Punctures and p-spin curves from matrix models II

We report here an extension of a previous work in which we have shown that matrix models provide a tool to compute the intersection numbers of p-spin curves. We discuss further an extension to half-integer p, and in more details for p=1/2 and p=3/2. In those new cases one finds contributions from the Ramond sector, which were not present for positive integer p.The existence of Virasoro constraints, in particular a string equation, is considered also for half-integral spins. The contribution of the boundary of a Riemann surface, is investigated through a logarithmic matrix model The supersymmetric random matrices provide extensions to mixed positive and negative p punctures.