Stable subgroups of finitely generated groups were introduced by Durham and Taylor as a generalisation of both the quasiconvex subgroups of hyperbolic groups, and the convex cocompact subgroups of mapping class groups. They also nicely coincide with many other classes of subgroups; for example in the general case they are the hyperbolic Morse subgroups, and in right-angled Artin groups they are the purely loxodromic subgroups. In this talk we will extend this to a characterisation of the stable subgroups of graph products with infinite vertex groups. This is joint work with Sahana Balasubramanya, Marissa Chesser, Johanna Mangahas, and Marie Trin.
