The group is specialized in some topics in Differential Geometry that go beyond classical Riemannian Geometry. In particular, we study SubRiemannian Geometry, Geometric Measure Theory and Optimal Transport on metric spaces. We are interested also in Geometric Mapping Theory, Geometric Topology, Hyperbolic Geometry, Minimal Surfaces, and Geometric Group Theory.
In the last 25 years there has been a surge of interest in the geometry of non-smooth spaces and in their corresponding analysis. This movement arose from the interaction between active areas of mathematics concerning the theory of analysis on metric spaces along with geometric group theory, rigidity, and quasi-conformal homeomorphisms. One of the purposes was to study mappings between non-Riemannian metric structures such as boundaries of hyperbolic groups and Carnot groups, equipped with their subRiemannian metrics.
