In this talk, I will present microscopic properties of the eigenvalues of random
normal matrices in the limit where the size of the matrices becomes large.
Specifically, this talk will focus on the random normal matrix model with a
singularity in the interior of the spectrum. I will discuss the existence and
uniqueness of the microscopic density of eigenvalues near a singularity and
describe how the rescaled Wards identity can be used to prove the universality.
This is based on joint work with Yacin Ameur.