Henri Cartan Explained

Henri Cartan
Birth Name:Henri Paul Cartan
Birth Date:8 July 1904
Birth Place:Nancy, Meurthe-et-Moselle, France
Death Place:Paris, France
Fields:Mathematics
Workplaces:University of Paris
Alma Mater:École Normale Supérieure
Father:Élie Cartan
Relatives:Anna Cartan (aunt), Pierre Weiss (father-in-law)
Thesis Title:Sur les systèmes de fonctions holomorphes a variétés linéaires lacunaires et leurs applications
Thesis Url:https://doi.org/10.24033/asens.786
Thesis Year:1928
Doctoral Advisor:Paul Montel
Doctoral Students:Jean-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
Known For:Cartan's theorems A and B
Cartan's lemma
Cartan–Eilenberg resolution
Projective module
Steenrod algebra
Weak dimension
Awards:Peccot Lectures (1932)
Émile Picard Medal (1959)
CNRS Gold Medal (1976)
Wolf Prize (1980)
Heinz R. Pagels Human Rights of Scientists Award (1989)

Henri Paul Cartan (in 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, physicist and mathematician, 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]

In 1923 he started studying mathematics at École Normale Supérieure, receiving an agrégation in 1926 and a doctorate in 1928. His PhD thesis, entitled Sur les systèmes de fonctions holomorphes a variétés linéaires lacunaires et leurs applications, was supervised by Paul Montel.

Cartan taught at Lycée Malherbe in Caen from 1928 to 1929, at University of Lille from 1929 to 1931 and at University of Strasbourg from 1931 to 1939. After the German invasion of France the university staff was moved to 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.

Cartan died on 13 August 2008 at the age of 104. His funeral took place the following Wednesday on 20 August in Die, Drome.[6] [7] [8]

Honours and awards

In 1932 Cartan was invited to give a Cours Peccot at the Collège de France.[9] In 1950 he was elected president of the Société mathématique de France[10] and from 1967 to 1970 he was president of the International Mathematics Union.[11] He was awarded the Émile Picard Medal in 1959,[12] the CNRS Gold Medal in 1976,[13] and the Wolf Prize in 1980.[14]

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[15] and in 1958 in Edinburgh.[16]

From 1974 until his death he had been a member of the French Academy of Sciences.[17] He was elected a foreign member of many academies and societies,[18] [19] including the American Academy of Arts and Sciences (1950),[20] London Mathematical Society (1959),[21] Royal Danish Academy of Sciences and Letters (1962), (1967),[22] Royal Society of London (1971),[23] Göttingen Academy of Sciences and Humanities (1971),[24] Spanish Royal Academy of Sciences (1971),[25] United States National Academy of Sciences (1972),[26] Bavarian Academy of Science (1974),[27] Royal Academy of Belgium (1978), Japan Academy (1979),[28] Finnish Academy of Science and Letters (1979), Royal Swedish Academy of Sciences (1981), Polish Academy of Sciences (1985) and Russian Academy of Sciences (1999).[29]

He was awarded Honorary Doctorates from Münster (1952),[30] ETH Zürich (1955), Oslo (1961), Sussex (1969), Cambridge (1969), Stockholm (1978), Oxford University (1980),[31] Zaragoza (1985)[32] and Athens (1992).

The French government named him Commandeur des Palmes Académiques in 1964, Officier de la Légion d'honneur in 1965 and Commandeur de l'Ordre du Mérite in 1971.[33]

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 Leonid Plyushch and Anatoly Shcharansky, imprisoned by the Soviet Union, Jose Luis Massera, imprisoned between 1975 and 1984 by the Uruguayan dictatorship, and Sion Assidon, imprisoned during the Moroccan Years of Lead. For his humanitarian efforts, he received in 1989 the Heinz R. Pagels Human Rights of Scientists Award from the New York Academy of Sciences.[34] [35] [36]

Since the 30's Cartan had tight 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.[37]

Cartan supported the idea of European Federalism and from 1974 to 1985 was president of the French section of the Union of European Federalists.[38] At the 1984 European elections he was the leader of the Liste pour les États-Unis d'Europe, which obtained 0.4% of votes and did not elect any candidate.[39]

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.

Research

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

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),[40] [41] Adrien Douady, Roger Godement, Max Karoubi, Jean-Louis Koszul, Jean-Pierre Serre and René Thom.

Cartan's first research interests, until the 40's, were in the theory of functions of several complex variables, which later gave rise to the theory of complex varieties and analytic geometry. Motivated by the solution to the Cousin problems, he worked on sheaf cohomology and 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,[42] he introduced the notion of Steenrod algebra,[43] and, together with Jean-Pierre Serre, developed the method of "killing homotopy groups".[44] [45] His 1956 book with Samuel Eilenberg on homological algebra[46] was an important text, treating the subject with a moderate level of abstraction with the help of category theory.[47] 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[48] [49] and in potential theory he developed the fine topology and proved Cartan's lemma. The Cartan model for equivariant cohomology[50] is also named after him.

Selected publications

External links

Notes and References

  1. News: Augereau . Jean-François . 19 August 2008 . Henri Cartan, mathématicien . fr . Henri Cartan, mathematician . . 16 April 2022.
  2. Web site: 8 June 2004 . Communiqué de presse pour le centenaire d'Henri Cartan (2004) . Press communication for the centenary of Henri Cartan (2004) . . fr.
  3. News: Weil . Martin . 31 August 2008 . Noted French mathematician and teacher . 25 April 2022 . . en-US.
  4. Jackson . Allyn . 1999 . Interview with Henri Cartan . . 46 . 7 . 782–788.
  5. News: 2008 . Henri Cartan: mathematician . en . . 18 April 2022 . 0140-0460. available also at News: Henri Cartan – Times obituary . en . . 18 April 2022.
  6. News: 18 August 2008 . Décès du mathématicien français Henri Cartan . fr . Death of French mathematician Henri Cartan . . 18 April 2022.
  7. News: Chang . Kenneth . 25 August 2008 . Henri Cartan, French Mathematician, Is Dead at 104 . en-US . . 16 April 2022 . 0362-4331.
  8. News: 18 August 2008 . Décès d'Henri Cartan, mathématicien français . Decease of Henri Cartan, French mathematician . 25 April 2022 . . fr.
  9. Web site: Liste chronologique des cours Peccot avec les intitulés depuis 1899 . Chronological list of the Peccot lectures with titles since 1899 . . fr.
  10. Web site: Les présidents de la SMF depuis 1873 . The presidents of the SMF since 1873 . 16 April 2022 . . fr.
  11. Web site: IMU Executive Committee . 16 April 2022 . International Mathematical Union.
  12. Web site: Médaille Émile Picard (Mathématique) . Émile Picard Medal (Mathematics) . . fr.
  13. Web site: Henri Cartan . 16 April 2022 . . December 1976 . fr.
  14. Web site: 9 December 2018 . Henri Cartan . 16 April 2022 . . en-US . 16 May 2022 . https://web.archive.org/web/20220516144443/https://wolffund.org.il/2018/12/09/henry-cartan/ . dead .
  15. Cartan, Henri. "Problèmes globaux dans la théorie des fonctions analytiques de plusieurs variables complexes." In Proc. Int. Cong. Math, vol. 1, pp. 152–164. 1950.
  16. Cartan, Henri. "Sur les fonctions de plusieurs variables complexes. Les espaces analytiques." In Proc. Intern. Congress Mathematicians Edinburgh, pp. 33–52. 1958.
  17. Web site: Henri Cartan – Les Membres de l'Académie des sciences . Henri Cartan – The members of the Académie des sciences . 18 April 2022 . . fr.
  18. Web site: 9 December 2019 . Henri Cartan . 18 April 2022 . . en.
  19. Web site: 1973 . Notices sur les travaux scientifiques de Henri Cartan . Academie de Sciences.
  20. Web site: Henri Paul Cartan . 24 April 2022 . . en.
  21. Web site: London Mathematical Society Honorary Members . 24 April 2022 . London Mathematical Society.
  22. Web site: Storia – Accademia Nazionale Scienze, Lettere, Arti . History – National Academy Science, Letters, Arts . 24 April 2022 . ansla.it . it.
  23. Web site: Cartan, Henri: certificate of election to the Royal Society . 24 April 2022 . Royal Society of London.
  24. Web site: Mitglieder: Henri Cartan . Member: Henri Cartan . 24 April 2022 . . de.
  25. Web site: 2003 . Relación de académicos desde el año 1847 hasta el 2003 . List of academics from 1847 to 2003 . . es.
  26. Web site: Henri P. Cartan . 24 April 2022 . National Academy of Sciences.
  27. Web site: Verstorbene Mitglieder – Prof. Dr. Henri Cartan . Deceased member – Prof. Dr. Henri Cartan . 24 April 2022 . . de.
  28. Web site: Deceased Honorary Members (Alphabetical Order) . 24 April 2022 . The Japan Academy.
  29. Web site: Картан А.. – Общая информация . 24 April 2022 . ras.ru . ru.
  30. Web site: Honory [sic] Doctors of the Faculty of Mathematics and Computer Science . 24 April 2022 . Münster University.
  31. Griffith . J. G. . 1981 . Eulogy: Henri Cartan . Bulletin of the London Mathematical Society . en . 13 . 3 . 263–264 . 10.1112/blms/13.3.263.
  32. Web site: Henri Cartan Honoris causa Universidad de Zaragoza . 24 April 2022 . . es.
  33. Web site: 1996 . Décret du 13 mai 1996 . Decree of 13 May 1996 . 24 April 2022 . . fr.
  34. Serre . Jean-Pierre . Jean-Pierre Serre . 2009 . Henri Paul Cartan. 8 July 1904 – 13 August 2008 . . 55 . 37–44 . 10.1098/rsbm.2009.0005 . free.
  35. Serre . Jean-Pierre . Jean-Pierre Serre . 2014 . Obituary: Henri Cartan 1904-2008 . Bulletin of the London Mathematical Society . en . 46 . 1 . 211–216 . 10.1112/blms/bdt079. free .
  36. Bourguignon . Jean-Pierre . Jean-Pierre Bourguignon . Hirzebruch . Friedrich . Friedrich Hirzebruch . Remmert . Reinhold . Reinhold Remmert . 2010 . Cartan, Europe, and Human Rights . . . 57 . 8 . 972–975.
  37. News: Ziegler . Günter . Günter M. Ziegler . 2009 . Der französische Freund . de . The French friend . . 18 April 2022.
  38. Web site: Archives de l'UEF-France et mémoire du fédéralisme . Archives of the UEF-France and memories of federalism . 25 April 2022 . uef.fr . 31 October 2015 . fr.
  39. Mabille . Xavier . 1984 . Les résultats des élections européennes de juin 1984 . The results of the European elections of June 1984 . Courrier Hebdomadaire du CRISP . fr . 1043 . 18 . 1–31 . 10.3917/cris.1043.0001 . 0008-9664.
  40. Web site: Joséphine Guidy-Wandja . 2023-03-25 . International Mathematical Union.
  41. Web site: Cassiau-Haurie . Christophe . 2008-02-20 . Les femmes peinent à percer les bulles . Women struggle to break through bubbles . 2023-03-25 . Africultures . fr-FR.
  42. Web site: 1954–1955 . Séminaire Henri Cartan, Tome 7 . Seminar Henri Cartan . 25 April 2022 . numdam.org . fr . 25 April 2022 . https://web.archive.org/web/20220425232321/http://www.numdam.org/volume/SHC_1954-1955__7/ . dead .
  43. Cartan . Henri . 1955 . Sur l'itération des opérations de Steenrod . On the iteration of Steenrod operations . . fr . 29 . 1 . 40–58 . 10.1007/BF02564270 . 124558011 . 0010-2571.
  44. Cartan . Henri . Espaces fibrés et groupes d'homotopie. I. Constructions générales . . 234 . 288–290 . 1952a . Paris . 0764-4442 . 0046045 . Serre . Jean-Pierre . Henri Cartan . Jean-Pierre Serre.
  45. Cartan . Henri . Espaces fibrés et groupes d'homotopie. II. Applications . Comptes Rendus de l'Académie des Sciences, Série I . 234 . 393–395 . 1952b . Paris . 0764-4442 . 0046046 . Serre . Jean-Pierre . Henri Cartan . Jean-Pierre Serre.
  46. Book: Cartan . Henri . Homological Algebra . Eilenberg . Samuel . . 1956 . 0691049912 . Samuel Eilenberg.
  47. Mac Lane, Saunders . Saunders Mac Lane . 1956 . Review: Homological algebra, by Henri Cartan and Samuel Eilenberg . Bull. Amer. Math. Soc. . 62 . 6 . 615–624 . 10.1090/S0002-9904-1956-10082-7 . free.
  48. Cartan . Henri . 1937 . Théorie des filtres . Theory of filters . . fr . 205 . 595–598.
  49. Cartan . Henri . 1937 . Filtres et ultrafiltres . Filters and ultrafilters . . fr . 205 . 777–779.
  50. Cartan . Henri . 1950 . La transgression dans un groupe de Lie et dans un espace fibré principal . Transgression in a Lie group and in a principal fibre bundle . Colloque de topologie (Espaces fibrés). Bruxelles . fr . 57–71 . 0045.30701.
  51. Mac Lane, Saunders. Saunders Mac Lane. Review: Homological algebra, by Henri Cartan and Samuel Eilenberg. Bull. Amer. Math. Soc.. 1956. 62. 6. 615–624. 10.1090/S0002-9904-1956-10082-7. free.
  52. News: Fresán, Javier. Review: Correspondance entre Henri Cartan et André Weil ed. by Michèle Audin. EMS Newsletter. June 2012. 58–60. 22 June 2016. 19 May 2020. https://web.archive.org/web/20200519020340/http://irma.math.unistra.fr/~maudin/EMS-review-cartan-weil.pdf. dead.

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