Orbifolds of 4d N=2 supersymmetric gauge theories

After recalling how some 4d N=2 gauge theories arise from reductions of 6d N=(2,0) superconformal theories on
a Riemann surface, I will discuss two discrete quotients with codimension 2 orbifold singularities. In the first
case the orbifold acts by rotations around one plane of the 4d N=2 theory; this is related to a Gukov-Witten
surface operator that imposes a monodromy around that plane. We deduce instanton partition functions in the
presence of surface operators; interestingly, instantons can fractionalize. In the second case the orbifold acts by
reflection on the 4d theory and the Riemann surface. We learn how boundaries are encoded in the AGT
correspondence. We are led to consider 4d N=2 quiver theories where some vector multiplets live on a
hemisphere and others on a projective space.