Abstract: Quivers are finite oriented graphs. Surprisingly, they enjoy a rich representation theory with connections to root systems of Lie algebras.
This link was established in full generality by Kac in the early 1980s. His proof relied on arithmetic geometry techniques applied to moduli spaces
of quiver representations and featured intriguing polynomials, which count representations of quivers over finite fields. Since then, a lot of work has
been done to strengthen the links between Kac’s polynomials, Lie algebras and the geometry of moduli spaces. In this talk, I will consider more recent countings of quiver representations over rings of finite depth. I will expose some of their recently proved properties and how they relate to geometric properties of the moduli spaces