There is no pre-seminar.

Given a finite subset $V$ of an $n$-dimensional lattice, it is natural to ask whether the whole lattice is tiled by translates of $V$. The periodic tiling conjecture states that such a tiling exists if and only if a periodic tiling exists, or in other words, that there is no "translationally aperiodic" tile in the lattice. We will look at a proof for tiles with prime size, and talk about connections with Fourier analysis and algebraic geometry. We will also discuss possible applications to other problems. This is based on joint work with Peter Horak.