Frances Clare Kirwan, FRS (born 1959) is a British mathematician, currently a Professor of Mathematics at the University of Oxford.
Her fields of specialisation are algebraic and symplectic geometry.
Professional career 
Educated at Oxford High School, she studied at the University of Cambridge. She took a D.Phil at Oxford in 1984, supervised by Michael Atiyah. From 1983 to 1985 she held a Junior Fellowship at Harvard, and from 1983 to 1986 a Fellowship at Magdalen College, before later becoming a Fellow of Balliol College.
In 1996 she was appointed a University Professor of Mathematics. From 2004-2006 she was President of the London Mathematical Society, the second-youngest president in the society's history. In 2005, she received a five-year EPSRC Senior Research Fellowship, to support her research on the moduli spaces of complex algebraic curves.
Awards and honours 
In 2012 she became a fellow of the American Mathematical Society.
- Cohomology of quotients in symplectic and algebraic geometry. Princeton University Press. 1984.
- An introduction to intersection homology theory. Longman Scientific and Technical. 1988. with Jonathan Woolf: 2nd edn. CRC Press. 2006.
- Complex algebraic curves. Cambridge University Press. 1992.