### Coarse Lipschitz embeddings and asymptotic structure of Banach Spaces

Lancien, G *(Franche-Comte)*

Wednesday 16 March 2011, 15:15-16:15

Seminar Room 1, Newton Institute

#### Abstract

The linear properties of Banach spaces considered in this talk will be the ex-
istence of an equivalent asymptotically uniformly smooth (or convex) equivalent
norm. We shall study the stability of these properties under various non linear
transformations, but we will concentrate on the coarse Lipschitz embeddings (i.e.
maps that are bi-Lipschitz for very large distances). These questions in relation
with uniform asymptotic smoothness are now quite well understood. We will try
to present the progress made last year by N.J. Kalton on the stability of uniform
asymptotic convexity under coarse embeddings. We will focus on the use of some
fundamental metric graphs or trees in the subject, and present a few open questions
that we find interesting.