4 problems

Let $\mathfrak{g}$ be the rank-three hyperbolic Kac–Moody Lie algebra of type $A_1^{++}$, with invariant bilinear form $(\cdot,\cdot)$, and let $p(n)$ denote the ordinary partition…

Let $\mathcal{P}_3$ be the class of convex three-dimensional parallelohedra, namely convex polyhedra that tile $\mathbb{R}^3$ by translations. For every $V>0$ and every…

Godara and Sarkar conjectured that, for every odd prime $p$, if $H_{p^3}=\operatorname{UT}_3(\mathbb{F}_p)$ is the Heisenberg group of order $p^3$, then $\mathsf{d}(H_{p^3})=3p-3$,…

For the incompressible Euler equations on boundary-free three-dimensional space, $\partial_t u+(u\cdot\nabla)u=-\nabla p$, $\nabla\cdot u=0$ on $\mathbb{R}^3\times[0,\infty)$, with…