In 1992, Hitchin introduced, using the theory Higgs bundles, the notion of what are now known as Hitchin representations. Later on, they were identified as dynamical objects. The plan of this course would be in a first part to recall the basics of Non Abelian Hodge Theory, the Hitchin bration, then the Hitchin section. The second part will describe these representations as dynamical objects, explaining Anosov representations, geodesics flows, cross ratios and the thermodynamic formalism.
This course is scheduled to be taught by incoming Chancellor's Professor François Labourie.