The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on June 21, 2016 at 14:00 in Room 478 of IMI.

A talk on:

The self-duality equations on a Riemann surface and symplectic geometry

will be delivered by Peter Dalakov.

Everybody is invited.

Abstract. In 1987 N. Hitchin introduced a system of gauge-theoretic equations associated with a compact Riemann surface X and a reductive complex Lie group G. These self-duality equations on a Riemann surface have been actively studied since then by differential geometers, algebraic geometers and representation theorists. The moduli space of solutions is a hyperkaehler orbifold, whose twistor family contains two non-isomorphic complex structures, both of which have interpretations as moduli of holomorphic (algebro-geometric) data. One of these corresponds to the moduli space of G-Higgs bundles on X and the other to the moduli space of G-local systems on X. The moduli space of (semi-stable) G-Higgs bundles is an algebraic integrable system. In the first part of the talk we shall review the main properties of Hitchin's moduli space. In the second part we shall discuss briefly some recent results (with U. Bruzzo) concerning the holomorphic symplectic and Poisson geometry of the generalised Hitchin system.