2 problems

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Erdős–Purdy–Straus conjecture on distinct simplex volumes
Erdős–Purdy–Straus conjecture. This construction is tight for all sufficiently large $n$ . The conjecture asks whether the displayed upper bound gives the exact minimum once $n$ is…
Conjecturesolveddiscrete-geometry distinct-distances simplex-volumesarXiv posted 2 days ago
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Sharp threshold conjecture for volumes of simplices
Simplex-volume threshold conjecture. The threshold $d-1$ is sharp for guaranteeing that $\mathcal V_d(E)$ has positive Lebesgue measure.
Conjectureopengeometric-measure-theory simplex-volumesarXiv posted 2 days ago

Erdős–Purdy–Straus conjecture on distinct simplex volumes