  We study the correspondence between four-dimensional supersymmetric gauge
theories and two-dimensional conformal field theories in the case of N=2* gauge
theory. We emphasize the genus expansion on the gauge theory side, as obtained
via geometric engineering from the topological string. This point of view
uncovers modular properties of the one-point conformal block on a torus with
complexified intermediate momenta: in the large intermediate weight limit, it
is a power series whose coefficients are quasi-modular forms. The all-genus
viewpoint that the conformal field theory approach lends to the topological
string yields insight into the analytic structure of the topological string
partition function in the field theory limit.
