Mikhael Gromov

1999 Balzan Prize for Mathematics

For his numerous, most original and profound contributions to geometry in its various forms, and for the way in which he has applied them to many other domains of mathematics and of theoretical physics.

Mikhael L. Gromov, born on 23 December, 1943, in Boksitogorsk, USSR, has been a naturalized French citizen since 1992.

He obtained his Masters degree (1965), his Doctorate (1969) and his Post-doctoral Thesis (1973) from Leningrad University, where he had also been teaching from 1967 to 1974 as an Assistant Professor; from 1974 to 1981, he was Professor at the University of New York at Stony Brook, and from 1981 to 1982 at the University of Paris VI; since 1982, he has been permanent Professor at the Institut des Hautes Etudes Scientifiques de Bures-sur-Yvette, near Paris.

He has received many national and international honours:

  • Award of the Mathematical Society of Moscow (1971),
  • the Oswald Veblen Prize in Geometry, American Mathematical Society (1981),
  • invited conference member at the International Congresses of Mathematicians in Nice (1970), Helsinki (1978) and Warsaw (1982),
  • Prix Elie Cartan of the Académie des Sciences of Paris (1984), invited conference member at the International Congress of Mathematicians in Berkeley (1986),
  • Foreign Associate Member, US National Academy of Sciences (1989),
  • Foreign Member of the American Academy of Art and Sciences (1989),
  • Associé étranger of the Académie des Sciences of Paris (1989),
  • Prix de l’Union des Assurances de Paris (1989), honorary degrees from the University of Geneva (1992),
  • Wolf Prize (1993),
  • Leroy P. Steele Prize for a Seminal Contribution to Research, American Mathematical Society (1997),
  • Member of the Institut de France, Académie des Sciences (1997) and the Lobatchewski Medal (1997).

The scientific contributions of Mikhael Gromov include more than one hundred articles and several books.
Among his most important publications, we cite:

  • Stable Maps of Foliations into Manifolds, 1969, Izv. Akad. Nauk SSSR, 33, 707-734;
  • Synthetic Geometry of Riemannian Manifolds, 1978, Int. Congress Math., 415-419, Helsinki; 
  • Homotopical Effects of Dilatation, 1978, J. Differential Geom., 13, 303-310;
  • Paul Levy’s Isoperimetric Inequality, 1980, re-issue, Institut des Hautes Etudes Scientifiques;
  • Groups of Polynomial Growth and Expanding Maps, 1981, Publ. Math., I.H.E.S., 53, 53-73;
  • Pseudo-holomorphic Curves in Symplectic Manifolds, 1985, Inventiones Math., 82, 307-347;
  • Partial Differential Relations, 1986, Ergeb. Math., 9, Springer, Heidelberg;
  • Hyperbolic Groups, 1987, in “Essays in Group Theory”, S. Gersten ed., MSRI Publications, 8. Springer-Verlag, Heidelberg-New York;
  • Foliated Plateau Problem, I, 1991, Geom. Anal. Functional Anal., 1, 14-79; idem, III, ibidem, 253-320;
  • Asymptotic Invariants of Infinite Groups, 1993, in “Geometric Group Theory”, G. Noble & M. Roller eds., London Math. Soc., 75-263;
  • Positive Curvature, Macroscopic Dimension, 1996, in “Functional Analysis in the Eve of the 21st Century”, S. Gindikin. J. Lepowski, & R. Wilsone eds., 1-213, Birkhäuser, Basle;
  • Metric Structures for Riemannian and non-Riemannian Manifolds (with M. La Fontaine and P. Pansu), 1999, Birkhäuser, Basle.

(October 1999)

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