Establishment of the symplectic picture for isomonodromic deformations
| Project/Area Number |
24740104
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Global analysis
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
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| Research Collaborator |
SAITO Masa-Hiko
HARAOKA Yoshishige
OSHIMA Toshio
HIROE Kazuki
BOALCH Philip
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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 |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 有理型接続 / 一般モノドロミー保存変形 / 一般モノドロミー保存変形方程式 / 有理型接続のモジュライ空間 / 一般モノドロミーデータのモジュライ空間 / 中島箙多様体 / Fourier-Laplace変換 / タウ関数 / 箙多様体 / Stokes係数 / 国際情報交換 / フランス / 分岐不確定特異点 |
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| Outline of Final Research Achievements |
I constructed the framed moduli spaces of meromorphic connections on the projective line as complex symplectic manifolds, and furthermore with Boalch, constructed the quasi-Hamiltonian spaces parametering local generalized monodoromy data of meromorphic connections with a link. Also, with Hiroe, I showed that the moduli spaces of meromorphic connections with an unramified irregular singularity and arbitrary number of regular singularities are isomorphic to Nakajima quiver varieties. Furthermore I checked that the isomonodromy tau functions induce the Hamiltonians for isomonodromic deformations in some sense, and showed that the Fourier-Laplace transform of meromorphic connections induce symmetry of isomonodromic deformation equations.
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Report
(4 results)
Research Products
(16 results)
