Matteo Sommacal is an expert in nonlinear waves, integrable systems and dynamical systems. In the theory of integrable systems, he mainly works on the mathematical models of 1- and 2-dimensional ferromagnetic systems at the nanometre length-scale, featuring uni-axial and bi-axial anisotropy, and on the problem of linear stability of scalar and multi-component, nonlinear partial differential equations of integrable type. In the theory of dynamical systems, he is one of the proponents of a mechanism to explain the onset of complex dynamics by means of an associated Riemann surface. He also researches on the appearance of slow chaos for a circular flow on a compact Riemann surface.