Speaker: Matei Ionita

Abstract:

For some linear, possibly singular ODEs, it’s easy to find formal solutions, which are series with zero radius of convergence. I will introduce the idea of Borel resummation: this produces an analytic solution, whose asymptotics are described by the original divergent series. Applying the same argument in families leads to exact WKB analysis for Schrödinger-type equations on a Riemann surface. Time permitting, I’ll describe some qualitative features of exact WKB analysis for higher order equations.