Wikinventia — Atlas of discoveries and inventions · Digital Age

Weil-Petersson volumes of moduli spaces — Maryam Mirzakhani

2007 AD · Transmission: Global
MathematicsTheoryPersian

Maryam Mirzakhani computes in 2007, in Inventiones Mathematicae and the Journal of the American Mathematical Society, the Weil-Petersson volumes of moduli spaces of Riemann surfaces with simple closed geodesics, also establishing a connection with intersection theory on these spaces that allows her to offer a new proof — via completely different geometric methods — of Witten's conjecture, already proved in 1992 by Maxim Kontsevich using algebraic techniques. Mirzakhani's work combines hyperbolic geometry, Teichmüller theory, and surface dynamics in a way considered exceptionally original by the mathematical community. Mirzakhani received the Fields Medal in 2014, the first woman and the first Iranian-born person to receive it; she died in 2017, at age 40, of breast cancer.

InstitutionStanford University
Historical regionIran / USA
Primary sourceMirzakhani, M. — "Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces" (Inventiones Mathematicae, 167, 2007); "Weil-Petersson volumes and intersection theory on the moduli space of curves" (Journal of the American Mathematical Society, 20, 2007)
Secondary sourceInternational Mathematical Union — Fields Medal citation 2014
Original languageEnglish
View this entry in the interactive atlas → View in graph →