Laurent Schwartz

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Laurent Schwartz (1970)

Laurent Schwartz (born March 5, 1915 in Paris , † July 4, 2002 ibid) was a French mathematician and Fields Medalist . He is considered to be the founder of the theory of distributions .

biography

Clanis schwartzi paratype

Laurent Schwartz was the son of the surgeon Anselme Schwartz, who moved to Paris after the annexation of Alsace by the German Reich and there became the first officially employed Jewish surgeon at a Paris hospital. Laurent Schwartz's uncle, Robert Debré , was the founder of UNICEF and Jacques Hadamard was his great-uncle.

Schwartz won the general entrance exams (Concours Generale) to the Grand Écoles in Latin, but then studied from 1934 at the École normal supérieure mathematics (Agrégation de Mathématiques 1937). In 1938 he married Marie-Hélène Lévy , daughter of the mathematician Paul Lévy . After the German Wehrmacht conquered France in 1940, Schwartz, as a Trotskyist and Jew, was in mortal danger. He used aliases (including Laurent-Marie Sélimartin). His wife called herself Lengé. In 1943 Schwartz received his doctorate from the University of Strasbourg , which was then evacuated to Clermont-Ferrand , where he lived nearby, half-submerged.

In Clermont-Ferrand Schwartz came under the influence of members of the mathematicians group Bourbaki (including Jean Dieudonné , Jean Delsarte , Henri Cartan ). In 1944/45 he was at the University (Faculté de Science) in Grenoble and after the war first professor at the University of Nancy , which made Dieudonne and Delsarte a mathematical center for the Bourbakists, to which Schwartz belonged. From 1952 he taught in Paris at the Sorbonne and from 1959 at the École polytechnique , where he was until 1980 and reformed the teaching and orientation towards scientific research - before that it was primarily an engineering school (subordinate to the military) and Career springboard for the French elite. In another concern of tightening the admission criteria for French universities, he was less successful. After that he was at the University of Paris VII until his retirement in 1983 .

Schwartz's doctoral students include Alexander Grothendieck , Louis Boutet de Monvel , Jacques-Louis Lions , Bernard Malgrange , André Martineau , François Treves , Gilles Pisier .

Schwartz's wife Marie-Hélène Schwartz was also a mathematician and one of the first women to study at the École Normale Supérieure. Their daughter, Claudine Robert, is a professor of statistics in Grenoble . Schwartz called himself an atheist. Schwartz owned one of the largest private butterfly collections, most of which he donated to museums. Several species of butterflies are named after him.

Distribution theory

In the years after the war Schwartz developed his theory of distributions , generalized functions, which he discovered during the war (November 1944). For this work he received the Fields Medal in 1950 at the International Congress of Mathematicians in Cambridge (Massachusetts) , where he also gave a plenary lecture ( Théorie des Noyaux ).

The theory of distributions had predecessors in the functions introduced by Oliver Heaviside and Paul Dirac in physics and also had some mathematical predecessors, for example by Salomon Bochner . In particular, the concept was developed by Sobolew in the Soviet Union in the 1930s as part of the Cauchy problem of linear hyperbolic partial differential equations. Schwartz himself did not know Sobolew's work and was primarily influenced by lectures by Jean Leray in 1934/35 at the Collège de France on weak solutions of partial differential equations and André Weil's work on integration on locally compact topological groups. He expanded the theory with the theory of topological vector spaces developed especially by the Bourbakists . Schwartz himself, together with Georges de Rham , applied distributions to differential forms on manifolds (de Rham's concept of currents) and also in quantum field theory. Schwartz later turned to probability theory, more precisely to stochastic analysis (for example, semimartingales on manifolds), which he became interested in at an early stage since conversations with his father-in-law Paul Lévy.

In addition to the Fields Medal, he received several prizes from the French Academy of Sciences and was honorary doctorates in Berlin, Brussels, Lund, Tel Aviv, Montreal and Athens. In 1972 he became a member of the French Académie des Sciences . In 1962 he was President of the Société Mathématique de France .

Political commitment

Schwartz was a very political person who, for example, got involved with the Trotskyists in the 1930s and 1940s , as he had been an avowed anti-Stalinist since the Moscow show trials of the 1930s. In 1956 he was publicly involved in the Hungarian uprising against the Soviet occupation. His political commitment led to a two-year exile in New York at the end of the 1950s : Maurice Audin , a mathematics doctoral student at the University of Algiers, Algerian communist and opponent of French rule in Algeria , was kidnapped by the French military in 1957 and tortured to death. Laurent Schwartz sought in vain to investigate the case, secured a posthumous doctorate for Audin and, after the affair, became one of the signatories of the Manifesto of 121 , a declaration calling for military disobedience in Algeria. He was then relieved of his professorship (the École Polytechnique was under the Minister of the Army), but it was returned after two years. Later he continued his political engagement, for example for politically persecuted mathematicians in all parts of the world, against the Vietnam War and the invasion of the Soviet Union in Afghanistan .

Fonts

  • Un mathématicien aux prices avec le siècle . Paris 1997, autobiography, English translation: A mathematician grappling with his century . Birkhäuser, 2001, ISBN 3-7643-6052-6 .
  • Theory of Distribution . Hermann, 2 volumes, 1950/1951, new edition 1966.
  • Tenseurs . Hermann, 1975.
  • Analysis . Hermann, 1998.
  • Analysis hilbertienne . Hermann, 1979.
  • Cours d'analysis . Hermann, 1981.
  • Analysis mathematiques . 2 volumes, Hermann, 1967.
  • Étude des sommes d'exponentielles . Hermann, 1959.
  • Mathematics for the physical sciences . Hermann, 1966, German translation: Mathematical methods of physics . BI university paperbacks, 1974.
  • Application of distributions to the theory of elementary particles in quantum mechanics . Gordon and Breach, 1968, 1988.
  • Semi-martingales and their stochastic calculus on manifolds . Press de l'Universitaire de Montreal, 1984.
  • Semi-martingales sur des variétés et martingales conformes sur des variétés analytiques complexes . Springer, 1980.
  • Geometry and probability in Banach Spaces . Springer, 1981.
  • Radon measures on arbitrary topological spaces and cylindrical measures . Oxford University Press, 1973 (Tata Lectures).
  • Lectures on complex analytic manifolds . Springer, 1986 (Lectures at the Tata Institute, Bombay 1955.)
  • Pour sauver l'université . Editions du Seuil, 1983.
  • Séminaire Schwartz in Paris 1953 to 1961 . Online edition: [1]

See also

Web links

Individual evidence

  1. ^ Laurent Schwartz: A Mathematician Grappling With His Century. Birkhäuser, Basel / Boston / Berlin 2000, ISBN 978-3-7643-6052-8 , p. 193. Quote: "My parents were atheists, I was an atheist, I never really felt like a Jew."
  2. ↑ Laurent Schwartz: Généralisation de la notion de fonction, de dérivation, de transformation de Fourier et applications mathématiques et physiques. In: Annales de l'Université de Grenoble. Vol. 21, 1945, pp. 57-74 ( PDF ; 1.4 MB), from Archive.Numdam.org, accessed on August 26, 2019.
  3. ↑ who always attributed the invention of distributions to Sobolev
  4. ^ Brigitte Vital-Durant: L'affaire Audin, un mensonge d'Etat. In: La Liberation. June 12, 2001 from Liberation.fr (French), accessed August 26, 2019.
  5. ↑ A book about it by Pierre Vidal-Naquet, for which Schwartz wrote the preface, appeared in 1958
personal data
SURNAME Schwartz, Laurent
BRIEF DESCRIPTION French mathematician, Fields Medalist
DATE OF BIRTH March 5, 1915
PLACE OF BIRTH Paris
DATE OF DEATH 4th July 2002
Place of death Paris