2013 Fiscal Year Final Research Report
Toplogical Field theory, Moduli spaces of connections and Geometric Langlands correspondence
| Project/Area Number |
23654010
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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 |
Algebra
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| Research Institution | Kobe University |
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Principal Investigator |
SAITO MASAHIKO 神戸大学, 理学(系)研究科(研究院), 教授 (80183044)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 可積分系 / パンルヴェ方程式 / 幾何学的ラングランズ対応 / モジュライ理論 / 量子コホモロジーとミラー対称性 / ラグランジュアンファイブレーション / 国際共同研究 / 国際情報交換 |
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| Research Abstract |
M. Inaba and I constructed the moduli spaces of stable parabolic connections over a nonsingular projective curve with fixed formal type of regular or irregular singularities as non singular algebraic varieties. Moreover,we proved that the Riemann-Hilbert correspondence for these cases give an analytic isomorphism, which implies the geometric Painleve property for iso-monodromic or iso-Stokes non-linear differential equations. Together with Frank Loray, we constructed a good model of the moduli space of rank 2 stable parabolic connections over the projective line as well as its compactification. We found unexpected relations between two Lagrangian fibrations of the moduli space of connections and the classical duality of the projective space and its dual projective space. S. Szabo and I are developing a theory of apparent singularities of connections and Higgs bundles and try to understand the geometric Langlands correspondence.
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