The simplicial volume is a homotopic invariant of manifolds introduced by Gromov in 1982. Despite being homotopical in nature, this invariant is strictly related to the geometric structures that a manifold can carry. I study this invariant even in the more mysterious case of non compact manifolds.
I am also interested in bounded cohomology of groups, which was introduced by Johnson and Trauber in the 70's. Bounded cohomology has since then found remarkable applications in many areas of mathematics (actions on the circle, stable commutator length, simplicial volume, geometric group theory), but is still very hard to compute in general.
