Kenji Fukaya

Kenji Fukaya (Japanese深谷 贤治, Kenji Fukaya; * March 12, 1959 Kanagawa Prefecture in Japan) is a Japanese mathematician, with symplectic geometry and differential geometry ( Riemannian geometry ) is concerned.

Career

Fukaya studied from 1978 at the University of Tokyo, where he in 1986 received his doctorate in mathematics. In 1987 he became an assistant professor at the University of Tokyo and since 1994 he is a professor at Kyoto University.

According to him the Fukaya categories are named in symplectic topology ( categories of Lagrangian submanifolds of a symplectic manifold with Floer chain groups as morphisms, see Floer homology). With Kaoru Ono, he proved a weak form of Arnold 's conjecture (1999).

It also deals with applications of differential geometry and symplectic geometry in string theory and gauge theories (including mirror symmetry).

In 2009 he was awarded the Asahi Prize, the 2003 Japan Academy Award, the 1994 Spring Price Japanese Mathematical Society, 2002 Inoue Prize and in 1989 the geometry price. He is since 2005 ( and 1996 to 2000 ) the Council of the Japanese Mathematical Society since 2006 and Chairman of the Mathematics Committee of the Science Council of Japan.

In 1990 he was invited speaker at the International Congress of Mathematicians in Kyoto ( Collapsing Riemannian Manifolds and its Application).

Writings

  • Collapsing Riemannian Manifolds and Eigenvalues ​​of the Laplace operator, Inventiones Mathematicae, Volume 87, 1987, p 517-557
  • With T. Yamaguchi The fundamental group of almost nonnegatively curved manifolds, Annals of Mathematics, Volume 136, 1992, pp. 253-333
  • Mikhail Gromov, Jeff Cheeger nilpotent structures and invariant metrics on collapsed manifolds, Journal of the American Mathematical Society, Volume 5, 1992, pp. 327-372
  • Conjecture with Kaoru Ono Arnold and Gromov - Witten invariant, Topology, Volume 38, 1999, pp. 933-1048
  • With Y. Oh, H. Ohta, K. Ono, Lagrangian Floer intersection theory - anomaly and obstruction, 2007
  • Morse homotopy, Category, and Floer homo logies, in HJ Kim (Editor) Proceedings of the Workshop on Geometry and Topology Garc, Seoul National University, 1994, pp. 1-102
  • Floer homology and mirror symmetry. II Minimal surfaces, geometric analysis and symplectic geometry, Adv Stud Pure Math 34, Math Soc. Japan, Tokyo, 2002, pp. 31-127
  • Multivalued Morse theory, asymptotic analysis and mirror symmetry in Graphs and patterns in mathematics and theoretical physics, Proc. Sympos.Pure Math, Volume 73, American Mathematical Society, 2005, pp. 205-278
  • Publisher Topology, Geometry and Field Theory, World Scientific 1994
  • Publisher Symplectic geometry and mirror symmetry ( Conference Korea Institute for Advanced Study, Seoul 2000), World Scientific 2001
  • Gauge theory and topology ( Japanese), Springer Verlag, Tokyo, 1995
  • Symplectic Geometry (in Japanese ), Iwanami Shoten, 1999
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