  We consider Laplacian growth problems using a field theory approach. In
particular we consider the Saffman-Taylor (ST) problem. The idealized settings
of the problem, with vanishing surface tension between the bubble and the
surrounding fluid, is singular due to the formation of cusps after a finite
time (for generic initial conditions). A natural regularization of the cusp, is
the addition of surface tension, but this complicates the mathematical
description of the problem a great deal. We discuss a different method of
regularization which arises from the relation of the ST problem with integrable
systems and matrix models.
