Quantization of simply-laced isomonodromy systems

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K17552
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Tokyo University of Science (2017); Tokyo Institute of Technology (2015-2016)
• Principal Investigator: Yamakawa Daisuke 東京理科大学, 理学部第一部数学科, 講師 (20595847)
• Research Collaborator: OSHIMA Toshio ; NAGOYA Hajime ; HARAOKA Yoshishige ; YANAGIDA Shintaro ; Boalch Philip ; Rembado Gabriele
• Project Period (FY): 2015-04-01 – 2018-03-31
• 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

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.

Free Research Field

シンプレクティック幾何学