Résume | The geometric Langlands correspondence has been linked to the S-duality of 4D quantum gauge theories in the works of Witten and others. But where does S-duality come from? It turns out that it has a natural geometric explanation from the point of view of a mysterious 6D quantum field theory predicted by string theory and M-theory, which appears to have no Lagrangian description. Although the existence of this theory and its properties are still conjectural, this information has been used to reveal surprising connections between 4D and 2D quantum field theories, some of which have now been proved. I will review some of these connections and their implications for the geometric Langlands Program. |