6 problems

Let $0<\alpha=\beta<\frac{1}{2}$ and set $\gamma=1-2\alpha$, so that $0<\gamma<1$. Consider the hexagonal circle patterns $z^{3\alpha}$ with an intersection point at the origin and…

Integrability conjecture. The discrete dynamics induced by the iteration of cluster maps $\psi_{D_{2N}}$ is a discrete integrable system.

Let $m\in\mathbb{Z}$ and let $\tilde z$ be an $m$-closed polygon recutting lattice map, meaning $\tilde z_{i,j}=\tilde z_{i+m,j-m}$ for all $i,j$. Assume $\tilde z_{i,0}=0$ for all…

Let $\mathcal{L}$ be the lattice on which the dSKP recurrence is defined, let $x:\mathcal{L}\to\hat{\mathbb{C}}$ be a solution, and set $a_{i,j}=x(i,j,[i+j]_2)$. Suppose…

Let $m\geq 1$, let $\tilde{f}:\mathbb{Z}^2\rightarrow {\mathbb{R}\mathrm{P}}^2$ be a $2m$-closed pentagram lattice map, equivalently let…

Let $(v_i)$ be a twisted polygon in $b2b2\text{?}b2b2$ and let $I$ be a multi-index defining a generalized pentagram map $T_{I,J}$. The map $T_{I,I}$ is the diagonal case in which…