Appears in collection : Higher Structures in Holomorphic and Topological Field Theory

In this talk, I am going to present certain conjectures (due to D. Gaiotto) which provide explicit examples of quantum local geometric Langlands duality for the group GL(n)\times GL(m). These conjectures lead to some interesting equivalences of categories involving representation theory of the Lie superalgebra GL(m|n). I will present some evidence for these conjectures and discuss proofs in some special cases.