6 problems

Kühn­el's componentwise minimality conjecture. The $f$-vector

Kühn­el–Lassmann 3-torus conjecture. The Kühn­el–Lassmann triangulation of $T^3$ with $15$ vertices is vertex-minimal and is unique with

Kühn­el–Lassmann torus conjecture. The Kühn­el–Lassmann series of combinatorial $d$-tori $T^d$ with $2^{d+1}-1$ vertices is vertex-minimal.

Kühn­el's minimal-vertex conjecture. The minimum numbers of vertices are: $12$ for $(S^2\times S^1)^{\#2}$ and $(S^2\times\!\_\!\_S^1)^{\#2}$; $13$ for the corresponding connected…

Kühn­el's conjecture. For $j=0,\dots,\lfloor(d-1)/2\rfloor$,

Kühn­el–Kalai conjecture.