| Project/Area Number |
15K17552
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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 |
Basic analysis
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| Research Institution | Tokyo University of Science (2017)
Tokyo Institute of Technology (2015-2016) |
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Principal Investigator |
Yamakawa Daisuke 東京理科大学, 理学部第一部数学科, 講師 (20595847)
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| Research Collaborator |
OSHIMA Toshio
NAGOYA Hajime
HARAOKA Yoshishige
YANAGIDA Shintaro
Boalch Philip
Rembado Gabriele
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 有理型接続 / モノドロミー保存変形 / タウ関数 / 非自励ハミルトン系 / 量子化 / 野性的指標多様体 / 国際情報交換 / フランス / 単純型モノドロミー保存変形 / 基本2次形式 / 頂点作用素代数 / フーリエ・ラプラス変換 / フィルター付き有理型接続 / フィルター付きストークス局所系 / リーマン・ヒルベルト・バーコフ対応 / wild character variety |
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| Outline of Final Research Achievements |
We partially quantized the simply-laced isomonodromy systems.
By joint work with Philip Boalch, we constructed the wild character varieties as algebraic Poisson varieties. Furthermore, we introduced the notions of filtered meromorphic connections on Riemann surfaces and filtered Stokes local systems, and established an equivalence between their categories.
We explicitly described the fundamental two-forms of the isomonodromic deformation equations for unramified meromorphic connections on the Riemann sphere. Furthermore, we use this result and some previous results to obtain a new description of the isomonodromic deformation equations as non-autonomous Hamiltonian systems.
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