Measures of finite energy in complex and non-Archimedean pluripotential theory

I will present a joint work with Mattias Jonsson, in which we develop a synthetic approach to global pluripotential theory, covering both the complex analytic and non-Archimedean settings. This allows in particular to study of the dependence of the energy of a measure with respect to the polarization, with applications to cscK metrics and K-stability.