Mikhail Leonidovich Gromov
Mikhail Gromov
Born	23 December 1943 (1943-12-23) (age 65) Boksitogorsk, Russian SFSR
Residence	France
Nationality	Franco-Russian
Fields	Mathematician
Institutions	IHÉS New York University
Alma mater	Leningrad (PhD)
Doctoral advisor	V. A. 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.

[edit] Work

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 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 V. A. Rokhlin. He is now a permanent member of IHÉS, and a Professor of Mathematics at New York University.

[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)
• Wolf Prize in Mathematics (1993)
• Leroy P. Steele Prize for Seminal Contribution to Research (AMS) (1997)
• Lobachevsky Medal (1997)
• Balzan Prize for Mathematics (1999)
• Kyoto Prize in Mathematical Sciences (2002)
• Nemmers Prize in Mathematics (2004)
• Bolyai prize in 2005
• Abel prize in 2009 “for his revolutionary contributions to geometry”

[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 de France - Académie des Sciences

[edit] See also

[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

[edit] External links

• Personal page at IHÉS
• Personal page at NYU
• Mikhail Leonidovich Gromov at the Mathematics Genealogy Project