Mathematics Research Seminar Series: Substitution Tilings with Rotational Symmetries

Mathematics Research Seminar Series
Substitution Tilings with Rotational Symmetries

by April Lynne D. Say-awen
Postdoc Fellow
Ateneo de Manila University

Date: Wednesday, 29 March 2023
Time: 4:00 - 5:00 pm
Venue: https://bit.ly/AdmuMathSeminar 

Abstract:
In this talk, we show constructions of aperiodic tilings of the Euclidean plane R^2 with rotational symmetries via substitutions. In a nutshell, a substitution σ with prototiles T_1,T_2,…,T_m and (real) substitution factor λ>1 is a rule on how to dissect λT_i into equivalent copies of some of the prototiles. Iterating this rule fills larger and larger regions of the plane.

We also discuss the notion of finite local complexity up to rigid motions and dense tile orientations.