• symmetric spaces
• proportionality principle
• simplicial volume
• bounded cohomology
• continuous cohomology

We will be mainly concerned with the notion of simplicial volume of closed, oriented manifolds, especially in the case of locally symmetric spaces of noncompact type.
We will give an exact computation for the simplicial volume of manifolds covered by H^2xH^2, following the work of Bucher-Karlsson. This is the only case, except the hyperbolic one, in which the precise value of the simplicial volume is known and nonzero. We will also show that, unlike in the hyperbolic case, the ratio between the Riemannian volume and the simplicial volume of manifolds covered by H^2xH^2 differs from the supremum of volumes of straight simplices in the universal covering.
Our main tools will be continuous cohomology and continuous bounded cohomology of topological groups and the interplay between these concepts and the usual notion of bounded cohomology for discrete groups and topological spaces.