• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to project page

2010 Fiscal Year Self-evaluation Report

Homological Mirror Symmetry of Isolated Hypersurface Singularities With Group Actions

Research Project

  • PDF
Project/Area Number 20684003
Research Category

Grant-in-Aid for Young Scientists (A)

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionOsaka University

Principal Investigator

TAKAHASHI Atsushi  Osaka University, 大学院・理学研究科, 准教授 (50314290)

Project Period (FY) 2008 – 2011
Keywords幾何学 / 代数学 / 数理物理学 / ミラー対称性
Research Abstract

ミラー対称性とは,リーマン面から多様体への正則写像の数え上げに対応するA模型と複素多様体の変形理論に対応するB模型という,2つの位相的弦理論の等価性のことである.ミラー対称性は多様体の定性的および定量的な性質に関するさまざまな予想を与え,これまで個別に研究されてきた数学を結び付けるので極めて興味深い.
本研究の目的は,離散群・特異点・ルート系・リー環・有限次元代数の間にある不思議な関係を解明するため,ホモロジー的ミラー対称性の観点から,群作用付孤立超曲面特異点に対して,「群作用付き行列因子化の圏およびその安定性条件の空間の構造解明」および「ミルナーファイバーの消滅ラグランジアン輪体の行列因子化による構成」という課題を解決することである.

  • Research Products

    (10 results)

All 2011 2010 2009 2008 Other

All Journal Article (4 results) (of which Peer Reviewed: 4 results) Presentation (5 results) Book (1 results)

  • [Journal Article] Weighted projective lines associated to regular systems of weights of dual type2010

    • Author(s)
      A.Takahashi
    • Journal Title

      Advanced Studies in Pure Mathematics 59

      Pages: 371-388

    • Peer Reviewed
  • [Journal Article] Categories of Graded Matrix Factorizations for Regular Systems of Weights with e=-12009

    • Author(s)
      H.Kajiura, K.Saito , A.Takahashi
    • Journal Title

      Advances in Mathematics 220

      Pages: 1602-1654

    • Peer Reviewed
  • [Journal Article] From Primitive Forms to Frobenius Manifolds2008

    • Author(s)
      K.Saito , A.Takahashi
    • Journal Title

      Proceedings of Symposia in Pure Mathematics 78

      Pages: 31-48

    • Peer Reviewed
  • [Journal Article] Strange duality of weighted homogeneous polynomials

    • Author(s)
      W.Ebeling , A.Takahashi
    • Journal Title

      to appear in Compositio Math 2011

    • Peer Reviewed
  • [Presentation] Mirror symmetry for weighted homogeneous polynomials2011

    • Author(s)
      A.Takahashi
    • Organizer
      Derived Category Tbkyo 2011
    • Place of Presentation
      東京大学
    • Year and Date
      2011-01-28
  • [Presentation] Strange duality of weighted homogeneous polynomials2010

    • Author(s)
      A.Takahashi
    • Organizer
      Workshop on Geometry and Physics of Landau-Ginzburg model
    • Place of Presentation
      Institut Fourier (Grenoble, France)
    • Year and Date
      2010-06-01
  • [Presentation] Triangulated categories for isolated hvpersurface singularitie and mirror symmetry2009

    • Author(s)
      A.Takahashi
    • Organizer
      可換環論シンポジウム
    • Place of Presentation
      ホテルアウィーナ大阪
    • Year and Date
      2009-11-27
  • [Presentation] Homological Mirror Symmetry for Cusp Singularities2009

    • Author(s)
      A.Takahashi
    • Organizer
      Workshop on Homological Mirror Symmetry and Related Topics
    • Place of Presentation
      University of Miami (Miami, USA)
    • Year and Date
      2009-01-23
  • [Presentation] Homological Mirror Symmetry for Isolated Hypersurface Similarities2008

    • Author(s)
      A.Takahashi
    • Organizer
      Workshop on Homological Mirror Symmetry and Symplectic Geometry
    • Place of Presentation
      MIT (Cambridge.USA)
    • Year and Date
      2008-05-27
  • [Book] ミラー対称性入門2009

    • Author(s)
      江口徹, 深谷賢治, 高橋篤史, 並河良典, 細野忍, 今野宏, マーティンゲスト, 藤隆史, 中島啓
    • Total Pages
      33-45,60-70,137-148
    • Publisher
      日本評論社

URL: 

Published: 2012-03-09   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi