Resurgence and Calabi-Yau geometries

The theory of resurgence provides powerful tools to access the non-perturbative sectors of the factorially divergent asymptotic series that arise naturally as perturbative expansions in quantum theories. After introducing the basics of resurgence, I will review recent progress on the resurgent analysis of the strong and weak coupling limits of the spectral theory of toric Calabi-Yau threefolds, which is conjecturally dual to the topological string theory compactified on the same background. In the case of the local P^2 geometry, a remarkable analytic number-theoretic structure unfolds, revealing an exact and explicit strong-weak symmetry underpinning the resurgent properties of the perturbative expansions and paving the way for further insights. This talk is based on arXiv:2212.10606. A follow-up with V. Fantini will be available soon.