In alphabetical order, linked to staff expertise, our specific research interests include:

- Algebraic Geometry, including its interactions with neighbouring fields (Sofos, Wemyss)
- Algebraic Number Theory, particularly Arithmetic Statistics (Bartel)
- Algebraic Topology (Baker, Stevenson)
- Analytic Number Theory (Sofos)
- Arithmetic Geometry (Sofos)
- Braid groups (Brendle)
- Birational Geometry (Wemyss)
- Cluster and Quantum Cluster Algebras (Gratz, Korff, Wemyss)
- Cohen-Lenstra heuristics (Bartel)
- Combinatorics (Bellamy, Meeks)
- Curve counting (DT/GW) invariants (Wemyss)
- Derived Categories and Moduli Spaces (Bellamy, Stevenson, Wemyss)
- Differential Geometry of Manifolds (Feigin, Strachan)
- Differential Graded Categories and Noncommutative Motives (Stevenson)
- Elliptic Curves (Bartel)
- Geometric Group Theory (Brendle)
- Graph Theory (Meeks)
- Homological and Commutative Algebra (Baker, Bellamy, Feigin, Gratz, Stevenson, Wemyss)
- Knots and Links (Owens)
- Noncommutative Geometry (Voigt, Whittaker, White, Zacharias)
- Noncommutative Ring Theory (Brown)
- Operator Algebras (Voigt, Whittaker, White, Zacharias)
- Symplectic Geometry and Topology (Bellamy, Wand)
- Representation Theory related to: Combinatorics, Lie theory, Mathematical Physics and Number Theory (Bartel, Bellamy, Feigin, Gratz, Korff)
- Representation Theory of Finite Dimensional Algebras (Gratz, Stevenson)
- Teichmuller Theory (Gadre)
- Topological dynamical systems (Gadre, Whittaker)
- Topology, with links to low-dimensional geometry (Brendle, Owens, Wand)

Conversely, our expertise listed by our members' names is available.