Dame Frances Clare Kirwan, DBE FRS (born 21 August 1959)[2] is a British mathematician, currently Savilian Professor of Geometry at the University of Oxford.

[3][4] Kirwan was educated at Oxford High School, and studied maths as an undergraduate at Clare College in the University of Cambridge.

[5] 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.

[7] Her work endeavours to understand the structure of geometric objects by investigation of their algebraic and topological properties.

[17] Kirwan served on the medal-selection committee that awarded the Fields medal to Maryam Mirzakhani.