6 problems

Let $d$ be the dimension of the unitary group and let $t$ denote the design order in a relation between $epsilon$-nets and $delta$-approximate $t$-designs on the space of unitary c…

A strong $\epsilon$-net for a range family is a set of points from the underlying ground set that intersects every range containing at least an $\epsilon$-fraction of the ground se…

Optimal-scaling conjecture. With some work, it should be possible to obtain

The epsilon-2-net transfer conjecture. In any reasonable setting, if an $\epsilon$-net exists with some order of magnitude, then an $\epsilon$-2-net exists with roughly the same or…

The t-VC-dimension bound. For general $t$, one has

Alon's conjecture. There are sets of points in the plane whose smallest $\varepsilon$-nets for the family of lines contain