Kenji Fukaya

Kenji Fukaya
Thâm cốc hiền trị
Kenji Fukaya 2010
Born	Kanagawa prefecture, Japan
Nationality	Japanese
Alma mater	University of Tokyo
Known for	Fukaya category Kuranishi structure
Scientific career
Fields	Mathematician
Institutions	Simons Center for Geometry and Physics Stony Brook University

Kenji Fukaya(Japanese: Thâm cốc hiền trị,Fukaya Kenji) is a Japanese mathematician known for his work insymplectic geometryandRiemannian geometry.His many fundamental contributions to mathematics include the discovery of theFukaya category.He is a permanent faculty member at theSimons Center for Geometry and Physicsand a professor of mathematics atStony Brook University.

Biography

Kenji Fukaya (left) withPaul Seidel,Oberwolfach 2002

Fukaya was both an undergraduate and a graduate student in mathematics at theUniversity 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 toKyoto Universityas a full professor in 1994. In 2013, he then moved to the United States in order to join the faculty of theSimons Center for Geometry and Physicsat Stony Brook.

TheFukaya category,meaning the$A_{\infty }$category of whose objects are Lagrangian submanifolds of a given symplectic manifold, is named after him, and is intimately related toFloer homology.Other contributions to symplectic geometry include his proof (withKaoru Ono) of a weak version of the Arnold conjecture and a construction of generalGromov-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 theJapanese Mathematical Society'sGeometry Prizein 1989andSpring Prizein 1994.He also received theInoue Prizein 2002, theJapan Academy Prizein 2003,theAsahi Prizein 2009,and theFujihara Awardin 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

• 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.S2CID122719694.
• with T. YamaguchiThe fundamental group of almost non negatively curved manifolds,Annals of Mathematics136, 1992, pp. 253 – 333
• Cheeger, Jeff;Fukaya, Kenji;Gromov, Mikhail(1992)."Nilpotent structures and invariant metrics on collapsed manifolds".Journal of the American Mathematical Society.5(2): 327–372.doi:10.1090/S0894-0347-1992-1126118-X.
• with Kaoru OnoArnold conjecture and Gromov-Witten invariant,Topology, 38, 1999, pp. 933–1048
• with Y. Oh, H. Ohta, K. OnoLagrangian intersection Floer theory- anomaly and obstruction,2007
• Morse homotopy,$A_{\infty }$-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 symmetryinGraphs 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.ISBN978-9811555619.S2CID234938865.

External links

• Kenji Fukayaat theMathematics Genealogy Project
• "Personal website".