5 problems

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Compactness conjecture for isospectral closed Riemannian manifolds
A closed Riemannian manifold is a compact manifold without boundary equipped with a Riemannian metric, and two such manifolds are isospectral when their Laplace spectra, counted wi…
Conjectureopenisospectral-manifolds spectral-geometryarXiv posted 2 days ago
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Ouyang–Pesce conjecture on isospectral deformations of nilmanifolds
Ouyang–Pesce conjecture. All isospectral deformations of nilmanifolds must arise from the Gordon–Wilson method for constructing isospectral nilmanifolds.
Conjectureopenisospectral-manifolds nilmanifolds spectral-geometryarXiv posted 2 days ago
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Conjecture on the growth of representation classes for symmetric groups
Conjecture. For every integer $n\geq 10$ ,
Conjectureopenisospectral-manifolds representation-theory symmetric-groupsarXiv posted 2 days ago
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The super-polynomial lower-bound conjecture for type A1 semisimple Lie groups
Let $H$ be a semisimple Lie group of type $\mathrm{A}_1$ with more than one simple factor, and let $\mathrm{IL}_{H}(x)$ denote the maximal size of a family of pairwise isospectral,…
Conjectureopenisospectral-manifolds riemannian-geometry semisimple-lie-groupsarXiv posted 2 days ago
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Torsion-homology conjecture for strongly isospectral hyperbolic 3-manifolds
Torsion-homology conjecture. For every prime number $p$ , there exist strongly isospectral closed hyperbolic $3$ -manifolds $M_1$ and $M_2$ such that
Conjectureopenhyperbolic-geometry isospectral-manifolds torsion-homologyarXiv posted 2 days ago

5 problems

Compactness conjecture for isospectral closed Riemannian manifolds

Ouyang–Pesce conjecture on isospectral deformations of nilmanifolds

Conjecture on the growth of representation classes for symmetric groups

The super-polynomial lower-bound conjecture for type A1 semisimple Lie groups

Torsion-homology conjecture for strongly isospectral hyperbolic 3-manifolds