Mutual local derivability and linear repetitivity for cubical vs. canonical cut and project sets
speaker: Alan Haynes (University of York)abstract: Cut and project sets are point patterns in Euclidean space which arise from a simple dynamical construction. They are the return times to fixed regions of linear Rd actions on higher dimensional tori. The desire to understand the structure and regularity properties of cut and project sets is a recurring theme in tiling theory, Diophantine approximation, and the theory of mathematical quasicrystals. In this talk we will discuss the relationship between cut and project sets formed from the same Rd action, but with different windows. We will focus on two natural choices of windows, `cubical’ and `canonical’. After surveying some results about local derivability of one set from the other, we will explain how to construct cut and project sets for which the cubical set is linearly repetitive, but the corresponding canonical one is not.
timetable:
Mon 4 Apr, 14:00 - 15:00, Aula Dini
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