Includes bibliographical references.

Variational problems arising in biology ; On the Cauchy problem for phase and vortices in the parabolic Ginzburg-Landau equation ; Nonlocal Cahn-Hilliard and isoperimetric problems: Periodic phase separation induced by competing long- and short-range interactions ; On a generalized Ginzburg-Landau energy for superconducting/normal composite materials ; Global questions for map evolution equations ; Pohozaev-type identities for an elliptic equation ; Some remarks on Monge-Ampere functions ; Variational versus pde-based approaches in mathematical image processing ; On the energy of a Chern-Simons-Higgs vortex lattice ; Some recent results about a class of singularly perturbed elliptic equations ; The dipole problem for ^1/2(\mathbb S^2 ; \mathbb S^1) maps and application ; Hodge decompositions, Gamma convergence and the Gross-Pitaevskii energy ; Bifurcation of vortex solutions to a Ginzburg-Landau equation in an annulus ; An Allen-Cahn type problem with curvature modification ; Rare events, action minimization, and sharp interface limits ; The Gauss-Green theorem for weakly differentiable vector fields