Integrable Systems and Moduli Spaces

The modern approach to integrable systems typically proceeds via a curve, the parameters of the curve encoding the actions and its Jacobian (or possibly some related Prym) encoding the angles. Physically relevant families of curves are often described by fixed relations amongst differentials on the curve: the constrained curves and associated Jacobians describe a moduli space for the physical system. We shall look at both problems and results in constructing such moduli spaces.