Open intersection numbers, matrix models and KP hierarchy

In their recent work R. Panharipande, J. Solomon and R. Tessler constructed intersection theory on the moduli spaces of Riemann surfaces with boundaries. The goal of my talk is to describe the generating function of this theory in terms of matrix models and integrable hierarchies. It appears that while open theory is much more complicated from the geometrical point of view, on the level of matrix models and integrable systems the difference is not so dramatic and the open case can be described by a natural deformation of the Kontsevich-Witten model.