Title: Exponential smallness and resurgence

Speaker: Arpan Saha, University of Hamburg, Germany

Abstract: In this talk, we investigate three seemingly unrelated puzzles: (a) the perturbative series that arise in QFT are typically divergent, yet truncating after one or two terms in practice yields accuracy surpassing those of convergent series, (b) series expansions of solutions of ODEs around irregular singularities are unable to detect splitting of modes, and (c) the asymptotic behaviour of complex analytic functions at infinity can discontinuously change across certain rays. We shall see that they are in fact different manifestations of "exponential smallness" and outline how the theory of resurgent functions introduced by Jean Écalle in the 80s may be used to resolve them.