Large genus asymptotics from exact WKB analysis


Exact WKB analysis consists in the Borel-resummation of the divergent series appearing in the context of singular perturbation theory of differential equations. However, beyond the obvious perks for those interested in genuine solutions, e.g. of some equivariant differential systems, it also provides a way to study asymptotic properties of certain enumerations through the generating function method. Applications of these procedures include for instance constructing physical solutions to Schrödinger equations in finite-dimensional Hilbert spaces, as well as obtaining large-genus asymptotics of generalised Catalan numbers.