Compactifications of (locally) symmetric spaces and ideal Poisson Voronoi tesselations

Higher rank symmetric spaces are nonpositively curved Riemannian manifolds, but they also admit interesting families of Finsler metrics. The horofunction compactifications of these different Finsler metrics realize many different compactifications. These compactifications play an important role when considering ideal Poisson Voronoi tesselations. I will  explain in particular that for some of these Finsler metrics the ideal Poisson Voronoi tesselations of a higher rank symmetric space exhibit rank one phenomena. This is joint work with Colin Davalo and Max Riestenberg.