On quasimorphisms invariant under automorphisms

Quasimorphisms comprise a good function theory on groups and many groups
admits an abundance of them. It was recently discovered by Brandenbursky and
Marcinkowski that the free group on two generators admits a quasimorphism
that is invariant under all automorphisms of F_2. I will present a more
recent construction, due to Bastien Karlhofer, of aut-invariant
quasimorphisms on various free products and graph products of groups.
Examples include groups like SL(2,Z), the braid group on three hair some
right angled Artin and Coxeter groups.