Establishment of the symplectic picture for isomonodromic deformations

2014 Fiscal Year Final Research Report

• Project/Area Number: 24740104
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Global analysis
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: YAMAKAWA Daisuke 東京工業大学, 理工学研究科, 助教 (20595847)
• Research Collaborator: SAITO Masa-Hiko ; HARAOKA Yoshishige ; OSHIMA Toshio ; HIROE Kazuki ; BOALCH Philip
• Project Period (FY): 2012-04-01 – 2015-03-31
• 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

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.

Free Research Field

シンプレクティック幾何学