From cyclic Higgs bundles to Anosov representations

Anosov representations generalize Fuchsian representations of surface groups, retaining key properties such as discreteness and faithfulness. Constructing new families of Anosov representations remains difficult. Via nonabelian Hodge theory, surface group representations can be studied through Higgs bundles. In this talk, I will present several families of cyclic Higgs bundles whose associated representations are Anosov, yielding new closed families of Anosov representations. This is based on work in progress with Samuel Bronstein and Colin Davalo.