5 problems

Let $P$ be a centrally symmetric $d$-dimensional polytope. A flag of $P$ is a chain of faces of $P$, one in each dimension. Kalai's full flag conjecture. $P$ has at least…

Klee–Nevo–Novik–Zheng's conjecture. There exists a unique polytopal complex ${\mathcal C}$ in ${\mathbb R}^d$ such that: (i) one face of ${\mathcal C}$ is the cross-polytope…

The polytopal cellulation conjecture. There exists a unique polytopal complex $\mathcal C$ in $\mathbb R^d$ such that: (i) one face of $\mathcal C$ is the cross-polytope…

Let $P$ be a centrally symmetric simplicial $d$-polytope. The higher cs lower bound conjecture. If, for some $3\leq r<\left\lfloor\frac d2\right\rfloor$, … then … Here…

Let $\Delta$ be a centrally symmetric simplicial complex of dimension $d-1\geq 3$. Assume that $\Delta$ is a homology sphere, a connected homology manifold, or a normal pseudomanif…