Nakajima quiver varieties form an important class of
examples of conical symplectic singularities. For example, such
varieties of dimension 2 are Kleinian singularities. Starting from
this, I will describe a combinatorial approach to classifying the next
case, affine quiver varieties of dimension 4. If time permits, I will
try to say the implications we obtained and how can one compute the
number of crepant symplectic resolutions of these varieties. This is based on a
joint project with Samuel Lewis (arXiv:2510.15160).