Research in Pure Mathematics is grouped around three main areas:
- Algebra and Combinatorics
- Logic (Model Theory and Set Theory)
- Number Theory, Ergodic Theory and Dynamical Systems
Research in Group Theory includes the automorphisms of designs, and the application of representation theory and incidence-transformation arguments to permutation groups. Research in Algebraic Combinatorics and finite permutation groups includes the invariant theory and homology of partially ordered sets and reconstruction problems. (Dr J Siemons) There is work on generation problems in profinite groups, probabilistic methods and asymptotic results. (Dr E Damian)
Research in Representation Theory includes: modular representation theory of the symmetric groups and related algebras, including the Hecke algebras of type A, the q-Schur algebras and the Ariki-Koike algebras (Dr S Lyle); representation theory of finite dimensional algebras, algebraic groups and related algebras, connections with Lie theory, homological methods, categorification (Dr V Miemietz).
Logic (Model Theory and Set Theory)
Research interests in Model Theory include model theoretic stability and simplicity theory, and algebraic model theory. There is particular interest in: the geometry of strongly minimal sets and Hrushovski constructions (Prof D Evans); exponential algebra, applications to number theory, transcendence questions (Dr J Kirby); model theory of infinitary logic, classification theory for non-elementary classes (Dr O Kolman), and classification theory for unstable theories (Prof M Dzamonja and Prof D Evans).
Set Theory research is on combinatorial set theory and independence results. Work is also done on interactions between set theory and other fields of mathematics, particularly set-theoretic model theory, topology and measure theory (Dr M Dzamonja); set theoretic algebra, including interactions with infinite abelian group theory (Dr O Kolman).
Number Theory, Ergodic Theory and Dynamical Systems
Our number theory research examines the representation theory of p-adic groups with a view to the Langlands programme (Prof S Stevens).
Research areas in Ergodic Theory and Dynamical Systems include higher dimensional Markov shifts, flows on homogeneous spaces of algebraic groups, examples of algebraic and geometric origin as well as examples motivated by number theory. Methods from commutative algebra, harmonic analysis, finite groups, Lie theory and representation theory are used to understand structural and rigidity properties of these dynamical systems. (Prof T Ward and Dr A Ghosh)
Further information on individual research interests can be obtained by following links to personal homepages. Most groups organise working seminars to discuss topics of current interest in their area.
