Mustafin degenerations: Between applied and arithmetic geometry

Mustafin varieties are degenerations of projective spaces induced by combinatorial data in a Bruhat--Tits building. In recent years, these objects have proved to be of great interest due to a wide array of applications in algebraic and arithmetic geometry. In this talk, we review these developments. Moreover, we introduce a generalisation - that we call Mustafin degeneration - which is obtained by considering combinatorial data in a compactification of the respective Bruhat-Tits building. This new notion provides a novel combinatorial framework for the study of one parameter families of so-called multiview varieties in computer vision.

This talk is partially based on joint work with Binglin Li and Annette Werner.