Document Type
Lecture
Publication Date
5-7-2018
Abstract
This talk begins with a brief history of the mathematics of aperiodic tilings of Euclidean space, highlighting their relevance to the theory of physical materials called quasicrystals. We then focus on an important class of point sets—cut and project sets—which provide mathematical models for quasicrystals. These sets have a dynamical description in terms of return times to certain regions under linear ℝᵈ-actions on higher-dimensional tori. As an application, we demonstrate how Diophantine approximation techniques help classify a subset of 'perfectly ordered' quasicrystals."
Relational Format
presentation
Recommended Citation
Haynes, Alan, "Repetitivity of Patterns in Mathematical Quasicrystals" (2018). Colloquium. 3.
https://egrove.olemiss.edu/math_colloquium/3
