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Too short a walk on the Riemann surface: Maryam Mirzakhani 1977–2017

13 October 2017

Maryam Mirzakhani, mathematics professor at Stanford University and Fields Medalist in 2014, passed away on 14 July aged just 40. She was the first woman and first Iranian citizen to win a Fields Medal.

Born in Teheran, at high-school age Maryam participated in two International Mathematics Olympiads, winning gold medals both times – once with a perfect score. After undergraduate studies at Sharif University, she moved to the US to enroll in a PhD course at Harvard University, under the supervision of Fields Medalist Curtis McMullen. Before joining Stanford in 2008 she was a fellow of the Clay Mathematics Institute in Cambridge (MA) and a professor at Princeton University.

Since her early career as a mathematician, Maryam obtained fundamental results on moduli spaces of Riemann surfaces and inhomogeneous space dynamics – topics at the intersections between mathematics and physics. One of her first major results was a counting theorem on closed geodesics that unexpectedly led to a new proof of Witten’s conjecture, related to the partition function of two-dimensional quantum gravity.

As Harvard string theorist Cumrun Vafa recalled in his speech at a memorial event held in August, results of Maryam’s work and the techniques she applied in her proofs might be applied to solve problems in string theory. Riemann surfaces are natural ingredients in string theory, where they appear both as 2D world-sheets of strings dynamically evolving in space–time, as well as 2D internal manifolds on which the theory is compactified to reduce its original 10 or 11 dimensions to a more familiar 4D scenario.

Both applications of Riemann surfaces are of great interest to theoretical physicists. Ongoing research in CERN’s theory department directly investigates string world-sheet and scattering amplitudes, as well as supersymmetric field theories, which are constructed through geometric engineering of branes wrapping Riemann surfaces. Maryam’s approach to moduli spaces provided powerful tools that, in the future, could lead to major advances in theoretical physics.

The premature departure of Maryam Mirzakhani represents a huge loss for the scientific community, not just for her scientific excellence. Winning a Fields Medal not only highlights the academic achievement of the recipient but, as Terrence Tao (Fields Medalist, UCLA) wrote in a note about Maryam Mirzakhani, it also promotes the recipient to a role model. In the case of Maryam Mirzakhani this was definitely true: as a female mathematician and the first woman to win a Fields Medal, she will remain a reference figure for future generations of female scientists.

In addition to an extraordinary scientific career, particularly noticeable were her generosity and humble personality.

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