Marcel Berger
Marcel Y. Berger (born in 1927 in Paris ) is a French mathematician who deals with differential geometry.
Life and work
Berger studied with André Lichnerowicz, Élie Cartan one pupil (who in turn a student of Gaston Darboux was ), and continued this line of outstanding Differentialgeometer in France continued. After his PhD ( " Holonomy groups of Riemannian manifolds " ) at Lichnerowicz he was from 1955 professor at the universities of Strasbourg, Nice and Paris ( University of Paris VII Denis Diderot, École normale supérieure ). 1974 to 1985 he was Directeur de Recherche at the CNRS and from 1985 to 1994 director of the IHES in Bures -sur -Yvette. In this role he also won the Russian Mikhail Gromov Differentialgeometer to France to the IHES. Berger was 1956/7 Visiting Professor at MIT and 1961/62 at the University of Berkeley. In 1981, he was " Rademacher Lecturer" at the University of Pennsylvania.
In 1955, he classified the Holonomiegruppen simply related, irreducible, non - locally symmetric Riemannian ( and pseudo- Riemannian ) manifolds.
With Wilhelm Klingenberg, he proved the late 1950s, building on the work of Harry smoke the spheres set.
With Jerry Kazdan he proved an inequality for the volumes of Riemannian manifolds with a given Injektivitätsradius ( Berger- Kazdan comparison theorem ). They thus contributing to the solution of a conjecture of Wilhelm Blaschke on Reunion manifolds.
He wrote several textbooks on differential geometry and geometry.
1972 to 1981 he was President of the French Mathematical Society. Since 1982 he is a corresponding member of the French Academy of Sciences. He was co-editor of the magazine since 1979, " Inventiones Mathematicae " and since 1982 the " fundamental doctrines of the mathematical sciences " by 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.
His doctoral include Yves Colin de Verdière, Jean -Pierre Bourguignon, Gérard Besson, Pierre Pansu and Sylvestre Gallot.
Also with a group of mathematicians under the pseudonym Arthur Besse, among other things, he published a book on Einstein manifolds.
Prices
Writings
- 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 Press Universitaire de France 1987)
- Geometry II, Universitext. Springer -Verlag, Berlin, 1987.
- Geometry I, Universitext. Springer -Verlag, Berlin, 1987, 1994, ISBN 3-540-11658-3 (in French appeared its geometry in 5 volumes 19777/8 at Nathan, in 3rd edition 2003, 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 de France, Association pour la diffusion de la pensée française ( ADPF ), 287 pages, 2005 online ( pdf ) 2.3 MB
- Convexity, American Mathematical Monthly, Bd.97, 1990, S.650 ( received the Writing Award from the Mathematical Association of America )
- Riemannian geometry falling on the second half of the twentieth century, annual report, DMV ( German mathematician club ), Bd.100, 1998, Issue 2 (Reprint in the University Lecture Series, vol 17, American Mathematical Society, Providence, Rhode Iceland, 2000, ISBN 0-8218-2052-4 )
- Convexité dans le plan dans l' espace et au delà -, 2 volumes, Ellipse, 2006
- Geometry tools vivante ou l' échelle de Jacob de mathematicien, Cassini, 2007