Marcel Berger

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Marcel Berger in Paris , 1968

Marcel Y. Berger (born April 14, 1927 in Paris ; † October 15, 2016 ) was a French mathematician who dealt with differential geometry .

Live and act

Berger studied with André Lichnerowicz , an Élie Cartan student (who in turn was a student of Gaston Darboux ), and continued this line of outstanding differential geometries in France. After completing his doctorate (“Holonomy Groups of Riemannian Manifolds”) with Lichnerowicz, he was professor at the Universities of Strasbourg , Nice and Paris (University of Paris VII Denis Diderot, École normal supérieure ) from 1955 . From 1974 to 1985 he was Directeur de Recherche at the CNRS and from 1985 to 1994 Director of the IHÉS in Bures-sur-Yvette. In this function he also brought the Russian differential geometer Michail Gromow to France at IHES. Berger was visiting professor at MIT in 1956/7 and at Berkeley University in 1961/62 . In 1981 he was "Rademacher Lecturer" at the University of Pennsylvania . Since 1982 he has been a corresponding member of the Académie des sciences .

In 1955 he classified the holonomy groups of simply connected, irreducible, not locally symmetrical Riemannian (and pseudo-Riemannian ) manifolds

With Wilhelm Klingenberg , he demonstrated the set of spheres at the end of the 1950s, building on the work of Harry Rauch .

With Jerry Kazdan he proved an inequality for the volumes of Riemann manifolds with a given injectivity radius (Berger-Kazdan comparison theorem). They thus contributed to the solution of a conjecture by Wilhelm Blaschke about reunion manifolds.

He wrote several textbooks on differential geometry and geometry.

Since 1982 he was a corresponding member of the French Academy of Sciences . Since 1979 he has been co-editor of the journal “Inventiones Mathematicae” and since 1982 of the “Basic Teachings of Mathematical Sciences” at Springer Verlag. In 1962 he was invited speaker at the International Congress of Mathematicians in Stockholm ( Les variétés riemanniennes dont la courbure satisfait certaines conditions ). Berger is a Fellow of the American Mathematical Society . 1979/80 he was president of the Société Mathématique de France .

His PhD students include Yves Colin de Verdière , Jean-Pierre Bourguignon , Gérard Besson , Pierre Pansu and Sylvestre Gallot .

He also published with a group of mathematicians under the pseudonym Arthur Besse , among other things, a book on Einsteinian manifolds .

Prices

  • 1956 Prix Peccot, Collège de France
  • 1962 Prix Maurice Audin
  • 1969 Prix Carrière, Académie des Sciences
  • 1978 Prix Leconte, Académie des Sciences
  • 1979 Prix Gaston Julia

Fonts

  • Geometry revealed. A Jacob's ladder to modern higher geometry , Springer Verlag 2010
  • with Paul Gauduchon , Edmond Mazet: Le specter d'une variété riemannienne, Lecture Notes in Mathematics, Vol. 194, Springer-Verlag, Berlin-New York 1971.
  • with Bernard Gostiaux: Differential geometry: manifolds, curves, and surfaces, Graduate Texts in Mathematics, Vol. 115, Springer-Verlag, New York, 1988, ISBN 0-387-96626-9 , 53-01 (French Presse Universitaire de France 1987)
  • Geometry II, university text. Springer-Verlag, Berlin, 1987.
  • Geometry I, university text. Springer-Verlag, Berlin, 1987, 1994, ISBN 3-540-11658-3 (his geometry appeared in French in 5 volumes 19777/8 by Nathan, in the 3rd edition 2003, also translated into Russian and Chinese)
  • with Berry, Pierre Pansu , St. Raymond: Problems in Geometry, Springer Verlag 1984
  • A panoramic view of Riemannian geometry. Springer-Verlag, Berlin, 2003 (824 pages), ISBN 3-540-65317-1
  • with Claude Reyraud: Cinq siècles de mathématiques en France, Association pour la diffusion de la pensée française (ADPF), 287 pages, 2005, online (pdf), 2.3 MB
  • Convexity, American Mathematical Monthly, Vol. 97, 1990, p. 650 (received the Mathematical Association of America's Writing Award )
  • Riemannian geometry during the second half of the twentieth century, annual report DMV (Deutsche Mathematiker-Vereinigung), Vol. 100, 1998, Issue 2 (Reprint in the University Lecture Series, Vol. 17. American Mathematical Society, Providence, Rhode Island, 2000 , ISBN 0-8218-2052-4 )
  • Convexité dans le plane, dans l´espace et au-delà, 2 volumes, Ellipse, 2006
  • Géométrie vivante ou l ´échelle de Jacob de mathématicien, Cassini, 2007

literature

  • Claude LeBrun (Ed.): Marcel Berger remembered, Notices AMS, 2017, No. 11, online

Web links

Remarks

  1. ↑ Décès de Marcel Berger SMF accessed on October 22, 2016
  2. ↑ that is, they are not local product spaces
  3. ↑ Berger Bulletin SMF, Vol. 83, 1955, p. 279, Annales ENS Vol. 74, 1957, p. 85. The list of holonomy groups can be found e.g. B. in Helga Baum Eichfeldtheorie , Springer 2009, p. 182.
  4. ↑ Berger points to an error in his classification of holonomy groups (1953) in Panorama of Riemannian Geometry , p. 679. It is precisely the groups that later became important in string theory , in seven-dimensional manifolds.
  5. ^ Mathworld
personal data
SURNAME Berger, Marcel
ALTERNATIVE NAMES Berger, Marcel Y.
BRIEF DESCRIPTION French mathematician
DATE OF BIRTH April 14, 1927
PLACE OF BIRTH Paris
DATE OF DEATH 15th October 2016