Mumford compactness for PSL(3,R)-Hitchin representations

Given a closed, oriented and connected surface S of genus at least two, the Hitchin component generalizes classical Teichmüller space as a distinguished component of the PSL(3,R)-character variety. To any such representation, one can define its systole and use Labourie's boundary curve to define its Liouville volume. In this talk, I will define the objects and explain (with some consequences) an analog of the Mumford compactness theorem: the space of Hitchin representations with Liouville volume bounded from above and systole bounded from below is compact