An integrable system, can be in principle reconstructed from the knowledge of its ``spectral curve'' (which is an algebraic curve embedded into C2). For instance for classical isospectral systems (thus with vanishing dispersion), Krichever showed how to reconstruct the Lax pair and the Tau function from the geometry of the spectral curve. par Inspired from the large size expansion of random matrices, we propose a method to reconstruct a dispersionful integrable system from the geometry of the spectral curve. par This method makes the link between integrable systems, geometry, combinatorics, topological strings. par We will show some examples of applications in statistical physics and enumerative geometry, and for instance knot theory.