Research in algebra spans both the core of the subject and its interfaces with adjacent areas of mathematics. See below for a detailed list of research topics.
The life of the group centres around the weekly Manchester Algebra Seminar. We also hold frequent reading groups, graduate-level courses and informal seminars, and host numerous workshops and conferences in specific subject areas.
Algebra also features heavily in the School's regular seminars on Geometry and Topology, Mathematical Logic, Discrete Mathematics, Dynamical Systems and Tropical Mathematics, and (for graduate students) the Pure Postgraduate Seminar.
Current core research in the algebra group includes:
- Group theory (finite and infinite, including computational)
- Homological algebra
- Lie algebras
- Commutative and non-commutative algebra
- Ordered algebraic structures
- Representation theory of groups (modular and ordinary)
- Semigroup theory
Topics spanning algebra and other areas include:
- Algebraic geometry (with Geometry and Topology group)
- Algebraic topology (with Geometry and Topology group)
- Category theory (with Geometry and Topology and Mathematical Logic groups)
- Model theory of algebraic structures (with Mathematical Logic group)
- Numerical linear algebra (with Numerical Analysis group)
- Tropical/max-plus algebra (with Dynamical Systems and Numerical Analysis groups)