| Project/Area Number |
12440022
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Keio University |
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Principal Investigator |
MAEDA Yoshiaki Keio University, Dept. of Mathematics, Professor, 理工学部, 教授 (40101076)
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| Co-Investigator(Kenkyū-buntansha) |
ICHII Ippei Keio University, Dept. of Mathematics, Professor, 理工学部, 助教授 (90051929)
TANI Atsushi Keio University, Dept. of Mathematics, Professor, 理工学部, 教授 (90118969)
KIKUCHI Norio Keio University, Dept. of Mathematics, Professor, 理工学部, 教授 (80090041)
KAMETANI Yokio Keio University, Dept. of Mathematics, Assistant Professor, 理工学部, 講師 (70253581)
MORIYOSHI Hitoshi Keio University, Dept. of Mathematics, Associate Professor, 理工学部, 助教授 (00239708)
下村 俊 慶應義塾大学, 理工学部, 教授 (00154328)
楯 辰也 慶應義塾大学, 理工学部, 助手 (00317299)
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| Project Period (FY) |
2000 – 2002
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| Project Status |
Completed (Fiscal Year 2002)
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| Budget Amount *help |
¥10,500,000 (Direct Cost: ¥10,500,000)
Fiscal Year 2002: ¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2001: ¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 2000: ¥3,900,000 (Direct Cost: ¥3,900,000)
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| Keywords | deformation quantizations / groupoids / Index theorem / D-brane / Hochshields cohomology / 変形量子化 / Navier-Stokes equatin / Seiberg Witten equatin / non commutative geometry / Painleve equatin / K-theory / 非可換微分幾何学 / 弦理論 / Seiberg-Witten不変量 / ポアソン構造 |
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| Research Abstract |
Poisson Geometry, which is the extended notion of symplectic geometry, is now developing quite recently. However, this research fields is not common in Japan, while this research field is much developing in Europe and the United State. In our Study, we have a mission to develop this research fields in Japan, and to coorporate with the researchers who are working on this fields in Europe and the Unites States. The first our development is to study the convergence problems on deformation quantizations. For the case of formal deformations, M. Kontsevich has given a pretty result. It is important problem to study the convergence for the deformation quantizations. Through our research, we found the totally different feature for the convergence of the deformation quantizations, and propose a new geometric objects on gerbes. We will extend our research on the convergence of the deformation quantization as a future task. By this grant, we have two major international symposia in 2001 and 2002, which has noncommutative geometry and D-brane as main Topics. We could have many visitors from abroad and also from domestic research institutes. We have published a proceedings for our research developments. Maeda has been invited to the Poisson 2002 international conference at Lisbon and gave a talk on this problem, which was very interesting for the participants. We have also visited various meetings in Japan and outside of Japan to make strong activities. As a results, we could have a international research groups on noncommutative geometry, which is able to develop the research.
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