Henri Cartan

Template:Short description Template:Use dmy dates Template:Infobox scientist Henri Paul Cartan (Template:IPA; 8 July 1904 – 13 August 2008) was a French mathematician who made substantial contributions to algebraic topology.<ref>Template:Cite news</ref><ref name=":3">Template:Cite web</ref><ref>Template:Cite news</ref>

He was the son of the mathematician Élie Cartan, nephew of mathematician Anna Cartan, oldest brother of composer Template:Interlanguage link, physicist Template:Interlanguage link and mathematician Template:Interlanguage link, 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.<ref name=":0">Template:Cite journal</ref> 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.<ref name=":4">Template:MacTutor Biography</ref><ref name=":5">Template:Cite news available also at Template:Cite news</ref>

In 1923 he started studying mathematics at École Normale Supérieure, receiving an agrégation in 1926 and a doctorate in 1928.<ref name=":4" /><ref name=":5" /> His PhD thesis, entitled Sur les systèmes de fonctions holomorphes à variétés linéaires lacunaires et leurs applications, was supervised by Paul Montel.<ref name=":1">Template:MathGenealogy</ref>

Cartan taught at Lycée Malherbe in Caen from 1928 to 1929, at the University of Lille from 1929 to 1931 and at the 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.<ref name=":4" /><ref name=":5" />

Cartan died on 13 August 2008 at the age of 104. His funeral took place the following Wednesday on 20 August in Die, Drome.<ref>Template:Cite news</ref><ref>Template:Cite news</ref><ref>Template:Cite news</ref>

Honours and awards

In 1932 Cartan was invited to give a Cours Peccot at the Collège de France.<ref>Template:Cite web</ref> In 1950 he was elected president of the Société mathématique de France<ref>Template:Cite web</ref> and from 1967 to 1970 he was president of the International Mathematics Union.<ref>Template:Cite web</ref> He was awarded the Émile Picard Medal in 1959,<ref>Template:Cite web</ref> the CNRS Gold Medal in 1976,<ref>Template:Cite web</ref> and the Wolf Prize in 1980.<ref>Template:Cite web</ref>

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<ref>Cartan, Henri. "Problèmes globaux dans la théorie des fonctions analytiques de plusieurs variables complexes." Template:Webarchive In Proc. Int. Cong. Math, vol. 1, pp. 152–164. 1950.</ref> and in 1958 in Edinburgh.<ref>Cartan, Henri. "Sur les fonctions de plusieurs variables complexes. Les espaces analytiques." Template:Webarchive In Proc. Intern. Congress Mathematicians Edinburgh, pp. 33–52. 1958.</ref>

From 1974 until his death he had been a member of the French Academy of Sciences.<ref>Template:Cite web</ref> He was elected a foreign member of many academies and societies,<ref>Template:Cite web</ref><ref name=":6">Template:Cite web</ref> including the American Academy of Arts and Sciences (1950),<ref>Template:Cite web</ref> London Mathematical Society (1959),<ref>Template:Cite web</ref> Royal Danish Academy of Sciences and Letters (1962), Template:Interlanguage link (1967),<ref>Template:Cite web</ref> Royal Society of London (1971),<ref>Template:Cite web</ref> Göttingen Academy of Sciences and Humanities (1971),<ref>Template:Cite web</ref> Spanish Royal Academy of Sciences (1971),<ref>Template:Cite web</ref> United States National Academy of Sciences (1972),<ref>Template:Cite web</ref> Bavarian Academy of Science (1974),<ref>Template:Cite web</ref> Royal Academy of Belgium (1978), Japan Academy (1979),<ref>Template:Cite web</ref> Finnish Academy of Science and Letters (1979), Royal Swedish Academy of Sciences (1981), Polish Academy of Sciences (1985) and Russian Academy of Sciences (1999).<ref>Template:Cite web</ref>

He was awarded Honorary Doctorates from Münster (1952),<ref>Template:Cite web</ref> ETH Zürich (1955), Oslo (1961), Sussex (1969), Cambridge (1969),<ref name=":6" /> Stockholm (1978), Oxford University (1980),<ref name=":2">Template:Cite journal</ref> Zaragoza (1985)<ref>Template:Cite web</ref> and Athens (1992).<ref name=":4" />

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.<ref>Template:Cite web</ref>

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.<ref name=":0" /><ref name=":7">Template:Cite journal</ref><ref name=":8">Template:Cite journal</ref><ref name=":9">Template:Cite journal</ref>

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.<ref name=":9" /><ref>Template:Cite news</ref>

Cartan supported the idea of European Federalism and from 1974 to 1985 was president of the French section of the Union of European Federalists.<ref>Template:Cite web</ref> At the 1984 European elections he was the leader of the Liste pour les États-Unis d'Europe,<ref name=":0" /> which obtained 0.4% of votes and did not elect any candidate.<ref>Template:Cite journal</ref>

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.<ref name=":9" />

Research

During the "Cartan celebration", at Orsay in 1975.

Cartan worked in several fields across algebra, geometry and analysis, focusing primarily on algebraic topology and homological algebra.<ref name=":7" /><ref name=":8" />

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),<ref>Template:Cite web</ref><ref>Template:Cite web</ref> Adrien Douady, Roger Godement, Max Karoubi, Jean-Louis Koszul, Jean-Pierre Serre and René Thom.<ref name=":1" /><ref name=":3" />

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,<ref>Template:Cite web</ref> he introduced the notion of Steenrod algebra,<ref>Template:Cite journal</ref> and, together with Jean-Pierre Serre, developed the method of "killing homotopy groups".<ref>Template:Cite journal</ref><ref>Template:Cite journal</ref> His 1956 book with Samuel Eilenberg on homological algebra<ref>Template:Cite book Template:Isbn.</ref> was an important text, treating the subject with a moderate level of abstraction with the help of category theory.<ref>Template:Cite journal</ref> 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<ref>Template:Cite journal</ref><ref>Template:Cite journal</ref> and in potential theory he developed the fine topology and proved Cartan's lemma. The Cartan model for equivariant cohomology<ref>Template:Cite journal</ref> is also named after him.

Selected publications

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• Espaces fibrés et homotopie, (Séminaire Henri Cartan Tome 2 (1949–1950))
• Cohomologie des groupes, suite spectrale, faisceaux, (Séminaire Henri Cartan Tome 3 (1950–1951))
• Algèbres d'Eilenberg – Mac Lane et homotopie, (Séminaire Henri Cartan Tome 7 no2. (1954–1955))
• Fonctions automorphes,(Séminaire Henri Cartan Tome 10 no2. (1957–1958))
• Quelques questions de topologie, 1958.
• Homological Algebra (with S. Eilenberg), Princeton Univ Press, 1956 Template:Isbn<ref>Template:Cite journal</ref>
• Séminaires de l'École normale supérieure (called "Séminaires Cartan"), Secr. Math. IHP, 1948–1964; New York, W.A.Benjamin ed., 1967.
• Théorie élémentaire des fonctions analytiques, Paris, Hermann, 1961 (translated into English, German, Japanese, Spanish and Russian).
• Calcul différentiel, Paris, Hermann, 1967 (translated into English, Spanish and Russian).
• Formes différentielles, Paris, Hermann, 1967 (translated into English, Spanish and Russian).
  • Differential Forms, Dover 2006
• Œuvres — Collected Works, 3 vols., ed. Reinhold Remmert & Jean-Pierre Serre, Springer Verlag, Heidelberg, 1967.
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• Relations d'ordre en théorie des permutations des ensembles finis, Neuchâtel, 1973.
• Théorie élémentaire des fonctions analytiques d'une ou plusieurs variables complexes, Paris, Hermann, 1975. Template:Isbn
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• Cours de calcul différentiel, Paris, Hermann, 1977.
• Template:Cite book.<ref>Template:Cite news</ref>

See also

• List of second-generation Mathematicians

External links

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• Illusie, Luc; Cartier, Pierre (ed.), Dossier. Notices of the American Mathematical Society, Sept. 2010, Template:Nobr, Template:Nobr
• Biographical sketch and bibliography by the Société Mathématique de France on the occasion of Cartan's 100th birthday. Template:In lang
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• Template:Citation (translations of above two articles from the SMF Gazette)
• Papers by Henri Cartan as member of the 'Association européenne des enseignants' (AEDE) and the 'Mouvement fédéraliste européen' (MFE) are at the Historical Archives of the EU in Florence