Resurgence and quantum topology

Abstract：

Quantum field theories and string theories often lead to perturbative series which encode geometric information. In this lecture I will argue that, in the case of complex Chern-Simons theory, perturbative series secretly encode integer invariants, related in some cases to BPS counting. The framework which makes this relation possible is the theory of resurgence, where perturbative series lead to additional non-perturbative sectors, and the integer invariants arise as Stokes constants. I will illustrate these claims with explicit examples related to quantum invariants of hyperbolic knots. If time permits, I will mention similar results in topological string theory.