Algebra and Algebraic Geometry
On
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
Algebra
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.
Members
- Professor Vladimir Bavula
- Dr Moty Katzman
- Dr Nicole Jarvis
- Professor John Greenlees
- Professor Rodney Sharp
- Professor David Jordan
- Ali Al khabyah
- Majed Almubark
- Maram Alossaimi
- David Carey
- Khalil Hakami
- Ali Hummdi
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