 Kirwan was educated at Oxford High School, and studied maths as an undergraduate at Clare College in the University of Cambridge.She took a D.Phil at Oxford in 1984, with the dissertation title "The Cohomology of Quotients in Symplectic and Algebraic Geometry", which was supervised by Michael Atiyah.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.