  Strebel differentials are a special class of quadratic differentials with
several applications in string theory. In this note we show that finding
Strebel differentials with integral lengths is equivalent to finding
generalized Argyres-Douglas singularities in the Coulomb moduli space of a U(N)
$\N=2$ gauge theory with massive flavours. Using this relation, we find an
efficient technique to solve the problem of factorizing the Seiberg-Witten
curve at the Argyres-Douglas singularity. We also comment upon a relation
between more general Seiberg-Witten curves and Belyi maps.
