Mikhail Leonidovich Gromov

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Mikhail Leonidovich Gromov
Gromov Mikhail Leonidovich.jpg
Mikhail Gromov
Born (1943-12-23) 23 December 1943 (age 70)
Boksitogorsk, Russian SFSR, Soviet Union
Residence France
Nationality Russian
Fields Mathematics
Institutions Institut des Hautes Études Scientifiques
New York University
Alma mater Leningrad (PhD)
Doctoral advisor Vladimir Rokhlin
Doctoral students Denis Auroux
Christophe Bavard
François Labourie
Pierre Pansu
Abdelghani Zeghib
Known for Geometry
Notable awards Oswald Veblen Prize in Geometry (1981)
Wolf Prize (1993)
Kyoto Prize (2002)
Nemmers Prize in Mathematics (2004)
Abel Prize (2009)

Mikhail Leonidovich Gromov (also spelled Mikhael Gromov or Michael Gromov; Russian: Михаи́л Леони́дович Гро́мов; born 23 December 1943), is a French–Russian mathematician known for important contributions in many different areas of mathematics. He is considered a geometer in a very broad sense of the word. In 2009 he was awarded the Abel Prize "for his revolutionary contributions to geometry".

Work[edit]

Gromov's style of geometry features a "coarse" or "soft" viewpoint, often analyzing asymptotic or large-scale properties.

His impact has been felt most heavily in geometric group theory, where he characterized groups of polynomial growth and created, along with James W. Cannon, the notion of hyperbolic group; symplectic topology, where he introduced pseudoholomorphic curves, and in Riemannian geometry. His work, however, has delved deeply into analysis and algebra, where he will often formulate a problem in "geometric" terms. For example, his homotopy principle (h-principle) on differential relations is the basis for a geometric theory of partial differential equations.

Gromov is also interested in mathematical biology.[1]

Gromov studied for a doctorate (1973) in Leningrad, where he was a student of Vladimir Rokhlin. He is now a permanent member of IHÉS, and a Professor of Mathematics at New York University.

Prizes and honors[edit]

Prizes[edit]

Honors[edit]

See also[edit]

Books and other publications[edit]

  • Gromov, M. Hyperbolic manifolds, groups and actions. Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N.Y., 1978), pp. 183–213, Ann. of Math. Stud., 97, Princeton Univ. Press, Princeton, N.J., 1981.
  • Gromov, M. Hyperbolic groups. Essays in group theory, 75–263, Math. Sci. Res. Inst. Publ., 8, Springer, New York, 1987.
  • Gromov, M. Asymptotic invariants of infinite groups. Geometric group theory, Vol. 2 (Sussex, 1991), 1–295, London Math. Soc. Lecture Note Ser., 182, Cambridge Univ. Press, Cambridge, 1993.
  • Gromov, Misha: Metric structures for Riemannian and non-Riemannian spaces. Based on the 1981 French original. With appendices by M. Katz, P. Pansu and S. Semmes. Translated from the French by Sean Michael Bates. Progress in Mathematics, 152. Birkhäuser Boston, Inc., Boston, MA, 1999. xx+585 pp. ISBN 0-8176-3898-9[5]
  • Gromov, M. Pseudoholomorphic curves in symplectic manifolds. Invent. Math. 82 (1985), no. 2, 307–347.
  • Gromov, Mikhael Groups of polynomial growth and expanding maps. Inst. Hautes Études Sci. Publ. Math. No. 53 (1981), 53–73.
  • Gromov, Mikhael Structures métriques pour les variétés riemanniennes. (French) [Metric structures for Riemann manifolds] Edited by J. Lafontaine and P. Pansu. Textes Mathématiques [Mathematical Texts], 1. CEDIC, Paris, 1981. iv+152 pp. ISBN 2-7124-0714-8
  • Gromov, Mikhael: Partial differential relations. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 9. Springer-Verlag, Berlin, 1986. x+363 pp. ISBN 0–387-12177-3[6]
  • Ballmann, Werner; Gromov, Mikhael; Schroeder, Viktor: Manifolds of nonpositive curvature. Progress in Mathematics, 61. Birkhäuser Boston, Inc., Boston, MA, 1985. vi+263 pp. ISBN 0-8176-3181-X
  • Gromov, Mikhael Carnot–Carathéodory spaces seen from within. Sub-Riemannian geometry, 79–323, Progr. Math., 144, Birkhäuser, Basel, 1996.
  • Gromov, Michael Volume and bounded cohomology. Inst. Hautes Études Sci. Publ. Math. No. 56 (1982), 5–99 (1983).

Notes[edit]

References[edit]

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