Rational singularities for moment maps of totally negative quivers

Moment maps of quivers are key to several geometric realizations of quantum groups and counting their points over finite fields has proven to be an efficient technique to compute graded dimensions of those. More recently, Wyss counted jets of quiver moment maps over finite fields in a particular case and related their asymptotic behaviour to Igusa zeta functions.
In the first half of the talk, I will introduce these countings of jets and relate their asymptotic behaviour to rational singularities of quiver moment maps. In the second part, I will prove that a large class of quiver moment maps have rational singularities, namely moment maps of totally negative quivers. If time allows, I will discuss some applications to singularities of other moduli spaces.