2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/24994We 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.PhD thesisSoft Condensed MatterStatistical MechanicsHigh Energy Physics - Theorytext