Thursday, August 14, 2014

A00049 - Maryam Mirzakhani, First Woman to Receive Fields Medal


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Maryam Mirzakhani (Persian: مریم میرزاخانی‎; born May[1] 1977) is an Iranian mathematician, and a full professor of mathematics (since 1 September 2008) at Stanford University.[5][6][7]
Her research interests include Teichmüller theory, hyperbolic geometry, ergodic theory, and symplectic geometry.[1] In 2014, Mirzakhani became the first woman, as well as the first Iranian and the second person from the Middle East (after Elon Lindenstrauss), to be awarded the Fields Medal.[8][9][10][11][12]
Mirzakhani found international recognition as a brilliant teenager after receiving gold medals at both the 1994 International Mathematical Olympiad (Hong Kong) and the 1995 International Mathematical Olympiad (Toronto),[13]where she was the first Iranian student to finish with a perfect score.[13][14][15]

Early life and education[edit]

Maryam Mirzakhani was born in 1977 in Tehran, Iran. She went to high school in the city at Farzanegan, National Organization for Development of Exceptional Talents (NODET). She competed and was recognized internationally for her math skills, receiving gold medals at both the 1994 International Mathematical Olympiad (Hong Kong) and the 1995 International Mathematical Olympiad (Toronto),[13] where she was the first Iranian student to finish with a perfect score.[13][16][17]
She obtained her BSc in mathematics (1999) from Sharif University of Technology in Tehran. She went to the United States for graduate work, earning a PhD from Harvard University (2004), where she worked under the supervision of the Fields Medalist Curtis McMullen. She was also a 2004 research fellow of the Clay Mathematics Institute and a professor at Princeton University.[18]

Research work[edit]

Mirzakhani has made several contributions to the theory of moduli spaces of Riemann surfaces. In her early work, Maryam 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 tautology classes on moduli space,[5] as well as an asymptotic formula for the growth of the number of simple closed geodesics on a compact hyperbolic surface.[19] Her subsequent work has 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.[20]
Mirzakhani was awarded the Fields Medal in 2014 for "her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces".[21]She was congratulated for her win by Iranian President Hassan Rouhani.[8]
At the time of the award, Wisconsin professor Jordan Ellenberg explained her research to a popular audience:
... [Her] work expertly blends dynamics with geometry. Among other things, she studies billiards. But now, in a move very characteristic of modern mathematics, it gets kind of meta: She considers not just one billiard table, but the universe of all possible billiard tables. And the kind of dynamics she studies doesn't directly concern the motion of the billiards on the table, but instead a transformation of the billiard table itself, which is changing its shape in a rule-governed way; if you like, the table itself moves like a strange planet around the universe of all possible tables ... This isn't the kind of thing you do to win at pool, but it's the kind of thing you do to win a Fields Medal. And it's what you need to do in order to expose the dynamics at the heart of geometry; for there's no question that they're there.[22]

Personal life[edit]

She is married to Jan Vondrak, a theoretical computer scientist who works at IBM Research. They have a daughter named Anahita.[23][24]

Awards and honours[edit]

  • Fields Medal 2014[9][25][26]
  • Plenary speaker at the International Congress of Mathematicians (ICM 2014)
  • Clay Research Award 2014[27]
  • The 2013 AMS Ruth Lyttle Satter Prize in Mathematics. "Presented every two years by the American Mathematical Society, the Satter Prize recognizes an outstanding contribution to mathematics research by a woman in the preceding six years. The prize was awarded on Thursday, 10 January 2013, at the Joint Mathematics Meetings in San Diego."[28]
  • Invited to talk at the International Congress of Mathematicians in 2010, on the topic of "Topology and Dynamical Systems & ODE" [29]
  • AMS Blumenthal Award 2009 [28]
  • Clay Mathematics Institute Research Fellow 2004[30]
  • Harvard Junior Fellowship Harvard University, 2003[1]
  • Merit fellowship Harvard University, 2003[1]
  • IPM Fellowship The Institute for theoretical Physics and Mathematics, Tehran, Iran, 1995–99[1]
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Top Math Prize Has Its First Female Winner

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    Winners of the 2014 Fields Medal in mathematics, from left: Maryam Mirzakhani, Artur Avila, Manjul Bhargava and Martin Hairer. International Mathematical Union

    An Iranian mathematician is the first woman ever to receive a Fields Medal, often considered to be mathematics’ equivalent of the Nobel Prize.
    The recipient, Maryam Mirzakhani, a professor at Stanford, was one of four winners honored on Wednesday at the International Congress of Mathematicians in Seoul, South Korea.
    The Fields Medal is given every four years, and several can be awarded at once. The other recipients this year are Artur Avila of the National Institute of Pure and Applied Mathematics in Brazil and the National Center for Scientific Research in France; Manjul Bhargava of Princeton University; and Martin Hairer of the University of Warwick in England.
    The 52 medalists from previous years were all men.
    “This is a great honor. I will be happy if it encourages young female scientists and mathematicians,” Dr. Mirzakhani was quoted as saying in a Stanford news release on Tuesday. “I am sure there will be many more women winning this kind of award in coming years.”
    Ingrid Daubechies, a professor of mathematics at Duke and president of theInternational Mathematical Union, called the news “a great joy” in an email.
    “All researchers in mathematics will tell you that there is no difference between the math done by a woman or a man, and of course the decision of the Fields Medal committee is based only on the results of each candidate,” she wrote. “That said, I bet the vast majority of the mathematicians in the world will be happy that it will no longer be possible to say that ‘the Fields Medal has always been awarded only to men.’ ”
    Much of the research by Dr. Mirzakhani, who was born in Tehran in 1977, has involved the behavior of dynamical systems. There are no exact mathematical solutions for many dynamical systems, even simple ones.
    “What Maryam discovered is that in another regime, the dynamical orbits are tightly constrained to follow algebraic laws,” said Curtis T. McMullen, a professor at Harvard who was Dr. Mirzakhani’s doctoral adviser. “These dynamical systems describe surfaces with many handles, like pretzels, whose shape is evolving over time by twisting and stretching in a precise way. They are related to billiards on tables that are not rectangular but still polygonal, like the regular octagon.”
    Dr. Avila, 35, investigated a different area of dynamical systems, including an understanding of fractals. Dr. Bhargava, 40, was recognized for new methods in the geometry of numbers, especially prime numbers, and Dr. Hairer, 38, made advances in the study of the effect of random noise on partial differential equations, capturing the effect of turbulence on ocean currents or the flow of air around airplane wings.
    While women have reached parity in many academic fields, mathematics is still dominated by men, who earn about 70 percent of the doctoral degrees. The disparity is even more striking at the highest echelons. Since 2003, the Norwegian Academy of Science and Letters has awarded the Abel Prize, recognizing outstanding mathematicians with a monetary award of about $1 million; all 14 recipients so far are men. No woman has won the Wolf Prize in Mathematics, another prestigious award.
    The Fields Medal was conceived by John Charles Fields, a Canadian mathematician, “in recognition of work already done” and as “an encouragement for further achievement.” Judges have interpreted the terms of the Fields trust to mean that the award should usually be limited to mathematicians age 40 or younger.
    Dr. McMullen, himself a Fields medalist, did not speculate on why it had taken so long for a woman to be recognized. “I would prefer to look forward and celebrate this occasion,” he said, “and see it as a sign of positive trends in society and in science.”
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