Degenerations in algebraic and applied geometry

The notion of degenerations has been at the forefront of algebraic geometry for the past decades. A particularly interesting class are so-called Mustafin degenerations, which are degenerations of projective varieties induced by combinatorial data in a Bruhat–Tits building. They were introduced in the 1970s by Mustafin in the context of uniformisation and have since found applications in several areas of algebraic and arithmetic geometry. In this talk, we give a classification of Mustafin degenerations in terms of combinatorial data and outline applications to p-adic non-abelian Hodge theory, computer vision and coding theory.