WKB Analysis and Stokes Geometry of Differential Equations

Abstract

In this article we survey the fundamental theory of the exact WKB analysis, that is, the WKB analysis based on the Borel resummation method. Starting with the exact WKB analysis for second order linear ordinary differential equations, we explain its application to the computation of monodromy groups of Fuchsian equations and its generalization to higher order equations. Some recent developments of the theory such as the exact WKB analysis for completely integrable systems are also briefly discussed.