Nonabelian Hodge theory is the study of three moduli spaces associated to an algebraic curve--the space of Higgs bundles, the space of local systems, and the space of representations of the fundamental group--which turn out to be diffeomorphic but algebraically distinct. After giving an overview of this picture for motivation, I'll talk about another collection of three spaces, much more concrete and explicit than those mentioned above, that exhibit a similar relationship. This construction will be particularly timely for those who are learning about toric varieties in my class. |