Tightness in Banach spaces 

In this talk, I will explore the concepts of tightness and minimality in Banach spaces, presenting their definitions and their role in classifying subspaces. I will show that every Banach space with an admissible system of blocks contains an infinite-dimensional subspace with a basis that is either -tight or -minimal, a key dichotomy involving these notions. This result is framed within the Banach space classification program initiated by T. Gowers. Finally, I will present some examples to illustrate these concepts.