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{{Short description|Indian mathematician (1932–2021)}}
{{Use Indian English|date=August 2015}}
{{Use dmy dates|date=May 2021}}
{{Infobox scientist
| name = M. S. Narasimhan
| image = NarasimhaninBengaluru2010 214.jpg
| image_size =
| caption = Narasimhan in 2010
| birth_name = Mudumbai Seshachalu Narasimhan
| birth_date = {{Birth date|1932|6|7|df=y}}
| birth_place = [[Tandarai]], [[Madras Presidency]], [[British India]]
| death_date = {{death date and age|2021|5|15|1932|6|7|df=yes}}
| death_place = [[Bangalore]], [[Karnataka]], [[India]]
| field = [[Mathematics]]
| work_institution = Tata Institute of Fundamental Research, [[International Center for Theoretical Physics]]
| alma_mater = [[Tata Institute of Fundamental Research]]
| doctoral_advisor = [[K. S. Chandrasekharan]]
| doctoral_students = {{Plainlist|
* [[M. S. Raghunathan]]
* [[S. Ramanan]]
* [[V. K. Patodi]]
* [[T. R. Ramadas]]
}}
| spouse = [[Sakuntala Narasimhan]]
| children = 2 (including [[Shobhana Narasimhan|Shobhana]])
}}

'''Mudumbai Seshachalu Narasimhan''' {{small|[[Fellow of the Royal Society|FRS]]}} (7 June 1932 – 15 May 2021) was an Indian [[mathematician]]. His focus areas included [[number theory]], [[algebraic geometry]], [[representation theory]], and [[partial differential equation]]s. He was a pioneer in the study of [[moduli space]]s of [[holomorphic vector bundle]]s on [[Projective variety|projective varieties]]. His work is considered the foundation for [[Kobayashi–Hitchin correspondence]] that links [[differential geometry]] and algebraic geometry of [[vector bundle]]s over [[complex manifold]]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 bundle]]s 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 for Science and Technology|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.<ref name=":3" /><ref>{{Cite web|title=A Versatile Ace at Bridge Building – Bhāvanā|url=https://bhavana.org.in/ms-narasimhan/|access-date=20 May 2021|language=en-US}}</ref> His family hailed from the [[North Arcot]] district. After his early education in rural part of the country, he joined [[Loyola College, Chennai|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]].<ref name=":1">{{Cite web|last=Ramanan|first=S.|title=Asia Pacific Math News – M. S. Narasimhan|url=http://www.asiapacific-mathnews.com/03/0302/0021_0024.pdf}}</ref> 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]], who was known for his work on number theory.<ref name=":1" />

== 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.<ref name=":0" /><ref name=":4">{{Cite web|title=TIFR – M. S. Narasimhan Obituary|url=http://www.math.tifr.res.in/sites/default/files/misc/MSN-obituary.pdf}}</ref> His areas of focus while at TIFR included studying [[partial differential operator]]s and [[elliptic operator]]s.<ref name=":1" /> 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]].<ref name=":1" /> 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 [[left-wing politics|leftist]] sympathies which were already triggered by his interactions with the [[Trotskyist]] Schwartz.<ref name=":1" />

During his time in France he also collaborated with Japanese mathematician [[Takeshi Kotake]] working on the analyticity theorems for determining specific types of [[elliptic operator]]s that satisfied [[Cauchy–Schwarz inequality|Cauchy–Schwarz inequalities]]. His work with Kotake was known as the [[Kotake–Narasimhan]] theorem for elliptic operators in the setting of ultradifferentiable functions.<ref name=":1" /><ref>{{Cite journal|last1=Boiti|first1=Chiara|last2=Jornet|first2=David|date=1 June 2017|title=A simple proof of Kotake-Narasimhan theorem in some classes of ultradifferentiable functions|journal=Journal of Pseudo-Differential Operators and Applications|volume=8|issue=2|pages=297–317|doi=10.1007/s11868-016-0163-y|arxiv=1604.03932|hdl=10251/107404|s2cid=50378672|issn=1662-9981}}</ref>

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.<ref name=":1" /><ref name=":2">{{Cite journal|last1=Narasimhan|first1=M. S.|last2=Seshadri|first2=C. S.|date=1 November 1965|title=Stable and Unitary Vector Bundles on a Compact Riemann Surface|journal=The Annals of Mathematics|volume=82|issue=3|pages=540|doi=10.2307/1970710|jstor=1970710}}</ref> The theorem derived the relation between the purely algebraic notion of [[Stable bundle|stable vector bundles]] on [[Riemann surface]]s.<ref name=":2" /> The theorem made a connection between two areas of modern geometry viz. [[differential geometry]] and [[algebraic geometry]].<ref name=":4" /> Both Seshadri and Narasimhan were elected [[Fellow of the Royal Society|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|Simha–Narasimhan measures]] on [[Riemann surface]]s.<ref>{{cite arXiv|last=Shivaprasad|first=Sanal|date=29 November 2020|title=Convergence of Narasimhan-Simha measures on degenerating families of Riemann surfaces|class=math.AG|eprint=2011.14471}}</ref>

For his work, Narasimhan was considered a pioneer in the study of [[moduli space]]s of [[holomorphic vector bundle]]s on [[Projective variety|projective varieties]].<ref name=":3" /> His work is considered the foundation for [[Kobayashi–Hitchin correspondence]] that links [[differential geometry]] and [[algebraic geometry]] of [[vector bundle]]s over [[complex manifold]]s.<ref name=":3" />

When the National Board of Higher Mathematics was established in India, Narasimhan was the first chairman of the board.<ref name=":1" /> 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]].<ref name=":0" /><ref name=":4" /> He had also served as a visiting scholar at the [[Institute for Advanced Study]], in [[Princeton, New Jersey]] in 1968.<ref name="ias">{{cite web|title=Community of Scholars Profile: Narasimhan, Mudumbai S.|url=http://www.ias.edu/people/cos/users/mnarasimha01|url-status=dead|archive-url=https://web.archive.org/web/20130107174137/http://www.ias.edu/people/cos/users/mnarasimha01|archive-date=7 January 2013|access-date=27 September 2012|publisher=[[Institute for Advanced Study]]}}</ref> After retiring from ICTP, he settled in [[Bangalore]].<ref name=":4" />

He was a [[Fellowship of the Royal Society|Fellow of the Royal Society]], London as well as recipient of [[National Order of Merit (France)|French National Order of Merit]] in 1989.<ref>{{Cite web|title=ICTP - In Memoriam|url=https://www.ictp.it/about-ictp/media-centre/news/2021/5/in-memoriam-narasimhan.aspx|access-date=20 May 2021|website=www.ictp.it}}</ref> He was awarded the [[Padma Bhushan]], India's third highest civilian honor, in 1990.<ref name="Padma Awards">{{cite web|date=2015|title=Padma Awards|url=http://mha.nic.in/sites/upload_files/mha/files/LST-PDAWD-2013.pdf|url-status=dead|archive-url=https://web.archive.org/web/20151015193758/http://mha.nic.in/sites/upload_files/mha/files/LST-PDAWD-2013.pdf|archive-date=15 October 2015|access-date=21 July 2015|publisher=Ministry of Home Affairs, Government of India}}</ref> He was also the recipient of the [[Shanti Swarup Bhatnagar Prize]] in 1975, [[TWAS Prize|Third World Academy of Sciences Prize]] for Mathematics in 1987, and the [[Srinivasa Ramanujan Medal]] in 1988.<ref>{{Cite journal|last=Malhotra|first=Richa|date=2010|title=Mathematicians speak|journal=Current Science|volume=99|issue=3|pages=38–46|jstor=24108278|issn=0011-3891}}</ref> He was also the recipient of the [[King Faisal International Prize for Science]] in 2006, an award that he won jointly with mathematician [[Simon Donaldson]], Imperial College.<ref name=":3">*[https://www.ams.org/notices/200603/comm-faisal.pdf Donaldson and Narasimhan Receive 2006 King Faisal Prize] - [[Notices of the American Mathematical Society]], March 2006, Volume 53, Number 3.</ref><ref name="Padma Awards" /><ref name="Prizes and Awards">{{Cite web|date=2016|title=Prizes and Awards|url=http://twas.org/opportunities/prizes-and-awards|publisher=The World Academy of Sciences}}</ref> As of 2021, he was the only Indian to have won the King Faisal International Prize for Science.<ref>{{Cite journal|last=Khan|first=Sameen Ahmed|date=2017|title=2017 King Faisal International Prize for Science and Medicine|journal=Current Science|volume=112|issue=6|pages=1088–1090|jstor=24912623|issn=0011-3891}}</ref><ref>{{Cite web|title=King Faisal Prize {{!}} Science|url=https://kingfaisalprize.org/science/|access-date=20 May 2021|language=en-US}}</ref> Also in 2021, he became a laureate of the [[Asian Scientist 100]] by the ''[[Asian Scientist]]''.<ref>{{cite web |url=https://www.asianscientist.com/as100/ |title=The Asian Scientist 100 |author=  |date= |website= |publisher= [[Asian Scientist]] |access-date= 13 March 2025 |quote= |language= }}</ref>

== 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]], and a son.<ref name=":4" /> Narasimhan was interested in [[Indian classical music]], contemporary art and painting, as well as [[Tamil literature]].<ref name=":1" />

Narasimhan died on 15 May 2021, in [[Bangalore]] at the age of 88. He had been undergoing treatment for [[cancer]] for the previous year.<ref name=":0">{{Cite web|title=PM Modi condoles demise of mathematician MS Narasimhan|url=https://www.aninews.in/news/national/general-news/pm-modi-condoles-demise-of-mathematician-ms-narasimhan20210516125411/|access-date=17 May 2021|website=ANI News|language=en}}</ref><ref name=":4" />

==Selected publications==
* {{Cite book | last1=Narasimhan | first1=M. S. | editor1-last=Nitsure | editor1-first=Nitin | title=The Collected Papers of M. S. Narasimhan |volume=I: 1956–1984; Volume II: 1985–2001 | publisher=Hindustan Book Agency and Indian National Science Academy | isbn=978-81-85931-77-7 | year=2007}}
* {{cite journal
| last1= Narasimhan|first1= M. S.|author2-link=C. S. Seshadri|last2=Seshadri|first2= C. S.
| title = Stable and unitary vector bundles on a compact Riemann surface
| journal = [[Annals of Mathematics]]
| volume = 82
| year = 1965
|issue= 3| pages = 540–567
| doi = 10.2307/1970710
|jstor= 1970710| mr=0184252
}}

==References==
{{reflist}}

==External links==
{{commons category}}
*{{cite journal |date=August 2022 | title = Remembering M. S. Narasimhan (1932–2021) | journal = [[Notices of the American Mathematical Society]] | volume = 69 | issue = 7 | pages = 1189–1203 | url = https://www.ams.org/journals/notices/202207/rnoti-p1189.pdf |doi = 10.1090/noti2512| doi-access = free| last1 = Beauville | first1 = Arnaud | last2 = García-Prada | first2 = Oscar | last3 = Hitchin | first3 = Nigel | last4 = Khare | first4 = Chandrashekhar | last5 = Kumar | first5 = Shrawan | last6 = Lange | first6 = Herbert | last7 = Nitsure | first7 = Nitin | last8 = Raghunathan | first8 = M. S. | last9 = Ramadas | first9 = T. R. | last10 = Ramanan | first10 = S. }}
* [http://www.iisc.ernet.in/currsci/aug252003/526.pdf Artless innocents and ivory-tower sophisticates: Some personalities on the Indian mathematical scene]—[[M. S. Raghunathan]]
* {{MathGenealogy|id=35413}}

{{SSBPST recipients in Mathematical Science}}
{{PadmaBhushanAwardRecipients 1990–99}}
{{Shanti Swarup Bhatnagar Laureates of Karnataka}}
{{FRS 1996}}
{{Authority control}}

{{DEFAULTSORT:Narasimhan, M. S.}}
[[Category:1932 births]]
[[Category:2021 deaths]]
[[Category:20th-century Indian mathematicians]]
[[Category:Algebraic geometers]]
[[Category:Differential geometers]]
[[Category:Fellows of the Royal Society]]
[[Category:Institute for Advanced Study visiting scholars]]
[[Category:Narasimhan family]]
[[Category:People from Kanchipuram district]]
[[Category:Recipients of the Padma Bhushan in science & engineering]]
[[Category:Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science]]
[[Category:Scientists from Tamil Nadu]]
[[Category:Tamil scholars]]
[[Category:Tata Institute of Fundamental Research alumni]]
[[Category:TWAS laureates]]
[[Category:University of Madras alumni]]

M. S. Narasimhan - Revision history

Garrisonroofing at 16:13, 3 May 2026