Title: Globally valued fields and Arakelov geometry

Abstract: I will present a framework of Globally Valued Fields introduced by Ben Yaacov and Hrushovski, that generalises the notion of global fields. Each number field can be equipped with a GVF structure in a unique way (up to scalar multiplication) and the study of GVF structures on other fields is related to e.g. Arakelov geometry, Berkovich spaces, and the Monge–Ampère equation. I will outline some of these connections and talk about some problems in the development of the theory. If time permits I will mention a joint work with Antoine Sedillot, where we use cohomological methods to understand some problems on families of Berkovich spaces.