4 problems

Let $S$ be a clean three-dimensional lattice simplex, meaning that the only lattice points on its boundary are its vertices, and suppose that $S$ has $k\geq 1$ interior lattice poi…

A Gorenstein simplex is a lattice simplex that is Gorenstein, and a lattice pyramid is a lattice polytope obtained as a lattice pyramid. Fix positive integers $k$ and $v\ge 2$, and…

Hensley's maximal-integral-points conjecture. The simplex $S^d_1$ contains the maximal number of integral points among all elements of $\mathcal{S}^d({1})$, the family of $d$-dimen…

Let $\mathcal{T}^d$ be the family of $d$-dimensional lattice simplices with a unique interior lattice point. For $T\in\mathcal{T}^d$, let $\beta_d(T)$ be the smallest barycentric c…