4 problems

For each integer $d\ge 1$, let $\mu_d$ be the minimum number of vertices among all simplicial complexes whose geometric realization is homeomorphic to real projective $d$-space…

Milman-moduli conjecture. For positive $\varepsilon$,

Day–Nordlander conjecture. The displayed inequalities hold.

Let ${\bf K}$ be an arbitrary $0$-symmetric convex body in ${\mathbb R}^3$. A truncated octahedron of the form ${\bf T}-{\bf T}$ is obtained from an arbitrary tetrahedron ${\bf T}$…