A basic problem in Representation theory is, given a group, or an algebra, to study its finite dimensional irreducible representations. The first question is how many there are. In my talk I will address this question for associative algebras that are quantizations of algebraic varieties admitting symplectic resolutions. These quantizations include universal enveloping algebras of semisimple Lie algebras, as well as W-algebras and symplectic reflection algebras. The counting problem is part of a more general program due to Bezrukavnikov and Okounkov relating the representation theory to quantum cohomology. I will consider the case of quotient singularities and will make the exposition non-technical.