Title: Higher Teichmuller and higher rank Schottky groups
Abstract: Schottky groups are the simplest and most classical examples of Kleinian groups, that is, of discrete subgroups of Mobius transformations. I will explain several generalisations of this notion to subgroups of higher rank Lie groups. One of these generalisations leads to an explicit description of positive representations of surfaces with non-empty boundary, a type of higher Teichmuller representation introduced by Fock and Goncharov in 2003. I will show how this description allows the construction of fundamental domains for an open domain of discontinuity in the projective space or the sphere, depending on the dimension. This talk will feature joint work with N. Treib, F. Kassel and V. Charette.