5 problems

The diluted $K$-spin model assigns spin configurations on a random $K$-uniform Erdős–Rényi hypergraph, with objective given by the cut density. A factor of i.i.d. process is a proc…

Montanari's local-algorithm conjecture. Local algorithms find asymptotically optimal configurations for Max-cut on random regular graphs. Consequently, this would imply

Let $d\in\{2,3\}$, and consider local algorithms that estimate the surface area, namely the intrinsic volume $V_{d-1}$, from digital images of sets on lattices whose resolution ten…

Hatami–Lovász–Szegedy conjecture. There exists a sequence of $r$-local independence functions $f_r$, $r\geq 1$, such that almost surely $I(f_r,n)$ is an independent set in…

Half-approximation conjecture. The same result should hold with $\gamma=1/2$.