Maryam Mirzakhani
Maryam Mirzakhani ( Persian مریم میرزاخانی Maryam Mirzachani , born on May 12, 1977 in Tehran ; died July 14, 2017 in Stanford , California ) was an Iranian mathematician who became the first and so far only woman and first Iranian person to be awarded the Fields Medal in 2014. Since 2008 she has been a professor at Stanford University .
Life
As a student at the Farzanegan School for particularly gifted girls in Tehran, Mirzakhani won a mathematical talent competition and gold medals at the International Mathematical Olympiads in 1994 and 1995 . In February 1998, she survived a bus accident when the bus that was supposed to bring Sharif University's mathematical elite back to Tehran from a competition in Ahvaz crashed into a ravine, killing seven of the mathematicians and two bus drivers.
In 1999 she received her bachelor's degree in mathematics from Sharif University in Tehran and then went to Harvard University , where she received her PhD in 2004 under Curtis McMullen on Simple Geodesics on Hyperbolic Surfaces and the Volume of the Moduli Space of Curves . In 2003 she was a Junior Fellow at Harvard and from 2004 to 2008 a Research Fellow at the Clay Mathematics Institute and an Assistant Professor at Princeton University . On September 1, 2008, Mirzakhani was appointed to a professorship at Stanford .
Mirzakhani was married to the Czech mathematician Jan Vondrák (* 1974), who teaches at Stanford University, and had a daughter with him in 2011.
In 2013 she was diagnosed with breast cancer, of which she died on July 14, 2017 at the age of 40. On the occasion of her death, some of the Iranian daily newspapers (such as Hamshahri ) broke the rule not to depict women without a headscarf ( hijab ). A group of Iranian parliamentarians introduced a bill to give the children of Iranian women abroad Iranian citizenship (the marriage of a Muslim Iranian woman to a non-Muslim is not recognized under Iranian law) in order to prevent complications when the daughter enters Iran .
Under the title Secrets of the Surface: The Mathematical Vision of Maryam Mirzakhani the author and produced filmmaker George Csicsery in the years 2018 and 2019, a 59-minute long film biography , which was published in early 2020th
research
Mirzakhani dealt with hyperbolic geometry , symplectic geometry , Teichmüller theory and ergodic theory . Her central research area was the theory of modular spaces (parameter spaces ) Riemann surfaces . This area is known for its connection with numerous other mathematical sub-areas, since in addition to the geometric aspects (as hyperbolic surfaces and symplectic structures) also complex-analytical and algebraic aspects (as algebraic curves ) are examined.
In 2009 she received the Blumenthal Award from the American Mathematical Society for her dissertation . The laudation emphasizes the original combination of methods of hyperbolic geometry , classical methods from the theory of automorphic forms and symplectic reduction, which led to results in three important problems:
- A recursive formula for the Weil - Petersson volumes of the modular spaces of Riemann surfaces , based on a generalization of the McShane identity .
- An asymptotic determination of the number of simple , closed geodetic tables on hyperbolic surfaces as a function of length . Their number for lengths less than or equal to , according to Mirzakhani, increases asymptotically as , where the exponent denotes the dimension of the module space of the associated Riemann surface with the topological gender . The formula for closed geodesics on hyperbolic surfaces ( prime number theorem for geodesics) has been known for a long time and showed exponential growth ( Atle Selberg , Heinz Huber ). The proof of the formula for the asymptotic number of simple geodesic follows from their volume calculations for modular spaces.
- A new proof of the Witten conjecture about the existence of exactly integrable structures of the Korteweg-de-Vries type in the determination of the intersection numbers in the module spaces of curves (first proven in 1992 by Maxim Lwowitsch Konzewitsch ). Mirzakhani, as part of her new proof, gave an interpretation of the counting of geodetic tables in modular rooms.
In 2010, in the dynamics on modular rooms ( Teichmüller rooms ), she proved William Thurston's long open conjecture that the Earthquake flow he introduced is ergodic. With Alex Eskin in 2014 she proved the rigidity properties of complex geodetic tables (and their closure) in modular spaces, similar to Marina Ratner's theorems for rivers in homogeneous spaces. This was surprising, because irregular or fractal behavior was expected here, because the modular rooms are the complete opposite of homogeneous rooms.
In 1999, she and her fellow student Roya Beheshti , who has been Associate Professor of Mathematics at Washington University in St. Louis since 2013 , published a book in Tehran on problems of elementary number theory . She also dealt with graph theory .
Fonts (selection)
- Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces. Inventiones Mathematicae, Volume 167, 2007, pp. 179-222, PDF .
- Weil-Petersson volumes and intersection theory on the moduli space of curves. Journal of the American Mathematical Society, Volume 20, 2007, pp. 1-23, PDF .
- Growth of the number of simple closed geodesics on hyperbolic surfaces. Annals of Mathematics, Series 2, Volume 168, No. 1, 2008, pp. 97-125, PDF .
- Growth of Weil-Petersson volumes and random hyperbolic surfaces of large genus. J. Differential Geom., Volume 94, 2013, No. 2, pp. 267-300, PDF .
- With Alex Eskin : Invariant and stationary measures for the SL (2, R) action on moduli space. Publ. Math. IHES, Volume 127, 2018, pp. 95-324, Preprint 2013, PDF .
- With Alex Eskin, Amir Mohammadi: Isolation, equidistribution, and orbit closures for the SL (2, R) action on moduli space. Annals of Mathematics (2), Volume 182, Issue 2, 2015, pp. 673–721, PDF .
- With Alex Wright: The boundary of an affine invariant submanifold. Inventiones Mathematicae, Volume 209, 2017, pp. 927-984, PDF .
Awards
In 2009 Mirzakhani received the Blumenthal Award from the American Mathematical Society and in 2013 the Ruth Lyttle Satter Prize in Mathematics . In 2014, together with Peter Scholze, she was awarded the Clay Research Award for significant contributions to geometry and ergodic theory , in particular for her proof of an analogue of Ratner's theorem about unipotent flows for modular spaces of surfaces . In addition, she was selected to be the plenary speaker at the International Congress of Mathematicians in Seoul in 2014 .
On August 13, 2014, she was the first and so far only woman and the first person from Iran to receive the Fields Medal for “outstanding contributions to the geometry and dynamics of Riemann surfaces and their modular spaces”, using “methods in various fields such as algebraic geometry , topology and probability theory ". In 2015 she was elected to the American Philosophical Society , in 2016 to the National Academy of Sciences and the Académie des sciences , and in 2017 to the American Academy of Arts and Sciences .
In 2018, the National Academy of Sciences renamed its NAS Award in Mathematics to the Maryam Mirzakhani Prize in Mathematics in her memory .
literature
- Curtis McMullen : The work of Maryam Mirzakhani. ICM 2014, Fields Medal Laudation ( PDF; 210 kB ).
- Kasra Rafi: Maryam Mirzakhani (1977-2017). In: Nature . Volume 549, p. 32, 2017 ( PDF; 207 kB ).
- Eugenia Sapir et al. a .: Maryam Mirzakhani (1977-2017). Notices AMS, November 2018 ( PDF; 1.1 MB ).
- Caroline Series : Maryam Mirzakhani and her work. Mathematics Today 2017 ( PDF; 630 kB ).
- Jan Vondrak: In memoriam Maryam Mirzakhani , Bulletin of the AMS, Volume 57, 2020, pp. 357-358, online
- Alex Wright: A tour through Mirzakhani's work on moduli spaces of Riemann surfaces , Bulletin of the AMS, Volume 57, 2020, pp. 359-408, online
- Scott A. Wolpert : Lectures and notes: Mirzakhani's volume recursion and approach for the Witten-Kontsevich theorem on moduli tautological intersection numbers. Park City Mathematics Institute, Graduate Summer School on Moduli Spaces of Riemann Surfaces, August 2, 2011 ( PDF; 380 kB ).
- Anton Zorich : The magic wand theorem of A. Eskin and M. Mirzakhani. Gazette des Mathematiciens, Volume 142, 2014, pp. 39–54 ( PDF; 291 kB ).
Web links
- Interview with Research Fellow Maryam Mirzakhani. (PDF; 266 kB) In: maths.ox.ac.uk. Oxford University Clay Mathematics Institute, August 27, 2009, accessed April 28, 2020 .
- Fields Medallists 2014 awardees with brief citations. In: mathunion.org. International Mathematical Union (IMU), accessed April 28, 2020 .
- Curriculum vitae. Maryam Mirzakhani. (PDF; 35 kB) In: ClayMath.org. July 19, 2004, archived from the original on November 24, 2005 ; accessed on April 28, 2020 (English).
- Oberwolfach Photo Collection. In: owpdb.mfo.de. Retrieved April 28, 2020 .
- John J. O'Connor, Edmund F. Robertson : Maryam Mirzakhani. In: MacTutor History of Mathematics archive .
- Ms. Kirschvogel: Fascinating researchers - Maryam Mirzakhani. Science comic. In: blogs.helmholtz.de. March 18, 2019, accessed April 28, 2020 .
References and comments
- ^ A b Andrew Myers, Bjorn Carey: Maryam Mirzakhani, Stanford mathematician and Fields Medal winner, dies. In: News.Stanford.edu. July 15, 2017, accessed April 28, 2020 .
- ↑ International Mathematical Olympiad. Retrieved April 28, 2020 .
- ↑ a b Saeed Kamali Dehghan: Maryam Mirzakhani: Iranian newspapers break hijab taboo in tributes. In: TheGuardian.com. July 16, 2017, accessed April 28, 2020 .
- ^ Maryam Mirzakhani: Simple geodesics on hyperbolic surfaces and the volume of the moduli space of curves. In: search.proquest.com. 2004, accessed April 28, 2020 .
- ^ Mathematics Genealogy Project. In: genealogy.math.ndsu.nodak.edu. Retrieved April 28, 2020 .
- ↑ Press Release: The Work of Maryam Mirzakhani. (PDF; 107 kB) In: mathunion.org. August 12, 2014, accessed April 28, 2020 .
- ^ Stanford Report: Report of the President to the Board of Trustees. In: news.stanford.edu. April 9, 2008, accessed April 28, 2020 .
- ^ Jan Vondrák: Jan Vondrák. (PDF; 115 kB) In: Stanford University . Accessed April 28, 2020 (English).
- ↑ a b Erica Klarreich: A Tenacious Explorer of Abstract Surfaces. In: QuantaMagazine.org. August 12, 2014, accessed April 28, 2020 .
- ↑ Iranian math genius battles cancer recurrence at US hospital. In: PressTV.ir. July 13, 2017, accessed April 28, 2020 .
-
↑ Secrets of the Surface website . On: zalafilms.com , last viewed on June 10, 2010.
Stirring biopic of the first woman to win top maths prize. On: nature.com from June 8, 2020. - ↑ Maryam Mirzakhani recieves 2009 Blumenthal Award. Eulogy. In: AMS.org. January 6, 2009, accessed April 28, 2020 .
- ↑ Roya Beheshti Zavareh. (PDF; 89 kB) CV. In: math.wustl.edu. Accessed April 28, 2020 (English).
- ↑ Fatemi Publishers, Tehran 1999 (in Farsi ).
- ^ Clay Research Awards 2014. In: claymath.org. July 14, 2014, accessed April 28, 2020 .
- ↑ Fields Medallists 2014 awardees with brief citations. Maryam Mirzakhani. In: mathunion.org. Accessed April 28, 2020 (English).
- ↑ Fields Medal - Highest mathematics prize for the first time for a woman. In: Deutschlandfunk.de. August 13, 2014, accessed April 28, 2020 .
personal data | |
---|---|
SURNAME | Mirzakhani, Maryam |
ALTERNATIVE NAMES | مریم میرزاخانی (Persian) |
BRIEF DESCRIPTION | Iranian mathematician |
DATE OF BIRTH | May 12, 1977 |
PLACE OF BIRTH | Tehran |
DATE OF DEATH | July 14, 2017 |
Place of death | Stanford , California |