7 problems

A rational discrete analytic function is a discrete analytic function represented as a rational function. Isaacs' conjecture. Every rational discrete analytic function is a polynom…

Let $Z^c$ be the square grid circle pattern with $0<c<2$, whose circles are labeled by … and which covers the infinite sector with angle $c\pi/2$, with the centers of the border ci…

Let $f$ be a polynomial of degree $k$ on a discrete Riemann surface, and let the ramification number of $f$ at a cycle $\gamma$ be its winding number around the origin, when define…

Let $R$ be a simply connected convex region of a discrete Riemann surface, and let the associated discrete exponentials be holomorphic functions on $R$. Exponential-generation conj…

Uniform discrete derivative bound. There is a uniform bound

A circle-packing immersion is a collection of discs tangent according to a prescribed pattern, without requiring the discs to have disjoint interiors. An immersion is entire when i…

Let $q\in[0,4]$, and consider the random cluster model on lattice domains. For the Ising model, let $F(z)$ denote the function in Proposition, which is discrete holomorphic and sat…