2 problems

Let $n\in\mathbb{N}$ and let $X$ be an $n$-point subset of $\ell_1$. Its Euclidean distortion is the least distortion among embeddings of $X$ into $\ell_2$. Goemans's conjecture. E…

Let $(X,\delta)$ be a diversity with induced metric $d$, and consider embeddings constructed solely from $d$. Induced-metric embedding conjecture. There exists such an embedding th…