Maryam Mirzakhani

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Maryam Mirzakhani
Born Persian: مریم میرزاخانی
May 1977 (age 37)[1]
Tehran, Iran
Residence Palo Alto, California, United States
Nationality Iranian[1]
Fields Mathematician
Institutions
Alma mater
Thesis Simple geodesics on hyperbolic surfaces and the volume of the moduli space of curves (2004)
Doctoral advisor Curtis T. McMullen[2][3][4]
Notable awards

Maryam Mirzakhani (Persian: مریم میرزاخانی‎; born May 1977) is an Iranian[1] mathematician working in the United States. Since 1 September 2008, she has served as a professor of mathematics at Stanford University.[5][6][7]

In 2014, Mirzakhani became both the first woman and the first Iranian honored with the Fields Medal, the most prestigious award in mathematics.[8] [9] [10] [11] [12] The award committee cited her work in understanding the symmetry of curved surfaces. Her research topics include Teichmüller theory, hyperbolic geometry, ergodic theory, and symplectic geometry.[1]

In 1994, Mirzakhani won a gold medal in the International Mathematical Olympiad, the first female Iranian student to do so. In the 1995 Olympiad, she became the first Iranian student to achieve a perfect score and to win two gold medals.[13] [14] [15]

Early life and education[edit]

Mirzakhani was born in 1977 in Tehran, Iran. She went to high school in Tehran 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][14][15]

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.[16]

Research work[edit]

Mirzakhani has 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 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.[17] 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.[18]

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.[19] 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.[19] 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."[19]

Mirzakhani was awarded the Fields Medal in 2014 for "her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces".[20]

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.[21]

President Hassan Rouhani of Iran congratulated her.[22]

Personal life[edit]

She is married to Jan Vondrák, a Czech theoretical computer scientist who works at IBM Almaden Research Center.[23][24] They have a daughter named Anahita.[25]

Awards and honors[edit]

Notes and references [edit]

  1. ^ a b c d e f g Mirzakhani, Maryam. "Curriculum Vitae". Archived from the original on 24 November 2005. Retrieved 13 August 2014. 
  2. ^ Maryam Mirzakhani at the Mathematics Genealogy Project
  3. ^ Mirzakhani, Maryam. "CurriculumVitae". Archived from the original on 29 August 2008. Retrieved 12 August 2014. 
  4. ^ Jonathan, Webb (2014). "First female winner for Fields maths medal". BBC News. Retrieved 13 August 2014. 
  5. ^ a b Mirzakhani, Maryam (2007). "Weil-Petersson volumes and intersection theory on the moduli space of curves". Journal of the American Mathematical Society 20: 1–23. doi:10.1090/S0894-0347-06-00526-1. MR 2257394. 
  6. ^ Mirzakhani, Maryam (January 2007). "Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces". Inventiones Mathematicae (Springer-Verlag) 167 (1): 179–222. doi:10.1007/s00222-006-0013-2. ISSN 1432-1297. 
  7. ^ "Report of the President to the Board of Trustees". Stanford University. 9 April 2008. Retrieved 12 August 2014. 
  8. ^ "President Rouhani Congratulates Iranian Woman for Winning Math Nobel Prize". Fars News Agency. 14 August 2014. Retrieved 14 August 2014. 
  9. ^ a b Ball, Philip (12 August 2014). "Iranian is first woman to nab highest prize in maths: Maryam Mirzakhani is among four young researchers to win Fields Medals, awarded every four years". Nature. doi:10.1038/nature.2014.15686. Retrieved 14 August 2014. 
  10. ^ "IMU Prizes 2014". International Mathematical Union. Retrieved 12 August 2014. 
  11. ^ Mathis-Lilley, Ben (8 August 2014). "A Woman Has Won the Fields Medal, Math's Highest Prize, for the First Time". Slate. Retrieved 13 August 2014. 
  12. ^ Polo, Susana. "Maryam Mirzakhani Becomes First Woman to Earn Fields Medal for Mathematics in Its 78 Year History". The Mary Sue. Retrieved 13 August 2014. 
  13. ^ a b c Maryam Mirzakhani's results at the International Mathematical Olympiad
  14. ^ a b "Iranian woman wins maths' top prize". New Scientist. 12 August 2014. Retrieved 13 August 2014. 
  15. ^ a b Newhall, Marissa (13 September 2005). "'Brilliant' minds honored: Maryam Mirzakhani". USA Today. 
  16. ^ Maryam Mirzakhani from the Scopus bibliographic database.
  17. ^ Mirzakhani, Maryam (2008). "Growth of the number of simple closed geodesics on hyperbolic surfaces". Annals of Mathematics 168 (1): 97–125. doi:10.4007/annals.2008.168.97. MR 2415399. Zbl 1177.37036. 
  18. ^ Mirzakhani, M. (July 2010). "Ergodic Theory of the Earthquake Flow". International Mathematics Research Notices. doi:10.1093/imrn/rnm116. 
  19. ^ a b c "The Work of Maryam Mirzakhani" (PDF) (Press release). International Mathematics Union. Retrieved 15 August 2014. 
  20. ^ "IMU Prizes 2014 citations". International Mathematical Union. Retrieved 12 August 2014. 
  21. ^ Ellenberg, Jordan (13 August 2014). "Math Is Getting Dynamic". Slate. 
  22. ^ "President hails Prof Mirzakhani, winner of topmost world math prize". Official Site of the President of The Islamic Republic of Iran. 13 August 2014. Retrieved 19 August 2014. 
  23. ^ "Jan Vondrák". Stanford University. Retrieved 15 August 2014. 
  24. ^ Jan Vondrak profile, ibm.com. Retrieved 13 April 2014.
  25. ^ "A Tenacious Explorer of Abstract Surfaces", simonsfoundation.org. Retrieved 13 April 2014.
  26. ^ "IMU Prizes 2014". International Mathematical Union. 
  27. ^ Larousserie, David (12 August 2014). "Médaille Fields de mathématiques : une femme promue pour la première fois". Le Monde (in French). Retrieved 13 August 2014. 
  28. ^ "2014 Clay Research Awards". 
  29. ^ a b American Mathematical Society. Retrieved 6 January 2009
  30. ^ "ICM Plenary and Invited Speakers since 1897". International Congress of Mathematicians. Retrieved 13 August 2014. 
  31. ^ "Interview with Research Fellow Maryam Mirzakhani". Oxford University. 2008. 

External links[edit]