5 problems

Curien–Kortchemski conjecture.

Classification conjecture. The dissections obtained by gluing towers are exactly the dissections into triangles and quadrilaterals that admit a unitary frieze.

Canonical 3d-dissection conjecture. Every element of $\mathrm{PSL}(2,\mathbb{Z})$ corresponds to a unique $3d$-dissection.

Serpent nest conjecture. For any hollow quadrangulation $\mathrm{Q}_\circ$, there is a bijection between the serpent nests of $\mathrm{Q}_\circ$ and the maximal $\mathrm{Q}_\circ$-…

Fair $d$-dissection enumeration conjecture. A strictly convex polygon with $2(d-1)n+2$ vertices has exactly