4 problems

Let $r\ge 1$ and $s\ge 1$ be integers, and let $H$ be an $r$-uniform hypergraph with $s(H)=s$. Asymptotic equivalence conjecture. Then … The quantity…

Let $r\ge 2$, $s\ge 2$, and $k\ge r+1$ be integers. Let … Let $H$ be an $r$-uniform hypergraph with $s(H)=s$ and $\delta_{s-1}(H)=\delta$. The gamma lower-bound conjecture. Then ……

Let $K_{s,s}$ be the balanced complete bipartite graph, let $\mathrm{wsat}(n,K_{s,s})$ denote its weak saturation number, and let $G$ be an erasable graph in the corresponding eras…

Let $K_{s,t}$ be the complete bipartite graph with $2<s\leq t$, and let $j$ satisfy $2\leq j\leq t-3$. Write $\mathrm{wsat}(n,K_{s,t})$ for the weak saturation number of $K_{s,t}$.…