We show that intersection numbers on the moduli space of stable bundles of coprime rank and degree over a smooth complex
curve can be recovered as highest-degree asymptotics in formulas of Vafa-Intriligator type. In particular, we explicitly evalu-
ate all intersection numbers appearing in the Verlinde formula.Our results are in agreement with previous computations of Wit-
ten, Jeffrey-Kirwan and Liu. Moreover, we prove the vanishing of certain intersections on a suitable Quot scheme, which can be
interpreted as giving equations between counts of maps to the Grassmannian.