Strategical Ramsey theory was developed in the nineties by Gowers in the

setting of Banach spaces; in this setting where the natural pigeonhole

principle does not always hold, this theory is an alternative to standard

infinite-dimensional Ramsey theory.

In this talk, I will present the formalism of Gowers spaces, an abstract

formalism unifying both strategical and standard infinite-dimensional

Ramsey theory. In this formalism, we can prove an abstract Ramsey theorem

implying both Gowers' Ramsey-type theorem in Banach spaces, and more

standard Ramsey results like Galvin-Prikry's theorem. I will also present

a result unifying infinite-dimensional Ramsey theory and determinacy.

I will then introduce a new family of Gowers spaces that arose from a

recent work in progress with Wilson Cuellar-Carrera and Valentin Ferenczi.

These examples from functional analysis are based on local properties of

subspaces of Banach spaces. We hope that exampl