Topological Methods for Aperiodic Tilings (08w5044)

The Banff International Research Station will host top researchers in its workshop on "Topological Methods for Aperiodic Tilings" next week, October 12 - October 17, 2008. Ordinary crystals, such as those found in materials ranging from grains of salt to precious gems, have been thoroughly studied by physicists. Mathematicians long ago developed theories classifying such periodic structures, those that consist of infinitely repeating patterns. In the 1980s, however, physicists discovered new substances called quasicrystals. The atomic structures of quasicrystals do NOT consist of periodic (or repeating) patterns, but they are nonetheless highly ordered. Even before the discovery of quasicrystals, mathematicians had discovered mathematical patterns, such as Penrose tilings, that likewise are non-periodic but highly ordered. The discovery that these mathematical patterns were useful in describing quasicrystals led to rapid advances in both physics and mathematics. This workshop will bring together researchers studying various aspects of this subject. They will be adapting techniques from the field of topology (the study of shape) to solve outstanding problems in this field.

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 US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnologí­a (CONACYT).