Gromov, Mikhail

Mikhail Gromov, in full Mikhail Leonidovich Gromov, (born December 23, 1943, Boksitogorsk, Russia, U.S.S.R.), Soviet-born French mathematician who was awarded the 2009 Abel Prize by the Norwegian Academy of Science and Letters “for his revolutionary contributions to geometry.” Gromov’s work in Riemannian geometry, global symplectic geometry, and geometric group theory was cited by the academy.

Gromov received master’s (1965), Ph.D. (1969), and D.Sc. (1973) degrees from Leningrad State University (now St. Petersburg State University), where he served as assistant professor (1967–74). He taught at the State University of New York at Stony Brook (1974–81) before moving to France, where in 1981–82 he taught at the University of Paris VI (now Pierre and Marie Curie University) and from 1982 at the Institut des Hautes Études Scientifiques. He became a French citizen in 1992. He continued to teach part of each academic year in the United States, first at the University of Maryland (1991–96) and then at New York University, where from 1996 he was Jay Gould Professor of Mathematics in the Courant Institute of Mathematical Sciences.

Among Gromov’s principal results were Gromov’s compactness theorem, the Gromov-Hausdorff convergence, the theorem of almost flat manifolds, Gromov’s Betti number theorem, and the Bishop-Gromov inequality in Riemannian geometry; the theory of pseudoholomorphic (or J-holomorphic) curves, the Gromov-Witten invariants, and the Gromov nonsqueezing theorem in symplectic geometry; Gromov’s theorem on groups of polynomial growth and Gromov hyperbolic groups in geometric group theory; and the homotopy principle (h-principle) and the theory of complex integration in the theory of partial differential equations. Gromov’s work had applications not only in mathematics but also in physics (for example, the measurement of black holes and heavy stars) and biology (for example, pattern recognition, which was a research interest of Gromov’s).

Gromov was elected to the American Academy of Arts and Sciences (1989) and the French Académie des Sciences (1997). In addition to the Abel Prize, he was the recipient of the Élie Cartan (1984), Wolf (1993), Steele (1997), Lobachevsky (1997), Balzan (1999), and Kyoto (2002) prizes.