Place: Fields Institute (Room 210)

Date: November 16 , 2018 (13:30-15:00)

Speaker: Noé de Rancourt

Title: Gowers spaces: unifying standard and strategical Ramsey theory

Abstract:

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 examples of the same kind could

be found in other areas of mathematics.