Jean Lagacé

Distribution statistics for cut-and-project sets

Cut-and-project sets, also known as quasi-crystals, are an aperiodic generalisation of lattices built from a lattice sitting in a higher dimensional space. In this talk, I will discuss statistics around the distribution of their points, in particular the discrepancy from average in large balls. I will explain how this discrepancy depends in a sharp way on diophantine properties of the lattice used to create the cut-and-project set, using methods from the geometry of numbers. This is joint work with Henna Koivusalo.