\noindent ``Integrability meeting ENS/IPhT'' \\ \\ From the seminal papers of Witten and Kontsevich we know that the intersection theory on the moduli spaces of complex curves is described by a tau-function of the KdV integrable hierarchy. Moreover, this tau-function is given by a matrix integral and satisfies the Virasoro constraints. Recently, an open version of this intersection theory was introduced. In my talk I will show that the open version can be described very similar to the closed one, in particular it is given by a tau-function of the integrable hierarchy. Moreover, it's W-constraints can be naturally described in terms of two free bosonic fields. \\ \\ (IPhT organizers: Ivan Kostov and Didina Serban)