Speaker
Description
I will present a variational formulation of the Hitchin system on a compact Riemann surface C of arbitrary genus, allowing simple poles in the Higgs field at finitely many points. The hierarchy of time flows is described within the framework of Lagrangian multiforms, which I will briefly review. Adapting Hitchin’s construction — via symplectic reduction of the space of stable holomorphic structures on a principal G-bundle P \to C — to this variational setting naturally produces a multiform version of the action of 3d mixed BF theory with defects, a lower-dimensional analogue of the celebrated 4d semi-holomorphic Chern–Simons theory. Working directly in holomorphic local trivialisations of principal G-bundles yields a simple 1d action that unifies several well-known integrable hierarchies — rational and elliptic Gaudin, including elliptic spin Calogero–Moser — within a single variational framework. This is based on joint work in progress with V. Caudrelier, D. Harland and A. A. Singh.
