Appears in collection : 2025 - T2 - WS2 - Low-dimensional phenomena: geometry and dynamics

An Anosov representation of a hyperbolic group $\Gamma$ quasi-isometrically embeds $\Gamma$ into a semisimple Lie group in a way which imitates and generalizes the behavior of a convex cocompact group acting on a rank-1 symmetric space; it is unknown whether every linear hyperbolic group admits an Anosov representation. In this talk, I will discuss joint work with Sami Douba, Balthazar Flechelles, and Feng Zhu, which produces new examples of Anosov representations by showing that every hyperbolic group that acts geometrically on a $\mathrm{CAT}(0)$ cube complex admits a 1-Anosov representation into $\mathrm{SL}(d,\mathbb R)$ for some $d$. Mainly, the proof exploits the relationship between the combinatorial $\mathrm{CAT}(0)$ geometry of right-angled Coxeter groups and the projective geometry of a convex domain in real projective space on which a Coxeter group acts by reflections.