Description
Quantising the mirror curve of a toric Calabi-Yau threefold gives rise to quantum operators whose fermionic spectral traces produce factorially divergent series in the Planck constant and its inverse. These are captured by the Nekrasov-Shatashvili and standard topological strings via the TS/ST correspondence. In this talk, I will discuss the resurgence of these dual asymptotic series and present an exact solution for the spectral trace of local P^2. A full-fledged strong-weak symmetry exchanges the perturbative/nonperturbative contributions to the holomorphic and anti-holomorphic blocks in the factorisation of the spectral trace. This exact symmetry builds upon the interplay of the L-functions with coefficients given by the Stokes constants and the q-series acting as their generating functions. Guided by this pivotal example, I will propose a new perspective on the resurgence of a particular class of formal power series conjectured to possess specific summability and quantum modularity properties, leading to the general paradigm of modular resurgence. This talk is based on arXiv:2212.10606, 2404.10695, and 2404.11550.
