Dear all, The next Banach spaces webinar is on Friday April 10th 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Pavlos Motakis, The University of Illinois at Urbana–Champaign Title: Coarse Universality Abstract. The Bourgain index is a tool that can be used to show that if a separable Banach space contains isomorphic copies of all members of a class C then it must contain isomorphic copies of all separable Banach spaces. This can be applied, e.g., to the class C of separable reflexive spaces. Notably, the embedding of each member of C does not witness the universality of X. We investigate a natural coarse analogue of this index which can be used, e.g., to show that a separable metric space that contains coarse copies of all members in certain “small" classes of metric spaces C then X contains a coarse copy of $c_0$ and thus of all separable metric spaces. This is joint work with F. Baudier, G. Lancien, and Th. Schlumprecht. Upcoming schedule April 17: Mikhail Ostrovskii, St. John’s April 24: Tomasz Kania, Czech Academy May 1: Dan Freeman, St Louis May 8: Chris Gartland, UIUC The video of last week’s talk is available here https://youtu.be/3U_e0Mc25cs For more information please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Thank you, and best regards, Bunyamin Sari