深谷賢治 - 北京雁栖湖应用数学研究院

单位: 北京雁栖湖应用数学研究院 , 清华丘成桐数学科学中心

邮箱: kfukaya@bimsa.cn

研究方向: 辛几何, 黎曼几何

个人简介

深谷賢治于2024年9月成为BIMSA和YMSC双聘教授。1981年，他在东京大学获得数学学士学位，1986年继续在东京大学攻读博士学位。他的论文题为“具有有界曲率和直径的黎曼流形集的边界”。1983年至1990年，他在东京大学工作，先后担任研究助理和副教授。他于1994年担任京都大学数学教授，并于2013年成为西蒙斯中心的永久成员。他于2003年获得日本学院奖，2009年获得朝日奖，2012年获得藤原奖。他是日本国家科学院院士。深谷賢治最近的工作是辛几何，特别是围绕拉格朗日子流形和与这些子流形交叉相关的Floer同调的研究。Fukaya发展并广泛研究了一种理论，其中给定辛流形的拉格朗日子流形是广义范畴的对象，现在称为Fukaya范畴，态射是Floer同调群。这项工作与Kontsevich的同调镜像对称猜想密切相关。现在，这被表述为一个猜想，即Kahler流形上的相干滑轮的导出范畴应该与“镜像”辛流形的Fukaya范畴同构。他早期的工作是黎曼几何，特别是在这种情况下处理坍缩结果。

教育经历

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

工作经历

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

荣誉与奖项

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

出版物

[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)
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[166] K. Fukaya, Collapsing Riemannian manifolds to ones with lower dimension II, Journal of The Mathematical Society of Japan, 41, 333-356 (1989)
[167] K. Fukaya, A boundary of the set of the Riemannian manifolds with bounded curvatures and diameters, Journal of Differential Geometry, 28, 1-21 (1988)
[168] S. Hayashi, K. Fukaya, H. Saito, Sintering of lanthanum chromite doped with zinc or copper, Journal of Materials Science Letters, 7, 457-458 (1988)
[169] K. Fukaya, K. Fukaya, A COMPACTNESS THEOREM OF A SET OF ASPHERICAL RIEMANNIAN ORBIFOLDS, A Fête of Topology, 391-413 (1988)
[170] K. Fukaya, Collapsing of Riemannian manifolds and eigenvalues of Laplace operator, Inventiones mathematicae, 87, 517-547 (1987)
[171] K. Fukaya, Collapsing of Riemannian manifolds and eigenvalues of Laplace operator, Inventiones mathematicae, 87, 517-547 (1987)
[172] K. Fukaya, Collapsing of Riemannian manifolds and eigenvalues of Laplace operator, Inventiones mathematicae, 87, 517-547 (1987)
[173] K. Fukaya, Collapsing Riemannian manifolds to ones of lower dimensions, Journal of Differential Geometry, 25, 139-156 (1987)
[174] K. Fukaya, Theory of convergence for Riemannian orbifolds, Japanese journal of mathematics. New series, 12, 121-160 (1986)
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更新时间: 2025-03-28 01:57:07