Craig Kaplan - Aperiodic monotiles: new shapes just dropped - Hatfest

A set of tiles is aperiodic when they can be used to tile the plane, but never in a way that repeats in a regular pattern of translations. Penrose's "Kite and Dart" tiles, discovered in the 1970s, show that a set of size two can be aperiodic, but since that time nobody had been able to find a set of size one---that is, a single tile---that displays the same behaviour. In 2023, David Smith, Joseph Samuel Myers, Chaim Goodman-Strauss and I showed that a simple shape called the "Hat" is an aperiodic monotile. We later also showed that a related family of shapes called "Spectres" tile aperiodically without using reflected tiles. In this talk I will introduce tilings and aperiodicity, and tell the story of the discovery of these marvellous shapes and of the collaboration that led to the proof of their aperiodicity. A talk from Hatfest at the Mathematical Institute, University of Oxford. See https://sites.google.com/view/thegrimmnetw... for more information.