In this talk, I am going to give an introduction to the exact WKB analysis, that is, WKB analysis based on the Borel resummation.
I start with review of basic notions and facts (such as Stokes geometry, Borel summability of WKB solutions etc.) for the prototypical equation namely second order linear ODE with a small (or large) parameter. Then I introduce WKB-theoretic transformations to canonical equations (Airy equation, Weber equation etc.) by Aoki-Kawai-Takei, explain their consequence and Borel summability.
I will also give an overview of the exact WKB analysis of higher order equations.