My main research interest is numerical analysis of differential equations, with a particular focus on geometric numerical integrators. This basically consists in the design and analysis of structure-preserving numerical methods for the approximation, in time, of solutions to deterministic and random dynamical systems. Such dynamical systems come, for instance, from applications in molecular dynamics, in astrophysics, in the field of modern communication systems, or in nonlinear wave phenomena. Concrete examples are highly oscillatory problems, multiscale problems, models for shallow water waves, or stochastic wave and Schrödinger equations.