5 problems

Let $M$ be a complete Riemannian manifold with nonnegative Ricci curvature, and fix a growth rate $d$. Consider the space of harmonic functions on $M$ having polynomial growth of r…

Non-negative curvature implies polynomial growth. If $G$ has bounded degrees and satisfies $\mathrm{CD}(0,\infty)$, then $G$ has polynomial growth. More precisely,

Let $G$ be a graph of polynomial growth, with growth rate $\rho(G)$, and let $\mathsf{emb}(G)$ be the least dimension $d$ such that $G$ embeds into the grid with diagonals…

Easo–Hutchcroft conjecture. There exists a universal constant $C$ such that

Polynomial growth conjecture. For fixed $m$, the size $|G_m|$ is of polynomial order in $n$ as $n$ tends to infinity.