Abstract：

There are three natural perspectives in which one could view Teichmüller space: Riemann surfaces as holomorphic objects, hyperbolic metrics as geometric objects, and Fuchsian representations as algebraic and topologic objects. In higher Teichmüller theory, one studies representations into higher rank Lie groups, where now the holomorphic objects are replaced with Higgs bundles. In certain cases, the new geometric objects are minimal surfaces inside symmetric spaces, and are linked to other geometric structures. In the same spirit as Thurston and Bonahon, we construct a compactification of a few Hitchin components and explicitly describe the boundary objects. This is joint work with A. Tamburelli.