Study to research symmetries in mathematics

An OU academic has been awarded over £330,000 to research symmetries in mathematics.

One of the benefits of studying symmetries in mathematics is so that mathematical quasicrystals can be classified. Quasicrystals are crystalline structures which do not have the translational symmetry of a normal crystal. Mathematicians and physicists had created many abstract models of quasicrystals in the 70s, but it was not till a decade later that they were observed to form naturally in metallic alloys.

Since then, classifying mathematical quasicrystals has interested researchers, in a desire to understand which of these models can be observed in nature and also in a quest to find new materials with novel physical properties, which can be used to innovate and create new products, such as surgical instruments.

Dr Reem Yassawi, Lecturer in Applied Mathematics in the Faculty of Science, Technology, Engineering and Mathematics is leading the project Computing algebraic invariants of substitutional dynamical systems which was funded by the Engineering and Physical Sciences Research Council.

Dr Yassawi is Principal Investigator for the project which will run from 1 June 2021 to 30 May 2024 and she will work closely with Professor Johannes Kellendonk at the Université Claude Bernard Lyon 1.

Dr Yassawi said: “Mathematicians study symmetry using abstract algebraic structures such as symmetry groups. We can characterize the structural properties of a tiling by associating to it algebraic constructions called invariants. If two tilings are equivalent, their invariants are the same.

So, an understanding of the algebraic invariants of a tiling leads to some answers to the question of which mathematical quasicrystals are the same. In this project, we seek to gain a better understanding of some of these invariants, how symmetries manifest in them, and how to compute them, so that we can make progress in classifying mathematical quasicrystals and focus on creating new quasicrystals.”

Find out more about OU research in mathematics and statistics