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2009 Fiscal Year Final Research Report

Development from Poisson Geometry to Noncommutative Differential Geometry via Integrating of Geometry and Physics

Research Project

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Project/Area Number 18204006
Research Category

Grant-in-Aid for Scientific Research (A)

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

Principal Investigator

MAEDA Yoshiaki  Keio University, 理工学部, 教授 (40101076)

Co-Investigator(Kenkyū-buntansha) MORIYOSHI Hitoshi  名古屋大学, 大学院・多元数理科学研究科, 教授 (00239708)
SHIMOMURA Shun  慶應義塾大学, 理工学部, 教授 (00154328)
ISHII Ippei  慶應義塾大学, 理工学部, 准教授 (90051929)
KAMETANI Yukio  慶應義塾大学, 理工学部, 准教授 (70253581)
MIYAZAKI Takuya  慶應義塾大学, 理工学部, 准教授 (10301409)
TAMURA Yozo  慶應義塾大学, 理工学部, 准教授 (50171905)
IKEDA Kaoru  慶應義塾大学, 理工学部, 教授 (40232178)
KURIHARA Masato  慶應義塾大学, 理工学部, 教授 (40211221)
OHTA Katsuhiro  慶應義塾大学, 理工学部, 教授 (40213722)
ATSUJI Atsushi  慶應義塾大学, 経済学部, 教授 (00221044)
TOSE Nobuyuki  慶應義塾大学, 経済学部, 教授 (00183492)
OMORI Hideki  慶應義塾大学, 理工学部, 訪問教授 (20087018)
Co-Investigator(Renkei-kenkyūsha) FUKAYA Kenji  京都大学, 理学研究科, 教授 (30165261)
TATE Tatsuya  名古屋大学, 多元数理科学研究科, 准教授 (00317299)
WATAMURA Satoshi  東北大学, 理学研究科, 准教授 (00201252)
KONNO Hiroshi  東京大学, 数理科学研究科, 准教授 (20254138)
KOHNO Toshitake  東京大学, 数理科学研究科, 教授 (80144111)
GUEST Martin  首都大学, 東京・理工学研究科, 教授 (10295470)
MIKAMI Kentaro  秋田大学, 工学資源学部, 教授 (70006592)
ONO Kaoru  北海道大学, 理学研究科, 教授 (20204232)
YAMAGUCHI Keizo  北海道大学, 理学研究科, 教授 (00113639)
MITSUMATSU Yoshihiko  中央大学, 理工学部, 教授 (70190725)
MIYAOKA Reiko  東北大学, 理学研究科, 教授 (70108182)
FUTAKI Akitp  東京工業大学, 理工学研究科, 教授 (90143247)
MATSUO Yuyaka  東京大学, 理学研究科, 准教授 (50202320)
MIZUTANI Tadayoshi  埼玉大学, 理工学研究科, 教授 (20080492)
OHTA Hiroshi  名古屋大学, 多元数理科学研究科, 教授 (50223839)
FUKAYA Kenji  京都大学, 理学研究科, 教授 (30165261)
Project Period (FY) 2006 – 2009
Keywords非可換幾何学 / 変形量子化 / ジャーブ / 超弦理論 / 量子化問題
Research Abstract

We obtain many results through the cooperation researches between noncommutative geometry and theoretical physics, namely for proposals on noncommutative gauge theory, p-adic Iwasawa theory, algebraic integrability for quantum Toda lattice, Bernstein measure, string theory and generalized complex structure, quantum cohomology and Frobenius manifolds, symplectic topology and contact topology. The results has been presented by the international conferences and published as monographs in 「Noncommutative Geometry and Physics」, 「Advaned Studies in Pure Mathematics 55」, 「Translations of Mathematical Monographs, 237」 and also published by individual researchers.

  • Research Products

    (34 results)

All 2010 2009 2008 2007 2006

All Journal Article (28 results) (of which Peer Reviewed: 28 results) Presentation (2 results) Book (4 results)

  • [Journal Article] Lagrangian Floer theory on compact toric manifolds. I.2010

    • Author(s)
      Fukaya, Kenji; Oh, Yong-Geun; Ohta, Hiroshi; Ono, Kaoru
    • Journal Title

      Duke Math. J. 151, no.1

      Pages: 23-174

    • Peer Reviewed
  • [Journal Article] 3-trees with few vertices of degree 3 in circuit graphs.2009

    • Author(s)
      Nakamoto, Atsuhiro; Oda, Yoshiaki; Ota, Katsuhiro
    • Journal Title

      Discrete Math. 309, no.4

      Pages: 666-672

    • Peer Reviewed
  • [Journal Article] Meromorphic solutions of difference Painleve equations.2009

    • Author(s)
      Shimomura, Shun
    • Journal Title

      J. Phys. A 42, no.31

      Pages: 315213

    • Peer Reviewed
  • [Journal Article] Thealgebraic integrability of the quantum Toda lattice and the Radon transform.2009

    • Author(s)
      Ikeda, Kaoru
    • Journal Title

      J. Fourier Anal. Appl. 15, no.1

      Pages: 80-100

    • Peer Reviewed
  • [Journal Article] Canonical models of filtered A∞-algebras and Morse complexes.2009

    • Author(s)
      Fukaya, Kenji; Oh, Yong-Geun; Ohta, Hiroshi; Ono, Kaoru
    • Journal Title

      New perspectives and challenges in symplectic field theory, CRM Proc. Lecture Notes(Amer. Math. Soc.) 49

      Pages: 201-227

    • Peer Reviewed
  • [Journal Article] A new nonformal noncommutative calculus: associativity and finite part regularization.2008

    • Author(s)
      Omori, Hideki; Maeda, Yoshiaki; Miyazaki, Naoya; Yoshioka, Akira
    • Journal Title

      Asterisque No.321

      Pages: 267-297

    • Peer Reviewed
  • [Journal Article] Noncommutative deformation of instantons.2008

    • Author(s)
      Maeda, Yoshiaki; Sako, Akifumi
    • Journal Title

      J. Geom. Phys. 58, no.12

      Pages: 1784-1791

    • Peer Reviewed
  • [Journal Article] Are vortex numbers preserved?2008

    • Author(s)
      Maeda, Yoshiaki; Sako Akifumi
    • Journal Title

      J. Geom. Phys. 58, no.8

      Pages: 967-978

    • Peer Reviewed
  • [Journal Article] Stickelberger elements, Fitting ideals of class groups of CM-fields, and dualisation.2008

    • Author(s)
      Greither, Cornelius; Kurihara, Masato
    • Journal Title

      Math. Z. 260, no.4

      Pages: 905-930

    • Peer Reviewed
  • [Journal Article] On 2-factors in r-connected( K1, k, P4)-free graphs.2008

    • Author(s)
      Egawa, Yoshimi; Fujisawa, Jun; Fujita, Shinya; Ota Katsuhiro
    • Journal Title

      Tokyo J. Math. 31, no.2

      Pages: 415-420

    • Peer Reviewed
  • [Journal Article] Forbidden subgraphs and the existence of paths and cycles passing through specified vertices.2008

    • Author(s)
      Fujisawa, Jun; Ota, Katsuhiro; Sugiyama, Takeshi; Tsugaki Masao
    • Journal Title

      Discrete Math. 308

      Pages: 6111-6114

    • Peer Reviewed
  • [Journal Article] K1, 3-factors in graphs.2008

    • Author(s)
      Egawa, Yoshimi; Fujita, Shinya; Ota, Katsuhiro
    • Journal Title

      Discrete Math 308

      Pages: 5965-5973

    • Peer Reviewed
  • [Journal Article] A second main theorem of Nevanlinna theory for meromorphic functions on complex submanifolds in Cn.2008

    • Author(s)
      Atsuji, Atsushi
    • Journal Title

      Potential Anal 29,no.2

      Pages: 119-138

    • Peer Reviewed
  • [Journal Article] Equi-distribution of values for the third and the fifth Painleve transcendents.2008

    • Author(s)
      Shimomura, Shun
    • Journal Title

      Nagoya Math. J 192

      Pages: 89-109

    • Peer Reviewed
  • [Journal Article] The monoidal transformation by Painleve divisor and resolution of the poles of the Toda lattice.2008

    • Author(s)
      Ikeda, Kaoru
    • Journal Title

      J. Math. Pures Appl (9)90,no.4

      Pages: 329-337

    • Peer Reviewed
  • [Journal Article] On a formula on the potential operators of absorbing Levy processes in the half space.2008

    • Author(s)
      Tamura, Yozo; Tanaka, Hiroshi
    • Journal Title

      Stochastic Process Appl. 118,no.2

      Pages: 199-212

    • Peer Reviewed
  • [Journal Article] Bernstein measures on convex polytopes. Spectral analysis in geometry and number theory2008

    • Author(s)
      Tate, Tatsuya
    • Journal Title

      Contemp. Math. 484

      Pages: 295-319

    • Peer Reviewed
  • [Journal Article] Expressions of algebra elements and transcendental, Noncommutative calculus.2007

    • Author(s)
      Omori, Hideki; Maeda, Yoshiaki; Miyazaki, Naoya; Yoshioka, Akira
    • Journal Title

      Noncommutative geometry and physics

      Pages: 3-30

    • Peer Reviewed
  • [Journal Article] String theory and deformation quantization.2007

    • Author(s)
      Maeda, Yoshiaki; Kajiura, Hiroshige
    • Journal Title

      Sugaku Expositions 20,no.2

      Pages: 191-214

    • Peer Reviewed
  • [Journal Article] Non-formal deformation quantization of Frechet-Poisson algebras: the Heisenberg and Lie algebra case. field theory2007

    • Author(s)
      Omori, Hideki; Maeda, Yoshiaki; Miyazaki, Naoya; Yoshioka, Akira
    • Journal Title

      Contemp. Math. 434

      Pages: 99-123

    • Peer Reviewed
  • [Journal Article] Orderings and non-formal deformation quantization.2007

    • Author(s)
      Omori, Hideki; Maeda, Yoshiaki; Miyazaki, Naoya; Yoshioka, Akira
    • Journal Title

      Lett. Math. Phys 82,no.2-3

      Pages: 153-175

    • Peer Reviewed
  • [Journal Article] Universal deformation formulae, symplectic Lie groups and symmetric spaces.2007

    • Author(s)
      Bieliavsky, Pierre; Bonneau, Philippe; Maeda, Yoshiaki
    • Journal Title

      Pacific J. Math 230,no.1

      Pages: 41-57

    • Peer Reviewed
  • [Journal Article] Geometric objects in an approach to quantum geometry. From geometry to quantum mechanics2007

    • Author(s)
      Omori, Hideki; Maeda, Yoshiaki; Miyazaki, Naoya; Yoshioka, Akira
    • Journal Title

      Progr. Math. 252

      Pages: 303-324

    • Peer Reviewed
  • [Journal Article] A secondary invariant of foliated spaces and type III_\lambda von Neumann algebras2007

    • Author(s)
      Moriyoshi, Hitoshi
    • Journal Title

      Progr. Math. 252

      Pages: 277-286

    • Peer Reviewed
  • [Journal Article] Two p-adic L-functions and rational points on elliptic curves with supersingular reduction.2007

    • Author(s)
      Kurihara, Masato; Pollack, Robert
    • Journal Title

      L-functions and Galois representations, London Math. Soc. Lecture Note Ser. 320

      Pages: 300-332

    • Peer Reviewed
  • [Journal Article] The Chvatal-Erdos condition and 2-factors with a specified number of components.2007

    • Author(s)
      Chen, Guantao; Gould, Ronald J. ; Kawarabayashi, Ken-ichi; Ota, Katsuhiro; Saito, Akira; Schiermeyer, Ingo
    • Journal Title

      Discuss. Math. Graph Theory 27,no.3

      Pages: 401-407

    • Peer Reviewed
  • [Journal Article] On the growth of Selmer groups of an elliptic curve with supersingular reduction in the Z2-extension of Q.2006

    • Author(s)
      Kurihara, Masato; Otsuki, Rei
    • Journal Title

      Pure Appl. Math. Q. 2,no.2,part2

      Pages: 557-568

    • Peer Reviewed
  • [Journal Article] Introduction to homological geometry. II. Integrable systems, geometry, and topology2006

    • Author(s)
      Guest, Martin A
    • Journal Title

      AMS/IP Stud. Adv. Math., 36, Amer. Math. Soc., Providence, R

      Pages: 123-150

    • Peer Reviewed
  • [Presentation] Geometry of Loop spaces2009

    • Author(s)
      Yoshiaki Maeda
    • Organizer
      Conference on Geometry and Physics 7
    • Place of Presentation
      中国・成都
    • Year and Date
      2009-07-08
  • [Presentation] Geometry and Analysis of star exponential functions, International conference on Differential Geometry2007

    • Author(s)
      Yoshiaki Maeda
    • Organizer
      Mathematical Physics, Mathematics and Society, IHES
    • Place of Presentation
      France Paris
    • Year and Date
      2007-08-29
  • [Book] Noncommutativity and Singularities, Advanced Studies in Pure Mathemtaics2009

    • Author(s)
      Maeda Yoshiaki, et al
    • Total Pages
      55
    • Publisher
      Mathematical Society of Japan
  • [Book] Operator algebras and geometry. Translated from the 2001 Japanese original by the authors. Translations of Mathematical Monographs2008

    • Author(s)
      Moriyoshi, Hitoshi; Natsume, Toshikazu
    • Total Pages
      237
    • Publisher
      American Mathematical Society
  • [Book] From quantum cohomology to integrable systems. Oxford Graduate Texts in Mathematics2008

    • Author(s)
      Guest, Martin A
    • Total Pages
      15
    • Publisher
      Oxford University Press
  • [Book] Noncommutative Geometry and Physics2007

    • Author(s)
      Maeda Yoshiaki, et al
    • Publisher
      World Scientific Publishing

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Published: 2011-06-18   Modified: 2021-08-23  

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