Moduli of vector bundles with connection and derived category

证明了从射影曲线上正则奇异抛物联络的模空间到基本群的模空间的Riemann-Hilbert态射是真态射。作为应用，模空间上的等单点形变具有几何Painleve性质.本系列研究始于与岩崎和齐藤的共同工作。在这个项目中，我对这个理论进行了极大的推广，并发表了最后一篇论文，从这个结果出发，我们可以用模空间的几何来理解经典的Painleve第六方程。

I proved that the Riemann-Hilbert morphism from the moduli space of regular singular parabolic connections on a projective curve to the moduli space of fundamental group is a proper morphism. As an application, the isomonodromic deformation on the moduli space has the geometric Painleve property. The series of this study started at the joint work with Iwasaki and Saito. During this project, I generalized the theory extremely and published the final paper.From this result, we can understand the classical Painleve sixth equation by the geometry of moduli spaces.