12 problems

Let $\beta^{3l+p-1}(T^{p,2l-1}_+)$ denote the beta invariant in the indicated dimension. The beta-invariant noninjectivity conjecture. The map … is not injective; consequently, the…

Consider domino tilings of the triangular lattice with periodic boundary conditions. ReCom moves define a metagraph on the tilings, and parity invariants partition it into four sec…

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

Let $p$ be a positive characteristic, and let Theorem on the correspondence between Dixmier–Ohno invariants and singularity types be denoted by the referenced theorem. Positive-cha…

Let $h_n$ denote the lower central homotopy invariants of links in closed orientable $3$-manifolds, and let the Almost-Concordance Conjecture be the conjecture asserting infinitely…

Let a finite or periodic point set be given in the Euclidean plane $\mathbb R^2$, and let $\mathrm{PDD}$ denote its pointwise distance distribution invariant. PDD completeness conj…

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…

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 $\lambda_{FO}(X)$ ar…

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