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