Directions in Aperiodic Order (25w5437)

The Banff International Research Station will host the “Directions in aperiodic order” workshop in Banff from July 27 to August 1, 2025.

The discovery, in March 2023, of the hat tile came after almost a 50 year search by the mathematical and scientific community. It had the desired property of being a two-dimensional tile which can tile the plane, but only aperiodically. The elegant simplicity of this tile came as a surprise to many. The hat tile followed Sir Roger Penrose’s discovery, in 1974, of a pair of tiles which also only tiled the plane aperiodically. Penrose’s tiling became important for mathematics in the 1980’s due to the Nobel prize discovery of quasicrystals by Daniel Shechtman. It was observed soon after this discovery that the Penrose tiling is a good mathematical model for quasicrystals. Aperiodic Order is the mathematical area whose goal is the study of theoretical models of these quasicrystals, and their properties. We are interested in models which are highly ordered, but in a way which does not repeat periodically in any direction.

The main goal of this meeting is to discuss some of the recent major developments surrounding the hat and spectre tiling, as well as any other monotilings of the plane, and their implications in aperiodic order and tiling dynamical systems.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada’s Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), and Alberta’s Advanced Education and Technology.