9 problems

Let $G=\prod_{i=1}^m G_i(k_i)$, where the $k_i$ are locally compact, non-discrete fields and the $G_i$ are connected, absolutely almost simple algebraic groups defined over $k_i$.…

Let $\Gamma$ be an irreducible lattice in a semisimple group over nondiscrete locally compact fields. Let $X_\Gamma$ be the product of the irreducible symmetric spaces and Euclidea…

Let $n\in\mathbb{N}$, and let $(\mathcal{M},d)$ be an $n$-point metric space. The space is of negative type when its $\frac{1}{2}$-snowflake $(\mathcal{M},d^{1/2})$ embeds isometri…

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…

Union distortion conjecture.

Let $X\to B$ be an almost Postnikov pair with $\pi_1X=\pi_1B=\Gamma$, monodromy representation $\rho$, and Euler class $\operatorname{eu}$. Suppose that for some $\gamma\in\Gamma$,…

Let $X$ be a space and consider the study of distortion functions of homotopy classes using rational equivalence, meaning that torsion information is ignored and spaces and maps ar…

For $2<q<p$ and $m,n\in\mathbb N$, let $[m]_q^n$ denote the $n$-dimensional integer grid with its $\ell_q$ metric, and let $c_p([m]_q^n)$ be its least bi-Lipschitz distortion in…

Distortion conjecture. An element in $\mathrm{Homeo}_{0}(S)$ which satisfies the conclusion of the proposition—that is, is non-spreading—is distorted.