8 problems

Let $T_{a,b,c,d}$ be a truly skew pentagram map, with parameters $(a,b,c,d)$ as in the paper, and let its dynamical degree be denoted by $\rho(T_{a,b,c,d})$. Khesin–Soloviev's conj…

Let $P$ be a $(k+3)$-gon in $\mathbb{RP}^k$, where $k\geq 2$, and let $J=(1,\ldots,1)$. For even $k$, let $I=(1,\ldots,1,2,1,\ldots,1)$ with the same number of $1$'s before and aft…

A convex Poncelet polygon is a polygon in the projective plane whose vertices lie on one conic and whose edges are tangent to another conic; convexity means convexity in an affine…

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…

Density and finite-to-one conjecture. The map $\pi_1$ has dense image. Restricted to twisted configurations, the map $\pi_1$ is finite-to-one. This predicts both generic realizabil…

Let $P\subset\mathbb{P}^2$ be an axis-aligned $2n$-gon. Let $T$ denote the pentagram map, and let … be its point of collapse. Let $\mathscr C(P)$ denote the center of mass of $P$.…

Let $T_{\mathcal I,\mathcal J}$ be a universal pentagram map on $d$-tuples of twisted $n$-gons in ${\mathbb {RP}}^d$, determined by matrices $\mathcal I$ and $\mathcal J$. Let…

Khesin–Soloviev higher-dimensional pentagram Devron conjecture. If $B=F^{n-3}(A)$, then $B_1,B_3,\ldots,B_{2n-1}$ are coplanar, and $B_2,B_4,\ldots,B_{2n}$ are also coplanar.