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Maryam Mirzakhani was a renowned mathematician who made significant contributions to the field of mathematics, particularly in the areas of geometry and topology. Some of her most notable achievements include:

Fields Medal: In 2014, Mirzakhani became the first woman and the first Iranian to receive the Fields Medal, which is considered the highest honor in mathematics. She was awarded the medal for her work on the dynamics and geometry of Riemann surfaces and their moduli spaces.

Research on hyperbolic geometry: Mirzakhani's doctoral thesis was on hyperbolic geometry, a non-Euclidean geometry that describes the geometry of surfaces with a constant negative curvature. Her research on this topic has had a significant impact on the field of mathematics.

Moduli space of Riemann surfaces: Mirzakhani made groundbreaking contributions to the study of the moduli space of Riemann surfaces, which is the space of all possible complex structures on a given surface. Her work has led to new insights into the geometry and topology of these surfaces and has applications in other fields, such as physics.

Invited speaker at prestigious conferences: Mirzakhani was invited to speak at many prestigious conferences, including the International Congress of Mathematicians in 2014, where she gave a plenary lecture on her work on the geometry of moduli spaces.