**WHITNEY PROBLEMS.**

Whitney problems originate from Hassler
Whitney seminal papers of 1934, they deal with the
following questions: given a function f on an arbitrary subset of a Euclidean
space, how can one tell if this functions is extendible to a function of a
prescribed smoothness on the whole Euclidean space?

Whitney was able to develop very important
techniques which allowed him to answer the question above in the case of the one-dimensional
space and the space of m times continuously differentiable functions on this
space. He also answered similar
questions in any dimension if you are given not just the function f but
actually a string of functions which are supposed to be the related derivatives
of f.

He also was able to give a simple geometric
sufficient condition for an open bounded domain in the Euclidean space to be an
extension domain, meaning that for every m any function on the domain with
bounded partial derivatives of orders less or equal to m, can be extended to an
m times differentiable function on the whole Euclidean space.

Recently Charles Fefferman was able to answer
the original question of Whitney in full generality. This led to a number of
very important developments in the field.

A WHITNEY PROBLEMS WORKSHOP was held at the

The Workshop was generously supported by a
grant from the Office of Naval Research, by the Office of Vice
Provost of the

WHITNEY PROBLEMS WORKSHOP 2008:

1. Schedule of talks and abstracts
whitney\whitneyschedule (1).pdf

2. List of open problems whitney\whitproblems.pdf.

3. Comments to the list
(continuously updated):

(a) Arie Israel: whitney\YossiCounterexample.pdf, whitney\CharlieProblemModification2.pdf

4.
Link to video
files of all lectures of the workshop http://whitneyworkshop2008.blip.tv.

5.
Photos.

FUTURE WHITNEY WORKSHOPS

We plan to have two more Whitney Problems
Workshops in 2009 and 2010. We shall post information about these
Workshops on this site. If you are interested in participating in these
Workshops, please contact Charles Fefferman cf@math.princeton.edu or me nxzobi@wm.edu.