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. Her fields of specialisation are algebraic and symplectic geometry.^[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.^[6]

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.^[7] Her work endeavours to understand the structure of geometric objects by investigation of their algebraic and topological properties.^[8] 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.^[9] She is an honorary fellow of Clare College, Cambridge^[10] and also at Magdalen College.^[11]

In 1996, she was awarded the Title of Distinction of Professor of Mathematics. From 2004 to 2006 she was president of the London Mathematical Society, the second-youngest president in the society's history and only the second woman to be president.^[12][13] In 2005, she received a five-year EPSRC Senior Research Fellowship, to support her research on the moduli spaces of complex algebraic curves.^[14]

In 2017, she was elected Savilian Professor of Geometry, becoming the first woman to hold the post.^[15] While this entailed a move to New College, Oxford she was elected an emeritus fellow at Balliol.^[16] She was the convenor of the 2008–9 meeting of European Women in Mathematics and deputy convenor of the following meeting in 2010–11.^[17]

• London Mathematical Society Whitehead Prize, 1989^[18]
• Fellow of the Royal Society, 2001^[19]
• President, London Mathematical Society, 2003–2005
• EPSRC Senior Research Fellowship, 2005–2010, for her work in algebraic geometry^[20]
• Fellow of the American Mathematical Society, 2012^[21]
• London Mathematical Society Senior Whitehead Prize, 2013^[18]
• DBE for services to mathematics, 2014^[22]
• Maths and Computing Suffrage Science award, 2016^[23]
• Member of Academia Europaea^[9]
• Chairman of the United Kingdom Mathematics Trust
• Sylvester Medal of The Royal Society, 2021
• Honorary degree, University of York, 2020^[24]
• Honorary degree, University of St Andrews, 2022^[25]
• L'Oréal-UNESCO For Women in Science Awards (Laureate for Europe – Mathematics), 2023^[26]

Kirwan served on the medal-selection committee that awarded the Fields medal to Maryam Mirzakhani.^[27]

• Cohomology of Quotients in Symplectic and Algebraic Geometry. Mathematical Notes. Vol. 31. Princeton University Press. 1984. ISBN 978-0691083704.
• An Introduction to Intersection Homology Theory. Longman Scientific and Technical. 1988.^[28] with Jonathan Woolf: 2nd edn. CRC Press. 2006. ISBN 978-1584881841.
• Complex Algebraic Curves. London Mathematical Society Student Texts. Cambridge University Press. 1992. ISBN 978-0521423533.