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Mikhail Leonidovich Gromov

Mikhail Gromov
Born 23 December 1943 (1943-12-23) (age 66)
Boksitogorsk, Russian SFSR
Residence France
Nationality Franco-Russian
Fields Mathematics
Institutions IHÉS
New York University
Alma mater Leningrad (PhD)
Doctoral advisor Vladimir Rokhlin
Known for Geometry
Notable awards see text

Mikhail Leonidovich Gromov (Russian: Михаил Леонидович Громов; born 23 December 1943) also romanized as Mikhael Gromov or Michael Gromov) is a Franco-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.

Contents

Work

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 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 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

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Prizes

Honors

See also

Books and other publications

  • 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
  • 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: 3-540-12177-3
  • 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).

References

External links


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