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