Maryam Mirzakhani (Persian: مریم میرزاخانی; 3 May 1977 – 14 July 2017) was an Iranian[7][1]mathematician and a professor of mathematicsat Stanford University.[9][10] Her research topics include Teichmüller theory, hyperbolic geometry, ergodic theory, and symplectic geometry.[1]
On 13 August 2014, Mirzakhani became both the first woman and the first Iranian honored with the Fields Medal, the most prestigious award in mathematics.[11][12] The award committee cited her work in "the dynamics and geometry of Riemann surfaces and theirmoduli spaces".[13]
Early life and education
Mirzakhani was born on 3 May 1977 inTehran, Iran.[14] 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.[15][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 in 2004, where she worked under the supervision of the Fields Medalist Curtis McMullen.
Career
Mirzakhani was a 2004 research fellow of the Clay Mathematics Institute and a professor atPrinceton University.[18] In 2008 she became a professor at Stanford University.[19][13]
Research work
Maryam Mirzakhani. August 2014
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 Wittenand Maxim Kontsevich on the intersection numbers of tautological classes on moduli space, 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.[20] Her subsequent work focused on Teichmüller dynamics of moduli space. In particular, she was able to prove the long-standing conjecture that William Thurston'searthquake flow on Teichmüller space is ergodic.[21]
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.[22][23] 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.[23]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."[23]
Mirzakhani was awarded the Fields Medal in 2014 for "her outstanding contributions to thedynamics and geometry of Riemann surfaces and their moduli spaces".[24] The award was made in Seoul at the International Congress of Mathematicians on 13 August.[25]
At the time of the award, 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 allpossible 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.[26]
In 2014, President Hassan Rouhani of Iran congratulated her for winning the topmost world mathematics prize.[27]
Mirzakhani has an Erdős number of 3.[28]
Personal life
Mirzakhani was married to Jan Vondrák, a Czech theoretical computer scientist and applied mathematician who is an associate professor at Stanford University;[29] their daughter is named Anahita.[30]
Mirzakhani described herself as a "slow" mathematician, saying that
You have to spend some energy and effort to see the beauty of math.
To solve problems, Mirzakhani would draw doodles on sheets of paper, and write mathematical formulas around the drawings. Her daughter described her mother's work as "painting".
I don’t have any particular recipe [for developing new proofs]... It is like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck you might find a way out.
— Maryam Mirzakhani, [31]
Death
Mirzakhani was diagnosed with breast cancer in 2013.[32] After four years, it spread to her bone marrow.[33] Mirzakhani died from breast cancer[34] on 14 July 2017 at the age of 40.[31][35]
Awards and honors
