Obstructions to embeddabillity of metric spaces in $L_p$ spaces: Property $\alpha$

I'll present a few inequalities on metric spaces holding for $L_p$ and other natural spaces. One of these inequalities can serve as the metric analogue of (Pisier's) property $\alpha$ and serves as an obstruction to the Lipschitz(and uniform) embeddability of (some discrete subsets of) Schatten classes into $L_p$ spaces. Joint work with Assaf Naor.Non UBCUnreviewedAuthor affiliation: Weizmann Institute of ScienceFacult