  S-duality is a nontrivial self-duality of type IIB string theory that
exchanges strong and weak coupling. We give a mathematically rigorous
description of how S-duality acts on a low-energy supersymmetry-protected
sector of IIB string theory, using a conjectural description of such protected
sectors in terms of topological string theory. We then give some applications
which are of relevance to Geometric Langlands Theory and the representation
theory of the Yangian.
