Forcing axioms and Banach spaces

• Grant number: 24/11202-8
• Support Opportunities: Scholarships in Brazil - Master
• Start date: November 01, 2024
• End date: July 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Christina Brech
• Grantee: Maurício Rossetto Corrêa
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 23/12916-1 - Geometry of Banach spaces, AP.TEM
• Associated scholarship(s): 25/08065-1 - Forcing Axioms and Banach Lattices, BE.EP.MS

Abstract

In this project we propose to study applications of combinatorial methods to uncountable structures in Banach spaces. In this sense, we will study two main results: a consequence of PFA on biorthogonal systems in non-separable spaces and a consequence of OCA on the Calkin algebra. The proposal will be complemented by an internship abroad, which will put the student in contact with a renowned researcher in the field and bring them into contact with research topics.