Henri Cartan

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Henri Cartan
École Normale Supérieure
Known forCartan's theorems A and B
Cartan's lemma
Cartan–Eilenberg resolution
Projective module
Steenrod algebra
Weak dimension
Parent
RelativesAnna Cartan (aunt), Pierre Weiss (father-in-law)
AwardsPeccot Lectures (1932)

Émile Picard Medal (1959)
CNRS Gold Medal (1976)
Wolf Prize (1980)

Heinz R. Pagels Human Rights of Scientists Award (1989)
Scientific career
FieldsMathematics
InstitutionsUniversity of Paris
ThesisSur les systèmes de fonctions holomorphes a variétés linéaires lacunaires et leurs applications (1928)
Doctoral advisorPaul Montel
Doctoral studentsJean-Paul Benzécri
Pierre Cartier
Jean Cerf
Jacques Deny
Adrien Douady
Pierre Dolbeault
Roger Godement
Max Karoubi
Jean-Louis Koszul
Jean-Pierre Ramis
Jean-Pierre Serre
René Thom

Henri Paul Cartan (French: [kaʁtɑ̃]; 8 July 1904 – 13 August 2008) was a French mathematician who made substantial contributions to algebraic topology.[1][2][3]

He was the son of the mathematician Élie Cartan, nephew of mathematician Anna Cartan, oldest brother of composer Jean Cartan [fr; de], physicist Louis Cartan [fr] and mathematician Hélène Cartan [fr], and the son-in-law of physicist Pierre Weiss.

Life

According to his own words, Henri Cartan was interested in mathematics at a very young age, without being influenced by his family.[4] He moved to Paris with his family after his father's appointment at Sorbonne in 1909 and he attended secondary school at Lycée Hoche in Versailles.[5][6]

In 1923 he started studying mathematics at

École Normale Supérieure, receiving an agrégation in 1926 and a doctorate in 1928.[5][6] His PhD thesis, entitled Sur les systèmes de fonctions holomorphes a variétés linéaires lacunaires et leurs applications, was supervised by Paul Montel.[7]

Cartan taught at

Clermont Ferrand, but in 1940 he returned to Paris to work at Université de Paris and École Normale Supérieure. From 1969 until his retirement in 1975 he was professor at Paris-Sud University.[5][6]

Cartan died on 13 August 2008 at the age of 104. His funeral took place the following Wednesday on 20 August in

Die, Drome.[8][9][10]

Honours and awards

In 1932 Cartan was invited to give a Cours Peccot at the Collège de France.[11] In 1950 he was elected president of the Société mathématique de France[12] and from 1967 to 1970 he was president of the International Mathematics Union.[13] He was awarded the Émile Picard Medal in 1959,[14] the CNRS Gold Medal in 1976,[15] and the Wolf Prize in 1980.[16]

He was an invited Speaker at the International Congress of Mathematics in 1932 in Zürich and a Plenary Speaker at the ICM in 1950 in Cambridge, Massachusetts[17] and in 1958 in Edinburgh.[18]

From 1974 until his death he had been a member of the

Royal Academy of Belgium (1978), Japan Academy (1979),[30] Finnish Academy of Science and Letters (1979), Royal Swedish Academy of Sciences (1981), Polish Academy of Sciences (1985) and Russian Academy of Sciences (1999).[31]

He was awarded

Sussex (1969), Cambridge (1969),[21] Stockholm (1978), Oxford University (1980),[33] Zaragoza (1985)[34] and Athens (1992).[5]

The French government named him

Officier de la Légion d'honneur in 1965 and Commandeur de l'Ordre du Mérite in 1971.[35]

Political and social activities

During the 70's and the 80's Cartan used his influence to help obtain the release of several dissident mathematicians, including

Heinz R. Pagels Human Rights of Scientists Award from the New York Academy of Sciences.[4][36][37][38]

Since the 30's Cartan had tied collaborations with many German mathematicians, including Heinrich Behnke and Peter Thullen. Right after World War II he put many efforts to improve the cooperation between French and German mathematicians and restore the flow of exchanges of ideas and students.[38][39]

Cartan supported the idea of

1984 European elections he was the leader of the Liste pour les États-Unis d'Europe,[4] which obtained 0.4% of votes and did not elect any candidate.[41]

In 1992 he gave a speech at the first European Congress of Mathematics in Paris, remarking the common heritage and future of European countries and praising the first reunion between mathematicians from the two previously separated parts of Europe.[38]

Research

Cartan has worked in several fields across algebra, geometry and analysis, focussing primarily on algebraic topology and homological algebra.[36][37]

He was a founding member of the Bourbaki group in 1934 and one of its most active participants. After 1945 he started his own seminar in Paris, which deeply influenced Jean-Pierre Serre, Armand Borel, Alexander Grothendieck and Frank Adams, amongst others of the leading lights of the younger generation. The number of his official students was small, but includes Joséphine Guidy Wandja (the first African woman to gain a PhD in mathematics),[42][43] Adrien Douady, Roger Godement, Max Karoubi, Jean-Louis Koszul, Jean-Pierre Serre and René Thom.[7][2]

Cartan's first research interests, until the 40's, were in the theory of

coherent sheaves and proved two powerful results, Cartan's theorems A and B
.

Since the 50's he became more interested in algebraic topology. Among his major contributions, he worked on cohomology operations and homology of the Eilenberg–MacLane spaces,[44] he introduced the notion of Steenrod algebra,[45] and, together with Jean-Pierre Serre, developed the method of "killing homotopy groups".[46][47] His 1956 book with Samuel Eilenberg on homological algebra[48] was an important text, treating the subject with a moderate level of abstraction with the help of category theory.[49] They introduced fundamental concepts, including those of projective module, weak dimension, and what is now called the Cartan–Eilenberg resolution.

Among his other contributions, in general topology he introduced the notions of filter and ultrafilter[50][51] and in potential theory he developed the fine topology and proved Cartan's lemma. The Cartan model for equivariant cohomology[52] is also named after him.

Selected publications

Notes

  1. ^ Augereau, Jean-François (19 August 2008). "Henri Cartan, mathématicien" [Henri Cartan, mathematician]. Le Monde (in French). Retrieved 16 April 2022.
  2. ^
    Academie des Sciences
    (in French). 8 June 2004.
  3. ^ Weil, Martin (31 August 2008). "Noted French mathematician and teacher". Los Angeles Times. Retrieved 25 April 2022.
  4. ^ a b c Jackson, Allyn (1999). "Interview with Henri Cartan" (PDF). Notices of the American Mathematical Society. 46 (7): 782–788.
  5. ^ a b c d O'Connor, John J.; Robertson, Edmund F., "Henri Cartan", MacTutor History of Mathematics Archive, University of St Andrews
  6. ^
    MacTutor History of Mathematics archive
    . Retrieved 18 April 2022.
  7. ^ a b Henri Cartan at the Mathematics Genealogy Project
  8. L'Obs
    (in French). 18 August 2008. Retrieved 18 April 2022.
  9. ISSN 0362-4331
    . Retrieved 16 April 2022.
  10. ^ "Décès d'Henri Cartan, mathématicien français" [Decease of Henri Cartan, French mathematician] (in French). France 24. 18 August 2008. Retrieved 25 April 2022.
  11. ^ "Liste chronologique des cours Peccot avec les intitulés depuis 1899" [Chronological list of the Peccot lectures with titles since 1899] (PDF). Collège de France (in French).
  12. Société Mathématique de France
    (in French). Retrieved 16 April 2022.
  13. ^ "IMU Executive Committee". International Mathematical Union. Retrieved 16 April 2022.
  14. Académie des sciences
    (in French).
  15. ^ "Henri Cartan". French National Centre for Scientific Research (in French). December 1976. Retrieved 16 April 2022.
  16. ^ "Henri Cartan". Wolf Foundation. 9 December 2018. Retrieved 16 April 2022.
  17. ^ Cartan, Henri. "Problèmes globaux dans la théorie des fonctions analytiques de plusieurs variables complexes." Archived 28 December 2013 at the Wayback Machine In Proc. Int. Cong. Math, vol. 1, pp. 152–164. 1950.
  18. ^ Cartan, Henri. "Sur les fonctions de plusieurs variables complexes. Les espaces analytiques." Archived 28 December 2013 at the Wayback Machine In Proc. Intern. Congress Mathematicians Edinburgh, pp. 33–52. 1958.
  19. Academie des Sciences
    (in French). Retrieved 18 April 2022.
  20. ^ "Henri Cartan". Institute for Advanced Study. 9 December 2019. Retrieved 18 April 2022.
  21. ^
    Academie de Sciences
    . 1973.
  22. ^ "Henri Paul Cartan". American Academy of Arts and Sciences. Retrieved 24 April 2022.
  23. ^ "London Mathematical Society Honorary Members" (PDF). London Mathematical Society. Retrieved 24 April 2022.
  24. ^ "Storia – Accademia Nazionale Scienze, Lettere, Arti" [History – National Academy Science, Letters, Arts]. ansla.it (in Italian). Retrieved 24 April 2022.
  25. Royal Society of London
    . Retrieved 24 April 2022.
  26. ^ "Mitglieder: Henri Cartan" [Member: Henri Cartan]. Göttingen Academy of Sciences and Humanities (in German). Retrieved 24 April 2022.
  27. Real Academia de Ciencias Exactas, Físicas y Naturales
    (in Spanish). 2003.
  28. ^ "Henri P. Cartan". National Academy of Sciences. Retrieved 24 April 2022.
  29. Bavarian Academy of Science
    (in German). Retrieved 24 April 2022.
  30. The Japan Academy
    . Retrieved 24 April 2022.
  31. ^ "Картан А.. – Общая информация". ras.ru (in Russian). Retrieved 24 April 2022.
  32. Münster University
    . Retrieved 24 April 2022.
  33. doi:10.1112/blms/13.3.263
    .
  34. Universidad de Zaragoza
    (in Spanish). Retrieved 24 April 2022.
  35. ^ "Décret du 13 mai 1996" [Decree of 13 May 1996]. Légifrance (in French). 1996. Retrieved 24 April 2022.
  36. ^
    doi:10.1098/rsbm.2009.0005
    .
  37. ^
    doi:10.1112/blms/bdt079
    .
  38. ^
    Notices of the AMS. 57 (8). American Mathematical Society
    : 972–975.
  39. ^ Ziegler, Günter (2009). "Der französische Freund" [The French friend]. Die Zeit (in German). Retrieved 18 April 2022.
  40. ^ "Archives de l'UEF-France et mémoire du fédéralisme" [Archives of the UEF-France and memories of federalism]. uef.fr (in French). 31 October 2015. Retrieved 25 April 2022.
  41. ISSN 0008-9664
    .
  42. ^ "Joséphine Guidy-Wandja". International Mathematical Union. Retrieved 25 March 2023.
  43. ^ Cassiau-Haurie, Christophe (20 February 2008). "Les femmes peinent à percer les bulles" [Women struggle to break through bubbles]. Africultures (in French). Retrieved 25 March 2023.
  44. ^ "Séminaire Henri Cartan, Tome 7" [Seminar Henri Cartan]. numdam.org (in French). 1954–1955. Archived from the original on 25 April 2022. Retrieved 25 April 2022.
  45. S2CID 124558011
    .
  46. MR 0046045
    .
  47. MR 0046046
    .
  48. ISBN 0691049912
    .
  49. doi:10.1090/S0002-9904-1956-10082-7
    .
  50. Comptes Rendus de l'Académie des Sciences
    (in French). 205: 595–598.
  51. Comptes Rendus de l'Académie des Sciences
    (in French). 205: 777–779.
  52. Zbl 0045.30701
    .
  53. doi:10.1090/S0002-9904-1956-10082-7
    .
  54. ^ Fresán, Javier (June 2012). "Review: Correspondance entre Henri Cartan et André Weil ed. by Michèle Audin" (PDF). EMS Newsletter. pp. 58–60. Archived from the original (PDF) on 19 May 2020. Retrieved 22 June 2016.

External links

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