Roman's research focuses on Random Matrix Theory. He is motivated by problems from physics such as power-spectrum analysis of long eigenlevel sequences in quantum chaology or two dimensional Coulomb gas. The latter is related to normal random matrices where in the limit of large matrix size the eigenvalues, which could be thought of as unit charges in the plane, fill a compact domain. This nodel is not yet as well understood as one-dimensional models. Roman obtained results for subleading corrections to the density and for the system of orthogonal polynomials associated with the gas of eigenvalues. One of his main goals is to find universal behavior of the Coulomb gas. At present he is working with Joshua Feinberg on Quasi-Hermitian Random Matrices. Roman's papers can be found here.