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2009 Fiscal Year Self-evaluation Report

Geometry of moduli spaces and its application to infinite diemensional integrable systems

Research Project

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Project/Area Number 19340007
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionTokyo Metropolitan University (2010)
Yokkaichi University (2009)
Kyoto University (2007-2008)

Principal Investigator

UENO Kenji  Kyoto University, 関孝和数学研究所, 研究員 (40011655)

Project Period (FY) 2007 – 2010
Keywordsモジュライ空 / 無限可積分系 / 共形場理論 / 位相的場の理論 / 剛幾何学 / 代数多様体の退化
Research Abstract

本研究はモジュライ空間の幾何学を種々の観点から考察しその性質を究明し、無限可積分系に応用することを目的として行う。申請者はこれまでモジュライ空間と無限可積分系との関係、特に共形場理論との関連に重点を置いて研究を行い、さらに共形場理論の応用としてモジュラー函手の構成と実3次元多様体の不変量(位相的場の理論)の研究を行ってきた。これらの研究では点付き安定曲線のモジュライ空間の研究が重要な働きをする。また、モジュライ空間は数学の種々の側面で登場し、様々な分野に応用されている。こうしたこれまでの研究成果に基づき、モジュライ空間の研究を軸として無限可積分系の様々な側面への応用をはかり、理論の進展を目指す。

  • Research Products

    (11 results)

All 2009 2008 2007

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (5 results) Book (1 results)

  • [Journal Article] Deformations of real rational dynamics in tropical geometry.2009

    • Author(s)
      Tsuyoshi Kato
    • Journal Title

      Geom.Funct.Anal. 19

      Pages: 883-901

    • Peer Reviewed
  • [Journal Article] Growth of Casson handles and transversality for ASD moduli spaces.2008

    • Author(s)
      Tsuyoshi Kato
    • Journal Title

      Geom. Topol. 12

      Pages: 1265-1311

    • Peer Reviewed
  • [Journal Article] On the Shimura variety having Mumford's fake projective plane as a connected component.2008

    • Author(s)
      Fumiharu Kato
    • Journal Title

      Math. Z. 259

      Pages: 631-641

    • Peer Reviewed
  • [Journal Article] Abelian conformal field theory and determinant bundles.2007

    • Author(s)
      J.A. Andersen, Kenji Ueno
    • Journal Title

      Internat. J.Math. 18

      Pages: 919-993

    • Peer Reviewed
  • [Journal Article] Geometric construction of modular functors from conformal field theory.2007

    • Author(s)
      J.A. Andersen, Kenji Ueno
    • Journal Title

      J.Knot theory and its Ramifications 16

      Pages: 127-202

    • Peer Reviewed
  • [Presentation] A rough equivalence on partial differential equations, International Conference.2009

    • Author(s)
      Tsuyoshi Kato
    • Organizer
      Geometry and Analysis
    • Place of Presentation
      Universite Paris 7, France
    • Year and Date
      2009-12-23
  • [Presentation] Loop spaces and conformal field theory.2009

    • Author(s)
      Yuji Shimizu
    • Organizer
      Hodge理論と代数幾何学
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-07-01
  • [Presentation] Artin-Schreier Mumford curves.2009

    • Author(s)
      Fumiharu Kato
    • Organizer
      Moduli and Discrete Groups
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-06-12
  • [Presentation] An index theory over Casson handles and complexity of smooth structure on K3 surface.2009

    • Author(s)
      Tsuyoshi Kato
    • Organizer
      Geometry Colloquium
    • Place of Presentation
      中国復旦大学
    • Year and Date
      2009-06-08
  • [Presentation] Conformal fields theory and modular functors.2007

    • Author(s)
      Kenji Ueno
    • Organizer
      International Conference on Algebra and Combinatorics
    • Place of Presentation
      中国北京航空航天大学
    • Year and Date
      2007-07-06
  • [Book] Fields Institute Monographs, 24.2008

    • Author(s)
      Kenji Ueno
    • Total Pages
      viii+168
    • Publisher
      American Mathematical Society

URL: 

Published: 2011-06-18   Modified: 2016-04-21  

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