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Ricardo Couso Santamaría, Instituto Superior Técnico

Resurgence in topological string theory

The theory of resurgence is the unified framework where to understand why many results in perturbation theory are asymptotic and divergent, how to relate this to nonperturbative effects, and how to go from a formal (trans)series to a proper function. Topological string theory is at the center of a net of dualities, equivalences, and connections to string and gauge theories, and to complex and enumerative geometry. The perturbative free energy is an asymptotic series in the string coupling constant that can be computed to high order. The nonperturbative completion is an open problem that has seen great advance this year from connections to the refined topological string and from the perspective of resurgence. In this talk I present the basic aspects of resurgence and asymptotics, and I explain how to apply them to reconstruct the nonperturbative (trans)series that represents the closed topological string free energy.