6 problems

Redundant symmetry-rigidity conjecture. For every such $\Gamma$ and $e$, $(G({\cal S})-e-e^*,*)$ is $\Gamma$-rigid in $\mathbb R^{k+1}$.

Higher-dimensional face lower bound conjecture. For $j=1,\dots,k$,

Let $\Delta$ be a balanced $d$-polytope, or more generally a balanced $\mathbf{k}$-homology $(d-1)$-sphere. Balanced GLBC. … The inequalities were established for all balanced poly…

Let $\Delta$ be a balanced normal pseudomanifold of dimension $d-1\geq 3$. Klee–Novik's balanced lower bound conjecture. … This extends the balanced Lower Bound Theorem by includin…

Let $d\geq 3$, and let $X$ be a connected, non-simply connected triangulated $d$-manifold. Lower bound conjecture for non-simply connected manifolds. Its face numbers satisfy … Equ…

Let $d$ and $k$ be integers with $d\geq 2k+1$, and let $X$ be a triangulated $d$-sphere with face-vector $(f_0,\dots,f_d)$. Generalized lower bound conjecture. For every $j$, the f…