classical trace and extension theorems characterize traces of spaces of generalized smoothness such as Sobolev and Besov to smooth submanifolds of Euclidean space. The subject originated from Hassler Whitney seminal papers of 1934, which deal with the following problem: given a real function on an arbitrary subset of Euclidean space, determine whether it is extendible to a function of a prescribed smoothness on the entire space.

Whitney developed important analytic and geometric techniques that allowed him to solve this problem for functions defined on subsets of the real line to be extended to m-times continuously differentiable functions on the entire real line. He also formulated and solved similar problems related to jets of functions defined on a subset of Euclidean space in any dimension. In the decades since Whitney's seminal work, fundamental progress was made by Georges Glaeser, Yuri Brudnyi, Pavel Shvartsman, Edward Bierstone, Pierre Milman, Wieslaw Pawlucki, and Charlie Fefferman.

It is natural also to consider similar extension and trace problems for functions in Sobolev spaces. These results are at a much earlier stage, though there has been significant progress of late. Another problem is to find the Lipschitz constant associated to m-jets.

The objective of the program is bringing together an international group of experts in the areas of function theory and functional and geometric analysis to report on and discuss recent progress and open problems in the area of Whitney type problems.