Maryam Mirzakhani

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Maryam Mirzakhani
Persian: مریم میرزاخانی
File:Maryam Mirzakhani 2014.jpg
Born(1977-05-03)3 May 1977
Tehran, Iran
Died15 July 2017(2017-07-15) (aged 40)
NationalityIranian,[4][5] American[6]
Alma mater
SpouseJan Vondrák
Children1
Awards
Scientific career
FieldsMathematics
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 (Persian: مریم میرزاخانی‎; 3 May 1977 – 15 July 2017) was an Iranian[7][4] mathematician and a professor of mathematics at Stanford University.[8][9][10] Her research topics include Teichmüller theory, hyperbolic geometry, ergodic theory, and symplectic geometry.[4]

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 their moduli spaces".[13]

Early life and education

Mirzakhani was born on 3 May 1977 in Tehran, 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 at Princeton 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 Witten and Maxim Kontsevich on the intersection numbers of tautological classes on moduli space,[8] 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's earthquake 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 the dynamics 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 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.[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 was diagnosed with breast cancer in 2013.[31] After four years, it spread to her bone marrow.[32]


Mirzakhani describes herself as "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. Here 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, [33]

Death

Mirzakhani died from breast cancer[34] on 15 July 2017 at the age of 40.[35]

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. ^ Valette, Alain. "The Fields Medalists 2014" (PDF). Neuchâtel, Switzerland: Institut de mathématiques, Université de Neuchâtel. Retrieved 15 July 2017.
  6. ^ "May 3, 2016: NAS Members and Foreign Associates Elected". www.nasonline.org. National Academy of Sciences. Retrieved 16 July 2017.
  7. ^ "Maryam Mirzakhani, first woman to win maths' Fields Medal, dies - BBC News". Bbc.com. 12 August 2014. Retrieved 16 July 2017.
  8. ^ 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.
  9. ^ 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.
  10. ^ "Report of the President to the Board of Trustees". Stanford University. 9 April 2008. Retrieved 12 August 2014.
  11. ^ "President Rouhani Congratulates Iranian Woman for Winning Math Nobel Prize". Fars News Agency. 14 August 2014. Retrieved 14 August 2014.
  12. ^ "IMU Prizes 2014". International Mathematical Union. Retrieved 12 August 2014.
  13. ^ a b Sample, Ian (13 August 2014). "Fields Medal mathematics prize won by woman for first time in its history". the Guardian. Retrieved 9 June 2016.
  14. ^ "Maryam Mirzakhani, Only Woman to Win a Fields Medal, Dies at 40". New York Times, 2017/07/16 Kenneth Chang
  15. ^ Maryam Mirzakhani's results at International Mathematical Olympiad
  16. ^ "Iranian woman wins maths' top prize". New Scientist. 12 August 2014. Retrieved 13 August 2014.
  17. ^ Newhall, Marissa (13 September 2005). "'Brilliant' minds honored: Maryam Mirzakhani". USA Today.
  18. ^ Maryam Mirzakhani's publications indexed by the Scopus bibliographic database. (subscription required)
  19. ^ "Maryam Mirzakhani, First Woman to Receive the Prestigious Fields Medal, Dies at the Age of 40 After Breast Cancer Battle". People Magazine, By Yvonne Juris on July 16, 2017
  20. ^ 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.
  21. ^ Mirzakhani, M. (2008). "Ergodic Theory of the Earthquake Flow". International Mathematics Research Notices. 2008. doi:10.1093/imrn/rnm116. MR 2416997.
  22. ^ 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.
  23. ^ a b c "The Work of Maryam Mirzakhani" (PDF) (Press release). International Mathematics Union. Retrieved 15 August 2014.
  24. ^ "IMU Prizes 2014 citations". International Mathematical Union. Retrieved 12 August 2014.
  25. ^ Stanford's Maryam Mirzakhani wins Fields Medal, Bjorn Carey, Stanford.edu, Retrieved 12 August 2016
  26. ^ Ellenberg, Jordan (13 August 2014). "Math Is Getting Dynamic". Slate.
  27. ^ "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.
  28. ^ "Collaboration paths to Paul Erdős". The Erdős Number Project.
  29. ^ "Jan Vondrák" (PDF). Stanford University. Retrieved 14 July 2017. {{cite web}}: Cite has empty unknown parameter: |dead-url= (help)
  30. ^ "A Tenacious Explorer of Abstract Surfaces", simonsfoundation.org. Retrieved 13 April 2014.
  31. ^ "PressTV-Iranian math genius battles cancer at US hospital". Presstv.ir. Retrieved 16 July 2017.
  32. ^ France-Presse, Agence. "Sorrow as Maryam Mirzakhani, the first woman to win mathematics' Fields Medal, dies aged 40". The Telegraph. Retrieved 15 July 2017.
  33. ^ University, Stanford (15 July 2017). "Maryam Mirzakhani, Stanford mathematician and Fields Medal winner, dies". Stanford News.
  34. ^ Chang, Kenneth (16 July 2017). "Maryam Mirzakhani, Only Woman to Win a Fields Medal, Dies at 40". The New York Times.
  35. ^ "Maryam Mirzakhani died" (in Persian). Mehr news Agancy. 15 July 2017.
  36. ^ "Interview with Research Fellow Maryam Mirzakhani" (PDF). Oxford University. 2008.
  37. ^ a b American Mathematical Society. Retrieved 6 January 2009
  38. ^ "ICM Plenary and Invited Speakers since 1897". International Congress of Mathematicians. Retrieved 13 August 2014.
  39. ^ 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. PMID 25519114.
  40. ^ "2014 Clay Research Awards".
  41. ^ "IMU Prizes 2014". International Mathematical Union.
  42. ^ Larousserie, David (12 August 2014). "Médaille Fields de mathématiques : une femme promue pour la première fois". Le Monde (in French). Retrieved 13 August 2014.
  43. ^ "Quinze nouveaux associés étrangers à l'Académie des sciences" (PDF). Institute de France Académie des Sciences. Retrieved 16 July 2017.
  44. ^ Newly Elected, American Philosophical Society, April 2015, retrieved 28 August 2015
  45. ^ "National Academy of Sciences Members and Foreign Associates Elected". Retrieved 5 May 2016.
  46. ^ Maryam Mirzakhani elected to American Academy of Arts and Sciences, Department of Mathematics, Stanford University, May 2017, retrieved 6 May 2017

External links

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