Fock bundles and the Hitchin component

The study of surface group representations into a Lie group is described by the character variety. I shall present a new approach to study character varieties, by so-called Fock bundles. Although similar to Higgs bundles, the new theory does not need a complex structure on the underlying surface. A Fock bundle induces a higher complex structure and gives a connection between these geometric structures and the Hitchin component. Joint work with Georgios Kydonakis and Charlie Reid.