7 problems

Generalized Glick conjecture. Let $k\geq 2$. If $n=3k+1$, the point $\widehat P_{\infty}$ is a fixed point for the projective action of $G_{P,k,k}$. If $n=3k+2$, the point…

Pre-compactness conjecture. The sequence $\{P^{\ell}\}$ is pre-compact modulo affine transformations. That is, this sequence has a convergent subsequence which converges to another…

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…

Vanishing-density conjecture. The dynamical domain has asymptotic density zero over the tower of finite fields:

Integrability conjecture. The map $T_{n,k}$ acting on ${\cal C}(n,k)$ is a discrete totally integrable system.

Uniqueness conjecture. For any $(n,k)$, the invariant $Z$ is uniquely maximized, and has a unique critical point, at the point representing the logarithmic pentagram spiral.

Singularity confinement conjecture. Singularity confinement holds generically on $X_S$ unless