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Gromov-Witten theory and mirror symmetry

Research Project

Project/Area Number 22740042
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionKyoto University

Principal Investigator

IRITANI Hiroshi  京都大学, 大学院・理学研究科, 准教授 (20448400)

Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywordsミラー対称性 / グロモフ・ウィッテン理論 / トーリック多様体 / 量子コホモロジー / ホッジ理論 / 軌道体 / 幾何学的量子化 / Seidel表現 / Gromov-Witten理論 / Seidel 元 / 量子化 / 収束 / Giventalの公式 / Gromov-Witten不変量 / Gromov-Wittenポテンシャル / 量子コホモロモジー / カラビ・ヤウ多様体 / FJRW理論 / Seidel元 / カラビ・ヤウ超曲面
Research Abstract

We studied a global structure of Gromov-Witten theory from a viewpoint of mirror symmetry. Our results include:
(1) mirror symmetry for complete intersections in toric orbifold and matching of integral structures from the A-model andthe B-model
(2) Landau-Ginzburg/Calabi-Yau correspondence for weighted projective Calabi-Yau hypersurfaces and its relation to Orlov’s derived equivalence
(3) Seidel representation for toric manifolds and the relation to mirror transformation.

Report

(4 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (29 results)

All 2013 2012 2011 2010 Other

All Journal Article (7 results) (of which Peer Reviewed: 7 results) Presentation (22 results) (of which Invited: 2 results)

  • [Journal Article] The Quantum Lefschetz Hyperplane Principle Can Fail For Positive Orbifold Hypersurfaces2012

    • Author(s)
      Tom Coates, Amin Gholampour, Hiroshi Iritani, Yunfeng Jiang, Paul Johnson, Cristina Manolache
    • Journal Title

      Math. Res. Lett.

      Volume: 19 Pages: 997-1005

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Seidel elements and mirror transformations2012

    • Author(s)
      Eduardo Gonzalez, Hiroshi Iritani
    • Journal Title

      Selecta Math. (N. S.)

      Volume: 18 Issue: 3 Pages: 557-590

    • DOI

      10.1007/s00029-011-0080-0

    • Related Report
      2012 Final Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Quantum Lefschetz Hyperplane Principle can Fail for Positive Orbifold Hypersurfaces2012

    • Author(s)
      Tom Coates, Amin Gholampour, Hiroshi Iritani, Yunfeng Jiang, Paul Johnson, Cristina Manolache,
    • Journal Title

      Mathematical Research Letters

      Volume: 19 Pages: 997-1005

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Ruan's conjecture and integral structures in quantum cohomology2010

    • Author(s)
      Hiroshi Iritani
    • Journal Title

      Ruan's conjecture and integral structures in quantum cohomology

      Volume: 59 Pages: 111-166

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Ruan's conjecture and integral structures in quantum cohomology2010

    • Author(s)
      Hiroshi IRITANI
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 59 Pages: 111-166

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Quantum Cohomology and Periods

    • Author(s)
      Hiroshi Iritani
    • Journal Title

      Ann. Inst. Fourier

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Landau-Ginzburg/Calabi-Yau Correspondence, Global Mirror Symmetry and Orlov Equivalence

    • Author(s)
      Alessandro Chiodo, Hiroshi Iritani, Yongbin Ruan
    • Journal Title

      Publ. IHES

    • NAID

      120005647499

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Presentation] Fock Sheaf of Givental Quantization2013

    • Author(s)
      Hiroshi Iritani
    • Organizer
      UK-Japan mathematical Forum
    • Place of Presentation
      慶応大学
    • Year and Date
      2013-01-23
    • Related Report
      2012 Final Research Report
  • [Presentation] Fock Sheaf of Givental Quantization2013

    • Author(s)
      Hiroshi Iritani
    • Organizer
      UK-Japan Mathematical Forum
    • Place of Presentation
      慶応大学日吉来往舎
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] 非可換Hodge構造の変動に付随するFock空間の層について2012

    • Author(s)
      Hiroshi Iritani
    • Organizer
      リーマン面に関連する位相幾何学
    • Place of Presentation
      東京大学
    • Year and Date
      2012-09-01
    • Related Report
      2012 Final Research Report
  • [Presentation] Gamma structure and functoriality in Gromov-Witten theory2012

    • Author(s)
      Hiroshi Iritani
    • Organizer
      Geometry and Physics of the Landau-Ginzburg model
    • Place of Presentation
      Kavli IPMU
    • Year and Date
      2012-06-25
    • Related Report
      2012 Final Research Report
  • [Presentation] Functoriality in Gromov-Witten theory2012

    • Author(s)
      Hiroshi Iritani
    • Organizer
      Singularites d'Equations Differentielles en Geometrie Algebrique
    • Place of Presentation
      CIRM Luminy, フランス
    • Year and Date
      2012-06-06
    • Related Report
      2012 Final Research Report
  • [Presentation] Serre duality and Fourier transformation2012

    • Author(s)
      Hiroshi Iritani
    • Organizer
      Motivic Structure in Quantum Cohomology
    • Place of Presentation
      Max-Planck Institute, Bonn, ドイツ
    • Year and Date
      2012-03-26
    • Related Report
      2012 Final Research Report
  • [Presentation] Orlov Equivalence and quantum singularity theory2012

    • Author(s)
      Hiroshi Iritani
    • Organizer
      Workshop on Integrable system and mirror symmetry
    • Place of Presentation
      神戸大学
    • Year and Date
      2012-02-23
    • Related Report
      2012 Final Research Report
  • [Presentation] Functoriality in Gromov-Witten theory2012

    • Author(s)
      Hiroshi Iritani
    • Organizer
      Singularites d'Equations Differentielles en Geometrie Algebrique
    • Place of Presentation
      CIRM, Luminy, France
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Quantum Cohomology and Periods2011

    • Author(s)
      Hiroshi Iritani
    • Organizer
      第10回環太平洋幾何学会議
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2011-12-04
    • Related Report
      2012 Final Research Report
  • [Presentation] Fock sheaf associated to the semi-infinite Hodge variation2011

    • Author(s)
      Hiroshi Iritani
    • Organizer
      Kobe Workshop on Quantum Cohomology and Integrable systems
    • Place of Presentation
      神戸大学
    • Year and Date
      2011-09-02
    • Related Report
      2012 Final Research Report
  • [Presentation] Quantum Cohomology of Toric Orbifold Hypersurfaces and mirror period integral2011

    • Author(s)
      Hiroshi Iritani
    • Organizer
      Workshop on Recent developments of orbifolds
    • Place of Presentation
      Nankai university, 天津,中国
    • Year and Date
      2011-07-25
    • Related Report
      2012 Final Research Report
  • [Presentation] Quantum Cohomology and Periods2011

    • Author(s)
      Hiroshi Iritani
    • Organizer
      Conference on Gromov-Witten theory
    • Place of Presentation
      Institut Fourier, Grenobel, フランス
    • Year and Date
      2011-07-04
    • Related Report
      2012 Final Research Report
  • [Presentation] Landau-Ginzburg/Calabi-Yau correspondence, analytic continuation and global mirror symmetry2011

    • Author(s)
      Hiroshi Iritani
    • Organizer
      Derived Categories
    • Place of Presentation
      Isaac Newton Institute for mathematical sciences,イギリス
    • Year and Date
      2011-04-13
    • Related Report
      2012 Final Research Report
  • [Presentation] Landau-Ginzburg/Calabi-Yau correspondence, analytic continuation and global mirror symmetry2011

    • Author(s)
      Hiroshi Iritani
    • Organizer
      Derived Categories
    • Place of Presentation
      Isaac Newton Institute for mathematical sciences(招待講演)
    • Year and Date
      2011-04-13
    • Related Report
      2011 Annual Research Report
  • [Presentation] Quantum Cohomology and Periods2011

    • Author(s)
      Hiroshi Iritani
    • Organizer
      New methods in geometry
    • Place of Presentation
      King's College London, イギリス
    • Year and Date
      2011-01-12
    • Related Report
      2012 Final Research Report
  • [Presentation] Global Study of Quantum D-modules2011

    • Author(s)
      Hiroshi Iritani
    • Organizer
      Workshop on Equivariant Quantum Cohomology
    • Place of Presentation
      Columbia University,アメリカ合衆国
    • Related Report
      2012 Final Research Report
  • [Presentation] トーリックスタックの大量子コホモロジーとmulti-GKZ 系2011

    • Author(s)
      入谷 寛
    • Organizer
      Mini workshop on Mirror Symmetry
    • Place of Presentation
      北海道大学
    • Related Report
      2012 Final Research Report
  • [Presentation] K-theory integral structure in quantum cohomology and mirror symmetry2010

    • Author(s)
      Hiroshi Iritani
    • Organizer
      代数幾何シンポジウム
    • Place of Presentation
      城崎大会議館,城崎
    • Year and Date
      2010-10-27
    • Related Report
      2012 Final Research Report
  • [Presentation] Gromov-Witten 理論における整構造2010

    • Author(s)
      入谷 寛
    • Organizer
      日本数学会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-22
    • Related Report
      2012 Final Research Report
  • [Presentation] Gromov-Witten理論における整構造2010

    • Author(s)
      入谷寛
    • Organizer
      日本数学会(幾何学分科会特別講演)
    • Place of Presentation
      名古屋大学(招待講演)
    • Year and Date
      2010-09-22
    • Related Report
      2010 Annual Research Report
  • [Presentation] Matrix factorization and enumeration of spin curves2010

    • Author(s)
      Hiroshi Iritani
    • Organizer
      Workshop on Geometry and Physics of the Landau-Ginzburg model
    • Place of Presentation
      Institut Fourier, Grenoble, フランス
    • Year and Date
      2010-06-01
    • Related Report
      2012 Final Research Report
  • [Presentation] Hodge Theory of Landau-Ginzburg model and its quantization2010

    • Author(s)
      Hiroshi Iritani
    • Organizer
      Summer School on mirror symmetry
    • Place of Presentation
      KIAS, ソウル,韓国
    • Related Report
      2012 Final Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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