Mikhail Leonidovich Gromov

Mikhail Leonidovich Gromov ( Michael or mixing Gromov, Russian Михаил Леонидович Громов; usually Mikhail Gromov cited; born December 23, 1943 in Boksitogorsk, Russia ) is a Russian- French mathematician, who researches primarily to differential geometry and analysis. Since 1992, Gromov is a French citizen. He is regarded as one of the leading geometers and is among other winners of the Abel Prize in 2009.

Career

Gromov attended school 217 ( Petri School ) in Leningrad. He then studied at the university there, where in 1965 he took his degree and received his doctorate at Vladimir Rokhlin 1969. From 1967 he was assistant professor there in 1973 he completed his habilitation (Russian doctoral degree ) in Saint Petersburg. In 1974 he became a professor at the University of Stony Brook in New York, in 1981 at the University of Paris and from 1982 to present at the IHES in Bures -sur -Yvette, near Paris, where he is a permanent member today. He was also 2008 Jay Gould Professor at the Courant Institute of Mathematical Sciences of New York University.

Research

In geometric group theory, Gromov examined groups of polynomial growth order and introduced the concept of hyperbolic groups. In the symplectic topology, he established the concept of pseudoholomorphen curve. His Homotopieprinzip for differential relations is important in the theory of partial differential equations; Gromov extended besides, older approaches, including the John Nash.

In particular, in the Riemannian geometry Gromov has many new perspectives opened, for example, by examining often asymptotic and global aspects and formulated in inequalities. He wrote concepts such as fast - flatness (almost flatness ) of metrics and contexts as well as simplicial volume. He also dealt with foliations, sub- Riemannian manifolds and index theory of operators.

The eulogy to the Abel Prize in 2009 identified the following posts Gromows to mathematics:

• A crucial role in the creation of the modern global Riemannian geometry. His solutions to major challenges of the Global geometry based on new, now named after him general concepts such as the convergence of Riemannian manifolds and the compactness principle.
• One of the founders of symplectic geometry. Holomorphic curves, previously an important tool in the geometry of complex manifolds were generalized by Gromov in his famous work 1985 J- holomorphic curves in symplectic manifolds. This led to the theory of Gromov -Witten invariants, now an extremely active area with links to modern quantum field theory and to the creation of symplectic topology, and it permeated and altered many other areas of mathematics.
• His work on groups of polynomial growth, which led to discrete infinite groups with their ideas introduced there to a completely different perspective. He discovered the geometry of discrete groups and sparked several outstanding problems. Due to its geometric access complicated combinatorial arguments have been much more natural and effective.

In the years 1970 (A topological technique for the construction of solutions of differential equations and inequalities ), 1978 (Synthetic geometry in Riemannian manifolds ) and 1983 ( Infinite groups as geometric objects), he was invited speaker at the International Mathematical Congresses (ICM). In 1986 in Berkeley, he held on the ICM a plenary lecture on " Soft and Hard Symplectic Geometry ". In 2012 he gave a plenary lecture at the European Congress of Mathematicians (ECM ) in Krakow ( In a search for a structure ).

Awards and Affiliations

• Price of the Moscow Mathematical Society (1971 )
• Oswald Veblen Prize in Geometry ( 1981)
• Elie Cartan Prize of the Académie des sciences (1984 )
• Wolf Prize (1993 )
• Leroy P. Steele Prize of the American Mathematical Society ( 1997)
• Lobachevsky Medal ( 1997)
• Balzan Prize ( 1999)
• Kyoto Prize (2002)
• Nemmers Prize ( 2004)
• Bolyai Medal ( 2005)
• Abel Prize (2009) "for his revolutionary contributions to geometry "
• Foreign member of the Royal Society ( 2011).

He holds honorary doctorates from the Universities of Geneva and Tel - Aviv.

He is a member of the Academie des Sciences ( 1997), the Academia Europaea, the American Academy of Arts and Sciences, the National Academy of Sciences, the Norwegian Academy of Sciences and an honorary member of the London Mathematical Society.

Writings

• Metric structures for Riemannian and non- Riemannian spaces (Appendices by M. Katz, P. Pansu, S. Semmes ), Birkhauser 1999
• Partial Differential Relations, Springer Verlag, results of mathematics and its applications, 1986
• Spaces and Questions, Noga Alon et al in (Editor) Visions in Mathematics, Geometric and functional analysis, special volume, GAF 2000, Birkhäuser, Volume 1, pp. 118-161
• Werner Ballmann, Viktor Schroeder: Manifolds of non positive curvature, Birkhauser 1985

Some online reach work:

• Gromov: Pseudoholomorphic curves in symplectic manifolds, Inventiones Mathematicae, Volume 82, 1985, p 307-347
• Gromov: Curvature, diameter and Betti numbers Comm.Math.Helv. In 1981.
• Gromov, Thurston: Pinching constants for hyperbolic manifolds, Inventiones Math 1987.
• Various works, especially in the Publ.Math.IHES
• Pauli Lectures 2009 at the ETH Zurich, records

Others

From October 21 2011 to 18 March 2012, the exhibition Mathematics found in the Paris Fondation Cartier: A Beautiful Elsewhere place for contributing exhibits including the film director and artist David Lynch in collaboration with Gromov.