Title: Topology at infinity of the Painlevé VI space;

Abstract: I will show how recent asymptotic abelianization results in
non-abelian Hodge theory imply a conjecture of Simpson on the topology at
infinity of Hodge moduli spaces in a simple special case. Time permitting, I
will also explain the relationship between this conjecture and the so-called
P=W conjecture of de Cataldo, Hausel and Migliorini.