Branes, rings and matrix models in minimal (super)string theory

We study both bosonic and supersymmetric (p,q) minimal models coupled to Liouville theory using the ground ring and the various branes of the theory. From the FZZT brane partition function, there emerges a unified, geometric description of all these theories in terms of an auxiliary Riemann surface Script M_p,q and the corresponding matrix model. In terms of this geometric description, both the FZZT and ZZ branes correspond to line integrals of a certain one-form on Script M_p,q. Moreover, we argue that there are a finite number of distinct (m,n) ZZ branes, and we show that these ZZ branes are located at the singularities of Script M_p,q. Finally, we discuss the possibility that the bosonic and supersymmetric theories with (p,q) odd and relatively prime are identical, as is suggested by the unified treatment of these models.