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For other persons of the same name, see
Gromov.
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.
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
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
- 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
External
links