14h-16h | Lucas Branco
The moduli space M(G) of Higgs bundles for a complex reductive group G on a compact Riemann surface carries a natural hyperkahler structure and it comes equipped with an algebraically completely integrable system through a flat projective morphism called the Hitchin map. Motivated by mirror symmetry, I will discuss certain complex Lagrangians (BAA-branes) in M(G) coming from real forms of G and give a proposal for the mirror (BBB-brane) in the moduli space of Higgs bundles for the Langlands dual group of G. In this talk, I will focus on the real groups SU^*(2m), SO^*(4m) and Sp(m,m). Higgs bundles for these groups have non-reduced spectral curves and we are led to describe certain subvarieties of the moduli space of rank 1 torsion-free sheaves on ribbons. If time permits we will also discuss another class of complex Lagrangians in M(G) which can be constructed from symplectic representations of G.