**Valentin
Ferenczi**, Universidade de São Paulo and l'Université
Pierre et Marie Curie - Paris 6

*On Gowers' classification program in Banach space
theory*

(slides)* *

We shall survey the program of classification of Banach spaces
proposed by Fields medalist W.T. Gowers in the 1990s. The famous
dichotomies of Gowers and their implications will be exposed,
classical results from the 1970s will be revisited, and recent
developments in the classification program will be presented.

**Christian Rosendal**, University of Illinois at Chicago

*On bounded representations and maximal*

symmetry (slides)

We study problems of maximal symmetry in Banach spaces. This
is done by providing an analysis of the structure of small subgroups
of the general linear group GL(X), where X is a separable reflexive
Banach space. In particular, we provide the first known example
of a Banach space X without any equivalent maximal norm, or
equivalently such that GL(X) contains no maximal bounded subgroup.
Moreover, this space X may be chosen to be super-reflexive.

** **

The **Back2Fields Colloquium Series** celebrates the accomplishments
of former postdoctoral fellows of Fields Institute thematic programs.
Over the past two decades, these programs attracted the rising
stars of their field and often launches very distinguished research
careers. As part of the 20th anniversary celebrations, this series
of colloquium talks will allow the general mathematical public
to become familiar with some of their work.

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