Mini Course: Anosov representations

Anosov representations are discrete, faithful (or finite-kernel) representations of word hyperbolic groups into semisimple Lie groups, with strong dynamical properties. They were introduced by Labourie in 2006 for fundamental groups of closed negatively-curved manifolds, and generalized by Guichard and Wienhard in 2012. They have been much studied in the past few years, and play an important role in higher Teichmüller-Thurston theory and in recent developments in the theory of discrete subgroups of Lie groups. We will introduce these representations, give examples, and discuss some characterizations.