In this talk I am going to present certain conjectures (due to D.Gaiotto) which provide explicit exmples of (quantum) local geometric Langlands duality for

the group GL(n)\times GL(m). These conjectures lead to some interesting equivalences of categories invloving representation theory of the Lie superalgebra gl(m|n). I will present some evidence for these conjectures and discuss proofs in some special cases.