I am a differential topologist that studies geometric structures. The questions I consider are often of the form: “What is the homotopy type of the space of all geometric structures of class X on a given manifold M?” There is a branch of Mathematics, called the h-principle, dedicated to answering things like this.

My main line of research has to do with a particular class of structures called tangent distributions (i.e. subbundles of the tangent bundle), so I am interested as well in the areas in which they play a role (Subriemannian Geometry, Control Theory, PDEs, Symplectic and Contact Topology). You can find more information in my personal website.