Dear all, The next Banach spaces webinar is on Friday June 12 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Noé de Rancourt (Kurt Gödel Research Center) Title: Local Banach-space dichotomies Abstract. I will present some results of a recent joint preprint with Wilson Cuellar Carrera and Valentin Ferenczi.<https://arxiv.org/abs/2005.06458> These results are generalizations of Banach-space dichotomies due to Gowers and to Ferenczi–Rosendal; the original dichotomies aimed at building a classification of separable Banach spaces "up to subspaces". Our generalizations are "local versions" of the original dichotomies, that is, we ensure that the outcome space can be taken in a prescribed family of subspaces. One of the most interesting examples of such a family is the family of all non-Hilbertian Banach spaces; hence, our results are a first step towards a classification of non-Hilbertian, $\ell_2$-saturated Banach spaces, up to subspaces. If time permits, I will present some applications of our work to a conjecture by Ferenczi and Rosendal about the number of subspaces of a separable Banach space. * For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Upcoming schedule June 19: Christian Rosendal, University of Illinois at Chicago and NSF Thank you, and best regards, Bunyamin Sari