5 problems

Morris–Soltan's conjecture. They conjectured that

Grid obstruction conjecture. There exists a $\gamma\in(1,2)$ such that the Erdős–Szekeres construction cannot be realized in an $n^\gamma\times n^\gamma$ integer grid. The paper co…

Integer-grid problem conjecture. The answer to this problem is no for all $\gamma\ge 1$; equivalently, for every $\gamma\ge 1$, there are arbitrarily large such point sets containi…

6-hole and empty 6-pseudo-triangle conjecture.

Let $h(n,k)$ be the least positive integer such that every planar set ${\cal X}$ in general position with at least $h(n,k)$ points contains $n$ points forming a convex $n$-gon whos…