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2012 Fiscal Year Final Research Report

Gromov-Witten theory and mirror symmetry

Research Project

  • PDF
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
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
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.

  • Research Products

    (23 results)

All 2013 2012 2011 2010 Other

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (18 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

    • Peer Reviewed
  • [Journal Article] Seidel elements and mirror transformations2012

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

      Selecta Math. (N. S.)

      Volume: 18 Pages: 557-590

    • DOI

      DOI:10.1007/s00029-011-0080-0

    • 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

    • Peer Reviewed
  • [Journal Article] Quantum Cohomology and Periods

    • Author(s)
      Hiroshi Iritani
    • Journal Title

      Ann. Inst. Fourier

    • 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

    • 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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
    • Year and Date
      20110916-18
  • [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
    • Year and Date
      20110000
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
    • Year and Date
      20100621-25
  • [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
  • [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
  • [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

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Published: 2014-08-29  

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