I am a mathematical physicists working in integrable systems, namely systems that are exactly solvable. In particular I am interest in analytic and probabilistic questions  related to  the  behaviour of solutions of dispersive nonlinear equations such  as  typical behaviour or  unlikely behaviour.   I consider initial data with a large number of solitary waves and my goal is to give  a statistical description of their behaviour over large times. The equations derived to obtain such description are called generalized hydrodynamic equations and their mathematical derivation is still an open problem in statistical mechanics.

I am interested in non-Hermitian random matrices. The type of   random matrices  considered are derived from Lax pairs of exactly solvable  classical  lattice models.  The relevant questions are the study of their eigenvalues, eigenvectors and their fluctuations that charctherize the statistical behaviour of solutions of  certain classes of  lattice models with random initial data.