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Fundamentals and Applications of Mathematics

Research Project

Project/Area Number 10304004
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionTohoku University

Principal Investigator

NISHIKAWA Seiki  Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (60004488)

Co-Investigator(Kenkyū-buntansha) BANDO Shigetoshi  Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (40165064)
SUNADA Toshikazu  Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (20022741)
ODA Tadao  Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (60022555)
BANNAI Eiichi  Kyushu University, Graduate School of Science, Professor, 大学院・数理学研究院, 教授 (10011652)
FUKAYA Kenji  Kyoto University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (30165261)
増田 久弥  東北大学, 大学院・理学研究科, 教授 (10090523)
Project Period (FY) 1998 – 2001
Project Status Completed (Fiscal Year 2001)
Budget Amount *help
¥32,220,000 (Direct Cost: ¥30,000,000、Indirect Cost: ¥2,220,000)
Fiscal Year 2001: ¥9,620,000 (Direct Cost: ¥7,400,000、Indirect Cost: ¥2,220,000)
Fiscal Year 2000: ¥7,700,000 (Direct Cost: ¥7,700,000)
Fiscal Year 1999: ¥6,900,000 (Direct Cost: ¥6,900,000)
Fiscal Year 1998: ¥8,000,000 (Direct Cost: ¥8,000,000)
KeywordsMathematical science / Global analysis / Symplectic geometry / Combinatorics / Class field theory / Group theory / Singularities / Integrable system / 微分幾何学 / リー群 / 幾何構造 / 微分方程式 / 組み合わせ論 / トポロジー / 特異点 / 表現論 / 等質空間 / 極小曲面 / シンプレクティック幾何学 / CR幾何学 / 過剰決定系 / 幾何解析
Research Abstract

The main objective of this project was twofold. One was to execute intensive cooperative researches beyond the borders of specific research fields with the aim of strengthening the foundation of mathematical sciences and its applications. The other was to promote the publication of the "Advanced Studies in Pure Mathematics" series (ASPM for short) in order to establish the prompt distribution of research results in official publication form.
As its outcomes, two international conferences were organized and accomplished with great success, and the following eight proceedings of international conferences were edited and published.
A. International Conferences :
(1) Minimal Surfaces, Geometric Analysis and Symplectic Geometry, held at the Japan-America Mathematics Institute, Johns Hopkins University in March, 1999.
(2) The Fifth Pacific Rim Geometry Conference, held at Tohoku University in July, 2000.
B. Proceedings :
(1) Arrangements - Tokyo 1998, ASPM Vol. 27
(2) Singularities - Sapporo 1998, ASPM Vol. 29
(3) Class Field Theory - Its Centenary and Prospect, ASPM Vol. 30
(4) Groups and Combinatorics - in memory of Michio Suzuki, ASPM Vol. 32
(5) Minimal Surfaces, Geometric Analysis and Symplectic Geometry, ASPM Vol. 34
(6) Proceedings of The Fifth Pacific Rim Geometry Conference, Tohoku Math. Publ., No. 20
(7) Surveys on Integrable Systems in Differential Geometry, to be published in 2002
(8) Lie Groups, Geometric Structure and Differential Equations - One Hundred Years after Sophus Lie-, to be published in 2002

Report

(5 results)
  • 2001 Annual Research Report   Final Research Report Summary
  • 2000 Annual Research Report
  • 1999 Annual Research Report
  • 1998 Annual Research Report
  • Research Products

    (45 results)

All Other

All Publications (45 results)

  • [Publications] Seiki Nishikawa: "Harmonic maps and negatively curved homogeneous spaces"Geometry and Topology of Submanifolds. 10. 200-215 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Shigetoshi Bando: "The existence problem of Einstein-Kahler metrics : the case of positive scalar curvature"Sugaku Expositions. 14. 91-101 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Kenji Fukaya: "Arnold conjecture and Gromov-Witten invariant"Topology. 38. 933-1048 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Kenji Fukaya: "Floer homology and mirror symmetry II"Advanced Studies in Pure mathematics. 34(印刷中). (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Eiichi Bannai: "Some results on modular forms-Subgroups of the modular group whose ring of modular forms is a polynomial ring"Advanced Studies in Pure mathematics. 32. 245-254 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Shigefumi Mori: "On a hyper plane section theorem of Gurjar"Mathematische Annalen. 319. 533-537 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Seiki Nishikawa: "Proceedings of the Fifth Pacific Rim Geometry Conference, Tohoku Mathematical Publications, No.20"Mathematical Institute, Tohoku University. 205 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Michael Falk: "Arrangements-Tokyo 1998 Advanced Studies in Pure Mathematics, Vol.27"Kinokuniya Company Ltd.. 283 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Jean-Paul Brasselet: "Singularities-Sapporo 1998 Advanced Studies in Pure Mathematics, Vol.29"Kinokuniya Company Ltd.. 326 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Katsuya Miyake: "Class Field Theory-Its Centenary and Prospect Advanced Studies in Pure Mathematics, Vol.30"Mathematical Society of Japan. 641 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Eiichi Bannai: "Groups and Combinatorics-in memory of Michio Suzuki Advanced Studies in Pure Mathematics, Vol.32"Mathematical Society of Japan. 483 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Kinji Fukaya: "Minimal Surfaces, Gesmetric Analysis and Symplectic Geometry Advanced Studies in Pure Mathematics, Vol.34"Mathematical Society of Japan(印刷中・予定). 275 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Seiki Nishikawa: "Harmonic maps and negatively curved homogeneous spaces"Geometry and Topology of Submanifolds. 10. 200-215 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Shigetoshi Bando: "The existence problem of Einstein-Kahler metrics : the case of positive scalar curvature"Sugaku Expositions. 14. 91-101 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Kenji Fukaya: "Arnold conjecture and Gromov-Witten invariant"Topology. 38. 933-1048 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Kenji Fukaya: "Floer homology and mirror symmetry II"Advanced Studies in Pure Mathematics. 34(in printing). (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Eiichi Bannai: "Some results on modular forms - Subgroups of the modular group whose ring of modular forms is a polynomial ring"Advanced Studies in Pure Mathematics. 32. 245-254 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Shigefumi Mori: "On a hyperplane section theorem of Gurjar"Mathematische Annalen. 319. 533-537 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Seiki Nishikawa: "Proceedings of The Fifth Pacific Rim Geometry Conference"Mathematical Institute, Tohoku University. 205 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Michael Falk: "Arrangements- Tokyo 1998, Advanced Studies in Pure Mathematics, Vol. 27"Kinokuniya Company Ltd.. 283 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Jean-Paul Brasselet: "Singularities - Sapporo 1998, Advanced Studies in Pure Mathematics, Vol.29"Kinokuniya Company Ltd.. 326 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Katsuya Miyake: "Class Field Theory - Its Centenary and Prospect, Advanced Studies in Pure Mathematics, Vol. 30"Mathematical Society of Japan. 641 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Eiichi Bannai: "Groups and Combinatorics - in memory of Michio Suzuki, Advanced Studies in Pure Mathematics, Vol. 32"Mathematical Society of Japan. 483 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Kenji Fukaya: "Minimal Surfaces, Geometric Analysis and Symplectic Geometry, Advanced Studies in Pure Mathemtics, Vol. 34"Mathematical Society of Japan (in printing). (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Eiichi Bannai: "Some results on modular forms-Subgroups of the modular group whose ring of modular forms is a polynomial ring"Advanced Studies in Pure Mathematics. 32. 245-254 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Kenji Fukaya: "Floer homology and Gromov-Witten invariant over Z of general symplectic manifolds -summary-"Advanced Studies in Pure Mathematics. 31. 75-91 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Shigefumi Mon: "On a hyperplane section theorem of Gunjar"Math. Ann. 319. 533-537 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Shigetoshi Bando: "The existence problem of Einstein-Kaehler metrics : the case of positive scalar curvature"Sugaku Expositions. 14. 91-101 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Kenji Fukaya: "Floer homology and mirror symmetry II"Advanced Studies in Pure Mathematics. 34. (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] Seiki Nishikawa: "Proceedings of The Fifth Pacific Rim Geometry Conference"Mathematical Institute, Tohoku University. 205 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Seiki Nishikawa: "Harmonic maps and negatively curved homogeneous spaces"Geometry and Topology of Submanifolds. 10. 200-215 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Eiichi.Bannai: "Some results on modular forms - subgroups of the modular group whose ring of modular form is a polynomial ring"Advanced Studies in Pure Mathematics. 32. (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] Michael Falk: "Arrangements - Tokyo 1998"Kinokuniya Company,Ltd.. 278 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Jean-Paul Brasselet: "Singularities - Sapporo 1998"Kinokuniya Company,Ltd.. 322 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] E.Bannai: "Modular invariance property of association schemes,TypeII codes over finite rings and finite abelian groups"Ann. Inst. Fourier. 49. 763-782 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] E.Bannai: "TypeII codes, even unimodular lattices and invariant rings"IEEE Trans. Inform.Theory. 45. 1194-1205 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] E.Bannai: "On the rings of simultaneous invariants for the Gleason-MacWilliams group"Erop. J. Combinatorics. 20. 619-627 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] K.Fukaya: "Arnold conjecture and Gromov-Witten invariant"Topology. 38. 933-1048 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] S.Nishikawa: "Homogeneous manifolds of negative curvature and harmonic maps"数理解析研究所講究録. 1104. 137-144 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] T.Kobayashi et al.: "Analysis on Homegeneous Spaces and Representation Theory of Lie groups, Okayama-Kyoto"Kinokuniya Company, Ltd. 500 (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] K.Fukaya: "Anti self dualequation on 4 manifolds with degenerate metric" Geometry And Functional Analysis. 8. 466-528 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Fukaya: "Arnold conjecture and Gromov Witten invariant" Topology. (印刷中). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Kotani: "Asymptotic behavior of the transition prebability of a random walk on an infinite graph" J.Funct.Anal.159. 664-689 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Miyake: "Class Field Theory-Its Centenary and Prospect(Advanced Studies in Pure Mathematics,vol.26)" Kinokuniya Company,Ltd, 500 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Suwa et al.: "Singularities-Arrangements,Sapporo-Tokyo 1998(Advanced Studies in Pure Mathematics,vol.27)" Kinokuniya Company,Ltd, 400 (1999)

    • Related Report
      1998 Annual Research Report

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Published: 1998-04-01   Modified: 2021-09-21  

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