Geometry of Banach spaces

• Grant number: 23/12916-1
• Support Opportunities: Research Projects - Thematic Grants
• Start date: June 01, 2024
• End date: May 31, 2029
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Valentin Raphael Henri Ferenczi
• Grantee: Valentin Raphael Henri Ferenczi
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Pesquisadores principais: Eloi Medina Galego
• Associated researchers: Christina Brech ; Leandro Candido Batista ; Pedro Levit Kaufmann ; Vinícius Colferai Corrêa Miranda ; Vinicius Morelli Cortes ; Willian Hans Goes Corrêa ; Wilson Albeiro Cuellar Carrera
• Associated scholarship(s): 25/00001-4 - Immersions and isomorphisms between spaces of continuous functions, BP.DR; 24/16659-6 - On non-self-conjugate operator ideals and complex structures on Banach spaces, BP.DR; 24/11202-8 - Forcing axioms and Banach spaces, BP.MS

Abstract

This thematic project involves a Principal and a Co-Principal Investigator, from the Department of Mathematics of IME-USP (Institute of Mathematics and Statistics of the University of São Paulo), Host Institution of the project, and between six and eight associated researchers, from IME-USP, from ICMC-USP, and from the Institute of Science and Technology (ICT) of UNIFESP. Graduate students and post-docs will also paricipate in the project. The lines of research of the group are concentrated in the Geometry of Banach spaces, in its interactions with combinatorics, Ramsey theory, set theory, homological theory, non-linear theory, operator theory, and theory of topological groups. Several lines of researchs and problems stand out, which are interrelated, and maybe gathered into four main lines of research:Structures and combinatorial principlesHomological theory of Banach spacesNon-linear theory and Lipschitz free spacesOperator theoryVisits of researchers are expected, leading to a better integration of the researchers of the group with national and international colleagues. (AU)

Scientific publications

(4)

(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)

GALEGO, ELOI MEDINA. The strongest forms of Banach-Stone theorem to C₀(K, lⁿ_p) spaces for all n ≥ 3 and p close to 2. Journal of Mathematical Analysis and Applications, v. 541, n. 2, p. 15-pg., 2024-08-01. (23/12916-1)

CANDIDO, LEANDRO; CUTH, MAREK; SMETANA, ONDREJ. Note on almost isometric ideals and local retracts in Banach and metric spaces. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, v. N/A, p. 25-pg., 2024-08-27. (23/12916-1)

CANDIDO, LEANDRO; CUTH, MAREK; VEJNAR, BENJAMIN. On the weak∗ separability of the space of Lipschitz functions. JOURNAL OF FUNCTIONAL ANALYSIS, v. 289, n. 1, p. 26-pg., 2025-03-07. (23/12916-1)

CACERES-RIGO, ALEJANDRA C.; FERENCZI, VALENTIN. Tight-minimal dichotomies in Banach spaces. STUDIA MATHEMATICA, v. N/A, p. 47-pg., 2025-04-06. (17/18976-5, 16/25574-8, 22/04745-0, 23/12916-1)