BIMSA

Affiliation: BIMSA , YMSC

Email: kfukaya@bimsa.cn

Research Field: Symplectic geometry, Riemannian geometry

Biography

Kenji Fukaya became a professor of BIMSA and YMSC in September 2024. He received his BA in Mathematics at the University of Tokyo in 1981, and continued graduate studies at the University of Tokyo, receiving his PhD in 1986. His thesis was entitled A boundary of the set of Riemannian manifolds with bounded curvatures and diameters. He was at the University of Tokyo from 1983 through 1990, where he was first a research assistant and then an Associate Professor. He was a Professor of Mathematics at Kyoto University in 1994, and became a permanent member of the Simons Center in 2013. He was awarded the Japan Academy Award in 2003, Asahi prize in 2009, and Fujiwara prize in 2012. He is a member of the Japanese National Academy of Sciences. Fukaya’s recent work has been in symplectic geometry and in particular has centered around the study of Lagrangian submanifolds and the Floer homology related to intersections of these submanifolds. Fukaya developed and has studied extensively a theory in which the Lagrangian submanifolds of a given symplectic manifold are the objects of a generalized category, now called the Fukaya category, and the morphisms are the Floer homology groups. This work is closely related to Kontsevich’s homological mirror symmetry conjecture . This is now formulated as the conjecture that the derived category of coherent sheaves on a Kahler manifold should be isomorphic to the Fukaya category of a `mirror’ symplectic manifold. His earlier work was in Riemannian geometry and especially dealt with collapsing results in this context.

Education Experience

- 1986 University of Tokyo Mathematics Ph.D
- 1981 University of Tokyo Mathematics Bachelor

Work Experience

2024 - BIMSA Professor
2013 - 2024 Simons Center for Geometry and Physics, Stony Brook University Simons Center for Geometry and Physics, Stony Brook University
1994 - 2013 Kyoto University Full Professor
1987 - 1994 University of Tokyo Associate Professor

Honors and Awards

2012 Fujihara Award
2009 Asahi Prize
2003 Japan Academy PrizeJapan Academy Prize
2002 Inoue Prize
1994 Spring Prize Japanese Mathematical Society
1989 Geometry Prize Japanese Mathematical Society

Publication

[1] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Exponential Decay Estimates and Smoothness of the Moduli Space of Pseudoholomorphic Curves, Memoirs of the American Mathematical Society, 299(1500) (2024)
[2] A. Daemi, K. Fukaya, M. Lipyanskiy, Lagrangians, SO(3)-Instantons and Mixed Equation, Geometric and Functional Analysis, 34, 659–732 (2024)
[3] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Construction of Kuranishi structures on the moduli spaces of pseudo-holomorphic disks: II, Advances in Mathematics, 442, 109561 (2024)
[4] K. Fukaya, Homological algebra and moduli spaces in topological field theories, Surveys in Differential Geometry (2023)
[5] K. Fukaya, Gromov-Hausdorff distance between filtered $A_{\infty}$ categories 1: Lagrangian Floer theory, arXiv:2106.06378 (2021)
[6] K. Fukaya, P. Seidel, Floer Homology, A ∞-categories and Topological Field Theory, Geometry and physics. CRC Press, 9-32 (2021)
[7] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Multivalued Perturbations, Springer Monographs in Mathematics (2020)
[8] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Fiber Product of Kuranishi Structures, Springer Monographs in Mathematics (2020)
[9] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, From Good Coordinate Systems to Kuranishi Structures and Back with CF-Perturbations, Springer Monographs in Mathematics (2020)
[10] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Linear K-Systems: Floer Cohomology III – Morse Case by Multisection, Springer Monographs in Mathematics (2020)
[11] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Linear K-Systems: Floer Cohomology I – Statement, Springer Monographs in Mathematics (2020)
[12] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Linear K-Systems: Floer Cohomology I – Statement, Springer Monographs in Mathematics (2020)
[13] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Linear K-Systems: Floer Cohomology I – Statement, Springer Monographs in Mathematics (2020)
[14] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Corner Smoothing and Composition of Morphisms, Springer Monographs in Mathematics (2020)
[15] K. Fukaya, Y. Oh, Hiroshi Ohta, K. Ôno, Tree-Like K-Systems: A ∞ Structure II – Proof, Springer Monographs in Mathematics (2020)
[16] K. Fukaya, Y. Oh, Hiroshi Ohta, K. Ôno, Tree-Like K-Systems: A ∞ Structure II – Proof, Springer Monographs in Mathematics (2020)
[17] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Stokes’ Formula, Springer Monographs in Mathematics (2020)
[18] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Stokes’ Formula, Springer Monographs in Mathematics (2020)
[19] K. Fukaya, Y. Oh, Hiroshi Ohta, K. Ôno, Introduction, Springer Monographs in Mathematics (2020)
[20] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Covering Space of Effective Orbifolds and K-Spaces, Springer Monographs in Mathematics (2020)
[21] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Covering Space of Effective Orbifolds and K-Spaces, Springer Monographs in Mathematics (2020)
[22] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Covering Space of Effective Orbifolds and K-Spaces, Springer Monographs in Mathematics (2020)
[23] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Covering Space of Effective Orbifolds and K-Spaces, Springer Monographs in Mathematics (2020)
[24] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Construction of Good Coordinate Systems, Springer Monographs in Mathematics (2020)
[25] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Construction of Good Coordinate Systems, Springer Monographs in Mathematics (2020)
[26] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Construction of Good Coordinate Systems, Springer Monographs in Mathematics (2020)
[27] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Construction of Good Coordinate Systems, Springer Monographs in Mathematics (2020)
[28] K. Fukaya, Y. Oh, Hiroshi Ohta, K. Ôno, Tree-Like K-Systems: A ∞ Structure I – Statement, Springer Monographs in Mathematics (2020)
[29] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Kuranishi Structures and Good Coordinate Systems, Springer Monographs in Mathematics (2020)
[30] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Introduction to Part II, Springer Monographs in Mathematics (2020)
[31] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Local System and Smooth Correspondence in de Rham Theory with Twisted Coefficients, Springer Monographs in Mathematics (2020)
[32] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Admissible Kuranishi Structures, Springer Monographs in Mathematics (2020)
[33] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Thickening of a Kuranishi Structure, Springer Monographs in Mathematics (2020)
[34] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Global Quotients and Orbifolds, Springer Monographs in Mathematics (2020)
[35] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Linear K-Systems: Floer Cohomology II – Proof, Springer Monographs in Mathematics (2020)
[36] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Orbifolds and Orbibundles by Local Coordinates, Springer Monographs in Mathematics (2020)
[37] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Notations and Conventions, Springer Monographs in Mathematics (2020)
[38] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Composition Formula of Smooth Correspondences, Fukaya, Kenji, et al. "Composition Formula of Smooth Correspondences." Kuranishi Structures and Virtual Fundamental Chains, 177-192 (2020)
[39] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Construction of CF-Perturbations, Kuranishi Structures and Virtual Fundamental Chains, 221-237 (2020)
[40] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, CF-Perturbations and Integration Along the Fiber (Pushout), Kuranishi Structures and Virtual Fundamental Chains, 113-146 (2020)
[41] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Construction of Multivalued Perturbations, Kuranishi Structures and Virtual Fundamental Chains, 239-251 (2020)
[42] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Zero-and One-Dimensional Cases via Multivalued Perturbation, Kuranishi Structures and Virtual Fundamental Chains, 253-273 (2020)
[43] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Extension of a Kuranishi Structure and Its Perturbation from Boundary to Its Neighborhood, Kuranishi Structures and Virtual Fundamental Chains, 345-398 (2020)
[44] K. Fukaya, K. Ôno, Y. Oh, H. Ohta, Kuranishi Structures and Virtual Fundamental Chains, Singapore: Springer (2020)
[45] M. Nishida, K. Fukaya, H. Fukaya, Yoshio Hayakawa, T. Ono, Reactions of Bifunctional Perfluoroarylsilanes with Activated C–F Bonds in Perfluorinated Arenes, ACS Omega, 4, 20807 - 20818 (2019)
[46] M. Nishida, K. Fukaya, H. Fukaya, Yoshio Hayakawa, T. Ono, Reactions of Bifunctional Perfluoroarylsilanes with Activated C–F Bonds in Perfluorinated Arenes, ACS Omega, 4, 20807 - 20818 (2019)
[47] M. Nishida, K. Fukaya, H. Fukaya, Yoshio Hayakawa, T. Ono, Reactions of Bifunctional Perfluoroarylsilanes with Activated C–F Bonds in Perfluorinated Arenes, ACS Omega, 4, 20807 - 20818 (2019)
[48] M. Nishida, K. Fukaya, H. Fukaya, Yoshio Hayakawa, T. Ono, Reactions of Bifunctional Perfluoroarylsilanes with Activated C–F Bonds in Perfluorinated Arenes, ACS Omega, 4, 20807 - 20818 (2019)
[49] D. Mcduff, M. Tehrani, K. Fukaya, D. joyce, Virtual Fundamental Cycles in Symplectic Topology, Mathematical Surveys and Monographs (2019)
[50] K. Fukaya, M. Hasegawa, [Oblique Lumbar Interbody Fusion Combined with Minimally Invasive Percutaneous Posterior Instrumentation for Adult Spinal Deformity]., No shinkei geka. Neurological surgery, 46 9, 771-781 (2018)
[51] K. Fukaya, M. Hasegawa, Oblique Lumbar Interbody Fusion Combined with Less Invasive Percutaneous Posterior Instrumentation for Adult Spinal Deformity, Spinal Surgery, 32, 334-337 (2018)
[52] A. Daemi, K. Fukaya, Atiyah-Floer conjecture: A formulation, a strategy of proof and generalizations, Proceedings of Symposia in Pure Mathematics (2018)
[53] K. Fukaya, Yong-Geun Oh, Hiroshi Ohta, K. Ôno, Corrigendum of"Construction of Kuranishi structures on the moduli spaces of pseudo holomorphic disks I, Surveys in Differential Geometry, XXII, 133-190 (2018)
[54] K. Fukaya, Lie Groupoids, Deformation of Unstable Curves, and Construction of Equivariant Kuranishi Charts, Publications of the Research Institute for Mathematical Sciences (2017)
[55] K. Fukaya, Lie Groupoids, Deformation of Unstable Curves, and Construction of Equivariant Kuranishi Charts, Publications of the Research Institute for Mathematical Sciences (2017)
[56] M. Tehrani, K. Fukaya, Gromov-Witten theory via Kuranishi structures, Virtual Fundamental Cycles in Symplectic Topology (2017)
[57] K. Fukaya, Categorification of invariants in gauge theory and symplectic geometry, Japanese Journal of Mathematics, 13, 1 - 65 (2017)
[58] K. Fukaya, M. Hasegawa, Mitsuru Shirato, Takashi Teshima, [Risk Factors for Predicting the Need for Additional Surgery for Symptomatic Adjacent Segment Disease after Minimally Invasive Surgery-Transforaminal Lumbar Interbody Fusion]., No shinkei geka. Neurological surgery, 45 4, 311-319 (2017)
[59] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Construction of Kuranishi structures on the moduli spaces of pseudo holomorphic disks: I, arXiv: Symplectic Geometry (2017)
[60] A. Daemi, K. Fukaya, Atiyah-Floer Conjecture: a Formulation, a Strategy to Prove and Generalizations, arXiv: Symplectic Geometry (2017)
[61] K. Fukaya, Unobstructed immersed Lagrangian correspondence and filtered A infinity functor, arXiv: Symplectic Geometry (2017)
[62] 오용근, K. Fukaya, H. Ohta, K. Ôno, Bulk deformations, tropicalization and non-displaceable Lagrangian tori (2016)
[63] K. Cieliebak, K. Fukaya, J. Latschev, Homological algebra related to surfaces with boundary, Quantum Topology (2015)
[64] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Kuranishi structure, Pseudo-holomorphic curve, and Virtual fundamental chain: Part 1, arXiv: Symplectic Geometry (2015)
[65] K. Fukaya, $SO(3)$-Floer homology of 3-manifolds with boundary 1, arXiv: Symplectic Geometry (2015)
[66] Sean Paul Wisconsin-Madison, K. Fukaya, Trends in Modern Geometry (2015)
[67] K. Fukaya, Takayasu cofibrations revisited, arXiv:1501.00271 (2015)
[68] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Shrinking good coordinate systems associated to Kuranishi structures, arXiv: Symplectic Geometry (2014)
[69] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Shrinking good coordinate systems associated to Kuranishi structures, arXiv: Symplectic Geometry (2014)
[70] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Shrinking good coordinate systems associated to Kuranishi structures, arXiv: Symplectic Geometry (2014)
[71] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Shrinking good coordinate systems associated to Kuranishi structures, arXiv: Symplectic Geometry (2014)
[72] Yu Li, K. Fukaya, On the equivalence of several deﬁnitions of compact infra-solvmanifolds (2013)
[73] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Technical details on Kuranishi structure and virtual fundamental chain, arXiv: Symplectic Geometry (2012)
[74] K. Fukaya, Weak (cid:2) -inequalities for the Haar system and diﬀerentially subordinated martingales (2012)
[75] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Spectral Invariants with Bulk, Quasi-Morphisms and Lagrangian Floer Theory, Memoirs of the American Mathematical Society (2011)
[76] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Lagrangian Floer theory over integers: spherically positive symplectic manifolds, arXiv: Symplectic Geometry (2011)
[77] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Displacement of polydisks and Lagrangian Floer theory, Journal of Symplectic Geometry, 11, 231-268 (2011)
[78] K. Fukaya, Floer homology of Lagrangian submanifolds, arXiv: Symplectic Geometry (2011)
[79] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Toric degeneration and non-displaceable Lagrangian tori in $S^2 \times S^2$, arXiv: Symplectic Geometry (2010)
[80] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Toric degeneration and non-displaceable Lagrangian tori in $S^2 \times S^2$, arXiv: Symplectic Geometry (2010)
[81] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Toric degeneration and non-displaceable Lagrangian tori in $S^2 \times S^2$, arXiv: Symplectic Geometry (2010)
[82] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Toric degeneration and non-displaceable Lagrangian tori in $S^2 \times S^2$, arXiv: Symplectic Geometry (2010)
[83] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Toric degeneration and non-displaceable Lagrangian tori in $S^2 \times S^2$, arXiv: Symplectic Geometry (2010)
[84] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Lagrangian Floer theory and Mirror symmetry on compact toric manifolds, Astérisque (2010)
[85] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Homotopy equivalence of _{∞} bimodules, 267-353 (2010)
[86] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Homotopy equivalence of _{∞} bimodules, 267-353 (2010)
[87] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Homotopy equivalence of _{∞} bimodules, 267-353 (2010)
[88] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Homotopy equivalence of _{∞} bimodules, 267-353 (2010)
[89] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Homotopy equivalence of _{∞} bimodules, 267-353 (2010)
[90] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Review: Floer cohomology, 39-76 (2010)
[91] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Lagrangian Floer theory on compact toric manifolds: survey, arXiv: Symplectic Geometry (2010)
[92] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, The _{∞} algebra associated to a Lagrangian submanifold (2010)
[93] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Homotopy equivalence of _{∞} algebras (2010)
[94] K. Fukaya, Differentiable Operads, the Kuranishi Correspondence, and Foundations of Topological Field Theories Based on Pseudo-Holomorphic Curves, Arithmetic and geometry around quantization. Boston, MA: Birkhäuser Boston, 123-200 (2010)
[95] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Lagrangian Intersection Floer Theory, Part 2: Anomaly and Obstruction, Part II, American Mathematical Soc. (2010)
[96] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Lagrangian Intersection Floer Theory: Anomaly and Obstruction, Part I, American Mathematical Soc. (2010)
[97] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Canonical models of filtered _{∞}-algebras and Morse complexes, 201-227 (2009)
[98] K. Fukaya, Cyclic symmetry and adic convergence in Lagrangian Floer theory, Kyoto Journal of Mathematics, 50, 521-590 (2009)
[99] K. Fukaya, Cyclic symmetry and adic convergence in Lagrangian Floer theory, Kyoto Journal of Mathematics, 50, 521-590 (2009)
[100] K. Fukaya, Cyclic symmetry and adic convergence in Lagrangian Floer theory, Kyoto Journal of Mathematics, 50, 521-590 (2009)
[101] K. Fukaya, Cyclic symmetry and adic convergence in Lagrangian Floer theory, Kyoto Journal of Mathematics, 50, 521-590 (2009)
[102] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Lagrangian Intersection Floer Theory (2009)
[103] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Lagrangian Intersection Floer Theory (2009)
[104] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Antisymplectic involution and Floer cohomology, Geometry & Topology, 21, 1-106 (2009)
[105] K. Fukaya, Counting pseudo-holomorphic discs in Calabi-Yau 3 fold, arXiv: Symplectic Geometry (2009)
[106] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Anchored Lagrangian submanifolds and their Floer theory, arXiv: Symplectic Geometry (2009)
[107] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Lagrangian Floer theory on compact toric manifolds II: bulk deformations, Selecta Mathematica, 17, 609-711 (2008)
[108] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Lagrangian Floer theory on compact toric manifolds II: bulk deformations, Selecta Mathematica, 17, 609-711 (2008)
[109] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Lagrangian Floer theory on compact toric manifolds II: bulk deformations, Selecta Mathematica, 17, 609-711 (2008)
[110] K. Fukaya, Y. Oh, H. Ohta, K. Ôno, Lagrangian Floer theory on compact toric manifolds II: bulk deformations, Selecta Mathematica, 17, 609-711 (2008)
[111] K. Fukaya, OH Y.-G., H. Ohta, K. Ôno, Canonical models of filtered $A_\infty$-algebras and Morse complexes, arXiv: Symplectic Geometry (2008)
[112] K. Fukaya, OH Y.-G., H. Ohta, K. Ôno, Canonical models of filtered $A_\infty$-algebras and Morse complexes, arXiv: Symplectic Geometry (2008)
[113] Y. Eliashberg, K. Fukaya, V. Muñoz, F. Presas, Foreword [Special issue: Proceedings of the VII Workshop on Symplectic and Contact Topology]. (2008)
[114] K. Fukaya, Loop space and holomorphic disc -summary- (2007)
[115] K. Fukaya, P. Seidel, I. Smith, The Symplectic Geometry of Cotangent Bundles from a Categorical Viewpoint, arXiv: Symplectic Geometry, 1-26 (2007)
[116] K. Fukaya, P. Seidel, I. Smith, Exact Lagrangian submanifolds in simply-connected cotangent bundles, Inventiones mathematicae, 172, 1-27 (2007)
[117] K. Fukaya, Differentiable operad, Kuranishi correspondence, and Foundation of topological field theories (2007)
[118] K. Fukaya, Chapter 4 Metric Riemannian geometry, 2, 189-313 (2006)
[119] K. Fukaya, Chapter 4 Metric Riemannian geometry, 2, 189-313 (2006)
[120] K. Fukaya, Chapter 4 Metric Riemannian geometry, 2, 189-313 (2006)
[121] K. Fukaya, APPLICATION OF FLOER HOMOLOGY OF LANGRANGIAN SUBMANIFOLDS TO SYMPLECTIC TOPOLOGY, 231-276 (2006)
[122] Y. Oh, K. Fukaya, Floer homology in symplectic geometry and in mirror symmetry, 879-906 (2006)
[123] K. Fukaya, On a compactification of the set of Riemannian manifolds with bounded curvatures and diameters, Curvature and Topology of Riemannian Manifolds: Proceedings of the 17th International Taniguchi Symposium held in Katata, Japan, Aug. 26–31, 1985. Berlin, Heidelberg: Springer Berlin Heidelberg, 89-107 (2006)
[124] K. Fukaya, Galois symmetry on Floer cohomology, Turkish Journal of Mathematics, 27, 11-32 (2003)
[125] K. Fukaya, M. Hasegawa, Tsuyoshi Mashitani, T. Kadoya, H. Horie, Y. Hayashi, H. Fujisawa, S. Kida, J. Yamashita, Oxidized Galectin‐1 Stimulates the Migration of Schwann Cells from Both Proximal and Distal Stumps of Transected Nerves and Promotes Axonal Regeneration after Peripheral Nerve Injury, JNEN: Journal of Neuropathology & Experimental Neurology, 62, 162–172 (2003)
[126] K. Fukaya, M. Hasegawa, Tsuyoshi Mashitani, T. Kadoya, H. Horie, Y. Hayashi, H. Fujisawa, S. Kida, J. Yamashita, Oxidized Galectin‐1 Stimulates the Migration of Schwann Cells from Both Proximal and Distal Stumps of Transected Nerves and Promotes Axonal Regeneration after Peripheral Nerve Injury, JNEN: Journal of Neuropathology & Experimental Neurology, 62, 162–172 (2003)
[127] M. Hasegawa, N. Muramatsu, Y. Tohma, K. Fukaya, H. Fujisawa, Y. Hayashi, O. Tachibana, S. Kida, J. Yamashita, K. Saito, Expression of E-cadherin-catenin complex in human benign schwannomas., Histology and histopathology, 17 1, 39-44 (2002)
[128] K. Fukaya, Mirror symmetry of abelian varieties and multi-theta functions, Journal of Algebraic Geometry, 11, 393-512 (2002)
[129] K. Fukaya, Floer Homology and Mirror Symmetry II, 31-127 (2002)
[130] K. Fukaya, K. Ôno, Floer Homology and Gromov-Witten Invariant over Integer of General Symplectic Manifolds – Summary –, 75-91 (2001)
[131] K. Fukaya, Deformation theory, homological algebra and mirror symmetry, 121-209 (2001)
[132] K. Fukaya, K. Ôno, ARNOLD CONJECTURE AND GROMOV–WITTEN INVARIANT, Topology, 38, 933-1048 (1999)
[133] K. Fukaya, K. Ôno, ARNOLD CONJECTURE AND GROMOV–WITTEN INVARIANT, Topology, 38, 933-1048 (1999)
[134] K. Fukaya, K. Ôno, ARNOLD CONJECTURE AND GROMOV–WITTEN INVARIANT, Topology, 38, 933-1048 (1999)
[135] K. Fukaya, K. Ôno, ARNOLD CONJECTURE AND GROMOV–WITTEN INVARIANT, Topology, 38, 933-1048 (1999)
[136] K. Fukaya, K. Ôno, Arnold conjecture and Gromov-Witten invariants for general symplectic manifolds (1999)
[137] K. Fukaya, MORSE HOMOTOPY AND ITS QUANTIZATION (1999)
[138] K. Fukaya, FLOER HOMOLOGY AND MIRROR SYMMETRY (1999)
[139] K. Fukaya, Anti-self-dual Equation on 4-manifolds with Degenerate Metric, Geometric & Functional Analysis GAFA, 8, 466-528 (1998)
[140] K. Fukaya, M. Hori, M. Hamaya, Masatoshi Suzuki, Air-fuel ratio sensor with rubber sealing bush (1997)
[141] K. Fukaya, Informal note on topology, geometry and topological field theory, Geometry from the Pacific Rim: Proceedings of the Pacific Rim Geometry Conference Held at National University of Singapore, Republic of Singapore, December 12-17, 1994. De Gruyter Proceedings in Mathematics, 99 (1997)
[142] K. Fukaya, Morse homotopy and Chern-Simons perturbation theory, Communications in Mathematical Physics, 181, 37-90 (1996)
[143] K. Fukaya, Floer homology of connected sum of homology 3-spheres, Topology, 35, 89-136 (1996)
[144] K. Fukaya, Geometry of Gauge Fields, /Lectures on Geometric Variational Problems. Tokyo: Springer Japan, 43-114 (1996)
[145] K. Fukaya, Takao Yamaguchi, Isometry groups of singular spaces, Mathematische Zeitschrift, 216, 31-44 (1994)
[146] K. Fukaya, M. Furuta, T. Kohno, D. Kotschick, Topology, Geometry and Field Theory, 1-266 (1994)
[147] K. Fukaya, Nonpositively curved manifolds with small volume, Journal of the Faculty of Science. University of Tokyo. Section IA. Mathematics, 40, 55-62 (1993)
[148] S. Hayashi, K. Fukaya, Hirokazu Kajima, H. Saito, Phase Transition and Thermal Expansion of LaCrO3 Solid Solutions, Journal of the Ceramic Society of Japan, 101, 1409-1414 (1993)
[149] J. Cheeger, K. Fukaya, M. Gromov, Nilpotent structures and invariant metrics on collapsed manifolds, Journal of the American Mathematical Society, 5, 327-372 (1992)
[150] J. Cheeger, K. Fukaya, M. Gromov, Nilpotent structures and invariant metrics on collapsed manifolds, Journal of the American Mathematical Society, 5, 327-372 (1992)
[151] J. Cheeger, K. Fukaya, M. Gromov, Nilpotent structures and invariant metrics on collapsed manifolds, Journal of the American Mathematical Society, 5, 327-372 (1992)
[152] J. Cheeger, K. Fukaya, M. Gromov, Nilpotent structures and invariant metrics on collapsed manifolds, Journal of the American Mathematical Society, 5, 327-372 (1992)
[153] K. Fukaya, Floer Homology for Oriented 3-Manifolds, 1-92 (1992)
[154] S. Hayashi, K. Fukaya, H. Saito, Li-Doped LaCrO3 Ceramics, Journal of the Ceramic Society of Japan, 100, 1078-1081 (1992)
[155] S. Hayashi, K. Fukaya, H. Saito, Li-Doped LaCrO3 Ceramics, Journal of the Ceramic Society of Japan, 100, 1078-1081 (1992)
[156] S. Hayashi, K. Fukaya, H. Saito, Li-Doped LaCrO3 Ceramics, Journal of the Ceramic Society of Japan, 100, 1078-1081 (1992)
[157] S. Hayashi, K. Fukaya, H. Saito, Li-Doped LaCrO3 Ceramics, Journal of the Ceramic Society of Japan, 100, 1078-1081 (1992)
[158] K. Fukaya, Takao Yamaguchi, The fundamental groups of almost nonnegatively curved manifolds, Annals of Mathematics, 136, 253-333 (1992)
[159] K. Fukaya, Takao Yamaguchi, Almost nonpositively curved manifolds, Journal of Differential Geometry, 33, 67-90 (1991)
[160] K. Fukaya, Hausdorff Convergence of Riemannian Manifolds and Its Applications, 143-238 (1990)
[161] K. Fukaya, Collapsing Riemannian manifolds to ones with lower dimension II, Journal of The Mathematical Society of Japan, 41, 333-356 (1989)
[162] K. Fukaya, Collapsing Riemannian manifolds to ones with lower dimension II, Journal of The Mathematical Society of Japan, 41, 333-356 (1989)
[163] K. Fukaya, Collapsing Riemannian manifolds to ones with lower dimension II, Journal of The Mathematical Society of Japan, 41, 333-356 (1989)
[164] K. Fukaya, Collapsing Riemannian manifolds to ones with lower dimension II, Journal of The Mathematical Society of Japan, 41, 333-356 (1989)
[165] K. Fukaya, Collapsing Riemannian manifolds to ones with lower dimension II, Journal of The Mathematical Society of Japan, 41, 333-356 (1989)
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Update Time: 2024-09-09 17:25:14