We study the inverse problem for semi-simple Frobenius manifolds of dimension 3 and we
explicitly compute a parametric form of the solutions of theWDVV equations in terms of Painlevé VI
transcendents. We show that the solutions are labeled by a set of monodromy data. We use our parametric
form to explicitly construct polynomial and algebraic solutions and to derive the generating
function of Gromov–Witten invariants of the quantum cohomology of the two-dimensional projective
space. The procedure is a relevant application of the theory of isomonodromic deformations
