Given an abelian group or semigroup $\mathcal{G}$ and sets $A,B\subseteq\mathcal{G}$, we define the sumset of $A$ and $B$ by $A+B=\lbrace a+b|a\in A,b\in B\rbrace$. We also denote by $hA=\lbrace a_1+...+a_h|a_i\in A\rbrace$ the $h$-fold sumset of $A$.
I'm curious about what applications sumsets may have in other areas of math, or even possibly other sciences.