Computer Science/Discrete Mathematics Seminar II

A finite set $F$ in $\mathbb{Z}^d$ is a translational tile of  $\mathbb{Z}^d$ if one can cover  $\mathbb{Z}^d$ by translated copies of $F$ without any overlaps, i.e., there exists a translational tiling of $\mathbb{Z}^d$ by $F$.  Suppose that $F$ is a translational tile; what can we say about the structure of tilings by $F$?  In the talk we will discuss this question and introduce techniques, conjectures, results, and open problems in the area.