Description:
Higher rank Teichmüller theory is the study of certain connected components of character varieties of surface groups in higher rank semisimple Lie groups, with the property that all elements in these components correspond to faithful representations with discrete image. Like classical Teichmüller theory, this relatively recent theory is very rich and builds on a combination of methods from various areas of mathematics. Its many facets were explored in detail during the Arbeitsgemeinschaft.