Pure Mathematics: Cutting edge research in pure mathematics with emphasis on algebra and topology. Our research also ranges over new and exciting potential applications of pure mathematics techniques to real world problems.

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Degree Qualification

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The department has a very active research group in pure mathematics and its applications. The following broad research themes are particularly emphasized:

  • Algebra
  • Algebraic geometry and mathematical physics
  • Algebraic topology
  • Applied algebraic topology
  • Geometric Topology

For informal inquiries please contact Professor Levi (Postgraduate Coordinator) or any potential supervisor whose research themes fit with your interests. All formal applications must be done through the Graduate School.

Research Interests


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

Algebraic Topology

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, 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.

Geometric Topology

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


Students with PhD degrees in Mathematics are recruited by universities, research institutes, and a range of industrial and commercial organisations.

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Contact Details

Postgraduate Research School - School of Engineering, Geosciences and Natural and Computing Science
University of Aberdeen
Crombie Hall
AB24 3TS