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, Dr Henke, 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.
Supervisors: Professor Gorbunov, Dr Sevastyanov
Geometry and Topology
Research in topology and geometry includes a wide range of themes: geometric group theory and symplectic topology (Kedra), algebraic and differential topology and their applications (Grant), homological stability, magnitude homology and string topology (Hepworth), homotopy theory and interactions with group and representation theory (Levi, Libman), applications of combinatorial and algebraic topology to neuroscience (Levi), and stable homotopy theory, homological algebra and algebraic K-theory (Patchkoria).
Supervisors: Dr Grant, Dr Hepworth, Professor Kedra, Professor Levi, Dr Libman, Dr Patchkoria.
Research in tropical mathematics includes semiring theory, commutative algebra, matrix algebra, semigroup representations, and polyhedral algebraic geometry.
Supervisor: Dr Izhakian