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This is the 11th article in the collection of reviews "Exact results in N=2supersymmetric gauge theories", ed. J. Teschner. It describes an approach tounderstanding the 4d/2d relations discovered by Alday, Gaiotto and Tachikawa byestablishing a triangle of relations between the zero mode quantum mechanicsobtained by localisation of class $\cal S$ theories, the quantum theoryobtained by quantisation of Hitchin moduli spaces, and conformal field theory.

Supersymmetric gauge theories, quantisation of moduli spaces of flat connections, and Liouville theory