Cut and project sets and Diophantine approximation
speaker: Henna Koivusalo (University of York)abstract: Cut and project sets give a way of defining discrete point patterns through a data of a linear subspace and an acceptance strip. The points in the pattern are obtained through first intersecting the integer lattice with the acceptance strip (cut) and then projecting these intersection points to the subspace (project). We establish a connection between finite patches in cut and project sets and an action of a toral rotation defined by the cut and project data.
Based on this connection, we use methods from Diophantine approximation to measure how well ordered cut and project sets are, in terms of repetitivity functions and pattern frequencies. Finally, we see that the existence of extremely well ordered cut and project sets turns out to be equivalent to the negation of the Littlewood conjecture.
The material is based on several recent works, joint with Alan Haynes, Antoine Julien, Lorenzo Sadun and James Walton.
timetable:
Mon 4 Apr, 15:00 - 15:45, Aula Dini
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