  We argued in the paper "Geometry from Donaldson-Thomas invariants" that, when
a certain sub-exponential growth property holds, the Donaldson-Thomas
invariants of a 3-Calabi-Yau triangulated category should define a geometric
structure on its space of stability conditions. In this paper we show how to
associate a generating function to these geometric structures which we call the
tau function. In the case of the derived category of the resolved conifold,
this function reproduces the non-perturbative topological string partition
function introduced in the paper "Riemann-Hilbert problems for the resolved
conifold". In the case of the A2 quiver it is the Painleve I tau function. The
definition of the tau-function depends on certain choices of additional data
which we discuss in the paper. There is still much to understand!
