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Geometry of Moduli Spaces and its Application to Infinite Analysis

Research Project

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  首都大学東京, 大学院・理工学研究科, 研究員 (40011655)

Co-Investigator(Kenkyū-buntansha) TOKUNAGA Hiroo  首都大学東京, 大学院・理工学研究科, 教授 (30211395)
KATO Tsuyoshi  京都大学, 大学院・理学研究科, 教授 (20273427)
KATO Fumiharu  京都大学, 大学院・理学研究科, 准教授 (50294880)
SHIMIZU Yuji  国際基督教大学, 教養学部, 教授 (80187468)
望月 新一  京都大学, 数理解析研究所, 教授 (10243106)
三輪 哲二  京都大学, 大学院・理学研究科, 教授 (10027386)
井上 義也  京都大学, 大学院・理学研究科, 助教 (10232571)
Project Period (FY) 2007 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥18,200,000 (Direct Cost: ¥14,000,000、Indirect Cost: ¥4,200,000)
Fiscal Year 2010: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2009: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2008: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2007: ¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Keywords代数科学 / 共形場理論 / モジュラー函手 / 位相的場の理論 / タイヒミュラー / GNS構成法 / ゲージ対称性 / 分岐被覆 / 剛幾何学 / モジュライ空 / 無限可積分系 / 代数多様体の退化 / 重複ファイバー / トロピカル幾何学 / 変形パラメータ / 導来圏 / モジュライ空間 / 接続 / ゲージ理論 / 代数曲線 / 退化 / ユニタリ性 / 写像類群 / 射影的平坦接続 / Hitchin接続 / p進剛幾何学 / ペンローズ変換
Research Abstract

From conformal field theory with gauge symmetry constructed by Tsuchiya, Yamada and Ueno I and Joergen E. Andersen constructed modular functors so that we had topological filed theory for three manifolds. When the Lie algebra for gauge symmetry is sl(n, C) we proved that our topological field is isomorphic to the one constructed by Reshetikhin and Turaev by using GNS construction of representations of Hecke algebra. As a corollary to our proof we could also prove that conformal block bundles on the Teichmueller space of pointed Riemann surfaces of genus 0 carry unitary structure compatible with KZ connections.
Ueno also constructed a family of curves over a field of characteristic p, which contain multiple fiber pD where D is any divisor appearing a degeneration of a family of curves of genus 2 and p is any prime number.

Report

(6 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report   Self-evaluation Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (46 results)

All 2011 2010 2009 2008 2007

All Journal Article (28 results) (of which Peer Reviewed: 28 results) Presentation (15 results) Book (3 results)

  • [Journal Article] On Hausdorff completions of commutative rings in rigid geometry2011

    • Author(s)
      Fujiwara, K.; Gabber, O.; Kato, F.
    • Journal Title

      Journal of Algebra

      Volume: 322 Pages: 293-321

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The relation between rigid-analytic and algebraic deformation parameters for Artin-Schreier-Mumford curves2010

    • Author(s)
      Cornelissen, G. Kato, F. & Kontogeorgis, A.
    • Journal Title

      Israel J. Math.

      Volume: vol.180 Pages: 345-370

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Pattern formation from projectively dynamical systems and iterations by families of maps2010

    • Author(s)
      Kato, T.
    • Journal Title

      Advanced Studies in Pure Math.

      Volume: vol.57 Pages: 243-262

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Geometry of irreducible plane quartics and their quadratic residue conics2010

    • Author(s)
      Tokunaga, H.
    • Journal Title

      J. Singularity

      Volume: vol.2 Pages: 170-190

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Geometry of. irreducible plane quartics and their quadratic residue conics2010

    • Author(s)
      Tokunaga, H.
    • Journal Title

      Journal of Singularity

      Volume: 2 Pages: 170-190

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The relation between rigid-analytic and algebraic deformation parameters for Artin-Schreier-Mumford curves2010

    • Author(s)
      Cornelissen, G.; Kato, F.; Kontogeorgis, A.
    • Journal Title

      Israel Journal of Mathematics

      Volume: 180 Pages: 345-370

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Pattern formation from projectively dynamical systems and iterations by families of maps2010

    • Author(s)
      Tsuyoshi Kato
    • Journal Title

      Advanced studies in pure mathematics Vol.57

      Pages: 243-262

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Deformations of real rational dynamics in tropical geometry2009

    • Author(s)
      Kato, T.
    • Journal Title

      Geometric and Functional Analysis

      Volume: vol.19 Pages: 842-882

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Deformations of real rational dynamics in tropical geometry.2009

    • Author(s)
      Tsuyoshi Kato
    • Journal Title

      Geom.Funct.Anal. 19

      Pages: 883-901

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Deformations of real rational dynamics in tropical geometry2009

    • Author(s)
      Tsuyoshi Kato
    • Journal Title

      Geometric and Functional Analysis Vol.19

      Pages: 842-882

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Grassmann structure in the XXZ model. II. Cretion operators.2009

    • Author(s)
      Boos, H., Jimbo, M., Miwa, T., Smirnov, F., Takeyama, Y. Hidden
    • Journal Title

      Comm. Math Phys. 286-3

      Pages: 875-932

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Conformal field theory and modular functor, in Advances in Algebraic and Combinatrics2008

    • Author(s)
      Ueno, K.
    • Journal Title

      World Scientific

      Pages: 335-352

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the Shimura variety having Mumford's fake projective plane as a connected component2008

    • Author(s)
      Kato, F.
    • Journal Title

      Math. Zeitschrift

      Volume: vol.259 Pages: 613-641

    • Related Report
      2010 Final Research Report
    • 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

    • Related Report
      2009 Self-evaluation Report
    • 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

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Conformal field theory and modular functor.2008

    • Author(s)
      Ueno, Kenji
    • Journal Title

      Advances in Algebra and Comb inatorics. 1

      Pages: 335-352

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

    • Author(s)
      Kato, Fumiharu
    • Journal Title

      Math. Z. 259-3

      Pages: 631-641

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

    • Author(s)
      Kato, Tsuyoshi
    • Journal Title

      Geom. Topol. 12-3

      Pages: 1265-1311

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The geometry of Frobenioids. II. Poly-Frobenioids.2008

    • Author(s)
      Mochizuki, Shinichi
    • Journal Title

      Kyushu J. Math. 62-2

      Pages: 401-460

    • NAID

      130000063242

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The geometry of Frobenioids. I. The general theory.2008

    • Author(s)
      Mochizuki, Shinichi
    • Journal Title

      Kyushu J. Math. 62-2

      Pages: 293-400

    • NAID

      130000063241

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The algebraic and anabelian geometry of configuration spaces.2008

    • Author(s)
      Mochizuki, Shinichi, Tamagawa, Akio
    • Journal Title

      Hokkaido Math. J. 37-1

      Pages: 75-131

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Geometric construction of modular functors from conformal field theory2007

    • Author(s)
      Andersen, J. E. & Ueno, K.
    • Journal Title

      Journal of Knot theory and its Ramifications

      Volume: vol.16 Pages: 127-202

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Abelian Conformal Field Theory and Determinant Bundles2007

    • Author(s)
      Andersen, J. E. & Ueno, K.
    • Journal Title

      International J. Math

      Volume: vol.18 Pages: 919-998

    • Related Report
      2010 Final Research Report
    • 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

    • Related Report
      2009 Self-evaluation Report
    • 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

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Geometric construction of modular functor from conformal _eld theory2007

    • Author(s)
      J.E. Andersen & K. Ueno
    • Journal Title

      J. Knot Theory and its Rami_cation 16

      Pages: 127-202

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Abelian Conformal Field Theory and Determinant Bundles2007

    • Author(s)
      J.E. Andersen & K. Ueno
    • Journal Title

      International J. Math. 18

      Pages: 919-993

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Penrose transform on conformally Bochner-Kahler manif olds2007

    • Author(s)
      Y. Inoue
    • Journal Title

      J. Math. Kyoto Univ. 47

      Pages: 327-357

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] Hecke algebra at root of unity and quantum invariants of three-manifolds2010

    • Author(s)
      Ueno, K.
    • Organizer
      研究集会「代数幾何学とその周辺」
    • Place of Presentation
      高知大学
    • Year and Date
      2010-12-18
    • Related Report
      2010 Final Research Report
  • [Presentation] Hecke algebra at root of unity and quantum invariants of three-manifolds2010

    • Author(s)
      上野健爾
    • Organizer
      研究集会「代数幾何学とその周辺」
    • Place of Presentation
      高知大学理学部
    • Year and Date
      2010-12-18
    • Related Report
      2010 Annual Research Report
  • [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
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] A rough equivalence on partial differential equations2009

    • Author(s)
      Tsuyoshi Kato
    • Organizer
      International Conference, Geometry and Analysis
    • Place of Presentation
      Universite Paris 7, France
    • Year and Date
      2009-12-23
    • Related Report
      2009 Annual Research Report
  • [Presentation] DG圏の代数化2009

    • Author(s)
      清水勇二
    • Organizer
      Workshop on Derived Algebraic Geometry I
    • Year and Date
      2009-11-24
    • Related Report
      2010 Final Research Report
  • [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
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] Loop spaces and conformal field theory2009

    • 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
    • Related Report
      2009 Annual Research Report
  • [Presentation] Loop spaces and conformal field theory2009

    • Author(s)
      Shimizu, Y.
    • Organizer
      研究集会「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
      2009-06-29
    • Related Report
      2010 Final Research Report
  • [Presentation] Artin-Schreier Mumford curves2009

    • Author(s)
      Kato, F.
    • 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
    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [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
    • Related Report
      2009 Self-evaluation Report
  • [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
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] An index theory over Casson handles and complexity of smooth structure on K3 surface2009

    • Author(s)
      Tsuyoshi Kato
    • Organizer
      Geometry Colloquium
    • Place of Presentation
      中国 復旦大学
    • Year and Date
      2009-06-08
    • Related Report
      2009 Annual Research Report
  • [Presentation] 離散力学系とトロピカル幾何学2009

    • Author(s)
      加藤毅
    • Organizer
      日本数学会2009年度年会企画特別講演
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-29
    • Related Report
      2008 Annual Research Report
  • [Presentation] From Conformal Field Theory to Topological Field Theory2007

    • Author(s)
      K. Ueno
    • Organizer
      The second International Congress of Algebra and Combinatorics
    • Place of Presentation
      北京
    • Year and Date
      2007-08-17
    • Related Report
      2007 Annual Research Report
  • [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
    • Related Report
      2009 Self-evaluation Report
  • [Book] Conformal Field Theory with Gauge Symmetry.(Fields Institute Monographs,24),Fields Institute for Research in Mathematical Sciences2008

    • Author(s)
      K. Ueno
    • Publisher
      American Mathematical Society
    • Related Report
      2010 Final Research Report
  • [Book] Fields Institute Monographs, 24.2008

    • Author(s)
      Kenji Ueno
    • Publisher
      American Mathematical Society
    • Related Report
      2009 Self-evaluation Report
  • [Book] Conformal field theory with gauge symmetry.2008

    • Author(s)
      Ueno, Kenji
    • Publisher
      American Mathematical Society
    • Related Report
      2008 Annual Research Report

URL: 

Published: 2007-04-01   Modified: 2016-04-21  

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