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Homological and descriptive set theory methods in Banach spaces

Abstract

This project deals with two directions of research within the theory of Banach spaces. In a first line we study homological theory in Banach spaces (also called twisted sum theory) from elements of interpolation theory. In the second part, we use methods of descriptive set theory to address Banach space classification problems. More specifically, we are interested in the study of the unconditional structure and local notions of singularity of twisted sums; and in the study of the complexity of isomorphism between separable Banach spaces. (AU)