SUSY field theories and geometric Langlands: The other side of the coin

Inclusion of surface operators leads to interesting generalisations of the correspondence discovered by Alday, Gaiotto and Tachikawa between four-dimensional N=2 SUSY field theories and conformal field theory. My goal will be to outline how this generalisation is related to the geometric Langlands correspondence and to a certain quantum generalisation of this correspondence. The resulting picture has interesting relations both to the CFT-based approach to the geometric Langlands correspondence developed by Beilinson and Drinfeld, and to the gauge-theoretic approach of Kapustin and Witten, offering the perspective to integrate all these approaches into a unified picture