  Conformal theories of the Argyres-Douglas type are notoriously hard to study
given that they are isolated and strongly coupled thus lacking a lagrangian
description. In flat space, an exact description is provided by the
Seiberg-Witten theory. Turning on a $\Omega$-background makes the geometry
``quantum" and tractable only in the weak curvature limit. In this paper we use
the AGT correspondence to derive $\Omega$-exact formulae for the partition
function, in the nearby of monopole points where the dynamics is described by
irregular conformal blocks of the CFT. The results are checked against those
obtained by the recursion relations coming from a conformal anomaly in the
region where the two approaches overlap. The Nekrasov-Shatashvili limit is also
discussed. Finally, we comment on the existence of black holes in De Sitter
space whose low energy dynamics is described by an Argyres-Douglas theory.
