A focus on quasicrystals

Professor Pavel Kurasov will receive funding from Knut and Alice Wallenberg Foundation to recruit an international researcher for a postdoctoral position at the Department of Mathematics, Stockholm University.

Quasicrystals comprise a new field of research in mathematical analysis and are the subject of this project. The Israeli chemist Dan Shechtman discovered quasicrystals in 1982 but his discovery was initially met with skepticism. Thirty years later, in December 2011, he was invited to Stockholm to receive the Nobel Prize in Chemistry. 

Quasicrystals, like ordinary crystals, build up metals and other solids with atoms that are very regularly ordered in a symmetric pattern. However, unlike crystals where the pattern is periodically repeated, quasicrystals do not possess this property. 

A decade before the discovery of quasicrystals, mathematicians had become interested in patterns that are quasisymmetric and are never fully repeated. Among the most famous are the refined tiling constructed in the 1970s, by the British mathematician Roger Penrose. Soon, it was shown that similar patterns could be found on centuries-old walls in mosques in Iran, Central Asia and Turkey. 

However, the modern mathematical exploration of quasicrystals has just begun. Last year, Pavel Kurasov and Peter Sarnak (IAS Princeton) presented a mathematical construction that gives rise to many yet unknown quasicrystals and thus answered questions posed by Yves Meyer (Abel Prize 2017). This has inspired other researchers to produce their own constructions. The purpose of the proposed project is to analyze how the constructions relate to each other and to try to classify all quasicrystals.

Photo Annemarie Luger