Noé de Rancourt: Ramsey theory, games, and Banach-space dichotomies, part 2

Data: quinta-feira, 17 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 2

Resumo: In this talk, I will give an introduction to Ramsey theory and discuss how this theory can apply to give a proof of Gowers' first dichotomy (which I introduced in the last talk). 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 begin with introducing Mathias-Silver theorem, which is a Ramsey result in the contexts of sets without structure, and explain what difficulties can happen when we try to adapt this result to other contexts, like Banach spaces with bases. Then, in an abstract and purely combinatorial formalism, I will discuss how these difficulties can be solved and I will present a general Ramsey result, where the possible conclusions will be formulated in terms of the existence of winning strategies in two-players games with perfect information. This theorem, in the context of Banach spaces, is a form of the Ramsey-type theorem Gowers used to prove his dichotomies.

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

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