The focus of my research is to develop mathematical modeling and scientific computing techniques to study problems arising in the areas of fluid mechanics, biology and materials science. I am particularly interested in applications where hydrodynamics are coupled to phase transformation processes. These problems can often be formulated in terms of ordinary or partial differential equations and typically involve free boundaries. The methods I use to study these problems include asymptotic and perturbation methods, bifurcation and stability techniques, and numerical techniques.