Algebra and Algebraic Geometry

Parabola and cubic curve in projective space

Algebraic Geometry

Group members have a variety of interests including combinatorial algebraic geometry, moduli spaces, derived categories, enumerative invariants, mirror symmetry and cluster varieties. Current topics include:

  • Homological Algebra, Geometry and K-theory of Singularities
  • Mirror Symmetry, Derived Categories, and Bridgeland stability conditions
  • Hall algebras and Donaldson-Thomas Theory
  • Moduli spaces of curves, Gromov-Witten theory
  • Frobenius manifolds and integrable systems
  • Topological field and string theory, relations to quantum topology
  • Grothendieck Ring of Varieties
  • Combinatorics

Group website


The algebra group has worked extensively on tight closure and related questions in commutative algebra.

Another major theme is the study of local cohomology; this connects with the work of the Topology group via the work of Greenlees on the local cohomology of equivariant cohomology rings.

On the noncommutative side, the group has studied classes of rings such as (generalised) Weyl algebras, rings of difference operators, quantum algebras, and Frobenius skew polynomial rings.


Past grants

  • Prime characteristic methods in commutative algebra, EPSRC
  • Common threads in the theories of Local Cohomology, D-modules and Tight Closure and their interactions, EPSRC

A global reputation

Sheffield is a research university with a global reputation for excellence. We're a member of the Russell Group: one of the 24 leading UK universities for research and teaching.