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Research of non-commutative geometry, singular point, and geometric asymptotics

Research Project

Project/Area Number 22540095
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionKeio University

Principal Investigator

MIYAZAKI Naoya  慶應義塾大学, 経済学部, 教授 (50315826)

Project Period (FY) 2010-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Keywords非可換幾何学 / シンプレクティック幾何学 / 一般複素幾何学 / 量子化 / 指数定理 / フーリエ積分作用素 / quantization / poisson structure / Kaehler structure / noncommutative geometry / poisson geometry / 一般複素幾何 / 一般ケーラー幾何 / Courant algebroid / symplectic geometry / bi-Hermitian structure / 非可換幾何 / 幾何学的漸近解析 / 微分幾何 / 特異点論 / 局所指数定理 / 変形量子化 / Poisson幾何 / symplectic幾何 / asymptoric analysis / index theorem / ディラック作用素 / ポアソン構造 / エータ関数 / 圏
Outline of Final Research Achievements

First, I introduced non-commutative deformation of structure sheaves of schemes, and I cnstructed a concrete example via complex projective spaces. Furthermore, I computed exponential map with respect to a new product. Second, with Hideki Omori, Yoshiaki Maeda, Akira Yoshioka, we studied the ordering problem on a flat space, and convergent problem with respect to a parameter h. Third, with Yasushi Homma, Tatsuya Tate, we sudy eta functions for Dirac operators on 3-manifolds (e.g. Heisenberg manifold, Lenz spaces etc.). Fourth, with Tadashi Taniguchi, we study quantization of super Calabi-Yau twistor spaces endowed with super Poisson structure via Penrose double fibration.

Report

(6 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Annual Research Report
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (9 results)

All 2015 2014 2013 2012 2011 2010

All Journal Article (7 results) (of which Open Access: 1 results,  Acknowledgement Compliant: 1 results,  Peer Reviewed: 2 results) Presentation (2 results)

  • [Journal Article] Quantization of holomorphic Poisson structure -related to generalized Kaehler structure-2014

    • Author(s)
      Naoya Miyazaki
    • Journal Title

      arXiv:math.DG

      Volume: 1403.7709v2 Pages: 1-20

    • Related Report
      2014 Annual Research Report
    • Open Access / Acknowledgement Compliant
  • [Journal Article] Deformation of expressions for elements of an algebra2014

    • Author(s)
      H. Omori, Y. Maeda, N. Miyazaki and A. Yoshioka
    • Journal Title

      Poisson and noncommutative Geometry, MSRI, Cambridge University Publication

      Volume: vol.62 Pages: 171-210

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Quantization of Holomorphic Poisson structure---related to Generalized Kaehler structure---2014

    • Author(s)
      Naoya Miyazaki
    • Journal Title

      arXiv:submit/0945317[math.DG] 30.Mar.2014

      Volume: 094531 Pages: 1-24

    • Related Report
      2013 Annual Research Report
  • [Journal Article] Symbol calculus on a projective space2013

    • Author(s)
      Naoya Miyazaki
    • Journal Title

      arXiv: [math.DG] 31 Mar 2013

      Volume: 1304.0184v1 Pages: 1-11

    • Related Report
      2012 Annual Research Report
  • [Journal Article] Deformation Expression for Elements of Algebra2011

    • Author(s)
      H.Omori, Y.Maeda, N.Miyazaki, A.Yoshioka
    • Journal Title

      Math-archive

      Pages: 1-25

    • Related Report
      2011 Annual Research Report
  • [Journal Article] On non (anti) commutative super twistor spaces2010

    • Author(s)
      T.Taniguchi
    • Journal Title

      International Journal of Geometric Method in Modern Physics

      Volume: Vol.7, No.4 Pages: 655-668

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Remarks on deformation quantization2010

    • Author(s)
      N.Miyazaki
    • Journal Title

      Kyoto University RIMS Kokyuroku (Geometric Mechanics)

      Volume: 1692 Pages: 1-16

    • Related Report
      2010 Annual Research Report
  • [Presentation] On holomorhic Poisson structures on toric projective schemes with polytopes2015

    • Author(s)
      Naoya Miyazaki
    • Organizer
      幾何学と解析学の交錯
    • Place of Presentation
      慶應義塾大学日吉キャンパス来往舎
    • Year and Date
      2015-02-13
    • Related Report
      2014 Annual Research Report
  • [Presentation] Noncommutative structures on affine spaces and projective spaces2012

    • Author(s)
      宮崎直哉
    • Organizer
      International Mathematics Conference "Topology and Analysis on foliations"
    • Place of Presentation
      名古屋大学(招待講演)
    • Year and Date
      2012-03-23
    • Related Report
      2011 Annual Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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