Description
Most perturbative series in quantum theory are factorially divergent. In the 1970s-1980s, many physicists, starting with the work of Bender and Wu, understood that these divergences are closely related to non-perturbative sectors, and in particular to instantons. In this talk I will first review these results, and then show how they can be applied in a very different context, suggesting new conjectures in algebraic geometry. This is yet another example of physical mathematics, in which physics intuition leads to new conjectures and research directions in pure mathematics.