Mikhael Gromov (mathematician)

For other people named Gromov, see Gromov (disambiguation).

Mikhail Leonidovich Gromov
Mikhail Gromov
Born	(1943-12-23) 23 December 1943 Boksitogorsk, Russian SFSR, USSR
Nationality	Russian
Alma mater	Leningrad (PhD)
Known for	Geometry
Awards	see text
Scientific career
Fields	Mathematics
Institutions	IHÉS New York University
Doctoral advisor	Vladimir Rokhlin
Doctoral students	Denis Auroux Christophe Bavard François Labourie Pierre Pansu Abdelghani Zeghib

Mikhail Leonidovich Gromov (also Mikhael Gromov or Michael Gromov; Russian: Михаи́л Леони́дович Гро́мов; born 23 December 1943), 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.

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 is also interested in mathematical biology.

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

• 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”

Honors

• Invited speaker to International Congress of Mathematicians: 1970 (Nice), 1978 (Helsinki), 1982 (Warsaw), 1986 (Berkeley)
• Foreign member of the National Academy of Sciences, the American Academy of Arts and Sciences and the Norwegian Academy of Science and Letters
• Membre de l'Institut de France - Académie des Sciences

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

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

• 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

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