3 problems

Let $R(\ell,k)$ be the two-colour Ramsey number, and suppose that $k$ and $\ell$ are sufficiently large with $\log k\ll\ell\ll k$. Super-exponential gap conjecture. For every fixed…

The iterated-tripartite classification conjecture. For a 3-graph $H$, there exists a constant $c$ depending only on $H$ such that

For a fixed $3$-graph $H$, write $r(H,K_n^{(3)})$ for the least $N$ such that every red-blue coloring of the edges of $K_N^{(3)}$ contains a red copy of $H$ or a blue copy of…