Higgs bundles, branes, and application

Higgs bundles are pairs of holomorphic vector bundles and holomorphic 1-forms taking values in the endomorphisms of the bundle. Their moduli spaces carry a natural Hyperkahler structure, through which one can study Lagrangian subspaces (A-branes) or holomorphic subspaces (B-branes). Notably, these A and B-branes have gained significant attention in string theory. After introducing Higgs bundles and the associated Hitchin fibration, we shall look at  natural constructions of families of different types of branes, and relate these spaces to the study of 3-manifolds, surface group representations and mirror symmetry.