Look up Assouad, Indyk (for value of embedding theorem from CS perspective)
bi-holder problem.
Topics for Seminar
1. Assouad embedding and some overview (me)
2. Rademacher theorem (grad student for this)
3. Poincare inequality and doubling. (Polynomial growth as opposed to exponential growth...) Colding-Minicozzi theorem. (Sauer)
4. Some results about bi-Lipschitz embedding of finite metric spaces (see Matousek book, Abert).
5. Pansu's theorem (?) and application to bi-Lipschitz.(60 page Annals paper, but it does other things)
6. Semmes stuff. What is involved in Poincare inequality? (Some more spaces that have Poincare inequality, Me.)
7. Some other funny spaces that are Ahlfors regular of fractional Hausdorff dimension, Why they don't bi-Lipschitz embed.
8. Kleiner's proof of polynomial growth theorem (sauer)
9. Mendel-Naor's theory of metric cotype and why is it that Lp doesn't uniformly embed in Lq unless it's obvious.