Data: quinta-feira, 28 de setembro de 2017, às 10h
Sala: Auditório Antonio Gilioli
Palestrante: Christina Brech (IME-USP)
Título: Um espaço de Tsirelson não separável
Resumo: Apresentaremos elementos da construção obtida conjuntamente com J. Lopez-Abad e S. Todorcevic de um espaço de Tsirelson não separável: um espaço de Banach reflexivo de densidade não enumerável que não possui cópias dos espaços $\ell_p$. A construção envolve famílias de subconjuntos finitos de um conjunto de índices não enumerável similares às famílias de Schreier.
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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"
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"
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