Ramsey theory methods in Banach spaces

• Grant number: 13/24827-1
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Duration: May 05, 2014 - May 04, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Valentin Raphael Henri Ferenczi
• Grantee: Valentin Raphael Henri Ferenczi
• Visiting researcher: Jorge Lopez-Abad
• Visiting researcher institution: Instituto de Ciencias Matemáticas (ICMAT), Spain
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

This project refers to the visit of Prof. Jorge Lopez-Abad to the Math Department of IME-USP, by invitation of Prof. Valentin Ferenczi, to participate, for a 12 months period (April 2014 - March 2015) as collaborator in several ongoing research projects. In particular, apart from Prof. Ferenczi, the visitor will collaborate with Profa. Christina Brech, the post-doc Brice Rodrigue Mbombo Dempowo and the graduate students of the group. This will be realized by meetings with V. Ferenczi and C. Brech on a regular basis, by the participation in the Functional Analysis Seminar, by a minicourse on Ramsey theory, by the joint organization of the BWB 2014 event, and participation in several student defenses. The research program during the visit of Professor Jorge will be concentrated on the following lines: 1) unconditional bases and complex structures, 2) operators in C([0,1]), 3) quotients of C(K)-spaces, 4) quasi-unconditionnality, 5) the separable quotient problem, 6) Existence of unconditional sequences, 7) Asplund spaces, 8) Amenable and extremely amenable groups. (AU)

Scientific publications

(7)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

BARTOSOVA, DANA; LOPEZ-ABAD, JORDI; LUPINI, MARTINO; MBOMBO, BRICE. THE RAMSEY PROPERTIES FOR GRASSMANNIANS OVER R, C. COMBINATORICA, NOV 2021. (12/20084-1, 13/24827-1, 13/14458-9)

LOPEZ-ABAD, J.; TRADACETE, P.. BASES OF RANDOM UNCONDITIONAL CONVERGENCE IN BANACH SPACES. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v. 368, n. 12, p. 32-pg., 2016-12-01. (13/24827-1)

BARTOSOVA, DANA; LOPEZ-ABAD, JORDI; LUPINI, MARTINO; MBOMBO, BRICE. The Ramsey property for Banach spaces and Choquet simplices, and applications. COMPTES RENDUS MATHEMATIQUE, v. 355, n. 12, p. 1242-1246, DEC 2017. (12/20084-1, 13/24827-1, 13/14458-9)

LOPEZ-ABAD, J.; TRADACETE, P.. BASES OF RANDOM UNCONDITIONAL CONVERGENCE IN BANACH SPACES. Transactions of the American Mathematical Society, v. 368, n. 12, p. 9001-9032, DEC 2016. (13/24827-1)

BRECH, C.; LOPEZ-ABAD, J.; TODORCEVIC, S.. Homogeneous families on trees and subsymmetric basic sequences. ADVANCES IN MATHEMATICS, v. 334, p. 322-388, AUG 20 2018. (15/26654-2, 12/24463-7, 13/24827-1)

BARTOSOVA, DANA; LOPEZ-ABAD, JORDI; LUPINI, MARTINO; MBOMBO, BRICE. The Ramsey property for operator spaces and noncommutative Choquet simplices. JOURNAL OF FUNCTIONAL ANALYSIS, v. 281, n. 9, NOV 1 2021. (13/24827-1, 12/20084-1, 13/14458-9, 16/25574-8)

BARTOSOVA, DANA; LOPEZ-ABAD, JORDI; LUPINI, MARTINO; MBOMBO, BRICE. The Ramsey property for Banach spaces and Choquet simplices. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, v. 24, n. 4, p. 36-pg., 2022-01-01. (12/20084-1, 13/24827-1, 13/14458-9)