Study on mirror symmetry and noncommutative Hodge structures

• Project/Area Number: 23654009
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Osaka University
• Principal Investigator: TAKAHASHI ATSUSHI 大阪大学, 理学(系)研究科(研究院), 准教授 (50314290)
• Co-Investigator(Renkei-kenkyūsha): IRITANI Hiroshi 京都大学, 理学研究科, 准教授 (20448400)
• Project Period (FY): 2011 – 2013
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000); Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 代数学 / 幾何学 / 数理物理学 / ミラー対称性

Research Abstract

Homological mirror symmetry is a symmetry which interchanges the role of the symplectic geometry and the complex algebraic geometry. The purpose of this research is a trial to solve one of the most important problems in the theory of homological mirror symmetry.
Assuming a certain formality conjecture for a homotopy calculas algebra associated to a Calabi-Yau dg category, we obtain a primitive form and hence a Frobenius structure on the versal deformation space for the category.

Research Products

• [Presentation] From Calabi-Yau dg categories to Frobenius manifolds via primitive forms : a work in progress (2014)
  • Author(s): Atsushi Takahashi
  • Organizer: 研究集会「Primitive forms and related subjects」
  • Place of Presentation: 東京大学国際高等研究所数物連携宇宙研究機構
  • Year and Date: 2014-02-11
• [Presentation] From Calabi-Yau dg categories to Frobenius manifolds via primitive forms : a work in progress (2013)
  • Author(s): Atsushi Takahashi
  • Organizer: Algebraic geometry seminar
  • Place of Presentation: Leibniz University Hannover (GERMANY)
  • Year and Date: 2013-02-18
• [Presentation] From Calabi-Yau dg categories to Frobenius manifolds via primitive forms : a work in progress (2013)
  • Author(s): Atsushi Takahashi
  • Organizer: UK-Japan MATHEMATICAL FORUM on Algebraic Geometry and Symplectic Geometry
  • Place of Presentation: 慶應義塾大学
  • Year and Date: 2013-01-27
• [Presentation] 原始形式の構成方法について (2012)
  • Author(s): 高橋 篤史
  • Organizer: 研究会「原始形式とラグランジアンフレーアー理論」
  • Place of Presentation: KKR函館
  • Year and Date: 2012-11-21
• [Presentation] Mirror symmetry of orbifold projective lines (2012)
  • Author(s): Atsushi Takahashi
  • Place of Presentation: 神戸大学
  • Year and Date: 2012-02-23
• [Presentation] Mirror symmetry of weighted projective lines (2012)
  • Author(s): Atsushi Takahashi
  • Place of Presentation: 香港科学技術大学
  • Year and Date: 2012-01-14
• [Presentation] Categories of matrix factorizations and mirror symmetry for weighted homogeneous polynomials (2012)
  • Author(s): Atsushi Takahashi
  • Place of Presentation: 香港科学技術大学
  • Year and Date: 2012-01-13
• [Presentation] Mirror Symmetry of orbifold projective lines (2012)
  • Author(s): Atsushi Takahashi
  • Organizer: Workshop on integrable systems and MS(招待講演)
  • Place of Presentation: 神戸大学
• [Presentation] Cat. of m. f. and MS for w. homog. polynomials (2012)
  • Author(s): Atsushi Takahashi
  • Organizer: Hong Kong geometry seminar(招待講演)
  • Place of Presentation: 香港科学技術大学
• [Presentation] Mirror Symmetry of weighted projective lines (2012)
  • Author(s): Atsushi Takahashi
  • Organizer: Hong Kong Geometry Colloquium
  • Place of Presentation: 香港科学技術大学
• [Presentation] From Calabi--Yau dg categories to Frobenius manifolds via primitive forms: a work in progress
  • Author(s): Ａｔｓｕｓｈｉ Ｔａｋａｈａｓｈｉ
  • Organizer: Primitive forms and related subjects
  • Place of Presentation: 東京大学国際高等研究所数物連携宇宙研究機構
  • Invited
• [Presentation] From Calabi--Yau dg categories to Frobenius manifolds via primitive forms: a work in progress
  • Author(s): Atsushi Takahashi
  • Organizer: Algebraic Geometry Semiar
  • Place of Presentation: Leibnitz University Hannover (GERMANY)
  • Invited
• [Presentation] From Calabi--Yau dg categories to Frobenius manifolds via primitive forms: a work in progress
  • Author(s): Atsushi Takahashi
  • Organizer: UK-JAPAN MATHEMATICAL FORUM on Algebraic Geometry and Symplectic Geometry
  • Place of Presentation: 慶應義塾大学
  • Invited
• [Presentation] 原始形式の構成方法について
  • Author(s): Atsushi Takahashi
  • Organizer: 原始形式とラグランジアンフレーアー理論
  • Place of Presentation: KKR函館
• [Book] 弦理論の代数的基礎 (2012)
  • Author(s): 高橋篤史
  • Total Pages: 204
  • Publisher: サイエンス社
• [Book] サイエンス社 (2012)
  • Author(s): 高橋 篤史
  • Total Pages: 204
  • Publisher: 弦理論の代数的基礎
• [Remarks] 下記アドレス(研究集会「Primitive forms and related subjects」の「Slides」というウェブページ)から, 「学会発表①, From Calabi-Yau dg categories to Frobenius manifolds via primitive forms : a work in progress 」のために用いたスライド(Takahashi.pdf)を取得することが可能である.
  • URL: http://indico.ipmu.jp/indico/materialDisplay.py?materialId=slides&confId=30