Introduction -- A phase-field model with a double obstacle potential -- Cahn and Hilliard fluid on an oscillating boundary -- Mathematical models of phase boundaries in alloys: phase field and sharp interface -- New ideas in calculus of variations and geometric measure theory -- The minimum time problem and its applications to front propagation -- Planar motion of an anisotropic interface -- Singular limit for an Allen-Cahn equation with a nonlocal term -- Axiomatization of shape analysis and application to texture hyperdiscrimination -- Variational approximation of the geometric motion of fronts -- On radial growth in crystallization theories of hyperbolic nature -- Physics and geometry of flow under curvature: singularity formation, minimal surfaces, geodesics, and surface tension -- Computing hypersurfaces which minimize surface energy plus bulk energy -- Boundary regularity for flows of nonparametric surfaces driven by mean curvature -- Some questions of De Giorgi about mean curvature flow of triply-periodic surfaces -- List of Contributors -- List of Participants.