10 problems

A pointed pseudotriangulation is a pseudotriangulation whose vertices are pointed, and a flexible flat cylinder is a flat cylindrical surface whose metric parameters may vary. Flex…

Weak flexible 2-periodic placement characterization. There exists a full placement-lattice $(p,L)$ of $G$ in $\mathbb{R}^2$ such that $(G,p,L)$ is a flexible full $2$-periodic fram…

Type 3 exclusion conjecture. Then $G$ has either a type 1 or type 2 flexible 2-lattice NBAC-colouring, a fixed lattice NBAC-colouring, or

Type 3 realization conjecture. If $G$ has a type 3 flexible 2-lattice NBAC-colouring, then there exists a full placement-lattice $(p,L)$ of $G$ in $\mathbb{R}^2$ such that…

Flexible 2-periodic placement characterization. There exists a full placement-lattice $(p,L)$ of $G$ in $\mathbb{R}^2$ such that $(G,p,L)$ is a flexible full $2$-periodic framework…

Let $langle H,mrangle$ be a body-bar orbit framework on the fixed torus $mathcal T0^d$, and let $mathcal G{mathcal C}(Y)$ denote the collection of connected components associate…

A periodic orbit graph is a graph with edges carrying gains in the fixed torus setting. Let $\langle H,m\rangle$ be a periodic orbit graph in dimension $d$, and let…

Periodic bar-body rigidity sufficiency conjecture. The conditions provided by Theorem also provide sufficient conditions for the generic rigidity of periodic bar-body orbit framewo…

Incidentally periodic rigidity conjecture. If $(\langle G,m\rangle,p)$ is infinitesimally rigid on the flexible torus, then it is infinitesimally rigid as an incidentally periodic…

Let $\tilde{G}(\mathbf{p},\mathbf{L})$ be an infinitesimally rigid periodic framework with periodic graph $(\tilde{G},\varphi)$. Let $\Lambda<\mathbb{Z}^2$ be any sub-lattice, and…