Noé de Rancourt: Ramsey theory, games, and Banach-space dichotomies, part 1

Data: quinta-feira, 10 de agosto de 2017, às 13h30h

Sala: Auditório Antonio Gilioli (Bloco A do IME)

Palestrante: Noé de Rancourt (Université Paris 7)

Título: Ramsey theory, games, and Banach-space dichotomies, part 1

Resumo: This is the first of a series of three talks, during which I will present some combinatorial tools that can be used in the study of Banach-space dichotomies. These dichotomies are one of the fundations of Gowers' loose classification project, which aims to build a list of "well-understood" classes of separable Banach spaces such that every space has a subspace in at least one class. In this first talk, I will present in more details Gowers' project, its motivations and some of the dichotomies Gowers obtained, and then I will give an introduction to Ramsey theory, the combinatorial tool the most used in the proof of dichotomies. This theory consists in a collection of results ensuring that given a partition of a structure, at least one of the pieces of the partition contains a sufficiently large substructure. I will in particular introduce Mathias-Silver theorem (one of the main results in Ramsey theory) and begin to explain how it can be adapted to the setting of Banach spaces.

Apoio: Projeto USP-Cofecub "Geometria dos espaços de Banach"