2 problems

Normalizer-equivalence conjecture. If $\operatorname{Fix}(G)^{\perp}$ contains a rational $G$-invariant subspace other than $\{0\}$ and $\operatorname{Fix}(G)^{\perp}$ itself, then…

Herr–Rehn–Schürmann conjecture. If $G$ is not $2$-homogeneous, then $G$ has infinitely many core points up to translation equivalence.