Nonlinear partial differential equations: Cahn-Hilliard equations, phase-field systems and related models Hyperbolic equations and related models Fluid dynamics: the study of incompressible multiphase flows, Navier-Stokes equations Elliptic and parabolic boundary value problems Dynamic boundary conditions for PDEs Nonlocal mathematical models Attractor's theory of dissipative systems Perturbation theory, convergence rates to steady states, stability issues