Marcel Berger Explained

Marcel Berger
Birth Name:	Marcel Yves Marie Joseph Berger
Birth Date:	14 April 1927
Birth Place:	Paris, France
Death Place:	Paris, France
Nationality:	French
Fields:	Mathematics
Workplaces:	University of Strasbourg Université Nice-Sophia-Antipolis Paris Diderot University Institut des Hautes Études Scientifiques
Alma Mater:	École normale supérieure (Paris) University of Paris
Thesis Title:	Sur des groupes d'holonomies des variétés riemanniennes et des variétés affinés sans torsion
Thesis Url:	https://dx.doi.org/10.24033/bsmf.1464
Thesis Year:	1954
Doctoral Advisor:	André Lichnerowicz
Doctoral Students:	Jean-Pierre Bourguignon Yves Colin de Verdière Sylvestre Gallot Dominique Hulin François Labourie Pierre Pansu
Known For:	Berger–Kazdan comparison theorem Berger classification Berger's sphere Berger's inequality for Einstein manifolds
Awards:	Leconte Prize (1978)

Marcel Berger (14 April 1927 – 15 October 2016) was a French mathematician, doyen of French differential geometry, and a former director of the Institut des Hautes Études Scientifiques (IHÉS), France.

Biography

After studying from 1948 to 1951 at the École normale supérieure in Paris, Berger obtained in 1954 his PhD from the University of Paris, with thesis written under the direction of André Lichnerowicz. From 1958 to 1964 he taught at the University of Strasbourg and had visiting positions at the Massachusetts Institute of Technology and the University of California, Berkeley. From 1964 to 1966 he taught at the University of Nice, after which he joined the University of Paris VII. From 1985 to 1993 he served as director of the IHÉS.

Formerly residing in Le Castera in Lasseube, Berger was instrumental in Mikhail Gromov's accepting positions both at the University of Paris and at the IHÉS.^[1]

Awards and honors

• 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
• 1979–1980 President of the French Mathematical Society.^[2]
• 1991 Lester R. Ford Award^[3]

Selected publications

• Berger, M.: Geometry revealed. Springer, 2010.
• Berger, M.: What is... a Systole? Notices of the AMS 55 (2008), no. 3, 374–376. online text
• Book: Berger, Marcel. A Panoramic View of Riemannian Geometry. Springer-Verlag. 2003. 3-540-65317-1. xxiv+824 pp.. ^{[4] [5]}
• Berger. Marcel. Encounter with a Geometer, Part I. Notices of the AMS. 47. 2. 183–194. Feb 2000.
• Berger. Marcel. Encounter with a Geometer, Part II. Notices of the AMS. 47. 3. 326–340. Mar 2000.
• Berger, Marcel; Gauduchon, Paul; Mazet, Edmond: Le spectre d'une variété riemannienne. (French) Lecture Notes in Mathematics, Vol. 194 Springer-Verlag, Berlin-New York 1971.
• Berger, Marcel: Sur les groupes d'holonomie homogène des variétés à connexion affine et des variétés riemanniennes. (French) Bull. Soc. Math. France 83 (1955), 279–330.
• Berger, Marcel: Les espaces symétriques noncompacts. (French) Ann. Sci. École Norm. Sup. (3) 74 1957 85–177.
• Berger, Marcel; Gostiaux, Bernard: Differential geometry: manifolds, curves, and surfaces. Translated from the French by Silvio Levy. Graduate Texts in Mathematics, 115. Springer-Verlag, New York, 1988. xii+474 pp. 
• Berger, Marcel: Geometry. II. Translated from the French by M. Cole and S. Levy. Universitext. Springer-Verlag, Berlin, 1987.
• Berger, M.: Les variétés riemanniennes homogènes normales simplement connexes à courbure strictement positive. (French) Ann. Scuola Norm. Sup. Pisa (3) 15 1961 179–246.
• Berger, Marcel: Geometry. I. Translated from the French by M. Cole and S. Levy. Universitext. Springer-Verlag, Berlin, 1987. xiv+428 pp. 
• Berger, Marcel: Systoles et applications selon Gromov. (French) [Systoles and their applications according to Gromov] Séminaire Bourbaki, Vol. 1992/93. Astérisque No. 216 (1993), Exp. No. 771, 5, 279–310.
• Berger, Marcel: Geometry. I. Translated from the 1977 French original by M. Cole and S. Levy. Corrected reprint of the 1987 translation. Universitext. Springer-Verlag, Berlin, 1994. xiv+427 pp. 
• Berger, Marcel: Riemannian geometry during the second half of the twentieth century. Reprint of the 1998 original. University Lecture Series, 17. American Mathematical Society, Providence, Rhode Island, 2000. x+182 pp. 
• Besse, A.L.: Einstein Manifolds. Springer-Verlag, Berlin, 1987.

See also

• Arthur Besse
• Berger's inequality for Einstein manifolds
• Berger–Kazdan comparison theorem
• Musical isomorphism
• Parametrix
• Quaternion-Kähler manifold
• Spin(7)-manifold
• Symmetric space
• Systolic geometry

Further reading

• Claude LeBrun (Editor and Translator). "Marcel Berger Remembered", Notices of the American Mathematical Society, December 2017, Volume 64, Number 11, pp. 1285–1295.

External links

• Web site: Correspondant de l'Académie des sciences: Marcel Berger. fr. French Academy of Sciences. www.academie-sciences.fr.

Notes and References

1. Web site: Décès de Marcel Berger | Société Mathématique de France . 2016-10-19 . https://web.archive.org/web/20161022191528/http://smf.emath.fr/content/d%C3%A9c%C3%A8s-de-marcel-berger . 2016-10-22 . dead .
2. Web site: Anciens Présidents | Société Mathématique de France . 2016-10-23 . https://web.archive.org/web/20161024023304/http://smf.emath.fr/content/anciens-presidents . 2016-10-24 . dead .
3. Berger. Marcel Y.. Convexity. The American Mathematical Monthly. 97. 1990. 8 . 650–678. 10.2307/2324573. 2324573 .
4. Osserman. Robert. 2005-01-01. Review of A Panoramic View of Riemannian Geometry. 20453617. SIAM Review. 47. 1. 186–188. 10.1137/SIREAD000047000001000163000001.
5. Giblin. Peter. 2005-01-01. Review of A Panoramic View of Riemannian Geometry. 3620688. The Mathematical Gazette. 89. 514. 162–163. 10.1017/s0025557200177289. 126075408 .