No dimension reduction for doubling spaces of $\ell_q$ for $q>2$

I'll discuss 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. 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.