Algebra research at the University of Birmingham covers a wide range of topics across group and representation theory.
These areas lie at the heart of algebra and give a mathematical abstraction for the study of symmetry. Although symmetry has been studied for millennia as represented in the art and architecture of many different cultures, it was not until the work of Galois in the early 19th century on the symmetries of roots of polynomials that the definition of a symmetry group was introduced.
Subsequently group theory and representation theory have found profound applications across the physical sciences, for example in the chemistry of molecular vibrations and in particle physics, and have a close relationship with geometry, number theory and combinatorics.
The research of algebraists in Birmingham involves an interaction of algebraic, geometric and combinatorial methods, collaboration with mathematicians worldwide and is or has been supported by the Engineering and Physical Sciences Council, the European Union, the Leverhulme Trust and the Royal Society.
Information about the weekly seminar can be found on the algebra seminar page. A list of upcoming talks, and an extensive archive of past talks, may be found at the seminar's talks@bham page.
A list of recent grants obtained by the Group can be found on the grants page. Previous PhD students in the Algebra Group, together with their theses, can be found on the previous PhD students page.
Head of Algebra Group
Professor of Pure Mathematics
Prof. Parker's research interests lie in finite group theory and fusion systems. In finite group theory he is heavily involved in the programme to produce a new proof of the Classification of Finite Simple Groups. In fusion systems he works on understanding saturated fusion systems on 'small' p-groups, for exaple restricted by rank or class.
Academic Staff
Senior Birmingham Fellow
Dr Craven's research interests are mostly connected to groups and their representations. He has worked on finite group theory, particularly the maximal subgroups of simple groups, fusion systems, modular representation theory of finite groups, and other topics such as the combinatorial representation theory of symmetric groups and the structure of group rings of torsion-free groups.
Professor of Pure Mathematics
Prof. Goodwin's research interests are in representation theory and Lie theory. His most recent research is on representation theory of modular Lie algebras and finite W-algebras.
Assistant Professor
It is notoriously difficult to determine whether one group is (almost) a subgroup of another. As methods for describing subgroups have advanced, the study of obstructions to subgroup inclusion has slowed. Dr Hume's research corrects this, using techniques from many different mathematical areas, including combinatorics, analysis, topology, fractal geometry and neural network theory.
Assistant Professor in Algebra
Dr Law's research interests are in the representation theory of finite groups and algebraic combinatorics. Her research focuses include the representation theory of symmetric groups, their Sylow subgroups and related algebras, and plethysms of Schur functions.
Professor of Pure Mathematics
Professor Shpectorov's research interests are in algebra, geometry, and combinatorics. The unifying theme is actions of groups: on geometries, graphs, Riemann surfaces, and, recently, axial algebras, which form a new interesting class of non-associative structures having applications in physics.
PhD Students
Note that not all PhD researchers have requested profiles.
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