Abstract: Berkovich spaces are an analog of complex manifolds/complex analytic spaces when the field of complex numbers is replaced by a non-archimedean field. They in particular enjoy nice topological properties, which contrasts with the ultrametric nature of the field. The goal of this talk is to explain how to perform (pluri)potential theory on those spaces, similar to the classical complex one. If time permits I will also present some applications to problems coming from differential geometry.
