Appears in collection : Logarithmic and non-archimedean methods in Singularity Theory - Thematic Month Week 1 / Méthodes logarithmiques et non-archimédiennes en théorie des singularités - Mois thématique semaine 1

Let $\mathrm{X}$ be a fixed abelian variety. In this talk I will outline a framework to classify semi-homogeneous vector bundles on $\mathrm{X}$ using a suitably modified Fourier–Mukai transform that generalizes the well-known homogeneous situation. This will allow us to explicitly construct moduli spaces of semi-homogeneous vector bundles on $\mathrm{X}$. Using the perspective of non-Archimedean uniformization, we can use our insights to understand the tropicalization of the moduli space of semihomogeneous vector bundles in terms of its essential skeleton.This talk is based on joint work with Andreas Gross, Inder Kaur, and Annette Werner.