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Research on Fundamental Mathematical Sciences

Research Project

Project/Area Number 03302006
Research Category

Grant-in-Aid for Co-operative Research (A)

Allocation TypeSingle-year Grants
Research Field 解析学
Research InstitutionNagoya University

Principal Investigator

AOMOTO Kazuhiko  Nagoya Univ.Sci.Professor, 理学部, 教授 (00011495)

Co-Investigator(Kenkyū-buntansha) MUKAI Shigeru  Nagoya Univ.Sci.Professor, 理学部, 教授 (80115641)
MORITA Shigeyuki  Tokyo Inst.of Tech.Sci.Professor, 理学部, 教授 (70011674)
SUNADA Toshikazu  Tohoku Univ.Sci.Professor, 理学部, 教授 (20022741)
HASHIHARA Masaki  Kyoto Univ.RIMS Professor, 数理解析研究所, 教授 (60027381)
IHARA Yasutaka  Kyoto Univ.RIMS Professor, 数理解析研究所, 教授 (70011484)
Project Period (FY) 1991 – 1993
Project Status Completed (Fiscal Year 1993)
Budget Amount *help
¥20,000,000 (Direct Cost: ¥20,000,000)
Fiscal Year 1993: ¥5,200,000 (Direct Cost: ¥5,200,000)
Fiscal Year 1992: ¥8,300,000 (Direct Cost: ¥8,300,000)
Fiscal Year 1991: ¥6,500,000 (Direct Cost: ¥6,500,000)
KeywordsMathematical Sciences / Infinite Analysis / Algebraic Combinatories / Quantum Analysis / Information Science / Non-linear Analysis / 情報数理 / モジュライ / 基礎数理 / 無限次久力学系 / 非線形現象 / 散乱理論 / カオス / 無限解析 / 特殊微分方程式
Research Abstract

The main purpose of this project was to continue and promote the research of fundamental mathematical aciences. As was seen in International Conference of Mathematics heid at Kyoto in 1990, the recent trend in mathematics is to have motivation and strong impetus from other fields in mathematical sciences including physics, biology and engeneering. Under this circumstance, the existing fields in pure mathematics is in the process of reorganization. This project has taken up this trend and promoted the reorganization. To establish a favorable environment, we made intensively the following activities.
1. Backing up the research projects in Research Institute of Mathematical Sciences including "Infinite Analysis", "Research on Nonlinear Phenomena" and "Number Theory and Moduli".
2. Supporting the international conferences including "Uniformization and Hypergeometric Integrals", "Spectral Scattering Theory", "Quantum Analysis", Algebraic Combinatorics" and "Global Geometry".
3. Supporting the domestic conferences including "Mathematical Foundation of Information Science".
4. Publication of Advanced Studies in Pure Mathematics as Proceedings of several important meetings.

Report

(4 results)
  • 1993 Annual Research Report   Final Research Report Summary
  • 1992 Annual Research Report
  • 1991 Annual Research Report
  • Research Products

    (36 results)

All Other

All Publications (36 results)

  • [Publications] Kazuhiko AOMOTO: "Gauss decompsition of connection matrices and application to Yang-Baxter equations,I." Proc.Japan Acad.89. 238-242 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Masaki KASHIHARA: "Global crystal bases of quantum groups" Duke Math.J.69. 455-485 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Toshikazu SUNADA: "On the spectrum of gauge-periodic elliptic operators" Asterisque. 20. 65-74 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Shigeyuki MORITA: "The extension of Johnson's homomorphism from the Torelli group to the mapping class group" Invent.Math.111. 197-224 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Shigeru MUKAI: "Curves and Grassmannians" Algebraic geometry and related topics. (to appear). (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Tadao ODA: "The algebraic de Rham theorem for toric varieties" Tohoku Math.J.45. 231-247 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Masaaki YOSHIDA et al.: "From Gauss to Painleve-A modern theory of special functions" Vieweg Verlag, 347 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] 谷島賢二: "数理物理学入門" 東京大学出版会(3月出版予定), (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Kazuhiko AOMOTO: "Gauss decompsition of connection matrices and a-plication to Yang-Baxter equations, I" Proc.Japan Acad.89. 238-242 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Masaki KASHIHARA: "Global crystal bases of quantum groups" Duke Math.J.69. 455-485 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Toshikazu KUNADA: "On the spectrum of gaugeperiodic elliptic operators" Asterisque. 20. 65-74 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Shigeyuki MORITA: "The extention of Johnson's homomorphism from the Torelli group to the mapping class group" Invent.Math.111. 197-224 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Shigeru MUKAI: "Curves and Grassmannians" Algebraic geometry and related topics to appear. (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Tadao ODA: "The algebraic de Pham theorem for toric varieties" Tohoku Math.J.45. 231-247 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Masaaki YOSHIDA et al.: From Gauss to Painleve - A modern theory of special functions. Vieweg Verlag, 347 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Kenji YAJIMA: Introduction to Mathematical Physics (in Japan). Univ.of Tokyo Pub. (in press), (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Kazuhiko AOMOTO: "Gauss decompition of connection matrices and application to Yang-Baxter equations,I" Proc.Japan Acad.89. 238-242 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Masaki KASHIHARA: "Global crystal bases of quantum groups" Duke Math.J.69. 455-485 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Toshikazu SUNADA: "On the spectrum of gauge-periodic elliptic operators" Asterisque. 20. 65-74 (1992)

    • Related Report
      1993 Annual Research Report
  • [Publications] Shigeyuki MORITA: "The extension of Johnson's homomorphism from the Torelli group to the mapping class group" Invent.Math.111. 197-224 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Shigeru MUKAI: "Curves and Grassmannians" Algebraic geometry and related topics. to appear (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Tadao ODA: "The algebraic de Rham theorem for toric varieties" Tohoku Math.J.45. 231-247 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Masaaki YOSHIDA et al.: "From Gauss to Painleve-A modern theory of special functions" Vieweg Verlag, 347 (1991)

    • Related Report
      1993 Annual Research Report
  • [Publications] 谷島賢二: "数理物理学入門" 東京大学出版会(3月出版予定), (1994)

    • Related Report
      1993 Annual Research Report
  • [Publications] K.Aomoto,Y.Kato,K.Mimachi: "A solution of the Yang-Baxter equation" Intern.Math.Res.Notes. 1. 7-15 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] K.Aomoto: "Hyperlogarithmic expansion.and the volume of a hyperbolic simplex" Banach Centre Pub.27. 9-21 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] T.Sunada: "Discrete Schrodinger operators on a graph" Nagoya Math.J.125. 141-150 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] T.Sunada: "Homology,Wiener integrals,and Integrated densities of states" J.Funct.Analy.106. 50-58 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] S.Mukai: "Curves and symmetric spaces" Proc.Japan Acad.68. 7-10 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] S.Mukai: "Curves and Granssmannians" Algebraic Geometry and Related Topics. (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] Kazuhiko AOMOTO: "Point spectrum on a quasi homogeneous tree." Pacific J.of Math.147. 231-242 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] Kazuhiko AOMOTO: "Finiteness of a cohomology associated with certain Jackson Integrals." Tohoku J.of Math.43. 75-101 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] Yasutaka IHARA: "Braids,Galois groups and some arithemtic functions." Proc.Int.Congress of Math,Kyoto 1990. 1. 99-120 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] Masaki KASHIWARA: "On crystal bases of the qーanalogue of universal enceloping algebras." Duke Math.J.63. 465-516 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] Toshikazu SUNADA: "Trace formulae in spectral geometry." Proc.ICMー90,Kyoto. 577-585 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] Shigeyuki MORITA: "On the structure of the Torelli group and the Casson invariant." Topology. 30. 603-621 (1991)

    • Related Report
      1991 Annual Research Report

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Published: 1991-04-01   Modified: 2016-04-21  

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