My work is about Riemannian Geometry in its broadest meaning and with interactions with other branches of geometry such as: topology of manifolds and singular spaces, dynamics, global analysis, metric geometry and geometric group theory.

During the years, I have become interested in :

• Einstein manifolds and other special structures (symmetric spaces, asymptotically harmonic manifolds etc.),

• geometric structures in dimension 3 (hyperbolic, Heisenberg and Sol geometries, non-geometric manifolds etc.)

• some topological and differential invariants of manifolds related to systolic geometry and minimizing problems in Riemannian geometry (simplicial volume and bounded cohomology, minimal volume and minimal entropy, Seiberg-Witten invariants etc.)

• topological and geometric rigidity (moduli space of special Riemannian structures, convergence theory in Riemannian geometry, pinching, collapsing and finiteness problems)

• geometry and dynamics of negatively curved manifolds (counting geodesics, entropy, quasi-conformal measures, ergodicity etc.)

• geometry of CAT(0) and Gromov-hyperbolic spaces

• geometric group theory (problems related to growth, splittings etc.)

I am also interested in scientific dissemination: I have long been involved in mathematics competitions, I translated the Topologicon of J.P. Petit and I partecipated to many popular science events and meetings (Caffè Scienza, Caffè Matematici, Scienza 3, La Scienza a Scuola etc.).