In order to study the weakly coupled regime of theory we often make use of perturbative expansion of the physical quantities of interest. But such expansions are often divergent and defined only as asymptotic series. In fact, this divergence is connected to the existence of nonperturbative contributions, i.e. instanton effects that cannot be captured by a perturbative analysis. The theory of resurgence is a mathematical tool which allows us to effectively study this connection and its consequences. In this talk we will make use of this theory in order to show how to construct a full nonperturbative solution from perturbative data. To write this full nonperturbative solution we need to introduce generalised multi-instanton sectors, which can then be checked by precision tests on the asymptotic data. Finally, the study of this nonperturbative sectors in matrix models allows us to have a full picture of the phase diagram of this models.

University of Lisbon