Moduli theory and Hall algebra

• Project/Area Number: 22840023
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Nagoya 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: ¥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.

Research Products

• [Journal Article] Derived categories of small toric Calabi-Yau 3-folds and counting invariants (2012)
  • Author(s): K. Nagao
  • Journal Title: The Quarterly Journal of Mathematics Volume: 63 Issue: 4 Pages: 965-1007
  • DOI: 10.1093/qmath/har025
  • Peer Reviewed
• [Journal Article] Motivic Donaldson-Thomas invariants of the conifold and the refined topological vertex (2012)
  • 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
  • Peer Reviewed
• [Journal Article] Counting invariant of perverse coherent sheaves and its wall-corssing (2011)
  • 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
  • Peer Reviewed
• [Journal Article] Refinde open noncommutative Donaldson-Thomas invariants for small crepant resolution (2011)
  • 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
  • Peer Reviewed
• [Journal Article] Non-commutative Donaldson-Thomas invariants and vetex operators (2011)
  • 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
  • Peer Reviewed
• [Journal Article] Non-commutative topological vertex and wall crossing phenomena (2010)
  • Author(s): Kentaro Nagao, Masahito Yamazaki
  • Journal Title: Adv. Theor. Math. Phys Volume: 4 Pages: 1147-1181
  • Peer Reviewed
• [Presentation] Hyperbolic 3-manifolds and cluster algebras (2012)
  • 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
• [Presentation] Refined topological vertex and matrix counting (2011)
  • Organizer: 組合せ論的表現論の拡がり
  • Place of Presentation: RIMS
  • Year and Date: 2011-10-13
• [Presentation] Refined topological vertex and matrix counting (2011)
  • 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
• [Presentation] Motivic Hall algebras (2011)
  • Organizer: Cluster algebras, representation theory, and Poisson geometry
  • Place of Presentation: BIRS
  • Year and Date: 2011-09-05
• [Presentation] Motivic Hall algebras (2011)
  • 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
• [Presentation] Motivic Hall algebra (2011)
  • Author(s): Kentaro Nagao
  • Organizer: Cluster algebras, representation theory, and Poissongeometry
  • Place of Presentation: BIRS, Banff
  • Year and Date: 2011-09-05
• [Presentation] Motivic Donaldson-Thomas invariants and wall-crossing (2011)
  • Organizer: Workshop on Derived Categories
  • Place of Presentation: Newton Institute, Cambridge
  • Year and Date: 2011-04-16
• [Presentation] Motivic Donaldson-Thomas invariants and wall-crossing (2011)
  • 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
• [Presentation] Refined topological vertex via motivicDonaldson-Thomas theory (2011)
  • Organizer: Mini-workshop on Moduli of Instantons
  • Place of Presentation: 名古屋大学
  • Year and Date: 2011-03-29
• [Presentation] Motivic Donaldson-Thomas invariants and wall-crossing (2011)
  • Organizer: WORKSHOP ON NON-COMMUTATIVE GEOMETRY AND THE McKAY CORRESPONDENCE
  • Place of Presentation: 名古屋大学
  • Year and Date: 2011-03-16
• [Presentation] Donaldson-Thomas theory and clusteralgebras (2011)
  • Organizer: Representation Theory of Quivers and Finite Dimensional Algebras
  • Place of Presentation: MFO, Oberwolfach
  • Year and Date: 2011-02-23
• [Presentation] Donaldson-Thomas theory for triangulated surfaces (2011)
  • Organizer: Derived Categories 2011 Tokyo
  • Place of Presentation: 東京大学
  • Year and Date: 2011-01-27
• [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
• [Presentation] Donaldson-Thomas theory for triangulated surfaces (2010)
  • Organizer: 多元環セミナー
  • Place of Presentation: 東京大学
  • Year and Date: 2010-12-09
• [Presentation] Donaldson-Thomas theory and clusteralgebras (2010)
  • Organizer: 代数幾何シンポジウム
  • Place of Presentation: 城崎
  • Year and Date: 2010-10-26
• [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
• [Presentation] Cluster transformations and their quantization (2010)
  • Organizer: 日中幾何学研究会
  • Place of Presentation: 西安
  • Year and Date: 2010-09-07
• [Presentation] Donaldson-Thomas theory and cluster algebras Representation (2010)
  • Organizer: Theory of Algebraic Groups and quantum groups
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-08-04
• [Presentation] Non-commutative Donaldson-Thomas invariants and vetex operators (2010)
  • 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
• [Presentation] Donaldson-Thomas theory and cluster algebras (2010)
  • Organizer: DMMセミナー
  • Place of Presentation: IPMU
  • Year and Date: 2010-06-28
• [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
• [Presentation] Donaldson-Thomas theory and cluster algebras (2010)
  • 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
• [Presentation] Instant on counting with adjoint matters viaaffine Lie algebras (2010)
  • Organizer: 幾何学セミナー
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-04-27
• [Presentation] Donaldson-Thomas theory and cluster algebras (2010)
  • Organizer: 代数幾何セミナー
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-04-19