Domains of discontinuity for Anosov representations

We construct open domains of discontinuity for Anosov representations acting on some homogeneous spaces, including (pseudo-Riemannian) symmetric spaces. This generalizes work of Kapovich-Leeb-Porti on flag spaces. Our results complement those of Gueritaud-Guichard-Kassel-Wienhard, who constructed proper actions of Anosov representations. For Zariski dense Anosov representations with respect to a minimal parabolic subgroup acting on some symmetric spaces, we show that our construction describes the largest possible open domains of discontinuity. This is joint work with Florian Stecker.