Noé de Rancourt: Ramsey theory, games, and Banach-space dichotomies, part 3

Data: quinta-feira, 24 de agosto de 2017, às 13h30h

Sala: Sala B-05 (Bloco B do IME)

Palestrante: Noé de Rancourt (Université Paris 7)

Título: Ramsey theory, games, and Banach-space dichotomies, part 3

Resumo:  In this talk, which is a sequel of the two preceding ones, I will explain the difficulties that make it impossible to have a real analogue of Mathias-Silver theorem in a general setting, and discuss how these
difficulties can be solved. Then, in the abstract setting defined in the last talk, 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. I will then present Gowers' Ramsey-type theorem for block-sequences, which is an approximate version of the last result in the setting of Banach spaces with a basis, and use it to end the proof of Gowers' first dichotomy. If time remains, I will present a generalisation of the abstract Ramsey theorem which also implies Borel determinacy of games on the integers, and hence is much stronger than an usual Ramsey theorem, in a matemathical way.
Apoio: Projeto USP-Cofecub "Geometria dos espaços de Banach"