Quivers are finite oriented graphs. They enjoy a wild representation theory, which shows surprising links with Lie algebras. Representations of quivers are typically classified by some moduli space. In the early 1980s, Kac introduced countings of quiver representations over finite fields in order to gain geometric information on moduli spaces of quiver representations. Since then, a lot of work has been done to understand properties of these countings and their relations with Lie algebras. In this talk, I will consider more recent countings of quiver representations over rings of finite depth. I will expose some recent results on the asymptotic behaviour of these countings and how it relates to singularities of the moment map associated to a given quiver.