Methods of set theory in the theory of complex structures

• Grant number: 12/00631-8
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: March 18, 2013
• End date: March 17, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Valentin Raphael Henri Ferenczi
• Grantee: Wilson Albeiro Cuellar Carrera
• Supervisor: Jordi Lopez Abad
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: Consejo Superior de Investigaciones Científicas (CSIC), Spain
• Associated to the scholarship: 10/17512-6 - Banach spaces with various complex structures, BP.DR

Abstract

This research project is a study of two problems of the theory of complex structures on real Banach spaces, as part of the candidate's PhD project at the Institute of Mathematics and Statistics (IME-USP). Based on the methods developed in the study of a space defined by the advisor in Brazil Valentin Ferenczi, and methods used in another space defined by the adviser abroad Jordi Lopez-Abad, the candidate will attempt to define a space with exactly a countable infinite number of complex structures. In addition, the student will use the descriptive set theory applied to the theory of Banach spaces to study the number of complex structures in a given space, in the framework of the classification of equivalence relations on Polish spaces. (AU)

Scientific publications

(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)

CARRERA, W. CUELLAR. A Banach space with a countable infinite number of complex structures. JOURNAL OF FUNCTIONAL ANALYSIS, v. 267, n. 5, p. 1462-1487, SEP 1 2014. (10/17512-6, 12/00631-8)