Nicolas Chopin , ENSAE, Institut Polytechnique de Paris, France
Christoph Richard (Erlangen)
Abstract: We define a notion of uniform density on translation bounded measures in unimodular amenable locally compact Hausdorff groups, which is based on a group invariant introduced by Leptin in 1966. We show that this density notion coincides with the Banach density. We illustrate uselfulness of Leptin densities for a geometric proof of the model set density formula, which expresses the density of a uniform regular model set in terms of the volume of its window. This is based on joint work with Felix Pogorzelski (Leipzig) and Nicolae Strungaru (Edmonton), see https://arxiv.org/abs/2107.04760.