Sala Seminari (Dip. Matematica).
The simplicial volume is a homotopy invariant of closed manifolds defined by Gromov in 1982. For a manifold M, it is bounded from above by the minimal number of top-dimensional simplices in a triangulation of M, and roughly speaking it measures the minimal size of triangulations of M “with real coefficients”. A long-standing conjecture by Gromov asserts that, for aspherical manifolds, the vanishing of the simplicial volume implies the vanishing of the Euler characteristis. In this talk I describe an approach to this conjecture that makes use of discrete approximations of the simplicial volume in towers of coverings.