Mirror symmetry

• Project/Area Number: 24740043
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: The University of Tokyo (2015); Osaka University (2012-2014)
• Principal Investigator: Ueda Kazushi 東京大学, 数理科学研究科, 准教授 (60432465)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: ミラー対称性 / シンプレクティック幾何学 / 代数幾何学 / Lagrangeトーラスファイブレーション / 深谷圏 / K3曲面 / ダイマー模型

Outline of Final Research Achievements

With Kwokwai Chan and Daniel Pomerleano, we have studied homological mirror symmetry for some toric Calabi-Yau manifolds. With Yuichi Nohara, we have studied integrable systems on Grassmannians and their Floer-theoretic properties. With Susumu Tanabe, we have studied the relation between monodromy of twisted I-functions of Calabi-Yau hypersurfaces in weighted projective spaces and autoequivalences of derived categories.

Research Products

• [Int'l Joint Research] 香港中文大学(香港)
• [Int'l Joint Research] Imperial College London(英国)
• [Journal Article] Lagrangian torus fibrations and homological mirror symmetry for the conifold (2016)
  • Author(s): Kwokwai Chan, Daniel Pomerleano and Kazushi Ueda
  • Journal Title: Communications in Mathematical Physics Volume: 341 Issue: 1 Pages: 135-178
  • DOI: 10.1007/s00220-015-2477-7
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Goldman systems and bending systems (2015)
  • Author(s): Y. Nohara and K. Ueda
  • Journal Title: Canad. J. Math. Volume: 67 Issue: 5 Pages: 1109-1143
  • DOI: 10.4153/cjm-2015-004-2
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] The special McKay correspondence and exceptional collections (2015)
  • Author(s): Akira Ishii and Kazushi Ueda
  • Journal Title: Tohoku Math. J. Volume: 67 Issue: 4 Pages: 585-609
  • DOI: 10.2748/tmj/1450798075
  • NAID: 130007961945
  • Peer Reviewed
• [Journal Article] Dimer models and the special McKay correspondence (2015)
  • Author(s): Akira Ishii and Kazushi Ueda
  • Journal Title: Geometry and Topology Volume: 19 Issue: 6 Pages: 3405-3466
  • DOI: 10.2140/gt.2015.19.3405
  • Peer Reviewed / Open Access
• [Journal Article] A note on bimodal singularities and mirror symmetry (2015)
  • Author(s): Makiko Mase, Kazushi Ueda
  • Journal Title: Manuscripta Mathematica Volume: 146 Issue: 1-2 Pages: 153-177
  • DOI: 10.1007/s00229-014-0693-7
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Weighted projective lines as fine moduli spaces of quiver representations (2015)
  • Author(s): Tarig Abdelgadir, Kazushi Ueda
  • Journal Title: Communications in Algebra Volume: 43 Issue: 2 Pages: 636-649
  • DOI: 10.1080/00927872.2013.842245
  • Peer Reviewed
• [Journal Article] Invariants of hypergeometric groups for Calabi-Yau complete intersections in weighted projective spaces (2013)
  • Author(s): Susumu Tanabe, Kazushi Ueda
  • Journal Title: Communications in Number Theory and Physics Volume: Volume 7, Number 2 Issue: 2 Pages: 327-359
  • DOI: 10.4310/cntp.2013.v7.n2.a4
  • Peer Reviewed
• [Journal Article] Dual torus fibrations and homological mirror symmetry for An-singularities (2013)
  • Author(s): Kwokwai Chan, Kazushi Ueda
  • Journal Title: Communications in Number Theory and Physics Volume: Volume 7, Number 2 Issue: 2 Pages: 361-396
  • DOI: 10.4310/cntp.2013.v7.n2.a5
  • Peer Reviewed
• [Journal Article] Homological mirror symmetry for the quintic 3-fold (2012)
  • Author(s): Yuichi Nohara, Kazushi Ueda
  • Journal Title: Geometry & Topology Volume: 16 Issue: 4 Pages: 1967-2001
  • DOI: 10.2140/gt.2012.16.1967
  • Peer Reviewed
• [Presentation] 箙の関係式のモジュライ (2015)
  • Author(s): 植田一石
  • Organizer: 日本数学会年会特別講演
  • Place of Presentation: 明治大学
  • Year and Date: 2015-03-21
  • Invited
• [Remarks]
  • URL: http://www.ms.u-tokyo.ac.jp/~kazushi/index.html
• [Remarks] Kazushi Ueda
  • URL: http://www.math.sci.osaka-u.ac.jp/~kazushi/
• [Remarks] Researchmap
  • URL: http://researchmap.jp/uedakazushi/