| Project/Area Number |
24654017
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Tokyo City University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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)
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| Keywords | ゲージ理論 / 共形場理論 / モジュライ / ４次元多様体 / 暗黒エネルギー / 国際情報交換 |
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| Outline of Final Research Achievements |
To develop mathematical analysis on the dark energry and accelerating universe, we should study Lorentz geometry, Riemannian geometry, nonlinear elliptic partial differentia equations on a noncompact space (space with infinite size), especially the behavior on the ends at infinity, and new framework on those issues. We took an algebraic-complex analytic approach to these problems. We investigated the behavior of the vector spaces called "conformal blocks" at the infinity of moduli spaces of compact Riemann surfaces, and developped the theory of spectral analysis of the operator algebras asssociated with these.
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