Research in algebra is centred on group theory and related topics. These include representation theory (Gramain, Martin, Turner), Hopf algebras (Meir), algebraic groups and geometric invariant theory (Martin, Meir) and applications of algebra to music (Turner). There are close links with Geometry/Topology (Levi, Libman) and Algebraic Geometry/Mathematical Physics (Gorbunov, Sevastyanov).
Supervisors: Dr Gramain, Professor Martin, Dr Meir, Dr Turner
Algebraic Geometry and Mathematical Physics
Research in mathematical physics ranges between discreet models of statistical mechanics and mathematical models for quantum field theories. The main tools we use are from Algebraic Geometry and Topology, Representation theory, and Graph Theory.
Supervisor: Dr Sevastyanov
Research in algebraic topology ranges across a variety of themes. In particular, topological complexity (Grant), homological stability, magnitude homology and string topology (Hepworth), homotopy theory and interactions with group and representation theory (Levi, Libman), and stable homotopy theory, homological algebra and algebraic K-theory (Patchkoria, Hebestreit).
Supervisors: Dr Grant, Dr Hebestreit, Dr Hepworth, Professor Kedra, Professor Levi, Dr Libman, Dr Patchkoria.
Applied Algebraic Topology
The main themes of applied algebraic topology we study are in applications of combinatorial and algebraic topology to neuroscience (Levi), and topological robotics (Grant).
Supervisors: Dr Grant, Professor Levi.
Research in Geometric Topology ranges between geometric group theory and symplectic topology (Kedra), and differential topology and its applications (Grant).
Supervisors: Professor Kedra, Dr Grant