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Jackiw-Teitelboim dilaton-quantum-gravity localizes on a double-scaledrandom-matrix model, whose perturbative free energy is an asymptotic series.Understanding the resurgent properties of this asymptotic series, including itscompletion into a full transseries, requires understanding the nonperturbativeinstanton sectors of the matrix model for Jackiw-Teitelboim gravity. Thepresent work addresses this question by setting-up instanton calculusassociated to eigenvalue tunneling (or ZZ-brane contributions), directly in thematrix model. In order to systematize such calculations, a nonperturbativeextension of the topological recursion formalism is required -- which is hereinboth constructed and applied to the present problem. Large-order tests of theperturbative genus expansion validate the resurgent nature of Jackiw-Teitelboimgravity, both for its free energy and for its (multi-resolvent) correlationfunctions. Both ZZ and FZZT nonperturbative effects are required by resurgence,and they further display resonance upon the Borel plane. Finally, theresurgence properties of the multi-resolvent correlation functions yield newand improved resurgence formulae for the large-genus growth of Weil-Peterssonvolumes.

Resurgent Asymptotics of Jackiw-Teitelboim Gravity and the Nonperturbative Topological Recursion