Mikhail Leonidovich Gromov

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Residence France Fields Mathematics Role Mathematician		Nationality Russian and French Name Mikhail Gromov Known for Geometry

Born 23 December 1943 (age 80) Boksitogorsk, Russian SFSR, Soviet Union ( 1943-12-23 ) Institutions Institut des Hautes Etudes ScientifiquesNew York University Alma mater Leningrad State University (PhD) Doctoral students Denis AurouxChristophe BavardFrancois LabourieYashar MemarianPierre PansuAbdelghani Zeghib Education Saint Petersburg State University Doctoral advisor Vladimir Abramovich Rokhlin Awards Abel Prize, Wolf Prize in Mathematics, Nemmers Prize in Mathematics Books Metric Structures for Riema, Partial Differential Relations, Manifolds of Nonpositi, Mathematical slices of molecular Similar People Yakov Eliashberg, Simon Donaldson, Pierre Pansu, Niels Henrik Abel, Marcel Berger

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Mikhail Leonidovich Gromov (also spelled Mikhael Gromov or Michael Gromov; Russian: Михаи́л Леони́дович Гро́мов; born 23 December 1943), is a French–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. In 2009 he was awarded the Abel Prize "for his revolutionary contributions to geometry".

Biography

Mikhail Gromov was born on 23 December 1943 in Boksitogorsk, Soviet Union. His father was Leonid Gromov and his mother was Lea Rabinovitz. Both his parents were pathologists. Gromov was born during World War II, and his mother, who worked as a medical doctor in the Soviet Army, had to distance herself from the front line in order to give birth to him. When Gromov was nine years old, his mother gave him the book Numbers and Figures, by Hans Rademacher and Otto Toeplitz, a book that piqued his curiosity and had a great influence on him.

Gromov studied for a doctorate (1973) in Leningrad, where he was a student of Vladimir Rokhlin. He is now a permanent member of IHES, and a Professor of Mathematics at New York University.

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, along with Eliyahu Rips, 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.

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, the Norwegian Academy of Science and Letters, and the Royal Society (2011).

Membre de l'Institut de France – Academie des Sciences

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. Birkhauser 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 Etudes Sci. Publ. Math. No. 53 (1981), 53–73.

Gromov, Mikhael Structures metriques pour les varietes riemanniennes. (French) [Metric structures for Riemann manifolds] Edited by J. Lafontaine and P. Pansu. Textes Mathematiques [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 0–387-12177-3

Ballmann, Werner; Gromov, Mikhael; Schroeder, Viktor: Manifolds of nonpositive curvature. Progress in Mathematics, 61. Birkhauser Boston, Inc., Boston, MA, 1985. vi+263 pp. ISBN 0-8176-3181-X

Gromov, Mikhael Carnot–Caratheodory spaces seen from within. Sub-Riemannian geometry, 79–323, Progr. Math., 144, Birkhauser, Basel, 1996.

Gromov, Michael Volume and bounded cohomology. Inst. Hautes Etudes Sci. Publ. Math. No. 56 (1982), 5–99 (1983).

References

Mikhail Leonidovich Gromov Wikipedia

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