Research activity in geometry occurs in several areas, including: algebraic, complex and differential geometry; geometric group theory; and interactions with differential equations, representation theory and the physics of string theory.

The members of the Geometry group at the University of Glasgow are:

• Dr C. Athorne works on representation theory associated with algebraic and geometric aspects of differential equations.  Most recently he has written papers on linking Lie symmetry theory with differential Galois theory, the role of the Hirota derivative in finite and infinite dimensional representations of sl_n and developed an sl_n module based approach to Padé approximants. His publications can be found here

• Prof. K.A. Brown is interested in the interactions between noetherian ring theory and geometry. His work uses Poisson and algebraic geometry to deduce structural results on noetherian rings and their modules. His publications can be found here
• Dr A. Craw is interested in links between algebraic geometry and representation theory using techniques from toric geometry, quiver representations and devived categories. Much of his work to date has been motivated by the McKay correspondence and its generalisations. His publications can be found here
• Dr M. Feigin is interested in Coxeter and other hyperplane arrangements in relations with Frobenius manifolds structures, rings of quasi-invariants, algebraic integrability. He is also interested in topological realisation of rings of quasi-invariants, in intertwining relations on Riemannian manifolds. His publications can be found here
• Dr M. McQuillan works in diophantine, complex algebratic and hyperbolic geometry. His recent work investigates the arithmetic properties of certain algebraic (log)-surfaces. His publications can be found here
• Dr I.A.B. Strachan is interested in special structures in Differential Geometry, particularly those associated with integrable systems and twistor theory. He is also interested in Frobenius manifolds, their submanifolds, the geometry of bi-Hamiltonian systems and the deformation of integrable structures. His publications can be found here
• Dr C. Stroppel works on connections between representation theory of Lie algebras and geometry, mostly to obtain structural results for representations of Lie algebras.  She is interested in quiver varieties, flag varieties and Springer fibres, in particular in their combinatorial descriptions. Her publications can be found here

• Dr M. Verbitsky is interested in complex algebraic geometry in interaction with differential geometry and string physics. He studies geometric structures on manifolds, primarily those related to quaternions and octonions. He has written papers on various topics in hyperkaehler geometry, hypercomplex and HKT-geometry, locally conformally Kaehler geometry, G2-manifolds and nearly Kaehler manifolds. His publications can be found here