October 8, 2021

https://hos.ifindia.in/

Indo-French Cooperation in Mathematics
Michel Waldschmidt
Professeur Émérite, Sorbonne Université,Institut de Mathématiques de Jussieu, Paris
http://www.imj-prg.fr/~michel.waldschmidt/

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Brahmagupta (598 – 670)
Brāhmasphut.asiddhānta - The Opening of the Universe (628) :11512 − 92 · 1202 = 1.
1 324 801 − 92 · 14 400 = 1
The smallest solution ofx2 − 92y 2 = 1
is
x = 1151,

y = 120.

Composition method : samasa – Brahmagupta identity
http://mathworld.wolfram.com/BrahmaguptasProblem.html
http://www-history.mcs.st-andrews.ac.uk/HistTopics/Pell.html
2 / 67Bhāskara II or Bhāskarāchārya (1114 - 1185)
Bijagan.ita (1150)
1 766 319 0492 − 61 · 226 153 9802 = 1

The smallest solution ofx2 − 61y 2 = 1
is
x = 1 766 319 049,

y = 226 153 980.

Cyclic method (Chakravala) – continued fraction expansion
http://www-history.mcs.st-andrews.ac.uk/HistTopics/Pell.html

3 / 67Narayan.a Pand.it ∼ 1340 – ∼ 1400
227 5282 − 103 · 22 4192 = 1
51 768 990 7842 − 103 · 502 611 5612 = 1

The smallest solution ofx2 − 103y 2 = 1
isx = 227 528,

y = 22 419.

https://mathshistory.st-andrews.ac.uk/Biographies/Narayana/
4 / 67References to Indian mathematics
A. Bag, Mathematics in ancient and medieval India,
Chaukhamba Orientala, Benarès, (1979).
G. R. Kaye, Indian mathematics., Calcutta & Simla,
Thaker, Spink & co,, (1915).
K. Plofker, Mathematics in India, Princeton University
Press, Princeton, NJ, 2009.
C. N. Srinivasiengar, The history of ancient Indianmathematics, The World Press Private, Ltd., Calcutta,
1967.
V. S. Varadarajan, Algebra in ancient and modern
times, vol. 12 of Mathematical World, American
Mathematical Society, Providence, RI, 1998.
5 / 67References

André Weil
Number theory :An approach through history.
From Hammurapi toLegendre.
Birkhäuser Boston, Inc.,
Boston, Mass., (1984) 375
pp. — Reprint 2007.
MR 85c:01004

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Pell – Fermat equation

John Pell(1610 – 1685)

Pierre de Fermat(1601 ?–1665)

It is often said that Euler mistakenly attributed Brouncker’s
work on this equation to Pell. However the equation appears ina book by Rahn which was certainly written with Pell’s help :some say entirely written by Pell. Perhaps Euler knew what he
was doing in naming the equation.
Johann Rahn (1622 - 1676) was a Swiss mathematician who
was the first to use the symbol ÷ for division.
https://mathshistory.st-andrews.ac.uk/Biographies/Pell/
https://fr.wikipedia.org/wiki/John_Pell
7 / 67

On the Brahmagupta – Pell – Fermat equation

Lord William Brouncker(1620–1684)

Pierre de Fermat(1601 ?–1665)

Correspondence from Pierre de Fermat to Brouncker.
1657 : letter of Fermat to Frenicle de Bessy (1604–1674).
https://mathshistory.st-andrews.ac.uk/Biographies/

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Challenge from Fermat to Brouncker“ pour ne vous donner pas trop de peine” (Fermat)“ to make it not too difficult”
x2 − dy 2 = 1, with d = 61 and d = 109.

Solutions respectively :(1 766 319 049 , 226 153 980)
(158 070 671 986 249, 15 140 424 455 100)

8092 −2020·182 = 1,

45 4952 −2021·10122 = 1,

1 3492 −2022·302 = 1.

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History (continued)

Leonard Euler(1707–1783)

Joseph–Louis Lagrange(1736–1813)

L. Euler : Book of algebra in 1770 + continued fractions
The complete theory of the equation x2 − dy 2 = ±1 wasworked out by Lagrange.
https://mathshistory.st-andrews.ac.uk/Biographies/

10 / 67Indian mathematical tradition (continued)
The Indian mathematical school flourished in Kerala between the
14th and the 17th Century. After the work on astronomy and onseries by Madhava of Sangamagramma (1350–1425), the fourmost important works on astronomy and mathematics from that
period are Tantrasan̄graha of Nı̄lakan.t.ha Somayaji (1444–1544),
Yuktibhasa by Jyesthdeva, Karana Paddhati by Putamana
Somayaji and Sadratnamala by Sankara Varman. Another Indianmathematician from the 14th Century is Narayana(∼1340–∼1400), who studied Fibonacci–like sequences.
One of the main features of the mathematics from the Kerala
School is the geometric treatment of algebraic problems. An
example is the text Karanamrta by Citrabhanu written in 1530.
https://mathshistory.st-andrews.ac.uk/Biographies/Madhava/

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The Kerala school
In his treatise on astronomy Madhava used a series for π andobtained 11 decimal digits, while Viète in 1579 could obtain only 9
decimal digits by computing the perimeter of a polygon with
393 216 sides. Three centuries before Newton, Madhava knew the
expansionsx3 x5 x7+−
+ ···sin x = x −
3!
5!
7!
and
x2 x4 x6
cos x = 1 −
+
−
+ ···
2!
4!
6!
The invention of infinitesimal calculus in India was motivated by
the predictions of eclipses. Āryabhat.a I, and later Brahmagupta,
used the concept of instant motion. Bhāskarācārya used thederivative of the sine function to compute the angle of the ecliptic.
These works were later pursued by the Kerala school.
One may consider Madhava as one of the founders of modern
analysis.
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French mathematical tradition

Henri PoincaréNicolas Bourbaki(1854 – 1912)
French mathematician, theoreticalphysicist, engineer, and philosopher
of science.

(1935 – )First Bourbaki Conference 1935
Standing (L to R) : Cartan, dePossel, Dieudonné, Weil Seated :Mirlès, Chevallez, Mandelbrojt

https://mathshistory.st-andrews.ac.uk/Biographies/Poincare/https://mathshistory.st-andrews.ac.uk/Biographies/Bourbaki/
13 / 67Indian mathematical tradition
Fellows of the Royal Society

Srinivasa Ramanujan(1887 – 1920)

Fellow of Trinity College,
Cambridge.

An equation for me has no meaning unless it expresses athought of God
https://mathshistory.st-andrews.ac.uk/Biographies/Ramanujan/
https://mathshistory.st-andrews.ac.uk/Biographies/Bourbaki/

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André Weil in India

André Weil
(1906 – 1998)

In 1929 Syed Ross Masood, Vice-Chancelor of Aligarh Muslim
University, proposed a chair of French civilization to André
Weil, who was recommended to him by a specialist ofIndology, Sylvain Levi. A few months later this offer wasconverted into a chair of mathematics. Weil reached India inearly 1930 and stayed there for more than two years.
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Sylvie Weil

Sylvie Weil
Chez les Weil. André andSimoneBuchet-Chastel, Paris (2009)

At home with André andSimone Weiltranslated from the French by
Benjamin Ivry
Northwestern Univ. Press(2010).

The Mathematical Intelligencer volume 34, pages 76-78 (2012)https://fr.wikipedia.org/wiki/Sylvie_Weil

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PV numbers

Charles Pisot

Tirukkannapuram Vijayaraghavan(1910 – 1984)(1902 – 1955)

Among the Indian colleagues of André Weil were
T. Vijayaraghavan, D. Kosambi and S. Chowla whose intellectual
qualities he appreciated.
T. Vijayaraghavan, who later became the first director of theRamanujan Institute in Madras (at that time it was independent of
the department of mathematics of the University) is known for his
study of the so–called P.V. numbers, which were studied by
C. Pisot. The influence of Weil on Vijayaraghavan was important.
https://mathshistory.st-andrews.ac.uk/Biographies/Pisot/
https://fr.wikipedia.org/wiki/Tirukkannapuram_Vijayaraghavan
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André Weil in India

Weil wrote two reports on the situation of the universities inIndia. In his first report 1931 for the Indian MathematicalSociety, he had suggested actions for the improvement ofIndian mathematics.
The conclusion of his second report in 1936 deals with thepotential of this country and the possibility for India to soontake one of the leading places in the international
mathematical community.

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References to André Weil
A. Weil, Mathematics in Indian Universities, Seventh
Conference of the Indian Mathematical Society,
Trivandrum, (1931).
Scientific works. Collected papers pp. 127–128.
, Mathematics in India, Usp. Mat. Nauk 3, I (1936),
pp. 286–288.
Scientific works. Collected papers pp. 129–131.
, Scientific works. Collected papers. Vol. I(1926–1951), Springer-Verlag, New York, 1979.
, Souvenirs d’apprentissage, vol. 6 of Vita
Mathematica, Birkhäuser Verlag, Basel, 1991. English
translation by Jennifer Gage, The Apprenticeship of a
Mathematician, Birkhäuser, Basel, 1992.
19 / 67

Father Racine

Fr Charles Racine

Father Racine reached India in
1937 as a Jesuit missionary
after having taken his
Doctorate in Mathematics in1934 under Élie Cartan.

(1897 – 1976)

He taught mathematics first at St Joseph’s College in
Tiruchirappally (Trichy, Tamil Nadu) and from 1939 onwards
at Loyola College (Madras). He spent forty-two years in India.
He had connections with many important Frenchmathematicians of that time like J. Hadamard, J. Leray,
A. Weil, H. Cartan.
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Charles Racine’s thesis° D ORDRE
2350
SÉRIE A.
DE SÉRIE *.
1484—~v^^-

THÈSESPRÉSENTÉESA LA FACULTÉ DES SCIENCES DE PARIS
POUR OBTENIRLE GRADE DE DOCTEUR ES SCIENCES MATHÉMATIQUESPARM.

CHARLESRACINEl i e T H È S E . — L E PROBLÈJIE DES N COUPS DANS LA THÉORIE DE LA RELATIVITÉ.
2e

T H È S E . — SUR LES COURBES DÉFINIES PAR UNE ÉQUATION

Soutenues le

DIFFÉRENTIELLE.

1934 devant la Commission d'examen.

MM. E. CARTAN,
J. CHAZY,)G. DARMOIS, )Doctorate in Mathematics in1934 under Élie Cartan.
Le problème des N corps dansla théorie de la relativité.
Thèse 1934
http://www.numdam.org/item?id=THESE_1934__158__1_0

Président.

PARIS
GAUTH1ER-V1LLARS, ÉDITEUR
LIBRAIRE DU BUREAU DES LONGITUDES, DE L'ÉCOLE POLYTECHNIQUE
Quai des Grands-Augustins, 55

M. Santiago, International conference on teaching andresearch in mathematics, in Birth Centenary Celebrations ofFather Charles Racine, S.J. Loyola College, Racine ResearchCentre, Chennai, January, 1997.
21 / 67

Fr D’Souza, rector, Loyola College, June 1, 1946

22 / 67

Fr D’Souza, rector, Loyola College, June 1, 1946
Le P. Racine. Le P. de Grangeneuve m’a demandé confidentiellement si je croyais
qu’il doit retourner aux Indes après sa visite prochaine en Europe. Mon Révérend Père,il m’est difficile de répondre à cette question catégoriquement. Le P. Racine avaitespéré faire un grand apostolat - intellectuel et religieux - aux Indes. Il s’était formé
une idée de l’Inde très au dessus de la réalité. D’où, déception profonde. Je crois qu’il
n’a pas pu s’adapter à la réalité - l’optimisme lui manque. Il a dû certainement penser
parfois à un retour en Europe pourvu qu’un genre de ministère lui agréable y soit
trouvé.
Une des raisons pourquoi il n’a pas pu d’adapter ici avec plein contentement est qu’il
ne comprend pas par certains côtés, il me semble, la psychologie indienne. Il regarde
nos élèves, pratiquement parlant, comme s’ils étaient des jeunes Universitaires de Paris
et il attend d’eux des réactions naturelles dans les cercles européens. Les remarques et
les critiques qu’il fait devant eux, les directives qu’il leur donne quelquefois feraientplus de mal que de bien - ce que le Père ne s’en rend pas toujours compte.
Si en vue de tout cela, et en particulier en vue de la situation de sa famille, le P.
Racine lui même se montre incliné de rester en Europe, surtout si Votre Révérence
croit qu’il pourra faire plus de bien en Europe, je crois qu’il ne doit pas être pressé derentrer ici, mais plutôt approuvé dans cette idée. Si, d’autre part, le Père, examinantla situation dans le recul, se sent plus réconcilié aux conditions de l’Inde, plus disposé
d’être patient avec les hommes et les situations, moins sévère dans ses jugements surelles, et par conséquent sincèrement désireux de recommencer, je crois qu’on doit lui
permettre de revenir. Ses grandes qualités personnelles, et ses solides vertus religieuses
lui assureraient encore un bel apostolat chez nous.
23 / 67

Father Racine

His erudition was clear from his lectures, his courses wereresearch oriented in contrast with the traditional way ofteaching which aimed only at leading the largest number ofstudents to success in their exams. At that time with Ananda
Rao, a noted analyst, and Vaidyanathaswamy, who had
broader interests, Madras was the best place in India forstudying mathematics and starting into research.
In the words of C. S. Seshadri, he was not a good teacher inthe classroom but nevertheless a great teacher.

24 / 67

Father Racine
Father Racine taught his students to read recent books, likethe one of L. Schwartz on distributions.
Racine wrote a letter to the French mathematician Leray,commending the names Seshadri and Narasimhan to his
attention.
The French government conferred on him the coveted Légion
d’honneur in 1962. In all the 42 years he spent in India, hemade only two trips to France ; yet he remained very much a
Frenchman. But there can be little doubt that he loved India
more than France.

25 / 67

Students of Father Racine
Father Racine encouraged his best students to join the newly
founded Tata Institute of Fundamental Research (TIFR) in
Bombay with K. Chandrasekharan and K.G. Ramanathan. This
explains why so many mathematicians from that generation
who were the leaders in TIFR came from Tamil Nadu.
The list of the former students of Father Racine who became
well known mathematicians is impressive : Venugopal Rao,
P.K. Raman, M.S. Narasimhan, C.S. Seshadri, Ramabhadran,K. Varadarajan, Raghavan Narasimhan, C.P. Ramanujam,
Ramabhadran Narasimhan, Ananda Swarup, S. Ramaswamy,
Cyril D’Souza, Christopher Rego, V.S. Krishnan and S. Sribala.

26 / 67

M.S. Narasimhan

M.S. Narasimhan

Recipient of the Padma Bhushan in
1990
Ordre national du Mérite in 1989
King Faisal International Prize for
Science in 2006

(1932–2021)

Head of the research group in Mathematics at theInternational Centre for Theoretical Physics (ICTP) in Trieste
from 1993 to 1999.
R. Narasimhan, The coming of age of mathematics inIndia, in Miscellanea mathematica, Springer, Berlin, 1991,
pp. 235–258.
https://www.ictp.it/about-ictp/media-centre/news/2021/5/in-memoriam-narasimhan.aspx
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M.S. Narasimhan
M.S. Narasimhan visited France in the 60’s under theinvitation of Laurent Schwartz and was exposed to the worksof 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 ”realFrance” and further strengthening his leftist sympathies whichwere already triggered by his interactions with Laurent
Schwartz.
S Ramanan. M S Narasimhan, The Man and the Mathematician — A
Personal Perspective. Asia Pacific Mathematics Newsletter, April 2013,
Volume 3 No 2, 21–24.
http://www.asiapacific-mathnews.com/03/0302/0021_0024.pdf

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C.S. Seshadri
Paris 1957 - 1960
Doctorat honoris causa, Université
Pierre-et-Marie-Curie (UPMC),
Paris, 2013

C.S. Seshadri(1932 – 2020)

Recipient of the Padma Bhushan in2009

M.S. Narasimhan and C.S. Seshadri were among the first
graduate students of the School of Mathematics, headed by K.
Chandrasekharan.
https://fr.wikipedia.org/wiki/C._S._Seshadri

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M.S. Ragunathan
PhD under M.S. Narasimhan in
1966
Recipient of the Padma Bhushan in
2012

Madabusi Santanam Raghunathan
M. S. Raghunathan, Artless innocents and ivory-towersophisticates : Some personalities on the Indianmathematical scene, Current Science, 85 (2003),
pp. 526–536.
http://www.ias.ac.in/currsci/aug252003/526.pdf
M. S. Raghunathan, India and the world ofmathematics, ICM 2010 (Hyderabad).
https://en.wikipedia.org/wiki/M._S._Raghunathan
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Tata Institute of Fundamental Research
The creation of the Tata Institute of Fundamental Research in
Bombay is due to a physicist of the Indian Institute of Scienceof Bangalore, Homi J. Bhabha (1909–1966), who had politicalsupport from J. Nehru and financial support from the Tatas, aParsi industrial family which is still extremely powerful. At theend of the 19th Century a member of this family, Jamsetji
Nusserwanji Tata, was at the origin of the creation of the
Indian Institute of Science in Bangalore. The goal of Bhabha
was for India to acquire nuclear power, and for this purpose it
was necessary to create a research school in physics of highlevel ; in turn, this objective made it necessary to create astrong mathematical research school.
https://www.tifr.res.in/

31 / 67Laurent Schwartz

Alexandre Grothendieck

Laurent Schwartz

Alexandre Grothendieck(1915 – 2002)(1928 - 2014)

Right after its creation, many influential French mathematicians
visited the Tata Institute of Bombay and gave courses. In the 50’s,
L. Schwartz visited it several times, followed by H. Cartan,
F. Bruhat, J.L. Koszul, P. Samuel, B. Malgrange, J. Dieudonné,P. Gabriel, M. Demazure, A. Douady and many others, invited by
the Director of that time, K. Chandrasekharan. Later, at the end of
the 60’s, A. Weil and A. Grothendieck visited TIFR.
https://mathshistory.st-andrews.ac.uk/Biographies/Schwartz/
https://mathshistory.st-andrews.ac.uk/Biographies/Grothendieck/32 / 67

CMI
CMI began as the School of Mathematics, SPIC Science
Foundation, in 1989. The SPIC Science Foundation was set up
in 1986 by Southern Petrochemical Industries Corporation Ltd(SPIC), one of the major industrial houses in India, to foster
the growth of Science and Technology in the country. The
driving force was C.S. Seshadri.
In 1996, the School of Mathematics became an independent
institution and changed its name to SPIC Mathematical
Institute. In 1998, in order to better reflect the emerging roleof the institute, it was renamed the Chennai Mathematical
Institute (CMI).
Chennai Mathematical Institute is a centre of excellence forteaching and research in the mathematical sciences.
https://www.cmi.ac.in/about/history.php
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Agreement CMI - ENS

Etienne Guyon

Pierre CartierThanks to an agreement (MoU) between the CMI (Chennai
Mathematical Institute) and ENS (École Normale Supérieure,rue d’Ulm, Paris), every year since 2000, some three young
students from ENS visit CMI for two months and delivercourses to the undergraduate students of CMI, and three
students from CMI visit ENS for two months. The French
students are accommodated in the guest house of IMSc, which
participates in this cooperation.
https://fr.wikipedia.org/wiki/Etienne_Guyon
https://mathshistory.st-andrews.ac.uk/Biographies/Cartier/
34 / 67

PICS
The influence of French mathematicians on the developmentof mathematics in India has played a leading role in at least
two topics : algebraic geometry in the 1960’s and theoreticalpartial differential equations in the 1970’s.

Jean-Louis Verdier

J-L. Verdier was responsible of a
PICS Inde (PICS=ProgrammeInternational de Coopération
Scientifique) of the CNRS (Centre
International de la Recherche
Scientifique) from 1986 to 1989.

(1935 – 1989)

https://opc.mfo.de/person_detail?id=3393
https://fr.wikipedia.org/wiki/Jean-Louis_Verdier
35 / 67

PICS

A report on this cooperation was published in the Gazette desMathématiciens of the Société Mathématique de France (n◦49, juin 1991, pp. 59–61).
A second report dealing with the activities from 1986 and1995 was published in the same Gazette des Mathématiciens(n◦ 71, 1997, pp. 62–65).

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Applied mathematics
Jacques-Louis Lions(1928 – 2001)

In applied mathematics also the cooperation between
mathematicians from France and from India is quite strong. While
J.L. Lions was at the head of INRIA (Institut National deRecherche en Informatique et Automatique) in Rocquencourt, hedeveloped close relations with several Indian institutions : IISc
(Indian Institute of Science) in Bangalore, IIT Indian Institute ofTechnology in Delhi, and most of all with the small group ofmathematicians working on partial differential equations in the
Bangalore section of TIFR.
https://mathshistory.st-andrews.ac.uk/Biographies/Lions_Jacques-Louis/

37 / 67

Applied mathematics
Olivier Pironneau
In September 1997 a Master of Scientific Calculus was createdat the University of Pondicherry, thanks to a cooperation
directed by O. Pironneau. The cooperation on ScientificCalculus for Mechanics and Engineering between thelaboratory of Numerical Analysis of Paris VI and INRIA
Rocquencourt in France and ISSc Bangalore, TIFR Bangaloreand IIT Delhi in India, started in 1975 and the agreements
have been renewed in 1993 ; this program is supported by
IFCPAR, the French Ministry of Foreign Affairs and the Pôlede recherche commun Dassault-Aviation/Université Paris VI.
https://fr.wikipedia.org/wiki/Olivier_Pironneau

38 / 67

Coordination of the Indo–French cooperation inmathematics

Jean–Louis Colliot-ThélèneGilles Lachaud(1946 – 2018)

Data base - calls for applications

39 / 67

CEFIPRA – IFCEPAR

T
Indo–French Centre for the Promotion of Advanced Research(IFCPAR, CEFIPRA in French) is a bilateral programme ofscientific cooperation between India and France under the
Department of Science and Technology, Government of India
and the Ministry of Foreign Affairs, Government of France.

http://www.cefipra.org/

40 / 67

CEFIPRA – IFCEPAR Annual Report 2019–2020

p-ADIC aspects of automorphic
forms and their L-functions
Project No. 5601-1 Nov. 2016 toOct. 2019

Interactions between dynamicalsystems, geometry and number
theoryProject No. 5801-1 Jan. 2018 toJan. 2021
http://www.cefipra.org/Publication/Annual_Report/AR_2019-20_Web.pdf
41 / 67

CEFIPRA – IFCEPAR Annual Report 2019–2020
High performance formation
control in the presence of
uncertainties and communication
constraints
Project No. 6001-1 Feb. 2019 toJan. 2022

Maximal abelian subalgebras inoperator algebras
Project No. 6101-1 Jun 2019 to
May 2022

http://www.cefipra.org/Publication/Annual_Report/AR_2019-20_Web.pdf
42 / 67IFIM
The Indo–French Institute ofMathematics (IFIM=Institut
Franco–Indien deMathématiques) is a virtual
institute which was created in
2003

with the support of NBHM (National Board for Higher
Mathematics) and DST (Department of Science andTechnology) on the Indian side and MAE (Ministère desAffaires Étrangères) and CNRS (Centre National de laRecherche Scientifique) on the French side. One of the main
objectives is to provide financial supports for doctoral,
postdoctoral and research positions.
43 / 67

LIA CFIM
LIA ”Centre franco-indien pour les mathématiques” (CFIM)

https://india.cnrs.fr/cnrs-collaboration-in-india/

44 / 67Indo-French Program in Mathematics (IFPM)

IFPM is the new name for CFIM, it is scheduled to continue until 2022.
https://cnrsindiacom.wpcomstaging.com/wp-content/uploads/2017/11/IFPM.pdf
45 / 67

International research Laboratory (IRL)

http://www.math.iisc.ac.in/~ifcam/index.html
46 / 67

UMI Relax à Chennai
Unite mixte internationale franco-indienne en informatique

Director Madhavan Mukund, deputy director Pascal Weil.
https://www.cnrs.fr/fr/creation-dune-unite-mixte-internationale-franco-indienne-en-informatique

47 / 67

The MODULI IRSES projectIndo European Collaboration on Moduli Spaces
January 1, 2014 – December 31, 2017
The main objective of this project is to establish newcollaborations and reinforce existing collaborations between Europe
and India in the field of moduli spaces, as well as training young
researches. This will be done through the exchange of bothexperienced and early stage researchers, and the organization ofconferences, specialized workshops and schools.
The project is a Marie Curie International Research Staff Exchange
Scheme (irses) project in the 7th European Framework Program.
https://www.icmat.es/projects/irsesmoduli/home.xhtml
48 / 67

The MODULI IRSES project

Sinnou DavidFirst conference of the
Indo-French Program forMathematics
ORGANISER : Sinnou David
from CNRSVENUE : IMSc
DATE : 11 - 24 January 2016

Former deputy scientific director at INSMI
Institut National des Sciences Mathématiques et leurs Interactions
https://www.icmat.es/projects/irsesmoduli/events.xhtml
49 / 67

IRP – Indo French Center for Applied Mathematics

https://cnrsindiacom.wpcomstaging.com/wp-content/uploads/2020/05/IRL-IFCAM.pdf
50 / 67

MOU• There are several MoU (Memorandum of Understanding)between French and Indian Universities. One of them involved
the University of Pondicherry in India and the universities ofParis VI and Poitiers in France. During a number of years
there were many scientific exchanges under this agreementwith a strong support of the French Embassy in Delhi.

51 / 67

MOU• Another MoU has been signed in 2009 between the
University of Paris VI Pierre et Marie Curie and the two
institutes of Chennai, CMI (Chennai Mathematical Institute)and IMSc (Institute of Mathematical Sciences). An item inthis MoU follows a recommendation of the COPED(Committee for Developing Countries) of the French Academyof Sciences : each year, one full time teaching duty of amathematician from Paris VI will be given in Chennai. In
practice, two professors from Paris 6 will go to CMI each year
to teach an graduate program for one term each.

52 / 67

Further supports• Several other sources of funding enable seniormathematicians from India and France to visit the othercountry. Among them are supports from CNRS and theMinistry of Education in France, from the NBHM (National
Board of Mathematics) in India. As an example, an agreement
between CNRS and NBHM from 1999 to 2003 enabled eachyear some three mathematicians from each country to visit theother one, when no other support from one of the otherprograms was suitable. There are also agreements between the
Académie des Sciences de Paris and the Indian National
Science Academy (INSA) in New Delhi.

53 / 67

Scholarships• A number of scholarships enable young mathematicians from
India (as well as from other countries) to pursue their studies
in France. This includes cotutelle theses (codirection). The
website of the French Embassy gathers some information on
this matter and proposes a number of links to several
institutions in France : Campus France, Egide, CNOUS(Centre National des Œuvres Universitaires et Scolaires),
ONISEP (a French provider of student career and job
information), CEFI (Centre de ressources et de prospective surles Grandes écoles d’ingénieurs et de gestion, et sur les emplois
d’encadrement). . .
http://ambafrance-in.org/france_inde/spip.php?article4158

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Centre International de Mathématiques Pures et Appliquées

The CIMPA, already mentioned, a non-profit internationalorganization established in Nice (France) since 1978, whose
aim is to promote international cooperation in higher education
and research in mathematics and related subjects, particularly
computer science, for the benefit of developing countries,
organized several research schools in India, starting in 1996.

https://www.cimpa.info/

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Waring’s Problem

Edward Waring

F.D, R.B, J-M.D(1736 – 1798)

E. Waring, 1770 : Every integer is a cube or the sum of two,
three, . . . nine cubes ; every integer is also the square of asquare, or the sum of up to nineteen such ; and so forth.
Similar laws may be affirmed for the correspondingly defined
numbers of quantities of any like degree.
g(4) = 19 : R. Balasubramanian, J–M. Deshouillers, F. Dress(1986)
https://mathshistory.st-andrews.ac.uk/Biographies/Waring/
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Serre’s Modularity Conjecture

Jean-Pierre Serre

Chandrashekhar Khare

Jean-Pierre Wintenberger(1954–2019)

Serre’s Modularity Conjecture was proved in 2006 in a joint
work by Chandrashekhar Khare and Jean–Pierre Wintenberger.
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K. Ramachandra
PhD 1965
1965 –1995 Tata Institute ofFundamental Research Bombay

Kanakanahalli Ramachandra(1933 – 2011)

1995 – 2011 National Institute ofAdvanced Studies, Bangalore

K. Ramachandra, Contributions to the theory oftranscendental numbers. Acta Arith. 14, (1968), pp. 65–88.
1976 : my first visit to India at TIFR.
https://en.wikipedia.org/wiki/Kanakanahalli_Ramachandra
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French Science Today 2006
12 lectures from November 13 to November 24, 2006
Indore, CAT = Raja Ramanna Centre For Advanced Technology
Indore, Devi Ajilya University
Bhopal, Regional Sciences Centre
Chandigarh, Punjab Engineering College
Chandigarh, Colloquium du Département de Maths de l’UniversitéDelhi, St Stephen’s College
Ranchi, Birla Institute of Technology Mesra
Kolkata, Bose InstituteKolkata, M.P. Birla Planetarium
Kolkata, College RKM Vidyamandira (Belur Math)
Kolkata, Indian Statistical Institute (ISI)
Chennai, Institute of Mathematical Sciences (IMSc)
http://www.imj-prg.fr/~michel.waldschmidt/articles/pdf/MissionIndeFST2006.pdf
https://in.ambafrance.org/-Science-Technology-

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French Science Today 2007
13 lectures from October 17 to November 10, 2007
Mumbai, Tata Institute of Fundamental Research TIFR
University of Mumbai, Department of Mathematics
Pune, Bhaskaracharya PratishthanaPune, Department of Mathematics
Hyderabad, Planetarium, B.M. Birla Science Centre
Hyderabad Central University
Kolkata, Indian Statistical InstituteKolkata, M.P. Birla Planetarium
Guwahati, Indian Institute of Technology
Bangalore, Indian Institute of Science
Trivandrum, St. Thomas School
Trivandrum, Kerala University, Department of Mathematics
Chennai, The Institute of Mathematical Sciences IMSc.
http://www.imj-prg.fr/~michel.waldschmidt/articles/pdf/MissionIndeFST2007.pdf
https://in.ambafrance.org/-Science-Technology61 / 67

IHÉShttps://www.ihes.fr/

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Kerala School of Mathematics (KSoM)

https://sites.google.com/view/iccgnfrt2021/home

63 / 67Indian Mathematical Society

http://www.mgmu.ac.in/ims/

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Special functions
November 22 - 24, 2018 : 17th Annual Meeting of SSFA International Conference on Special Functions & Applications(ICSFA-2018), Amal Jyothi College on Engineering,
Kanjirapalli, Kottayam (Kerala).

Aligarh Muslim University(AMU)
Department of Mathematics
M.A. Pathan

Lidstone interpolation

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References
Indo–French cooperation in Mathematics Special issue onMathematics Newsletter of the Ramanujan MathematicalSociety , Vol. 19, Sp. No. 1, August 2010, 1-12.

Seminar on Successful Indo–French S & T Co-operation
through CEFIPRA
May 17, 2013, Paris.
CEFIPRA 25th Anniversary Silver Jubilee Celebration and the
expansion of its activities
https://in.ambafrance.org/CEFIPRA-25th-Anniversary-7-March

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October 8, 2021

https://hos.ifindia.in/

Indo-French Cooperation in Mathematics
Michel Waldschmidt
Professeur Émérite, Sorbonne Université,Institut de Mathématiques de Jussieu, Paris
http://www.imj-prg.fr/~michel.waldschmidt/

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