In this talk, we introduce Higgs bundles and the Hitchin fibration with examples. We then discuss how Higgs bundles arise as the classical limits of the geometric Langlands duality (On both the Galois side and the Automorphic side, we see Higgs moduli arise as limits!), and we outline Ron and Tony's work for showing that the geometric Langlands holds in the classical limit.

Hitchin&RonNotes.pdf