Studies of D Module and Integrable System

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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.