3 problems

Let $X$ be an $n$-point subset of $L_1$, and let $c_2(X)$ denote its least distortion when embedding $X$ into Hilbert space. The hypercube conjecture. Every $n$-point subset of…

Let $V$ be a finite-dimensional Hilbert space, and let $\Gamma\leq \operatorname{E}(V)$ be an isometry group with closed orbits. The orbit space $V/\Gamma$ is equipped with its quo…

For $n\to\finity$ and $p>2$, let $\mathsf{c}_2^n(L_p)$ denote the maximum, over all $n$-point metric spaces, of the least distortion with which the space embeds into $L_p$ and then…