Abstract
A finite order automorphism of a complex semisimple Lie group determines a cyclic grading of its Lie algebra. Vinberg's theory is concerned with the geometric invariant theory associated to this grading. Important examples include the case of involutions and representations of cyclic quivers. After reviewing some basic facts about Vinberg's theory, in this talk I will discuss about its relation to the geometry of moduli spaces of Higgs bundles over a compact Riemann surface.
