Maryam Mirzakhani

Mirzakhani's work on the geometry of Teichmüller spaces and hyperbolic Riemann surfaces introduced a wealth of new ideas, allowing us to understand the asymptotics of length spectra on hyperbolic surfaces in great detail and to compute Weil-Petersson volumes of moduli spaces. She has clarified the ergodic theory of the 'earthquake flow' on Teichmüller space and shown how it can be extended to an action of SL(2,R). She has established analogues of the deep work of Margulis and Ratner (on symmetric spaces) in the much more challenging arena of moduli spaces Mg, providing new perspectives on ergodic theory, topology, and dynamics.