From quantum topology to topological strings

In the last years many interesting connections have been found between quantum invariants of links and three-manifolds, and topological strings on Calabi-Yau threefolds. In this talk I will focus on state integral invariants of hyperbolic knots, their perturbative expansion, and the resurgent structure of the latter. I will show that many of the structures found in these objects, as unveiled in particular in the work of Stavros Garoufalidis and his collaborators,  have counterparts in topological string theory, and suggest avenues for understanding non-perturbative aspects of the topological string.