Gromov-Witten theory and mirror symmetry

• Project/Area Number: 22740042
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: Kyoto 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: ¥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.

Research Products

• [Journal Article] The Quantum Lefschetz Hyperplane Principle Can Fail For Positive Orbifold Hypersurfaces (2012)
  • 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 transformations (2012)
  • 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
  • Peer Reviewed
• [Journal Article] The Quantum Lefschetz Hyperplane Principle can Fail for Positive Orbifold Hypersurfaces (2012)
  • Author(s): Tom Coates, Amin Gholampour, Hiroshi Iritani, Yunfeng Jiang, Paul Johnson, Cristina Manolache,
  • Journal Title: Mathematical Research Letters Volume: 19 Pages: 997-1005
  • Peer Reviewed
• [Journal Article] Ruan's conjecture and integral structures in quantum cohomology (2010)
  • Author(s): Hiroshi Iritani
  • Journal Title: Ruan's conjecture and integral structures in quantum cohomology Volume: 59 Pages: 111-166
  • Peer Reviewed
• [Journal Article] Ruan's conjecture and integral structures in quantum cohomology (2010)
  • Author(s): Hiroshi IRITANI
  • Journal Title: Advanced Studies in Pure Mathematics 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
  • NAID: 120005647499
  • Peer Reviewed
• [Presentation] Fock Sheaf of Givental Quantization (2013)
  • Author(s): Hiroshi Iritani
  • Organizer: UK-Japan mathematical Forum
  • Place of Presentation: 慶応大学
  • Year and Date: 2013-01-23
• [Presentation] Fock Sheaf of Givental Quantization (2013)
  • Author(s): Hiroshi Iritani
  • Organizer: UK-Japan Mathematical Forum
  • Place of Presentation: 慶応大学日吉来往舎
  • 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
• [Presentation] Gamma structure and functoriality in Gromov-Witten theory (2012)
  • 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 theory (2012)
  • 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 transformation (2012)
  • 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 theory (2012)
  • 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] Functoriality in Gromov-Witten theory (2012)
  • Author(s): Hiroshi Iritani
  • Organizer: Singularites d'Equations Differentielles en Geometrie Algebrique
  • Place of Presentation: CIRM, Luminy, France
  • Invited
• [Presentation] Quantum Cohomology and Periods (2011)
  • 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 variation (2011)
  • 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 integral (2011)
  • 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 Periods (2011)
  • 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 symmetry (2011)
  • 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] Landau-Ginzburg/Calabi-Yau correspondence, analytic continuation and global mirror symmetry (2011)
  • 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
• [Presentation] Quantum Cohomology and Periods (2011)
  • 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] Global Study of Quantum D-modules (2011)
  • Author(s): Hiroshi Iritani
  • Organizer: Workshop on Equivariant Quantum Cohomology
  • Place of Presentation: Columbia University,アメリカ合衆国
• [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
• [Presentation] K-theory integral structure in quantum cohomology and mirror symmetry (2010)
  • 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] 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
• [Presentation] Matrix factorization and enumeration of spin curves (2010)
  • 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
• [Presentation] Hodge Theory of Landau-Ginzburg model and its quantization (2010)
  • Author(s): Hiroshi Iritani
  • Organizer: Summer School on mirror symmetry
  • Place of Presentation: KIAS, ソウル,韓国