EPSRC Reference: 
EP/C523229/1 
Title: 
Multidisciplinary Critical Mass in Computational Algebra and Applications 
Principal Investigator: 
Linton, Professor S 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Computer Science 
Organisation: 
University of St Andrews 
Scheme: 
Standard Research (PreFEC) 
Starts: 
01 September 2005 
Ends: 
31 August 2010 
Value (£): 
1,094,497

EPSRC Research Topic Classifications: 
Algebra & Geometry 
Condensed Matter Physics 
Fundamentals of Computing 
Logic & Combinatorics 

EPSRC Industrial Sector Classifications: 

Related Grants: 

Panel History: 

Summary on Grant Application Form 
Symmetry is everywhere. Many things in the natural world are symmetrical, and many of the mental tools that we develop to deal with the world introduce additional symmetry. Studying objects and ideas through their symmetries  the transformations that can be applied to them while leaving some essential characteristic unchanged  has been a central plank of mathematics and science since the early nineteenth century. Chemistry and crystallography use geometric symmetries to study and classify possible compounds and crystals, and symmetry is at the core of Einstein's special theory of relativity.Group theory is the phenomenally successful mathematical tool developed to handle symmetry. A group is the mathematical abstraction of symmetry just as a number is the abstraction of quantity or repetition. Modern group theory developed in the early nineteenth century, and one of its earliest triumphs was a clear understanding of why there was no equivalent of the quadratic formula for equations involving fifth powers. Elementary group theory also provides an explanation of the seventeen essentially different ways to put a repeating pattern on a flat surface, known to Islamic artists since the fourteenth century. Today, it has applications in theoretical physics; chemistry; crystallography; structural biology; computer science; and in many other areas of mathematics.Since the invention of digital computers, group theory has led the increasing use of computation in mathematical and scientific research. Alan Turing suggested this as early as 1947. Today, computational group theory is an established international research area, in which the Centre for Interdisciplinary Research in Computational Algebra (CIRCA), established in 2000 at St Andrews, already plays a major role. GAP (Groups, Algorithms, Programming), a powerful integrated computational algebra system, developed by an international team now coordinated from CIRCA, incorporates the latest algorithms in a flexible and extensible system and is used by researchers at hundreds of sites worldwide. New disciplines such as computer science and artificial intelligence have thrown up entirely new problems in which symmetry is a central issue. Recent CIRCA projects, funded by EPSRC grants, have demonstrated that incorporating computational group theory algorithms and software into computational tools in these areas can produce dramatic benefits, turning the management of symmetry from a difficult problem requiring lengthy and errorprone manual intervention to a routine computation taking a few seconds in GAP.This proposal, involving a strategic investment of 1 m from EPSRC and 400K from the University of St Andrews, will dramatically expand the work of CIRCA, with a particular emphasis on developing the capabilities to rapidly and flexibly work with computational scientists across a broad range of disciplines who need to work with symmetry.We plan a number of new collaborations with other disciplines, and extensions of old ones. Believe it or not, an invisibility cloak is one subject of these new collaborations. Prof Ulf Leonhardt is studying the analogy between Stephen Hawking's theories of black holes and specialised optical media. There is at least a possibility that this might lead to objects containing a volume which is invisible to the outside world. To develop this research he needs exactly the mathematical tools we are developing. Other applications of our research are in the scheduling of real world problems like exams and slabs moving through steel mills, and in the development of highly specialised new materials in physics. Of course mathematicians will also benefit from our research, and we have a number of plans for specialised developments in computational algebra.Overall, this investment from EPSRC would make St Andrews the world's centre of expertise in using computers for working with symmetry.

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