Structure and symmetry

Structure and Symmetry research at Heriot-Watt comprises two broad groups: one in mathematical physics (MP) and its interface with other areas of mathematics and natural sciences; another in algebra, geometry and topology (AGT) and their interactions with computer science.

Mathematical physics is a broad field covering numerous areas and mathematical methods and tools, from string and gauge theories to statistical mechanics and quantum theory, aiming at solving key problems in various areas of modern physics.

The main aim of this research is to provide a deeper theoretical understanding of physical phenomena and to develop accurate mathematical models that describe fundamental physical processes. The search and study of the underlying algebraic structures that characterise the symmetries of physical systems, is also a central theme.

The core of the AGT group’s research is the study of symmetries – group theory – which helps describe how an object finds itself in the universe and predicts how it will develop and move. From the symmetries of the Rubik’s cube to virus molecules, understanding the regularity of both structure and movement can give us invaluable information on how to build an object or how the object will propagate and multiply. Understanding the symmetries of atoms, molecules, crystals, and all the building blocks of nature, is essential for physics, biology and medicine.

Another strand of our work is hyperbolic geometry, a model which assumes not everything in a plane is flat but curved, which is an essential model both in physical setups and in today’s big data world. A hyperbolic geometry setting has recently been proposed as a solution for storing, compressing and analysing data. A further part of our research is in leveraging deep algebraic and geometric results to affect computer science, in particular the creation, optimisation and verification of software.

Our award-winning researchers are at the core of training future scientists in the UK, through the only UKRI EPSRC Centre for Doctoral Training (CDT) in algebra, geometry, topology and mathematical physics, leading the Algebra, Geometry and Quantum Fields jointly with the University of Edinburgh and Glasgow University.

Mathematical Sciences are at the core of technological progress, driving innovations in artificial intelligence, data security, and computational modelling that shape critical sectors like finance, healthcare, and engineering. At the School of Mathematical and Computer Sciences (MACS), Heriot-Watt University brings together experts in mathematics, actuarial science, statistics, and computer science to tackle global challenges through interdisciplinary research.

By collaborating with industry and academic partners, MACS plays a pivotal role in supporting Heriot-Watt’s globally renowned research institutes, including The National Robotarium, The Lyell Centre for Earth and Marine Sciences and Technology, The Global Research Institute in Health and Care Technologies, and iNetZ+ Global Research Institute for Net Zero and Beyond. This ensures that MACS research has both theoretical significance and real-world impact, contributing to the university’s mission of advancing global innovation and societal benefit.