[Todos CMAT] Maryam Mirzakhani, 1977-2017

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Headlines    Maryam Mirzakhani, 1977-2017

  Maryam Mirzakhani , the only woman to win a Fields Medal, died on  
July 14 at the age of 40. Mirzakhani was a professor at Stanford  
University and a highly original mathematician who made a host of  
striking contributions to geometry and dynamical systems. Her work  
bridges several mathematical disciplines---including hyperbolic  
geometry, complex analysis, topology, and dynamics---and in return  
deeply influenced them all.

She gained widespread recognition for her early results in hyperbolic  
geometry, particularly on a problem known as the "prime number theorem  
for simple closed geodesics." The viewpoint developed in that work led  
to a proof of a conjecture that had been made by string theorist  
Edward Witten (1990 Fields Medalist). The conjecture was first proved  
in 1992 by Maxim Kontsevich (1998 Fields Medalist); 15 years later,  
Mirzakhani provided a new proof that came from a very different and  
totally unexpected viewpoint. These works led her to the study of  
dynamical systems associated with spaces of Riemann surfaces, where  
she and her collaborators made fundamental breakthroughs.

Her more-recent work (with A. Eskin and A. Mohammadi) constitutes one  
of the most sought-after advances in the area known as "Teichmüller  
dynamics." She proved a rigidity theorem that is an analogue, in this  
non-homogeneous context, of the celebrated "Ratner rigidity theorem"  
in homogeneous dynamics. (Marina Ratner, a Russian-American  
mathematician, died earlier this month at the age of 78.) Like  
Ratner's results, Mirzakhani's rigidity theorems, in asserting that  
the dynamics are much more rigid than one might initially expect, have  
numerous and far-reaching applications. That such rigidity is true and  
can be proven, in the highly intricate inhomogeneous setting of  
Teichmüller dynamics, came as a surprise. Indeed, the latter are so  
complicated that many assumed it would be impossible to work on them  
directly. Not Mirzakhani. Possessing strong geometric intuition and  
fluency in a remarkably diverse range of mathematical techniques and  
disparate mathematical cultures, she embodied a rare combination of  
superb technical ability, bold ambition, far-reaching vision, and deep  
curiosity.

In an obituary [  
https://www.nytimes.com/2017/07/16/us/maryam-mirzakhani-dead.html?_r=1  
]  by Kenneth Chang in  The   New York Times , Peter Sarnak reflected  
on Mirzakhani: "She was in the midst of doing fantastic work. ... Not  
only did she solve many problems; in solving problems, she developed  
tools that are now the bread and butter of people working in the  
field." Mirzakhani was also a tremendous inspiration to women  
mathematicians around the globe. In an article [  
https://www.timeshighereducation.com/comment/opinion/maryam-mirzakhani-the-right-woman-at-the-right-time/2015263.article ]  in  Times Higher Education , which appeared on August 21, 2014, just after Mirzakhani received the Fields Medal, British mathematician Caroline Series summed up what many women mathematicians felt at that moment: "The tectonic plates have shifted, and female mathematicians have finally come of  
age."

Mirzakhani grew up in Iran and came to the U.S. to attend graduate  
school, earning her PhD from Harvard University in 2004 under the  
direction of Curtis McMullen (1998 Fields Medalist). She was a  
professor at Princeton University before moving to Stanford in 2008.  
In addition to the Fields Medal, Mirzakhani also received the  
Blumenthal Award (2009), the Satter Prize (2013), and a Clay Research  
Award (2014). Survivors include her husband, Jan Vondrák, also a  
mathematics professor at Stanford, and their daughter, Anahita.

For more on Mirzakhani's work, see an article [  
http://www.math.harvard.edu/~ctm/papers/home/text/papers/icm14/icm14.pdf ]  by  
Curtis McMullen, which contains the  laudatio  he delivered during the  
2014 International Congress of Mathematicians in Seoul, where  
Mirzakhani received the Fields Medal. More information can be found in  
the news release [  
http://www.mathunion.org/fileadmin/IMU/Prizes/2014/news_release_mirzakhani.pdf  
]  the International Mathematical Union issued when Mirzakhani's  
Fields Medal was announced, a 2014 article [  
https://www.quantamagazine.org/maryam-mirzakhani-is-first-woman-fields-medalist-20140812 ]  in  Quanta Magazine  by Erica Klarreich, a 2015 emNotices/em article [ http://www.ams.org/notices/201511/rnoti-p1334.pdf ]  by Anton Zorich (pp. 1345-1349), and two pieces from this week: an article [ http://www.newyorker.com/tech/elements/maryam-mirzakhanis-pioneering-mathematical-legacy ]   
in
The New Yorker  by Siobhan Roberts, and a Beyond Reviews/em post
[ http://blogs.ams.org/beyondreviews/2017/07/17/maryam-mirzakhani ]   
by Ed Dunne that highlights MathSciNet reviews of her work.