Unsolved Problems

Find reasonable bounds for the maximal density of a set $A \subset \{1, \ldots, N\}$ not containing a 3-term progression with common difference a squa...

Define the 2-colour van der Waerden numbers $W(k, r)$ to be the least quantities such that if $\{1, \dots, W(k, r)\}$ is coloured red and blue then th...

What is $C$, the infimum of all exponents $c$ for which the following is true, uniformly for $0 < \alpha < 1$? Suppose that $A \subset \mathbb{F}_2^n$...