The origin of symmetry
University of St Andrews scientists have been awarded nearly £1.5 million to study symmetry, the crux of some of the world’s most baffling computational problems from airline scheduling to medical scanning.
The end result will be the largest research group of its kind in the world, providing new insights and solutions to people working in everything from computer graphics, electronics and medicine to aviation, optics and artificial intelligence.
The Centre for Interdisciplinary Research in Computational Algebra (CIRCA) has beaten off intense competition from other universities by securing £1m from the Engineering and Physical Sciences Research Council (EPSRC), together with £400,000 from the University itself. The funding will allow CIRCA to expand on its research activities in the long- term, developing new and exciting links with other disciplines, helping researchers in Mathematics, Computer Science and Physics understand each others issues, problems and techniques.
Examples of St Andrews based projects which will benefit from the funding include existing, interdisciplinary work on “symmetry and search” which could have real applications for airline scheduling.
Principal Investigator Dr Stephen Linton said, “Symmetry is everywhere and studying objects and ideas through their symmetries has been a central plank of mathematics and science since the early nineteenth century. Algebra, especially group theory, is the mathematics of symmetry and we are experts in using computers to apply this theory. Just one example is an airline combining hundreds of planes, air crew and so on, and various flights it needs to make. Sophisticated optimisation programs are used to schedule these to make best use of people and planes, minimize time away from home, and so on. The same techniques apply to very many other problems – laying out components on a circuit board or a chip, working out how to allocate orders to slabs of steel in a mill, planning computer networks and so on. In almost all of these problems, symmetry is an issue”.
University beneficiaries will include Professor Andrew Mackenzie’s group who are studying the fundamental properties of new materials which could lead to new kinds of electronic devices. Meanwhile, Professor Ulf Leonhardt’s group are looking at designing new optical devices, some of which have symmetries, including an “invisibility cloak”, a device – which could be used in radar – which bends electromagnetic waves from any direction perfectly around a space in the middle. His group are also developing an “optical black hole”, in an optical fibre which can be used to do experiments in a lab that would explain the quantum behaviour of “black holes”.
The project will also involve Professor Nik Ru¿kuc and Dr Martyn Quick (Mathematics) and Dr Ian Gent and Dr Ian Miguel (Computer Science).
It is hoped that the funding will also attract new talent, in the form of top, young researchers, who can interact with students and give seminars or lectures on their areas of expertise.
CIRCA, which was established in 2000, focuses on computational algebra, particularly on the development of the GAP system, together with computational techniques and algorithmic results. GAP – Groups, Algorithms, Programming – is a powerful, integrated, computational algebra system, used in teaching and research by mathematicians, computer scientists, physicists and chemists throughout the world.
The Engineering and Physical Sciences Research Council (EPSRC) is the UK’s main agency for funding research in engineering and the physical sciences. The EPSRC invests more than £500 million a year in research and postgraduate training, to help the nation handle the next generation of technological change. The areas covered range from information technology to structural engineering, and mathematics to materials science. This research forms the basis for future economic development in the UK and improvements for everyone’s health, lifestyle and culture. EPSRC also actively promotes public awareness of science and engineering. EPSRC works alongside other Research Councils with responsibility for other areas of research. The Research Councils work collectively on issues of common concern via Research Councils UK. Website address for more information on EPSRC: www.epsrc.ac.uk/.
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