, founded on 3 December 1963 by President Charles de Gaulle. The reason for the order's estab ...

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 or fundamental, in biology, ...

in 1975 and was the only Indian to receive the

King Faisal International Prize The King Faisal Prize ( ar, جائزة الملك فيصل, formerly King Faisal International Prize), is an annual award sponsored by King Faisal Foundation presented to "dedicated men and women whose contributions make a positive difference". T ...

in the field of science.

Early life

Narasimhan was born on 7 June 1932 into a rural family in

Tandarai Tandarai is a Panchayat town in Tiruvanamalai district, Tamil Nadu Tamil Nadu (; , TN) is a state in southern India. It is the tenth largest Indian state by area and the sixth largest by population. Its capital and largest city is ...

in present day Tamil Nadu, as the eldest among five children. His family hailed from the

North Arcot North Arcot was a former district in Madras Presidency, acquired by the annexation of the Arcot State in 1855 when its Nawab died without issue. It had Chittoor as its headquarters (currently in Andhra pradesh). On 1 April 1911, the Chittoor d ...

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 A geometer is a mathematician whose area of study is geometry. Some notable geometers and their main fields of work, chronologically listed, are: 1000 BCE to 1 BCE * Baudhayana (fl. c. 800 BC) – Euclidean geometry, geometric algebra * ...

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 geometr ...

. He joined the

Tata Institute of Fundamental Research Tata Institute of Fundamental Research (TIFR) is a public deemed research university located in Mumbai, India that is dedicated to basic research in mathematics and the sciences. It is a Deemed University and works under the umbrella of the ...

(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-m ...

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

University of Mumbai The University of Mumbai is a collegiate, state-owned, public research university in Mumbai. The University of Mumbai is one of the largest universities in the world. , the university had 711 affiliated colleges. Ratan Tata is the appointed h ...

in 1960 where his advisor was the mathematician K. S. Chandrasekharan, who was known for his work on number theory.

Career

Narasimhan started his career in 1960 when he joined the faculty of the

(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 operators. 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 ...

and was exposed to the works of other French mathematicians including

Jean-Pierre Serre Jean-Pierre Serre (; born 15 September 1926) is a French mathematician who has made contributions to algebraic topology, algebraic geometry, and algebraic number theory. He was awarded the Fields Medal in 1954, the Wolf Prize in 2000 and the ina ...

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 foun ...

, and

Jean Leray Jean Leray (; 7 November 1906 – 10 November 1998) was a French mathematician, who worked on both partial differential equations and algebraic topology. Life and career He was born in Chantenay-sur-Loire (today part of Nantes). He studied at Éc ...

. He contracted

pleurisy Pleurisy, also known as pleuritis, is inflammation of the membranes that surround the lungs and line the chest cavity ( pleurae). This can result in a sharp chest pain while breathing. Occasionally the pain may be a constant dull ache. Other sy ...

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 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 ...

Schwartz. During his time in France he also collaborated with Japanese mathematician Takeshi Kotake working on the analyticity theorems for determining specific types of elliptic operators 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

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. differential geometry and algebraic geometry. 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 In mathematics, an analytic manifold, also known as a C^\omega manifold, is a differentiable manifold with analytic transition maps. The term usually refers to real analytic manifolds, although complex manifolds are also analytic. In algebraic ge ...

. These measures were called Simha–Narasimhan measures on

s. For his work, Narasimhan was considered a pioneer in the study of moduli spaces of

s on

. His work is considered the foundation for

that links differential geometry and algebraic geometry of

s over complex manifolds. 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 Educatio ...

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 prov ...

. 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 schola ...

, 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 (), List of renamed places in India, officially Bengaluru (), is the Capital city, capital and largest city of the Indian state of Karnataka. It has a population of more than and a metropolitan area, metropolitan population of a ...

. 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 knowledge, including mathemat ...

, London as well as recipient of

French National Order of Merit French (french: français(e), link=no) may refer to: * Something of, from, or related to France ** French language, which originated in France, and its various dialects and accents ** French people, a nation and ethnic group identified with France ...

in 1989. He was awarded the

, 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 The Srinivasa Ramanujan Medal, named after the Indian mathematician Srinivasa Ramanujan, is awarded by the Indian National Science Academy for work in the mathematical sciences. Past recipients include: *1962 S. Chandrasekhar *1964 B. P. Pal *19 ...

in 1988. He was also the recipient of the King Faisal International Prize for Science in 2006, and award that he won jointly with mathematician

Simon Donaldson Sir Simon Kirwan Donaldson (born 20 August 1957) is an English mathematician known for his work on the topology of smooth (differentiable) four-dimensional manifolds, Donaldson–Thomas theory, and his contributions to Kähler geometry. H ...

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