Ricci iteration and semipositivity of relative log canonical bundle

In this talk I would like to explain how to use the Ricci iteration to show the semipositivity of relative(canonical) K\ahler-Einstein currents on the relative log canonical bundle of a family of KLT pairs with big log canonical bundles. If time permits I would like to show how to obtain the smooth dependence of the K\ahler-Einstein forms on a nonempty Zariski open subset of a
projective family.