Conférencier: Nathaniel Sagman, Université du Luxembourg

For S a closed surface of genus at least 2, Hitchin representations from pi_1(S) to PSL(n,R) naturally generalize Fuchsian representations to PSL(2,R). Labourie proved that every Hitchin representation comes with an invariant minimal surface in the corresponding symmetric space. Motivated by the mapping class group action and potential Kahler metrics on the space of Hitchin representations, he conjectured that uniqueness holds as well. 

In this talk we'll explain how we used Higgs bundles to produce large area minimal surfaces that give counterexamples to Labourie's conjecture, and we'll overview related advances in the theory of Higgs bundles at high energy. This is all joint with Peter Smillie.