My research mainly involves interpolation and approximation of functions in normed linear spaces, and the representation and computation of curves and surfaces. Recently, I have worked on approximation from sparse grids, subdivision on sparse grids, variational spline theory, local spline interpolation, and dual basis functions in subspaces. Recently, I provided a condition for the invertibility of submatrices of the Pascal matrix based on a connection with (lacunary) Birkhoff interpolation. This relates to my work on the linear independence of subsets of the dual Bernstein basis on polynomial spaces.