Casey Tompkins, Ramsey numbers of Boolean lattices

The poset Ramsey number $R(Q_m,Q_n)$ is the smallest integer $N$ such that any blue-red coloring of the elements of the Boolean lattice $Q_N$ has a blue induced copy of $Q_m$ or a red induced copy of $Q_n$. Axenovich and Walzer showed that $n+2\le R(Q_2,Q_n)\le 2n+2$. Recently, Lu and Thompson
improved the upper bound to $\frac{5}{3}n+2$. In this paper, we solve this problem asymptotically by showing that $R(Q_2,Q_n)=n+O(n/\log n)$.
Joint work with Dániel Grósz and Abhishek Methuku.