To provide a unified framework for median graphs, mapping class groups, and $\mathrm{CAT}(0)$ cube complexes, Bowditch introduced the notion of a coarse median on a metric space. Answering a question of Bowditch, Haettel showed that a higher-rank symmetric space of non-compact type admits a coarse median if and only if it is a product of rank-one spaces. In this talk, we will focus on the family of higher-rank symmetric spaces of noncompact type admitting a convex projective model. While these metric spaces do not admit a coarse median in Bowditch's sense, we will construct a generalized coarse median for them. We will conclude by discussing some properties of our ''coarse higher medians''.
This is joint work with Mitul Islam.
