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Moduli theory and Hall algebra

Research Project

Project/Area Number 22840023
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Algebra
Research InstitutionNagoya University

Principal Investigator

NAGAO Kentaro  名古屋大学, 多元数理科学研究科, 助教 (10585574)

Project Period (FY) 2010 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2011: ¥1,495,000 (Direct Cost: ¥1,150,000、Indirect Cost: ¥345,000)
Fiscal Year 2010: ¥1,625,000 (Direct Cost: ¥1,250,000、Indirect Cost: ¥375,000)
Keywordsドナルドソン・トーマス理論 / 壁越え / 団代数 / Donaldson-Thomas理論 / 双曲幾何 / モチーフ的DT理論
Research Abstract

We provide a proof of wall-crossing formula for motivic Donaldson-Thomas theory with its application to computations of generating functions. We also study Donaldson-Thomas theory and cluster algebras associated to punctured surfaces, in particular from the view point of mapping class group action.

Report

(3 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • Research Products

    (30 results)

All 2012 2011 2010

All Journal Article (6 results) (of which Peer Reviewed: 6 results) Presentation (24 results)

  • [Journal Article] Derived categories of small toric Calabi-Yau 3-folds and counting invariants2012

    • Author(s)
      K. Nagao
    • Journal Title

      The Quarterly Journal of Mathematics

      Volume: 63 Issue: 4 Pages: 965-1007

    • DOI

      10.1093/qmath/har025

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Motivic Donaldson-Thomas invariants of the conifold and the refined topological vertex2012

    • Author(s)
      Andrew Morrison, Sergey Mozgovoy, Kentaro Nagao, Balazs Szendroi
    • Journal Title

      Advances in Mathematics

      Volume: 230(掲載確定) Issue: 4-6 Pages: 2065-2093

    • DOI

      10.1016/j.aim.2012.03.030

    • Related Report
      2011 Annual Research Report 2011 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Counting invariant of perverse coherent sheaves and its wall-corssing2011

    • Author(s)
      K.Nagao, H.Nakajima
    • Journal Title

      Int.Math.Res.Notices

      Volume: 7(掲載確定) Pages: 3885-3938

    • DOI

      10.1093/imrn/rnq195

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Refinde open noncommutative Donaldson-Thomas invariants for small crepant resolution2011

    • Author(s)
      K.Nagao
    • Journal Title

      Pacific Journal of Mathematics

      Volume: 254(掲載確定) Issue: 1 Pages: 173-209

    • DOI

      10.2140/pjm.2011.254.173

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Non-commutative Donaldson-Thomas invariants and vetex operators2011

    • Author(s)
      K.Nagao
    • Journal Title

      Geometry & Topology

      Volume: 15(掲載確定) Issue: 3 Pages: 1509-1543

    • DOI

      10.2140/gt.2011.15.1509

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Non-commutative topological vertex and wall crossing phenomena2010

    • Author(s)
      Kentaro Nagao, Masahito Yamazaki
    • Journal Title

      Adv. Theor. Math. Phys

      Volume: 4 Pages: 1147-1181

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Presentation] Hyperbolic 3-manifolds and cluster algebras2012

    • Author(s)
      Kentaro Nagao
    • Organizer
      第7回代数・解析・幾何学セミナー
    • Place of Presentation
      鹿児島大学(招待講演)
    • Year and Date
      2012-02-16
    • Related Report
      2011 Annual Research Report
  • [Presentation] Refined topological vertex and matrix counting2011

    • Organizer
      組合せ論的表現論の拡がり
    • Place of Presentation
      RIMS
    • Year and Date
      2011-10-13
    • Related Report
      2011 Final Research Report
  • [Presentation] Refined topological vertex and matrix counting2011

    • Author(s)
      Kentaro Nagao
    • Organizer
      組合せ論的表現論の拡がり
    • Place of Presentation
      RIMS,京都大学(招待講演)
    • Year and Date
      2011-10-13
    • Related Report
      2011 Annual Research Report
  • [Presentation] Motivic Hall algebras2011

    • Organizer
      Cluster algebras, representation theory, and Poisson geometry
    • Place of Presentation
      BIRS
    • Year and Date
      2011-09-05
    • Related Report
      2011 Final Research Report
  • [Presentation] Motivic Hall algebras2011

    • Author(s)
      Kentaro Nagao
    • Organizer
      Cluster algebras, representation theory, and Poisson geometry
    • Place of Presentation
      BIRS, Banff(招待講演)
    • Year and Date
      2011-09-05
    • Related Report
      2011 Annual Research Report
  • [Presentation] Motivic Hall algebra2011

    • Author(s)
      Kentaro Nagao
    • Organizer
      Cluster algebras, representation theory, and Poissongeometry
    • Place of Presentation
      BIRS, Banff
    • Year and Date
      2011-09-05
    • Related Report
      2010 Annual Research Report
  • [Presentation] Motivic Donaldson-Thomas invariants and wall-crossing2011

    • Organizer
      Workshop on Derived Categories
    • Place of Presentation
      Newton Institute, Cambridge
    • Year and Date
      2011-04-16
    • Related Report
      2011 Final Research Report
  • [Presentation] Motivic Donaldson-Thomas invariants and wall-crossing2011

    • Author(s)
      Kentaro Nagao
    • Organizer
      Workshop on Derived Categories
    • Place of Presentation
      Newton Institute, Cambridge(招待講演)
    • Year and Date
      2011-04-16
    • Related Report
      2011 Annual Research Report
  • [Presentation] Refined topological vertex via motivicDonaldson-Thomas theory2011

    • Organizer
      Mini-workshop on Moduli of Instantons
    • Place of Presentation
      名古屋大学
    • Year and Date
      2011-03-29
    • Related Report
      2011 Final Research Report
  • [Presentation] Motivic Donaldson-Thomas invariants and wall-crossing2011

    • Organizer
      WORKSHOP ON NON-COMMUTATIVE GEOMETRY AND THE McKAY CORRESPONDENCE
    • Place of Presentation
      名古屋大学
    • Year and Date
      2011-03-16
    • Related Report
      2011 Final Research Report
  • [Presentation] Donaldson-Thomas theory and clusteralgebras2011

    • Organizer
      Representation Theory of Quivers and Finite Dimensional Algebras
    • Place of Presentation
      MFO, Oberwolfach
    • Year and Date
      2011-02-23
    • Related Report
      2011 Final Research Report
  • [Presentation] Donaldson-Thomas theory for triangulated surfaces2011

    • Organizer
      Derived Categories 2011 Tokyo
    • Place of Presentation
      東京大学
    • Year and Date
      2011-01-27
    • Related Report
      2011 Final Research Report
  • [Presentation] Donaldson-Thomas理論と壁越え公式量子可積分系の新展開2010

    • Place of Presentation
      富士教育研修所
    • Year and Date
      2010-12-21
    • Related Report
      2011 Final Research Report
  • [Presentation] Donaldson-Thomas theory for triangulated surfaces2010

    • Organizer
      多元環セミナー
    • Place of Presentation
      東京大学
    • Year and Date
      2010-12-09
    • Related Report
      2011 Final Research Report
  • [Presentation] Donaldson-Thomas theory and clusteralgebras2010

    • Organizer
      代数幾何シンポジウム
    • Place of Presentation
      城崎
    • Year and Date
      2010-10-26
    • Related Report
      2011 Final Research Report
  • [Presentation] クラスター変換とその周辺重力・幾何・素粒子2010

    • Place of Presentation
      大阪市立大学
    • Year and Date
      2010-09-29
    • Related Report
      2011 Final Research Report
  • [Presentation] Cluster transformations and their quantization2010

    • Organizer
      日中幾何学研究会
    • Place of Presentation
      西安
    • Year and Date
      2010-09-07
    • Related Report
      2011 Final Research Report
  • [Presentation] Donaldson-Thomas theory and cluster algebras Representation2010

    • Organizer
      Theory of Algebraic Groups and quantum groups
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-08-04
    • Related Report
      2011 Final Research Report
  • [Presentation] Non-commutative Donaldson-Thomas invariants and vetex operators2010

    • Organizer
      5-th Pacific Rim Complex and Symplectic Geometry Conference 2010
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-07-27
    • Related Report
      2011 Final Research Report
  • [Presentation] Donaldson-Thomas theory and cluster algebras2010

    • Organizer
      DMMセミナー
    • Place of Presentation
      IPMU
    • Year and Date
      2010-06-28
    • Related Report
      2011 Final Research Report
  • [Presentation] Instant on counting with adjoint matters viaaffine Lie algebras量子可積分系の展開2010

    • Place of Presentation
      RIMS
    • Year and Date
      2010-06-16
    • Related Report
      2011 Final Research Report
  • [Presentation] Donaldson-Thomas theory and cluster algebras2010

    • Organizer
      第13回代数群と量子群の表現論研究集会
    • Place of Presentation
      すいとぴあ江南
    • Year and Date
      2010-06-06
    • Related Report
      2011 Final Research Report
  • [Presentation] Instant on counting with adjoint matters viaaffine Lie algebras2010

    • Organizer
      幾何学セミナー
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-04-27
    • Related Report
      2011 Final Research Report
  • [Presentation] Donaldson-Thomas theory and cluster algebras2010

    • Organizer
      代数幾何セミナー
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-04-19
    • Related Report
      2011 Final Research Report

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Published: 2010-08-27   Modified: 2016-04-21  

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