New grant to bring mathematical meaning to the concept of order

An OU researcher is leading a research project aimed at understanding mathematical structures which display a particularly interesting kind of order, which could have implications for the design of smart materials.

Uwe Grimm, Professor of Mathematics in the OU’s Faculty of Science, Technology, Engineering and Mathematics, has been awarded £343,000 from the Engineering and Physical Sciences Research Council (EPSRC) for the three year research project which starts in early 2019.

The project, Lyapunov Exponents and Spectral Properties of Aperiodic Structures (LESPAS), will investigate two different properties which both characterise order, one linked to the scattering of radiation by such systems and the other to the motion of electrons in these structures. The main aim of the project is to understand how these two different quantities are related to each other.

“This project concerns fundamental mathematics which goes to the bottom of the question of what constitutes order and what consequences this entails,” said Professor Grimm. “Since ordered structures are prevalent both in nature and in any man-made materials, increasing our understanding of the structures and their properties is thus important not only from a fundamental perspective, but also in view of potential applications, for instance in the development of smart materials with designer properties.”

The research will involve collaborations with international groups. In particular, this includes a close collaboration with the group of Professor Michael Baake, Bielefeld University, Germany, with whom Professor Uwe Grimm has embarked on an ambitious book project with Cambridge University Press, with the first two volumes of the series on Aperiodic Order published in 2013 and 2017. Other collaborators include Natalie Priebe Frank (Vassar College, Poughkeepsie, USA), David Damanik (Rice University, Houston, USA) and E. Arthur Robinson Jr. (George Washington University, Washington, USA).

Find out more about a previous workshop on Quasicrystals: pattern formation and aperiodic order and a future workshop on: Aperiodic order meets number theory

Read about more OU research into mathematics