Alan Haynes
Title: Equivalence relations on separated nets arising from toral flows

Abstract: In 1998, Burago-Kleiner and McMullen independently proved the existence of separated nets (a.k.a. Delone sets) in R^d which are not bi-Lipschitz equivalent (BL) to a lattice. A finer equivalence relation than BL is bounded displacement after dilation (BDD). Separated nets arise naturally from R^d actions on the torus via the cut-and-project method. We show that generically these nets are BL to a lattice, and for some choices of dimensions, they are generically BDD to a lattice.