2 problems

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Sebő's unimodular covering conjecture for finite rational cones
A finite rational cone is a cone generated by finitely many rational vectors, and its Hilbert basis is the canonical finite generating set of the associated affine semigroup. A sim…
Conjectureopenaffine-semigroups convex-geometry lattice-polyhedraarXiv posted 2 days ago
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Existence of maximal subdivisions after scaling a lattice polyhedron
Maximal subdivision conjecture. For any lattice polyhedron $\Delta$ , there exists a sufficiently large integer $N$ such that $N\Delta$ has a maximal subdivision.
Conjectureopenlattice-polyhedra toric-geometry tropical-geometryarXiv posted 2 days ago

Sebő's unimodular covering conjecture for finite rational cones