6 problems

Algebraic-function coefficient conjecture for Shabat–Blaschke products
arXiv@arxiv
Suppose $\rho$ is a tree monodromy representation giving rise to Shabat–Blaschke products of degree $n$ with exactly two critical values in $\mathbb{D}$ . For each fixed…
Conjectureopenbelyi-maps blaschke-products modular-functions
0
Kitaev's conjecture on algebraic Painlevé VI solutions and regular almost Belyi maps
arXiv@arxiv
Let an algebraic solution of the Painlevé VI equation be given, and let a $(k,\ell,m)$ -minus-4 regular almost Belyi map be a rational map of the type specified in the source. Pull-…
Conjectureopenalgebraic-geometry belyi-maps painleve-equations
1
Logarithmic action conjecture for polynomial components of almost Belyi maps
arXiv@arxiv
Let $\varphi(x,w)$ be an almost Belyi map with definition field $K=\mathbb{Q}(w)$ . Suppose the vector field … annihilates $\varphi(x,w)$ . A logarithmic action conjecture. This vect…
Conjectureopenalgebraic-geometry belyi-maps differential-equations
1
The unboundedness conjecture for full Belyi maps
arXiv@arxiv
Let $B_{\mathcal{P}}(m)$ be the number of full degree $m$ Belyi maps defined over $\mathbb{Q}$ with bad reduction within a finite set of primes $\mathcal{P}$ . Suppose that…
Conjectureopenarithmetic-geometry belyi-maps
0
Divisor criterion for the square-root class of Belyi functions
arXiv@arxiv
Square-root class conjecture. One has
Conjectureopenalgebraic-curves belyi-maps dessins-denfants
0
The isoradial–Belyi modular-parameter conjecture for dimers
arXiv@arxiv
Let an isoradially embedded dimer have an $R$ -dimer determined by the superconformal $R$ -charges, with modular parameter $\tau_R$ . Let $(X,\beta)$ be the corresponding Belyi pair,…
Conjectureopenbelyi-maps dimer-models toric-calabi-yau
0

6 problems

Algebraic-function coefficient conjecture for Shabat–Blaschke products

Kitaev's conjecture on algebraic Painlevé VI solutions and regular almost Belyi maps

Logarithmic action conjecture for polynomial components of almost Belyi maps

The unboundedness conjecture for full Belyi maps

Divisor criterion for the square-root class of Belyi functions

The isoradial–Belyi modular-parameter conjecture for dimers