The next Banach spaces webinar is on Friday November 19 9AM Central time. Please join us at
https://unt.zoom.us/j/83807914306
Title: No dimension reduction for doubling spaces of $\ell_q$ for $q>2$.
Abstract: We'll provide a new elementary proof for the impossibility of dimension reduction for doubling subsets of $\ell_q$ for $q>2$. This is done by constructing a family of diamond graph-like objects based on the construction by Bartal, Gottlieb, and Neiman. We'll compare our approach with previous results and discuss their advantages and disadvantages. One noteworthy consequence of our proof is that it can be naturally generalized to obtain embeddability obstructions into non-positively curved spaces or asymptotically uniformly convex Banach spaces. Based on the work with Florent Baudier and Andrew Swift.
For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach
Best regards,
Bunyamin Sari