6 problems

Thurston's conjecture. This theorem should have a simpler proof based on more general principles, in particular the max flow/min cut principle, convexity, and…

Freedman–Headrick conjecture. The maximal flow and minimal cut on $(V,E)$ converge as

Cui et al.'s asymptotic quantum max-flow min-cut conjecture. For every quantum tensor network $\mathcal{N}=(G,d,S,T)$,

Let $G$ be a perfect graph, and let $\mathcal{C}$ be its clique clutter, whose edges are the maximal cliques of $G$. The clutter $\mathcal{C}$ is ideal when its covering polyhedron…

Kesten's flow-constant conjecture. The flow constant should exist for all $d \geq 2$.

Kesten's surface-law conjecture. The surface law should hold for all $F(0)<1-p_c$.