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Maryam Mirzakhani

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Maryam Mirzakhani
Born
Template:Lang-fa

(1977-05-13) 13 May 1977 (age 47)[4]
Tehran, Iran
NationalityIranian[4]
Alma mater
Awards
Scientific career
FieldsMathematician
Institutions
ThesisSimple geodesics on hyperbolic surfaces and the volume of the moduli space of curves (2004)
Doctoral advisorCurtis T. McMullen[1][2][3]

Maryam Mirzakhani (Template:Lang-fa; born May 13, 1977) is an Iranian-American mathematician and a professor of mathematics at Stanford University.[5][6][7]

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.[8][9] The award committee cited her work in "the dynamics and geometry of Riemann surfaces and their moduli spaces".[10]

Her research topics include Teichmüller theory, hyperbolic geometry, ergodic theory, and symplectic geometry.[4]

Early life and education

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).

In 1994, Mirzakhani won a gold medal 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.[11][12][13]

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.[14]

Research work

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 tautological 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, generalizing the theorem of the three geodesics for spherical surfaces.[15] 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.[16]

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.[17][18] 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.[18] 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."[18]

Mirzakhani was awarded the Fields Medal in 2014 for "her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces".[19] The award was made in Seoul at the International Congress of Mathematicians on 13 August.[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

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 (Template:Lang-fa) .[25]

Awards and honors

References

  1. ^ Maryam Mirzakhani at the Mathematics Genealogy Project
  2. ^ Mirzakhani, Maryam. "Curriculum Vitae" (PDF). Archived from the original (PDF) on 29 August 2008. Retrieved 12 August 2014.
  3. ^ Jonathan, Webb (2014). "First female winner for Fields maths medal". BBC News. Retrieved 13 August 2014.
  4. ^ a b c d e f Mirzakhani, Maryam. "Curriculum Vitae" (PDF). Archived from the original (PDF) on 24 November 2005. Retrieved 13 August 2014.
  5. ^ a b Mirzakhani, Maryam (2007). "Weil-Petersson volumes and intersection theory on the moduli space of curves" (PDF). 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. 167 (1). Springer-Verlag: 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. ^ "IMU Prizes 2014". International Mathematical Union. Retrieved 12 August 2014.
  10. ^ Sample, Ian (13 August 2014). "Fields Medal mathematics prize won by woman for first time in its history". the Guardian. Retrieved 9 June 2016.
  11. ^ Maryam Mirzakhani's results at International Mathematical Olympiad
  12. ^ "Iranian woman wins maths' top prize". New Scientist. 12 August 2014. Retrieved 13 August 2014.
  13. ^ Newhall, Marissa (13 September 2005). "'Brilliant' minds honored: Maryam Mirzakhani". USA Today.
  14. ^ Maryam Mirzakhani's publications indexed by the Scopus bibliographic database. (subscription required)
  15. ^ 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.
  16. ^ Mirzakhani, M. (2008). "Ergodic Theory of the Earthquake Flow". International Mathematics Research Notices. 2008. doi:10.1093/imrn/rnm116. MR 2416997.
  17. ^ Eskin, Alex; Mirzakhani, Maryam; Mohammadi, Amir (2015). "Isolation, equidistribution, and orbit closures for the SL(2,R) action on moduli space". Annals of Mathematics. 182 (2): 673–721. doi:10.4007/annals.2015.182.2.7.
  18. ^ a b c "The Work of Maryam Mirzakhani" (PDF) (Press release). International Mathematics Union. Retrieved 15 August 2014.
  19. ^ "IMU Prizes 2014 citations". International Mathematical Union. Retrieved 12 August 2014.
  20. ^ Stanford's Maryam Mirzakhani wins Fields Medal, Bjorn Carey, Stanford.edu, Retrieved 12 August 2016
  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" (PDF). 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. ^ "National Academy of Sciences Members and Foreign Associates Elected". Retrieved 5 May 2016.
  27. ^ "IMU Prizes 2014". International Mathematical Union.
  28. ^ Larousserie, David (12 August 2014). "Médaille Fields de mathématiques : une femme promue pour la première fois". Le Monde (in French). Retrieved 13 August 2014.
  29. ^ "2014 Clay Research Awards".
  30. ^ a b American Mathematical Society. Retrieved 6 January 2009
  31. ^ "ICM Plenary and Invited Speakers since 1897". International Congress of Mathematicians. Retrieved 13 August 2014.
  32. ^ "Interview with Research Fellow Maryam Mirzakhani" (PDF). Oxford University. 2008.
  33. ^ Gibney, E.; Leford, H.; Lok, C.; Hayden, E.C.; Cowen, R.; Klarreich, E.; Reardon, S.; Padma, T.V.; Cyranoski, D.; Callaway, E. (18 December 2014). "Nature's 10 Ten people who mattered this year". Nature. 516: 311–319. doi:10.1038/516311a.
  34. ^ Newly Elected, American Philosophical Society, April 2015, retrieved 28 August 2015.
  35. ^ http://www.academie-sciences.fr/pdf/communique/election_AE_2015.pdf
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