10 problems

Let $\mathcal{G}_{n,p}$ denote the Erdős–Rényi random graph, and let $\Gamma\sim\mathcal{G}_{n,p}$. For a group or graph, “thick of order at most $k$” is used in the sense of the p…

Hypergraph-index conjecture. These upper bounds are equalities: the following are equivalent:

Non-uniqueness conjecture. Under the stated integrability condition and suitable assumptions on $\beta$ and $T$, such a density $\rho$ and incompressible Sobolev vector field $u$ e…

Inclusion-divergence conjecture. Under these assumptions,

Let $W_\Gamma$ be a right-angled Coxeter group, and let $n$ denote its hypergraph index. Let thickness of order $n$ and divergence $x^{n+1}$ have their standard meanings for the gr…

Let $\Gamma$ be a simplicial graph and let $W_{\Gamma}$ be the corresponding right-angled Coxeter group. Fix an order $n$. Equivalence conjecture. The following are equivalent:…

Let $X$ be a nonpositively curved metric space, and let $Div(X)$ denote its divergence function, measuring the lengths of shortest paths avoiding a ball that connect points roughly…

Suppose that $\mathbb{N}=A\mathbin{\dot\cup}B$ is a partition of the natural numbers. Let $Q$ be a basic sequence, and say that it is fully divergent when the relevant divergence c…

Let $t\geq2$ be an integer and suppose that $\{1,\ldots,t\}=A\mathbin{\dot\cup}B$. Let $Q$ be a basic sequence, and say that it is $t$-divergent when the relevant divergence condit…

Linear divergence conjecture. Every lattice in a semisimple Lie group of higher rank has linear divergence.