Hochschild-Pirashvili homology is a construction associating to any topological space
X a homology theory HH^X of commutative algebras. In the first part of my talk,
I will discuss how to obtain representations of Aut(F_n) that do not factor through
GL_n(\mathbb{Z}) out of Hochschild--Pirashvili construction. In the second part, I will describe how
to get certain local systems on Outer space, which turn out to be related to
the moduli space of tropical curves. The talk is largely based on recent
work of V.Turchin and Th.Willwacher.