The Centre for Interdisciplinary Research in Computational Algebra (CIRCA) was established in 2000 to foster new and existing collaborative research between members of the Schools of Computer Science and of Mathematics and Statistics in the area of computational abstract algebra.

The Centre undertakes mathematical research with computer assistance, develops new techniques for computation in abstract algebra and develops and distributes software implementing these techniques. This work is supported by research grants from the EPSRC, the Leverhulme Trust, the British Council, the European Commission and the Royal Society of Edinburgh.

The Centre also organises conferences, seminars and training courses and coordinates the international efforts to develop maintain and promote the GAP (groups, algorithms and programming) software package, a leading integrated system for computational discrete mathematics and algebra.

News and Events

CIRCA Lunchtime Seminar (15.02.2018)

The next CIRCA Lunchtime Seminar will be on Thursday 15th February in Maths Lecture Theatre C at 1pm. Ian Gent and Markus Pfeiffer will be speaking.

Reed–Muller codes and Thomas’ conjecture

There will be a seminar on  Wednesday February 7th, 2018 at 1pm in Lecture Theatre D: Peter Cameron will speak on Reed–Muller codes and Thomas’ conjecture.

Abstract: A countable first-order structure is countably categorical if its automorphism group has only finitely many orbits on n-tuples of points of the structure for all n. (Homogeneous structures over finite relational languages provide examples.) For countably categorical structures, we can regard a reduct of the structure as a closed overgroup of its automorphism group. Simon Thomas showed that the famous countable random graph has just five reducts, and conjectured that any countable homogeneous structure has only finitely many reducts. Many special cases have been worked out but there is no sign of a general proof yet. In order to test the limits of the conjecture, Bertalan Bodor, Csaba Szabo and I showed that a vector space over GF(2) of countable dimension with a distinguished non-zero vector has infinitely many reducts. The proof can most easily be seen using an infinite generalisation of the binary Reed–Muller codes.