Mirrors of 3d Sicilian theories

We consider the compactification of the 6d N=(2,0) theories, or equivalently of M-theory 5-branes, on a punctured Riemann surface times a circle. This gives rise to what we call 3d N=4 Sicilian theories, and we find that their mirror theories are star-shaped quiver gauge theories. We also discuss an alternative construction of these 3d theories through 4d N=4 SYM on a graph, which allows us to obtain the 3d mirror via 4d S-duality.