Geometry research in York includes:

• Differential Geometry: harmonic maps and sections; variational theory of Riemannian G-structures; integrable surface theory (minimal surfaces, CMC surfaces, Willmore surfaces).
• Geometric Group Theory: the interplay between groups and manifolds, particularly in hyperbolic geometry.
• Geometric Invariant Theory: the theory of invariants of linear algebraic groups acting on algebraic varieties.

The geometry group interacts strongly with algebra research at York, and there is some interaction with mathematical physics.

Yorkshire-Durham Geometry Days: Together with Leeds and Durham, York belongs to this London Mathematical Society funded network, which run 3 or 4 differential geometry research days per year.