Research in this group explores the structural underpinning of our understanding of Mathematics, creating the potential for future applications. We benefit from wide international collaboration networks across the globe, which allow us both to disseminate our research and to bring world experts to UEA. Our research ranges from Logic, the study of the fundamentals which form the basis for mathematical discourse, to Combinatorics, the study of finite and countable structures, to Algebra, the study of abstract structures and of symmetry, with a particular view to implications for Number Theory, the study of integers and prime numbers.
Work in the group is wide in scope, with Pure Mathematicians within the School of Mathematics working on a range of fundamental problems. These areas of research include:
- Algebraic Combinatorics: finite permutation groups, the invariant theory and homology of partially ordered sets and reconstruction problems (Dr J Siemons).
- Group Theory: combinatorial and geometric group theory, semigroup theory, presentations, decidability, string rewriting systems and related homological finiteness conditions, and groups acting on graphs and other relational structures (Dr R Gray).
- Model Theory: 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) and classification theory for unstable theories (Prof M Dzamonja and Prof D Evans).
- Number Theory: the local Langlands programme, representations of p-adic groups, local factors (Prof S Stevens).
- Representation Theory: 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, derived categories and homological algebra/homotopical algebra, category theory and categorification (Dr V Miemietz and Dr J Grant).
- Set Theory: Combinatorial set theory and independence results (Dr D Aspero and Prof M Dzamonja); interactions between set theory and other fields of mathematics, particularly set-theoretic model theory, topology and measure theory (Prof M Dzamonja).