The energy functional of a Hitchin representation

In this talk we will discuss the energy functionals on Teichmüller space that are associated to Hitchin representations. We will show that these functionals are strictly plurisubharmonic functions on Teichmüller space. In the second half of this talk we consider the question whether a Hitchin representation is uniquely determined by its energy functional. We answer a similar question in a simpler setting and
discuss work in progress on how these results can be expanded to include Hitchin representations.