Antoine Julien: Links between cut-and-project tilings and Diophantine approximation

Antoine Julien, NTNU, will give a talk with title: Links between cut-and-project tilings and Diophantine approximation

Abstract: Cut-and-project tilings are obtained by cutting a slice of a higher dimensional lattice and projecting it on a lower dimensional space. The result is a point set which is regular enough (since it originates from a lattice), but is not periodic, provided the direction of the slice is irrational in a suitable sense. In one dimension, typical examples of this construction are Sturmian subshifts. It is known that some of their dynamical properties depend on the arithmetic properties of a certain parameter. In this talk, I will recall some known results by Hedlund and Morse on Sturmian subshifts. Then, I will describe how, even in higher dimensions, the repetition properties of some cut-and-project sets can be linked to problems of simultaneous Diophantine approximation. This is joint work with A. Haynes, H. Koivusalo and J. Walton.