Studies of D Module and Integrable System

Mikio Sato和Takahiro Kawai利用微局部分析方法研究了常微分方程的奇异摄动理论。Masaki Kashiwara和Tetsuji Miwa将晶体基理论应用于一个称为完全表示的大类的I点函数的计算，得到了1点函数由特征标给出的一般性结果，Kyoji Saito推广了Eichler积分，并构造了一个双重积分本文首先讨论了曲线模空间上向量丛的无穷级数，然后讨论了曲线模空间上向量丛的无穷级数，最后讨论了曲线模空间上向量丛的无穷级数，荒木厚弘证明了在扰动XY模型中返回平衡点的问题，松杉武将泛函分析应用于常角曲线，甚至在非凸的情况下，斋藤守彦应用Hodge模和D模的理论，证明了Dimca关于多项式映射纤维上同调的猜想。

Mikio Sato and Takahiro Kawai studied the singular perturbation theory of the ordinary differential equations by exploiting the method of micro-local analysis. They gave a conjecture about the relation between the WKB method and the Borel transform for unharmonic oscillator equation and its secular equation.Masaki Kashiwara and Tetsuji Miwa applied the theory of crystal base to the computation of I point functions for a large class called the perfect representations, and obtained the general result that the 1 point function is given by characters.Kyoji Saito generalized the Eichler integral and constructed doubly infinite series of vector bundles over the moduli spaces of curves.Huzihiro Araki showed that the return to the equilibrium happens in the perturbed XY model.Shigetake Matsuitra applied functional analysis to constant angle curve, even in non convex case.Morihiko Saito applied the theory of Hodge module and D module, and proved Dimca's conjecture about fiber cohomology of polynomial mappings.