A blog that discusses a mix of mathematical research, expository issues and topics of general interest to mathematicians.

Our main fields of interest are group theory, combinatorics and computation.

The Centre is a focal point for world-leading research in group theory, computation and combinatorics.

These principal areas have links to many other branches of the Mathematical Sciences.

They include fundamental tools used to analyse vast networks and the designs used in experiments across all of the sciences, in particular agriculture, together with the development of algorithms that are the key to solving many problems in complex systems.

Our research groups are dedicated to the study of mathematical structures with a high degree of symmetry. Our research covers the following areas:

- Computational Group Theory: Studying symmetry using computers, and in particular, the development of highly sophisticated algorithms for such a study.
- Permutation Groups: Researching the fundamental properties of permutation groups and use the developed theory to study classes of mathematical objects with a high degree of symmetry, such as graphs and geometries.
- Algebraic Graph Theory: Solving a number of important open problems on Cayley graphs, and have significantly changed the status of various important topics in the area.
- Finite Geometry: Linking geometry with a finite number of objects with experimental design, information security, particle physics and coding theory.
- Matroid Theory: Providing a very high level coarse description of any proper minor-closed class of graphs or binary matroids, but cannot be used to determine the fine-grained structure of any particular class.

The central focus of the Centre is research and research training through postgraduate and postdoctoral programs.

Research programs can be undertaken at master's degree by research level, or as PhDs and professional doctorates.