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In this talk I will review recent progress in generically defining perturbation theory even in non-Borel summable situations, by making use of resurgent analysis and transseries. As an example, I will address the large N perturbative expansion and discuss new nonperturbative contributions found deep in the large-order expansion of the genus expansion. If time allows, I will also briefly comment on the large N dual picture (via matrix models), where resurgence and transseries may also be used to obtain nonperturbative solutions of closed (topological) string theory.
