Kenji Fukaya

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Kenji Fukaya (left) with Paul Seidel , Oberwolfach 2002

Kenji Fukaya ( Japanese 深谷 賢治 , Fukaya Kenji ; born March 12, 1959 Kanagawa Prefecture in Japan ) is a Japanese mathematician who studies symplectic geometry and differential geometry ( Riemannian geometry ).

Career

Fukaya studied from 1978 at the University of Tokyo , where he received his doctorate in mathematics in 1986. In 1987 he became assistant professor at the University of Tokyo and in 1994 professor at the University of Kyoto . He has been at Stony Brook University since 2013 .

The Fukaya categories in the symplectic topology are named after him ( -categories of Lagrange submanifolds of a symplectic manifold with Floer chain groups as morphisms, see Floer homology ). With Kaoru Ono , he proved a weak form of the Arnold conjecture (1999).

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

In 2009 he received the Asahi Prize , in 2003 the Japan Academy Award, in 1994 the Spring Prize of the Japanese Mathematical Society , in 2002 the Inoue Prize and in 1989 the Geometry Prize. He has been on the Council of the Japanese Mathematical Society since 2005 (and 1996 to 2000) and since 2006 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 ).

Fonts

  • Collapsing Riemannian Manifolds and Eigenvalues ​​of Laplace Operators , Inventiones Mathematicae, Volume 87, 1987, pp. 517-557
  • with T. Yamaguchi The fundamental group of almost nonnegatively curved manifolds , Annals of Mathematics, Volume 136, 1992, pp. 253-333
  • with Michail Gromow , Jeff Cheeger Nilpotent structures and invariant metrics on collapsed manifolds , Journal of American Mathematical Society, Volume 5, 1992, pp. 327-372
  • with Kaoru Ono Arnold conjecture and Gromov-Witten invariant , Topology, Volume 38, 1999, pp. 933-1048
  • with Y. Oh, H. Ohta, K. Ono Lagrangian intersection Floer theory- anomaly and obstruction , 2007
  • Morse homotopy, Category, and Floer homologies , in HJ Kim (Editor) Proceedings of Garc Workshop on Geometry and Topology , 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., Vol. 73, American Mathematical Society, 2005, pp. 205-278
  • Edited by Topology, Geometry and Field Theory , World Scientific 1994
  • Editor 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 (Japanese), Iwanami Shoten 1999

Web links

Individual evidence

  1. ↑ The dissertation was published as A boundary of the set of the Riemannian manifolds with bounded curvatures and diameters , J. Differential Geometry, Volume 28, 1988, pp. 1-21
personal data
SURNAME Fukaya, Kenji
ALTERNATIVE NAMES 深谷 賢治 (Japanese)
BRIEF DESCRIPTION Japanese mathematician
DATE OF BIRTH March 12, 1959
PLACE OF BIRTH Kanagawa Prefecture , Japan