Variational Analysis and Computation of Cahn-Hilliard and Isoperimetric Problems with Long-Range Interactions: Self-Assembly of Diblock Copolymers and Liquid Drop Models.

Variational and Computational Analysis of Problems Involving Distance Functions, Generalized Voronoi Regions and Centroidal Voronoi Tessellations

Variational Analysis of Functionals with Competing Attractive and Repulsive Algebraic Potentials

Analysis of Grain Growth: Imaging, Statistics and the Phase Field Crystal Model

Variational Analysis of Problems Associated with the Shape of Biological Membranes

Variational Approaches to Image Processing and Barcode Reconstruction

Variational Analysis in Type 1 Superconductors and Ferromagnets: Scaling Laws and Branching of Domain Structures

Miscellaneous: Continuum Mechanics, Geometric Measure Theory, Conservation Laws.