Algebraic Geometry Seminar

A Higgs bundles (introduced by N. Hitchin in 1987) is a pair of a
holomorphic vector bundle and a holomorphic 1-form taking values in
the endomorphisms of the bundle.  The moduli space of Higgs bundles
carries a natural Hyperkahler structure, through which we can study
Lagrangian subspaces (A-branes) or holomorphic subspaces (B-branes)
with respect to each structure. Notably, these A and B-branes have
gained significant attention in string theory.

We shall begin the talk by first introducing Higgs bundles for complex
Lie groups and the associated Hitchin fibration, and recalling how to
realize Langlands duality through spectral data. We shall then look at
a natural construction of families of subspaces which give different
types of branes. Finally, by means of spectral data, we shall relate these
branes to the study of 3-manifolds, surface group representations. We
shall conclude with some conjectures related to Langlands duality.