The research of this group is divided into four main lines. The first one concerns different aspects of differential topology, as Engel structures, foliations and extensions of h-principle, as well as contact topology, specifically groups of contactomorphisms, Legendrian submanifolds and higher dimensional problems. The second one is focused on differential and Riemannian geometry, in particular on spectral problems, Poisson and symplectic geometry, field theories, Kahler geometry, geometric analysis and geometric theory of information. The third one studies geometric mechanics and control theory, including geometric integration, Hamilton-Jacobi theory and continuum mechanics. Finally, the fourth line is focused in the theory of dynamical systems and the geometry of PDEs, specifically in topological fluid mechanics, KAM theory and applications, and the study of level sets of solutions to elliptic and parabolic PDEs.