4 problems

Infinite-group recovery conjecture. In the extreme case $M\rightarrow\infty$, Theorem should still hold, and exact recovery of the clusters should be possible whenever the whole ne…

Scalar-overlap restriction conjecture. This restriction of the replica formula for the free energy is correct in general, including outside the setting of abelian groups.

AMP algorithmic threshold conjecture. Approximate Message Passing algorithms of the form developed in PWBM2018 are expected to achieve weak signal recovery from a random initializa…

Let $\mathcal{G}$ be a closed subgroup of the orthogonal group $\mathcal{O}(d)$, and let $\operatorname{conv}(\mathcal{G})$ denote its convex hull. For…