Geometric semi-norms in homology

The simplicial volume of a simplicial complex is a topological invariant
related to the growth of the fundamental group, which gives rise to a
semi-norm in homology. In this talk, we introduce the volume entropy
semi-norm, which is also related to the growth of the fundamental group
of simplicial complexes and shares functorial properties with the
simplicial volume. Answering a question of Gromov, we prove that the
volume entropy semi-norm is equivalent to the simplicial volume
semi-norm in every dimension. Joint work with I. Babenko.