Suppose E is a compact subset of R^n, and we are given a function f, mapping E to the real numbers. How can we tell if the function lies on a smooth convex function? Can we construct an almost optimal, smooth, convex interpolant of the function? These are examples of Whitney-type extension and trace problems; while theoretical, they are driven by practical questions of interpolation of data, where convexity is a natural constraint. I will begin with an answer to these questions by presenting work of mine proving there is a […]