Study on derived categories

• Project/Area Number: 21840030
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Kyoto University
• Principal Investigator: OKADA So Kyoto University, 数理解析研究所, 特定研究員(グローバルCOE) (50547015)
• Project Period (FY): 2009 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥2,223,000 (Direct Cost: ¥1,710,000、Indirect Cost: ¥513,000); Fiscal Year 2010: ¥1,066,000 (Direct Cost: ¥820,000、Indirect Cost: ¥246,000); Fiscal Year 2009: ¥1,157,000 (Direct Cost: ¥890,000、Indirect Cost: ¥267,000)
• Keywords: ホモロジカルミラー対称性 / 導来圏 / 安定性条件 / 保型形式

Research Abstract

We study derived categories, using stability conditions. In particular, we deal with homological mirror symmetry for Fermat polynomials. From studies on string theory, Kontsevich proposes the symmetry as equivalence of derived categories of coherent sheaves and Lagrangians. We give equivalence of derived categories of equivariant coherent sheaves and Fukaya-Seidel categories, and discuss categorical Pontryagin dualities. We give quiver descriptions of Fukaya-Seidel categories and discuss stability conditions. We study modularity, counting rigid semistable objects.

Research Products

• [Journal Article] Joyce invariants for K3 surfaces and mock theta functions, Commun. (2009)
  • Author(s): Anton Mellit、岡田崇
  • Journal Title: Number Theory Phys. Vol 3 Num 4 Pages: 655-676
  • Peer Reviewed
• [Journal Article] Joyce invariants for K3 surfaces and mock theta functions (2009)
  • Author(s): Anton Mellit, So Okada
  • Journal Title: Communications in Number Theory and Physics 3 Pages: 655-676
  • Peer Reviewed
• [Presentation] Rigid semistable objects and kinds of modular forms, School and Conference on Modular Forms and Mock Modular Forms and their Applications in Arithmetic, Geometry and Physics (2011)
  • Author(s): 岡田崇
  • Organizer: the Abdus Salam International Centre for Theoretical Physics
  • Place of Presentation: イタリア(トリエステ)
  • Year and Date: 2011-03-15
• [Presentation] Rigid semistable objects and kinds of modular forms (2011)
  • Author(s): 岡田崇
  • Organizer: School and Conference on Modular Forms and Mock Modular Forms and their Applications in Arithmetic, Geometry and Physics
  • Place of Presentation: Abdus Salam International Centre for Theoretical Physics, Trieste, Italy(招待講演)
  • Year and Date: 2011-03-15
• [Presentation] Homological mirror symmetry of Fermat polynomials (2010)
  • Author(s): 岡田崇
  • Organizer: XIV International Conference on Representations of Algebras
  • Place of Presentation: 国立オリンピック記念青少年総合センター(代々木)
  • Year and Date: 2010-08-15
• [Presentation] Homological mirror symmetry of Fermat polynomials (2010)
  • Author(s): 岡田崇
  • Organizer: XIV International Conference on Representations of Algebras
  • Place of Presentation: National Olympic Memorial Youth Center(東京)
  • Year and Date: 2010-08-15
• [Presentation] Homological Mirror symmetry of Fermat polynomials and related topics (2010)
  • Author(s): 岡田崇
  • Organizer: Workshop on Period Integrals and Motives
  • Place of Presentation: 東京大学
  • Year and Date: 2010-02-17
• [Presentation] Homological mirror symmetry of Fermat polynomials and some related topics (2010)
  • Author(s): 岡田崇
  • Organizer: 微分トポロジーセミナー
  • Place of Presentation: 京都大学
  • Year and Date: 2010-01-26
• [Presentation] Homological mirror symmetry of Fermat polynomials and some related topics (2010)
  • Author(s): 岡田崇
  • Organizer: 代数幾何セミナー
  • Place of Presentation: 京都大学
  • Year and Date: 2010-01-15
• [Presentation] K3曲面のジョイス不変量とモックテータ関数 (2009)
  • Author(s): 岡田崇
  • Organizer: 近畿大学数学講演会
  • Place of Presentation: 近畿大学
  • Year and Date: 2009-10-22
• [Remarks] ホームページ等
  • URL: http://www.kurims.kyoto-u.ac.jp/~okada/
• [Remarks]
  • URL: http://www.kurims.kyoto-u.ac.jp/~okada/
• [Remarks]
  • URL: http://www.kurims.kyoto-u.ac.jp/~okada/