2 problems

Density conjecture. For every $\epsilon>0$, there exists some positive integer $d$ such that if $I\subseteq\mathbb{Z}^2$ has upper density greater than $\epsilon$, then there is a…

Let $\delta>0$. Consider the collection of non-oriented graphs on the vertex set $[n]$, with density measured relative to the number of such graphs. Gowers' clique-difference conje…