2011 Fiscal Year Final Research Report
Confluence process of differential equation and deformation of complex analytic space
| Project/Area Number |
21654003
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Kyoto University |
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Principal Investigator |
ITO Koki 京都大学, 数理解析研究所, 研究員 (30456842)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 微分方程式 / q差分方程式 / オイラー型積分 / 周期 / ド・ラーム構造 / ベッチ構造 / 比較同型 / リーマン・ヒルベルト対応 |
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| Research Abstract |
Describing the natural phenomena or relationships among various quantities in such fields as physics, engineering, we use equation ; especially differential or difference equation. We study some interaction between equation and its solution. For example, such an interaction produces the important numberπ.(Such interactions as above are called"comparison between Betti structure and de Rham structure"or"period".) Various periods appear in various places, and we believe that there exists a common framework for all over the periods. However, nobody has found one yet. So, we have groped for an answer to this question. Finally, we found seeds of prototype.
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