Curvilinear Mesh Adaptation using RBF Interpolation and Smoothing
A Spectral/HP Element Framework
Thin-plate-Spline Curvilinear Meshing on a Calculus-of-Variations Framework
Structure-preserving function approximation via convex optimization

Some of my Projects
(Beware, clicking on them opens links to awesome journal articles!)

Structure-preserving nonlinear filtering for continuous and discontinuous Galerkin Spectral/HP element methods
Fast Barycentric-Based Evaluation Over Spectral/HP Elements