##
Gilles Lancien

Szlenk indices.
Applications to renorming theory and to the non linear classification of
Banach spaces.

### Abstract:

In this series of lectures we will introduce the Szlenk index of a
Banach space and cover some of the applications of this notion.
We will start with a brief description of its historical applications:
the non existence of universal spaces and the isomorphic classification
of $C(K)$ spaces where $K$ is a countable compact space.
Then we will show how it is related with locally uniformly rotund and
uniformly Kadec-Klee renormings.
Finally we will see how it can be used as an invariant under uniform
homeomorphisms between Banach spaces.