2 problems

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Conjecture on the maximal number of facets of a six-dimensional L-type domain
An $L$ -type domain is a cone of positive semidefinite quadratic forms whose Dirichlet–Voronoi polytopes have the same combinatorial-metric structure. Let $C_1$ be a primitive $L$ -t…
Conjectureopenquadratic-forms voronoi-theoryarXiv posted 2 days ago
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Closedness and discreteness of perfect forms in a Voronoi space
Let $(V,\mathcal{Q},Z,\mathbf{G})$ be a Voronoi space, and consider its set of perfect forms. Closedness and discreteness conjecture. The set of perfect forms in a Voronoi space is…
Conjectureopendiscrete-sets quadratic-forms voronoi-theoryarXiv posted 2 days ago

Conjecture on the maximal number of facets of a six-dimensional L-type domain