A sponge’s ability to be squeezed and stretched depends on the number of holes in its structure—and the same mathematical principle now lets researchers design materials with entirely new electrical and optical properties. Topological design uses counting rules—how many holes, bridges, or twists a structure has—to create materials whose properties stay stable even when the material is deformed. This approach has already sparked a wave of new materials that conduct electricity without resistance along their edges, or guide light in ways conventional optics cannot. But turning these laboratory discoveries into real-world products requires a workforce trained across physics, engineering, and materials science. This Centre for Doctoral Training will produce the first generation of researchers who combine deep topological theory with hands-on fabrication skills and industry awareness. Working with partners in communications, manufacturing, and defence, these PhD students will develop topological materials that can be scaled from the lab bench to factory production. If successful, the programme could transform how we build everything from fibre-optic networks and quantum computers to lightweight structural components—technologies that depend on materials whose properties are baked into their geometry, not just their chemistry.
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Topology is a particular study of the spatial structure of objects, based on counting discrete properties, such as the number of holes and bridges in a sponge. Whichever way the sponge is stretched or squeezed, these numbers stay the same. In fact, the elastic properties of the sponge depend on this structure. It turns out that topological properties like this play a role in the physical properties of certain materials, such as the way they conduct electricity or how light propagates through them. This has led to an explosion of research and development into new kinds of materials with unprecedented properties, designed using fundamental physical and mathematical principles which can be fabricated and, in the future, manufactured on a large scale. We will train the first cohort of doctoral topological scientists, who will have a broad expertise in topological science and design, focused towards the development of new topological materials that address the needs of industry. Drawn from mathematically-informed backgrounds including physics, engineering and materials science, they will develop a broad technical appreciation of topological design within all of these disciplines, and gain research experience in mini-projects in theoretical and experimental groups. Their main PhD research project can be with supervisors drawn from all academic Schools in the College of Engineering and Physical Sciences at the University of Birmingham, in partnership with our wide range of partners from industry. This technical education will be entwined with a programme of transferable skills developing the critical skills of innovation, entrepreneurship and responsible innovation. The academic leadership of this CDT has co-created the training programme in collaboration with a range of industrial partners who will contribute to the directions of the research projects, provide internships and help the students and academic supervisors focus on the needs of end users in their research. These partners will not only be drawn from relevant industries, such as communications, manufacturing and defence sectors, but more widely from knowledge industries including software developers and commercialisation lawyers. The resulting CDT will be a beacon for cross-disciplinary research across the physical sciences and spearheading academic-industrial partnership over the coming decades as topological design becomes a crucial principle for the development of future technologies, underpinning the future prosperity of the UK.
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