Higher Teichmüller-Thurston theory, among other things, deals with deformation spaces of locally homogeneous geometric structures on manifolds, representations of fundamental groups of surfaces, and flat connections.  This workshop will focus on the side of the subject dealing with conformally flat Lorentzian metrics, geometric structures arising from Anosov representations, and the geometry of the Hitchin components which extends the Weil-Petersson geometry of Teichmüller space. In particular recent work on realizing Anosov representations as geometric structures on closed manifolds, the pressure metric on Hitchin representations, as well as tameness results for flat Lorentzian manifolds, will be among the topics discussed at the workshop.