Speaker: Mitul Islam
Date: November 13, 2025
Affiliation: TIFR, Mumbai

Abstract: Bowditch introduced the notion of a ``coarse median'' on a metric space as a simultaneous generalization of metric trees, mapping class groups, and $\mathrm{CAT}(0)$ cube complexes. Answering a question of Bowditch, Haettel recently showed that the only higher-rank symmetric spaces that admit a ``coarse median'' are products of rank-one spaces, e.g.\ $\mathbb{H}^2 \times \mathbb{H}^2$. In this talk, we will introduce the notion of a ``coarse higher median'', which generalizes Bowditch’s medians. We will identify several families of irreducible higher-rank symmetric spaces that admit our generalized median, but not Bowditch’s medians. This is joint work in progress with Grazia Rago.