Dame Frances Kirwan is a prominent British mathematician known for her work in algebraic geometry and topology. She has made significant contributions to the understanding of Kähler manifolds and symplectic geometry, which are important areas in modern mathematics. Kirwan has held various academic positions, including a professorship at the University of Oxford. In addition to her research, Dame Frances Kirwan is recognized for her efforts in promoting mathematics and supporting women in the field. She has served as the president of the London Mathematical Society and has been involved in initiatives aimed at increasing diversity in mathematics.