4 problems

Rohatgi's conjecture. The lower bound is tight:

Gishboliner–Jin–Sudakov conjecture. The exponent in this bound can be chosen to be linear in $k$.

Gir27ao–Janzer–Janzer conjecture. The ordered Ramsey number of $P^<_{k,n}$ in $q$ colors admits the displayed bound with an exponent linear in $q$.

For integers $2\le k < s < n$ and $2\le t\le {s\choose k}$, let $r_k(s,t;P_n)$ be the minimum $N$ such that every red/blue coloring of the $k$-sets of $[N]$ contains a monochromati…