Algebra 

Algebra research at the University of Birmingham covers a wide range of topics across group and representation theory.

A petrie algebra spiralThese 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 Simon Goodwin

Professor Simon Goodwin

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.

Academic Staff

Dr David Craven

Dr David Craven

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 Paul Flavell

Professor of Pure Mathematics

Prof. Flavell's research focuses on the abstract theory of finite groups, in particular generation, automorphisms and the revision of the classification of the finite simple groups. A recent highlight, in joint work with Bernd Stellmacher, is a new proof of Stellmacher's Sym(4)-Free Theorem.

Professor Chris Parker

Professor Chris Parker

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.

Professor Sergey Shpectorov

Professor Sergey Shpectorov

Professor of Pure Mathematics

Prof. 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.

Research and Teaching Fellows

Dr Mark Butler

Dr Mark Butler

Teaching Fellow in Mathematics

Mark is a Teaching Fellow in the School of Mathematics and part of the Algebra group.

Dr Leyu Han

Dr Leyu Han

EPSRC Research Fellow

Dr Han's research interests are in the structure theory of simple Lie superalgebras.

Dr Ana Retegan

Research Fellow

Dr Retegan's research is in subgroup structure and irreducible representations of linear algebra groups.

Dr Matthew Westaway

Dr Matthew Westaway

Research Fellow in Representation Theory
Royal Commission for the Exhibition of 1851 Fellow

Dr Westaway's research focuses on representations of Lie algebras and algebraic groups, especially in positive characteristic. He is interested in how category-theoretic methods and geometric representation theory can be used to prove results in this area. He studies non-restricted representations of modular Lie algebras, and their relationship with representations of finite W-algebras.

PhD Students

Note that not all PhD researchers have requested profiles.

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