Appears in collection : Tropical Geometry, Berkovich Spaces, Arithmetic D-Modules and p-adic Local Systems

K-stability was introduced in complex differential geometry as a conjectural criterion (the YTD conjecture) for the existence of special Kšahler metrics, such as Kšahler-Einstein metrics, or constant scalar curvature Kšahler metrics. There has been a great deal of recent activity around K-stability : the YTD conjecture is solved in many cases, a nice picture for K-stable Fano varieties has emerged, and there is an increased understanding of the notion of K-stability itself. In my talk, I will explain how K-stability can be viewed through the lens of non-Archimedean geometry. This is based on joint work with Berman, Blum, Boucksom, and Hisamoto,