Kenji Fukaya (Japanese: 深谷賢治, ''Fukaya Kenji'') is a Japanese mathematician known for his work in

symplectic geometry Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed differential form, closed, nondegenerate form, nondegenerate different ...

and Riemannian geometry. His many fundamental contributions to mathematics include the discovery of the

Fukaya category In symplectic topology, a Fukaya category of a symplectic manifold (M, \omega) is a category \mathcal F (M) whose objects are Lagrangian submanifolds of M, and morphisms are Floer chain groups: \mathrm (L_0, L_1) = FC (L_0,L_1). Its finer structur ...

. He is a permanent faculty member at the

Simons Center for Geometry and Physics The Simons Center for Geometry and Physics is a center for theoretical physics and mathematics at Stony Brook University in New York. The focus of the center is mathematical physics and the interface of geometry and physics. It was founded in 2 ...

and a professor of mathematics at

Stony Brook University Stony Brook University (SBU), officially the State University of New York at Stony Brook, is a public research university in Stony Brook, New York. Along with the University at Buffalo, it is one of the State University of New York system's ...

Biography

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 , mottoeng = Freedom of academic culture , established = , type = National university, Public (National) , endowment = ¥ 316 billion (2.4 1000000000 (number), billion USD) , faculty = 3,480 (Teaching Staff) , administrative_staff ...

as a full professor in 1994. In 2013, he then moved to the United States in order to join the faculty of the

at Stony Brook. The

, meaning the

A_\infty

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 Kaoru Ono (小野薫, ''Ono Kaoru'', born 1962) is a Japanese mathematician, specializing in symplectic geometry. He is a professor at the Research Institute for Mathematical Sciences (RIMS) at Kyoto University. Ono received from the University ...

) 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's

Geometry Prize The Mathematical Society of Japan (MSJ, ja, 日本数学会) is a learned society for mathematics in Japan. In 1877, the organization was established as the ''Tokyo Sugaku Kaisha'' and was the first academic society in Japan. It was re-organized ...

in 1989 and

Spring Prize The Mathematical Society of Japan (MSJ, ja, 日本数学会) is a learned society for mathematics in Japan. In 1877, the organization was established as the ''Tokyo Sugaku Kaisha'' and was the first academic society in Japan. It was re-organized ...

in 1994. He also received the Inoue Prize in 2002, the Japan Academy Prize in 2003, the Asahi Prize in 2009, and the

Fujihara Award Fujihara (written: 藤原) is a Japanese surname and a place name, which may refer to: *Fujihara, Tochigi was a town located in Shioya District, Tochigi Prefecture, Japan. As of 2001, the town had an estimated population of 13,798 and a densi ...

in 2012. 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.''

Selected publications

* *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,

A_

-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 *

References

External links

* * {{DEFAULTSORT:Fukaya, Kenji 1959 births Living people People from Kanagawa Prefecture 20th-century Japanese mathematicians 21st-century Japanese mathematicians University of Tokyo alumni Kyoto University faculty Stony Brook University faculty Geometers