  We present exact results for partition functions of Jackiw-Teitelboim (JT)
gravity on two-dimensional surfaces of arbitrary genus with an arbitrary number
of boundaries. The boundaries are of the type relevant in the
NAdS${}_2$/NCFT${}_1$ correspondence. We show that the partition functions
correspond to the genus expansion of a certain matrix integral. A key fact is
that Mirzakhani's recursion relation for Weil-Petersson volumes maps directly
onto the Eynard-Orantin "topological recursion" formulation of the loop
equations for this matrix integral. The matrix integral provides a (non-unique)
nonperturbative completion of the genus expansion, sensitive to the underlying
discreteness of the matrix eigenvalues. In matrix integral descriptions of
noncritical strings, such effects are due to an infinite number of disconnected
worldsheets connected to D-branes. In JT gravity, these effects can be
reproduced by a sum over an infinite number of disconnected geometries -- a
type of D-brane logic applied to spacetime.
