2 problems

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The choir-number conjecture for four-, five-, and six-dimensional flat tori
Choir-number conjecture.
Conjectureopenflat-tori isospectral-geometry spectral-geometryarXiv posted 2 days ago
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Lauret–Linowitz conjecture on highest-volume isospectral spherical space forms
Let $d$ be an odd integer with $d\geq 5$ . An isospectral and non-isometric pair of $d$ -dimensional spherical space forms is said to have highest volume if its common volume is maxi…
Conjecturesolvedisospectral-geometry lens-spaces spherical-space-formsarXiv posted 2 days ago

The choir-number conjecture for four-, five-, and six-dimensional flat tori