5 problems

Two-sided limiting-threshold conjecture. For every $\epsilon>0$, there exists $\kappa^*(\epsilon)>0$ such that for every $kappalekappa^*(\epsilon)$: no polynomial-time search algorithm…

Let $\kappa>0$ be the SBP parameter and let the algorithmic threshold be the largest constraint density up to which efficient algorithms can find a solution with high probability. T…

Let $A\in(\mathbb{R}^N)^{\otimes p}$ have independent entries distributed as $\mathcal{N}(0,N^{-(p-1)})$, and let $\mathcal{B}_N\subset\mathcal{H}_N$ denote the binary and Hilbert-…

Hilbert-cube OGP conjecture. For every even $p\geq4$, there exist $\mu>0$ and $0<\nu_1<\nu_2<1$ such that $\mathcal{A}$ satisfies the OGP with domain $\mathcal{S}_N=\mathcal{H}_N$,…

Landscape conjecture. Suppose … If $k=o(\sqrt n)$, then: