# Bounded distance equivalence of Pisot substitution tilings

### Dirk Frettloeh (University of Bielefeld)

Thursday 29th November, 2018 16:00-17:00 Maths 311B

#### Abstract

A (compact) subset P of the d-torus is a bounded remainder set with respect to a vector v, if $| \sum\limits_{k=1}^n 1_P(kv \bmod 1) - n \lambda_d(P)|$ is uniformly bounded (Here 1_P denotes the indicator function of a set P, and \lambda_d denotes d-dimensional Lebesgue measure). This talk presents a connection between aperiodic point sets (cut-and-project sets) and bounded remainder sets and uses this to prove that several sets with fractal boundary are bounded remainder sets. In fact these sets with fractal boundary are the windows  of the cut-and-project sets considered. The talk has an introductory nature: All terms will be explained and accompanied by several images.