  This paper describes the reconstruction of the topological string partition
function for certain local Calabi-Yau (CY) manifolds from the quantum curve, an
ordinary differential equation obtained by quantising their defining equations.
Quantum curves are characterised as solutions to a Riemann-Hilbert problem. The
isomonodromic tau-functions associated to these Riemann-Hilbert problems admit
a family of natural normalisations labelled by the chambers in the extended
K\"ahler moduli space of the local CY under consideration. The corresponding
isomonodromic tau-functions admit a series expansion of generalised theta
series type from which one can extract the topological string partition
functions for each chamber.
