5 problems

Width law of large numbers. There exists a constant $W>0$ such that, as $n\to\infty$,

Homological width conjecture. For some dimensional constant $c_k$,

Universal-cover-of-balls conjecture. There exist positive dimensional constants $\delta_n$, $C_n$, and $R_n$ such that, for every $p\in M$,

Macroscopic curvature and codimension 2 width. There exist positive dimensional constants $\delta_n$, $C_n$, and $R_n$ such that, if every ball of radius $R_n$ in $M$ has volume at…

Let $P$ be a poset, let $\operatorname{width}(P)$ be the maximum size of an antichain, and let ${\operatorname{qn}}(P)$ denote its queue-number. Write $w=\operatorname{width}(P)$.…