Kenji Fukaya (left) with Paul Seidel, Oberwolfach 2002
Fukaya was both an undergraduate and a graduate student in mathematics at the University of Tokyo, receiving his BA in 1981, and his PhD in 1986. In 1987, he joined the University of Tokyo faculty as an associate professor. He then moved to Kyoto University as a full professor in 1994. In 2013, he then moved to the United States in order to join the faculty of the Simons Center for Geometry and Physics at Stony Brook.
The Fukaya category, meaning the category of whose objects are Lagrangian submanifolds of a given symplectic manifold, is named after him, and is intimately related to Floer homology. Other contributions to symplectic geometry include his proof (with Kaoru Ono) of a weak version of the Arnold conjecture and a construction of general Gromov-Witten invariants. His many other mathematical contributions include important theorems in Riemannian geometry and work on physics-related topics such as gauge theory and mirror symmetry.
Fukaya was awarded the Japanese Mathematical Society'sGeometry Prize in 1989 [2] and Spring Prize in 1994.[3] He also received the Inoue Prize in 2002, the Japan Academy Prize in 2003,[4] the Asahi Prize in 2009,[5] and the Fujihara Award in 2012.[6] He has served on the governing board of the Japanese Mathematical Society and on the Mathematical Committee of the Science Council of Japan.
Fukaya was an invited speaker at the 1990 International Congress of Mathematicians in Kyoto, where he gave a talk entitled, Collapsing Riemannian Manifolds and its Applications.[7]
Selected publications
Fukaya, Kenji (1987). "Collapsing Riemannian Manifolds and Eigenvalues of Laplace-Operators". Inventiones Mathematicae. 87 (3): 517–557. Bibcode:1987InMat..87..517F. doi:10.1007/BF01389241. S2CID 122719694.
with T. Yamaguchi The fundamental group of almost non negatively curved manifolds, Annals of Mathematics 136, 1992, pp. 253 – 333
with Kaoru Ono Arnold conjecture and Gromov-Witten invariant, Topology, 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 H. J. Kim (editor) Proceedings of 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. 73, American Mathematical Society, 2005, pp. 205–278
Editor: Topology, Geometry and Field Theory, World Scientific 1994
Editor: Symplectic geometry and mirror symmetry (Korea Institute for Advanced Study conference, Seoul 2000), World Scientific 2001
Gauge Theory and Topology (in Japanese), Springer Verlag, Tokyo 1995
Symplectic Geometry (in Japanese), Iwanami Shoten 1999
Fukaya, Kenji; Oh, Yong-Geun; Ohta, Hiroshi; Ono, Kaoru (2020). Kuranishi Structures and Virtual Fundamental Chains (Springer Monographs in Mathematics). Springer. pp. XV, 638. doi:10.1007/978-981-15-5562-6. ISBN 978-9811555619. S2CID 234938865.
