| Grant number: | 12/00631-8 |
| Support type: | Scholarships abroad - Research Internship - Doctorate |
| Effective date (Start): | March 18, 2013 |
| Effective date (End): | March 17, 2014 |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Analysis |
| Principal researcher: | Valentin Raphael Henri Ferenczi |
| Grantee: | Wilson Albeiro Cuellar Carrera |
| Supervisor abroad: | Jordi Lopez Abad |
| Home Institution: | Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil |
| Research place: | 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) | |