Logic Seminar
Christian Rosendal
UIUC
The rough classification of Banach spaces
Abstract: The geometric theory of Banach spaces underwent a tremendous
development in the decade 1990-2000 with the solution of several
outstanding conjectures by Gowers, Maurey, Odell and Schlumprecht.
Their discoveries both hinted at a previously unknown richness of the
class of separable Banach spaces and also laid the beginnings of a
classification program for separable Banach spaces due to Gowers.
However, since the initial steps done by Gowers, little progress was made
on the classification program. We shall discuss some recent advances due
to V. Ferenczi and myself on this by means of Ramsey theory and dichotomy
theorems for the structure of Banach spaces. This simultaneously allows us
to answer some related questions of Gowers concerning the quasiorder of
subspaces of a Banach space under the relation of isomorphic
embeddability.
Tuesday November 27, 2007 at 4:00 PM in SEO 427