Geometry of Banach Spaces

The course will cover the basics of the theory of Banach spaces with an emphasis on their nonlinear geometry. The course will start with the basics of the theory of Banach spaces. For example, we will cover bases on Banach spaces (e.g., Schauder bases, unconditional bases, shrinking and completely bounded bases), basic sequences, Banach-Mazur Theorem, geometry of l_p spaces, Pitt’s Theorem, etc. After these basic concepts have been covered, we will focus on nonlinear problems. These topics will include Lipschitz, coarse and uniform geometry of Banach spaces as well as their relationships to each other. We will also study graph embeddings in Banach spaces (e.g., Hamming Graphs and Interlaced Graphs) and asymptotic geometry of Banach Spaces. If time permits, additional topics will also be given (e.g., differentiating Lipschitz maps into Banach spaces, stable spaces, etc).

References:
1) Topics in Banach space theory, Fernando Albiac e Nigel Kalton.
2) Geometric Nonlinear Functional Analysis, Yoav Benyamini e Joram Lindenstrauss.
3) Artigo selecionados.
4) Notas de aula (pretendo escrever notas sobre os tópicos mais especializados sem um livro texto apropriado, essas notas devem ser parte do livro texto que estou escrevendo sobre geometria de larga escala).