3 problems

An orthoscheme is a non-Euclidean polytope whose relevant volume is under consideration. A classical polylogarithm is a polylogarithm of depth one, such as $\operatorname{Li}_n(z)$…

Nonzero volume-defect conjecture. As $\ell\to\infty$, the corresponding orthoschemes have a nonzero volume defect with probability at least $\varepsilon>0$.

Let $d$ be a positive integer and let $P$ be a convex polytope in $\mathbb R^d$. An orthoscheme is a simplex whose successive edges are pairwise orthogonal in the standard ordering…