Interests include the study of Morrey's quasiconvex functions and their properties. Quasiconvexity is the fundamental convexity condition for the existence of minimizers of problems in the calculus of variations. It is implied by polyconvexity - a tractable form of quasiconvexity which has applications in nonlinear elasticity theory and itself a subject of research. The functionals representing the stored energy of certain elastic materials are singular in the sense that their integrands assume the value infinity in an essential way. Thus the machinery of classical regularity theory cannot easily be brought to bear, and the smoothness properties of minimizers of such functionals remain largely unknown. It is well known that singularities in minimizers can have a physical significance: cavitation, for example, can correspond to a point of discontinuity of the minimizer. The relevance of singularities in the gradient is less well understood, though here there may be lessons to learn from liquid crystal theory. Other interests include the nucleation of martensite in shape-memory alloys, which may be studied by means of energy functionals that include surface energy terms. Such terms are designed to ensure the existence of global and local minimizers, and they introduce a lengthscale into the minimizing microstructures. These functionals are not yet fully understood, though notable progress in a specific case was made by Kohn and Müller by studying the scaling of the global minimum energy in the spirit of gamma convergence.