Frances Kirwan

Professorial Fellow; Savilian Professor of Geometry
BA Cantab, DPhil Oxon, FRS, DBE 

Frances Kirwan was an undergraduate in mathematics at Clare College, Cambridge. After Part III Mathematics in Cambridge she moved to Oxford for her DPhil supervised by Michael Atiyah. She was a Junior Fellow at Harvard (1983-85) before returning to Oxford, first as a Fellow by Examination at Magdalen College and then as a Tutorial Fellow in Mathematics at Balliol (1986-2017) before being appointed to the Savilian Professorship. She is a Fellow of the Royal Society, serving on its Council 2012-15, and she chaired the UK Mathematics Trust 2010-16.


Her teaching is in the Mathematics Department, where she has given a range of lecture courses, from first year pure mathematics, through more specialised third and fourth year undergraduate courses on geometry and algebra, to graduate courses focussed on areas close to her research.

Research Interests

Frances Kirwan’s research lies in the area of algebraic geometry (mostly over the field of complex numbers) and its links with other parts of geometry, especially symplectic (and hyperkähler) geometry. She is particularly interested in classification problems in algebraic geometry and the construction and study of moduli spaces.

Selected publications


An introduction to intersection homology theory
Kirwan, F; Woolf, J;
ISBN-13: 9781584881841 (2006)


Geometric invariant theory
Mumford, D; Fogarty, J; Kirwan, F;
ISBN-10: 3-540-56963-4 (1994)


Complex algebraic curves
Kirwan, F;
ISBN-13: 9780521412513 (1992)


Cohomology of quotients in symplectic and algebraic geometry
Kirwan, FC;
ISBN-13: 9780691083704 (1984)