 
Summary: MIRROR SYMMETRY, LANGLANDS DUALITY AND
THE HITCHIN SYSTEM
Abstract. Notes of talks by Tamas Hausel in Oxford, Trinity
Term, 2010. Notes by Gergely Berczi, Michael Groechenig and
Geordie Williamson.
1. Higgs bundles and the Hitchin system
1.1. The moduli space of vector bundle on a curve. Let C be a
complex projective curve of genus g > 1. We fix integers n > 0 and
d Z. We asssume throughout that (d, n) = 1.
1.1.1. GLn. A central object of study in these talks will be:
Nd
:=
moduli space of rank n vector bundles on C
which are semistable of degree d.
This space can be constructed using geometric invariant theory (GIT)
or gauge theory.
We recall that a vector bundle is called stable if ever subbundle F
satisfies
µ(F) =
deg F
