Free products of semi-simple algebras via quivers

We will see how quiver representation theory and stability allow us to understand the (finite dimensional) representation theory of a free product of semi-simple (associative) k-algebras. In particular, we will study the simple modules and modules in general position. We will see that a module in general position is always semisimple, and give an explicit numeral equation to decide when it is simple. If time permits, we will comment on the representation type (tame, wild) and discuss how to use moduli spaces of quivers to compute the number of parameters for the simple modules in a given dimension. This is joint work with A. Buchanan, I. Dimitrov, O. Grace, D. Wehlau and T. Xu.