Pure point diffractive, coincidence, and cut-and-project set in substitution point sets (tilings)

Pure point diffractive sets are point sets whose diffraction patterns consist of bright peaks (so called Bragg peaks). It is known that cut-and-project sets (model sets) with boundary measure zero on their windows are pure point diffractive. We show that dropping the condition on the boundary of the windows, model sets are in fact equivalent with pure point diffractive sets in substitutions. We introduce a notion of coincidence in the substitutions and show how this notion bridges the two concepts of model sets and pure point diffractive sets together.

Dr. Lee is a UFA candidate. Please plan to attend this special colloquium. She will also give a specialized talk on Friday, Sept. 30th at 4:00 p.m. in MATH 103, entitled ``Pure point diffractive substitution point sets are Meyer sets''.