6 problems

Triple-twist parity conjecture. For every slab tiling ${\mathbf t}$ of ${\cal R}$, the integers

Let $\mathcal{H}$ be a Poncelet family of $N$-gons interscribed between two homothetic, concentric ellipses, and let $A_1$ and $A_2$ be the areas of the two lateral harmonic polygo…

A bicentric pedal polygon is obtained from a bicentric polygon by taking its pedal polygon with respect to a limiting point, denoted by $\ell_1$ or $\ell_2$. Cosine-sum invariance…

Let $X$ be a smooth oriented homology-oriented $4$-manifold with the $\mathbb{Z}[\mathbb{Z}]$-homology of $S^1\times S^3$. The invariants $\lambda_{SW}(X)$ and $\lambda_{FO}(X)$ de…

Excentral $X_3$-inconic conjecture. The ratio $\mu'_3/\mu_3$ is invariant over all 3-periodics and is given by

Fenchel–Nielsen parameter conjecture. The subgroup $\langle A,B\rangle$ is determined up to conjugacy by