Forcing Axioms and Banach Lattices

• Grant number: 25/08065-1
• Support Opportunities: Scholarships abroad - Research Internship - Master's degree
• Start date: January 01, 2026
• End date: June 30, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Christina Brech
• Grantee: Maurício Rossetto Corrêa
• Supervisor: Antonio Aviles Lopez
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: Universidad de Murcia, Spain
• Associated to the scholarship: 24/11202-8 - Forcing axioms and Banach spaces, BP.MS

Abstract

This project proposes a research internship at the University of Murcia (ESP) to investigate certain combinatorial implications within Banach space theory focusing on exploring possible connections between the theory of Banach lattices and the techniques introduced on the main articles of the master's project. The candidate's master's project already studies combinatorical consequences in functional analysis, concentrating mostly in the use of forcing axioms, strong generalizations of the Baire category theorem. The internship would allow the student to expand his skillset with methods and concepts that are extremely relevant in contemporary mathematical research. The responsible professor from the foreign institution, Dr. Antonio Avilés Lopez, has a vast experience in such topics, which makes him suitable for guiding the candidate through the proposal.