2 problems

Zero-free locus conjecture. The zero-free locus of hypergraphs of maximum degree $\Delta$ is identical to the zero-free locus of graphs of maximum degree $\Delta$:

Galvin–McKinley–Perkins–Sarantis–Tetali conjecture. For each $k\geq 2$, there exists a constant $C_k>0$ such that, if $G$ is a $k$-uniform linear hypergraph of maximum degree…