Asymptotic analysis for hypergeometric systems and Garnier systems

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To generalize the exact WKB analysis to multidimensional problems, we consider completely integrable systems such as hypergeometric systems and Garnier systems from the viewpoint of the exact WKB analysis. We obtain the following fundamental results: "Coalescing phenomena of turning points" play an important role in determining the Stokes geometry of completely integrable systems as well as of higher order ordinary differential equations obtained as their restriction, in the case of linear completely integrable systems the Pearcey system gives a normal form at a point where a coalescing phenomenon of turning points occurs, and so on. Concerning the consolidation of the theory of exact WKB analysis, we also make a big progress in the analysis of the Voros coefficients of linear equations and Painleve equations by using the method of difference equations.