9 problems

Let $R$ be a rational function in $z_1$ with deformation dimension $m=1$, satisfying the conditions of Proposition[necessary condition], and suppose that its first three critical v…

Tricolour graph construction. For any tricolour graph there exists a function

Uniqueness conjecture. For each such passport, its realization as a dessin d'enfant is unique.

Projective-prime dessin conjecture. For each projective prime $p=1+q+\cdots+q^{n-1}>3$, there exists at least one dessin of type $(3,2,p)$ and degree $p$ with monodromy group…

General dessin conformal-block conjecture. For a dessin satisfying the proposition's conditions, it corresponds to a family of 4-point CBs whose states follow the stated table.

Unique coherent extension conjecture. This partial choice of factors has a unique coherent extension to $\tilde{\mathcal{A}}$, meaning that the ideal generated by $Z_\psi(\psi)$ fo…

A dessin d'enfant is a combinatorial object associated with a trigonal curve; it is maximal when it has one singular fiber in each region and is connected. Deformation conjecture.…

Let $\mathcal{L}$ be the lattice of biased dessins, let $\Gamma' = \operatorname{Aut}(\mathcal{L})$, and let $\Gamma'_0$ be the subgroup of $\Gamma'$ that fixes the three vertices…

Square-root class conjecture. One has