Mikhail Gromov
From Wikipedia, the free encyclopedia
| Mikhail Leonidovich Gromov | |
 Mikhail Gromov
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| Born | December 23, 1943 Russia |
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| Residence | France |
| Nationality | Russian |
| Fields | Mathematician |
| Institutions | IHÉS New York University |
| Alma mater | Leningrad (PhD) |
| Doctoral advisor | V. A. Rokhlin |
| Known for | geometry |
| Notable awards | see page |
Mikhail Leonidovich Gromov Russian: Михаил Леонидович Громов (born December 23, 1943, also known as Mikhael Gromov, Michael Gromov, or Misha Gromov) is a 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. His style of geometry features a "coarse" or "soft" viewpoint, often analyzing asymptotic or large-scale properties.
Gromov's 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 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 V. A. Rokhlin. He is now a permanent member of IHÉS, and Jay Gould Professor of Mathematics at New York University.
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[edit] Prizes and honors
[edit] Prizes
- Prize of the Mathematical Society of Moscow (1971)
- Oswald Veblen Prize in Geometry (AMS) (1981)
- Prix Elie Cartan de l'Academie des Sciences de Paris (1984)
- Prix de l'Union des Assurances de Paris (1989)
- Leroy P. Steele Prize for Seminal Contribution to Research (AMS) (1997)
- Wolf Prize in Mathematics (1993)
- Lobachevsky Medal (1997)
- Balzan prize for Mathematics (1999)
- Kyoto Prize in Mathematical Sciences (2002)
- Nemmers Prize in Mathematics (2004)
- Bolyai prize in 2005.
[edit] Honors
- Invited speaker to International Congress of Mathematicians: 1970 (Nice), 1978 (Helsinki), 1982 (Warsaw), 1986 (Berkeley)
- Foreign member of the National Academy of Sciences and American Academy of Arts and Sciences
- Membre de l'institut - l'Academie des Sciences de Paris
[edit] See also
- Gromov's theorem on groups of polynomial growth
- Gromov's theorem on almost flat manifolds
- Gromov's compactness theorem
- Gromov's inequality for complex projective space
- Gromov's systolic inequality for essential manifolds
- Gromov–Hausdorff convergence
- Bishop–Gromov inequality
- Lévy-Gromov inequality
- Gromov-Witten invariants
- Taubes's Gromov invariant
- Minimal volume
- localisation on the sphere
- Gromov norm
- Hyperbolic group
- Random group
- Ramsey-Dvoretzky-Milman phenomenon
- Systolic geometry
- Filling radius
- Gromov product
- Gromov δ-hyperbolic space
- Filling area conjecture
[edit] 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).
[edit] References
- Gromov Receives Nemmers Prize AMS Notices, vol. 51, number 7
- Marcel Berger, Encounter with a Geometer, Part I, AMS Notices, Volume 47, Number 2
- Marcel Berger, Encounter with a Geometer, Part II, AMS Notices, Volume 47, Number 3
