Kirwan's research interests include moduli spaces in algebraic geometry, geometric invariant theory (GIT), and in the link between GIT and moment maps in symplectic geometry. Her work endeavours to understand the structure of geometric objects by investigation of their algebraic and topological properties. She introduced the Kirwan map. From 1983 to 1985 she held a Junior Fellowship at Harvard. From 1983 to 1986 she held a Fellowship at Magdalen College, Oxford, before becoming a Fellow of Balliol College, Oxford. She is an honorary fellow at Clare College, Cambridge.