Oscar Garcia-Prada, ICMAT, Madrid
‘'Involutions of Higgs bundle moduli spaces”
We consider the moduli space M(G) of G-Higgs bundles over a compact Riemann surface X, where G is a complex semisimple Lie group. This is a hyperkhler manifold homeomorhic to the moduli space of representations of the fundamental group of X in G. In this talk we study involutions of M(G), and describe the subvarieties of fixed points, and their relation to representations of the fundamental group of X. We also comment on the relation of the fixed point sub varieties with Langlands duality and mirror symmetry for Higgs bundles.