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Maryam Mirzakhani
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| Maryam Mirzakhani | |
|---|---|
On the occasion of winning the Fields Medal at the international mathematical congress in Seoul, 2014, the first woman and the first Iranian to do so
| |
| Native name | Persian: مریم میرزاخانی |
| Born | 3 May 1977 Tehran, Imperial State of Iran |
| Died | 14 July 2017 (aged 40) Palo Alto, California, United States |
| Nationality | Iranian,[1][2] American[3] |
| Fields | Mathematics |
| Institutions | |
| Alma mater | |
| Thesis | Simple geodesics on hyperbolic surfaces and the volume of the moduli space of curves (2004) |
| Doctoral advisor | Curtis T. McMullen[4][5][6] |
| Notable awards |
|
| Spouse | Jan Vondrák |
| Children | 1 |
Maryam Mirzakhani (Persian: مریم میرزاخانی, pronounced [mæɾjæm miːɾzɑːxɑːniː]; 3 May 1977 – 14 July 2017) was an Iranian[7][8][1] mathematician and a professor of mathematics at Stanford University.[9][10][11] Her research topics include Teichmüller theory, hyperbolic geometry, ergodic theory, and symplectic geometry.[1]
On 13 August 2014, Mirzakhani was honored with the Fields Medal, the most prestigious award in mathematics.[12][13] She thus became both the first woman and the first Iranian to be honored with the award.[14] The award committee cited her work in "the dynamics and geometry of Riemann surfaces and their moduli spaces".[15]
On 14 July 2017, Mirzakhani died of breast cancer at the age of 40.[16]
Contents
[hide]Early life and education
Mirzakhani was born on 3 May 1977 in Tehran, Iran.[17] She attended Farzanegan School there, part of the National Organization for Development of Exceptional Talents.
In 1994, Mirzakhani achieved the gold medal level in the International Mathematical Olympiad, the first female Iranian student to do so. In the 1995 International Mathematical Olympiad, she became the first Iranian student to achieve a perfect score and to win two gold medals.[18][19][20]
She obtained her BSc in mathematics (1999) from Sharif University of Technology in Tehran. She then went to the United States for graduate work, earning her PhD in 2004 from Harvard University, where she worked under the supervision of the Fields Medalist Curtis T. McMullen.
Career
Mirzakhani was a 2004 research fellow of the Clay Mathematics Institute and a professor at Princeton University.[21] In 2008 she became a professor at Stanford University.[15][22]
Research work
Mirzakhani made several contributions to the theory of moduli spaces of Riemann surfaces. In her early work, Mirzakhani discovered a formula expressing the volume of a moduli space with a given genus as a polynomial in the number of boundary components. This led her to obtain a new proof for the formula discovered by Edward Witten and Maxim Kontsevich on the intersection numbers of tautological classes on moduli space,[9] as well as an asymptotic formula for the growth of the number of simple closed geodesics on a compact hyperbolic surface, generalizing the theorem of the three geodesics for spherical surfaces.[23] Her subsequent work focused on Teichmüller dynamics of moduli space. In particular, she was able to prove the long-standing conjecture that William Thurston's earthquake flow on Teichmüller space is ergodic.[24]
Most recently as of 2014, with Alex Eskin and with input from Amir Mohammadi, Mirzakhani proved that complex geodesics and their closures in moduli space are surprisingly regular, rather than irregular or fractal.[25][26] The closures of complex geodesics are algebraic objects defined in terms of polynomials and therefore they have certain rigidity properties, which is analogous to a celebrated result that Marina Ratner arrived at during the 1990s.[26] The International Mathematical Union said in its press release that, "It is astounding to find that the rigidity in homogeneous spaces has an echo in the inhomogeneous world of moduli space."[26]
Mirzakhani was awarded the Fields Medal in 2014 for "her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces".[27] The award was made in Seoul at the International Congress of Mathematicians on 13 August.[28]
At the time of the award, Jordan Ellenberg explained her research to a popular audience:
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