Maryam Mirzakhani

Maryam Mirzakhani
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Name	Maryam Mirzakhani
Birth date	12 May 1977
Birth place	Tehran, Iran
Death date	14 July 2017
Death place	Stanford, California, U.S.
Alma mater	Sharif University of Technology; Harvard University
Occupation	Mathematician; Professor
Known for	Work on Teichmüller theory; dynamics of moduli spaces; geometry of Riemann surfaces
Awards	Fields Medal; Clay Research Award; Blumenthal Award

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Maryam Mirzakhani Maryam Mirzakhani was an Iranian-born mathematician noted for deep results connecting Teichmüller space, Riemann surface geometry, and dynamical systems, and for becoming the first woman and first Iranian to receive the Fields Medal. Trained at Sharif University of Technology and Harvard University, she held faculty positions at Princeton University and Stanford University. Her work influenced research across complex analysis, hyperbolic geometry, symplectic geometry, and ergodic theory.

Early life and education

Born in Tehran, Mirzakhani attended Alzahra University-affiliated schools and competed in the International Mathematical Olympiad where she earned gold medals, joining fellow contestants from China, United States, Russia, South Korea, and Iran who distinguished themselves at the IMO program. She studied at Sharif University of Technology in Tehran under professors involved with Iranian Mathematical Society activities before earning a Ph.D. at Harvard University under Curtis McMullen, connecting her to a lineage including William Thurston, Benoit Mandelbrot, André Weil, and others in the history of Harvard mathematics. During graduate study she worked on problems related to moduli space, drawing upon techniques from complex dynamics, ergodic theory, and influences traced to seminars at Institute for Advanced Study, Mathematical Sciences Research Institute, and workshops organized by International Mathematical Union members.

Mirzakhani's research forged links between Teichmüller dynamics, moduli space of Riemann surfaces, and counting problems in hyperbolic geometry. She proved new identities for volumes of moduli spaces inspired by work of Maryam Mirzakhani collaborators and predecessors such as Maxim Kontsevich, Edward Witten, Scott Wolpert, and Shigeru Mukai, while employing techniques related to Weil–Petersson form, Mirzakhani's recursion (named after her), and the Selberg trace formula. Her breakthrough on the asymptotic growth of simple closed geodesics on hyperbolic surfaces built on foundations from William Thurston, Jennifer Schultens, Howard Masur, and Yair Minsky. She established measure-classification results for the SL(2,R) action on moduli space, connecting to work by Curtis McMullen, Alex Eskin, Maryam Mirzakhani coauthors, and Carlos Matheus, and influenced ongoing collaborations among researchers at University of Chicago, University of Cambridge, École Normale Supérieure, University of Bonn, and University of California, Berkeley. Her papers invoked tools from ergodic theory, symplectic geometry, algebraic geometry, and geometric topology, engaging with problems addressed in conferences at International Congress of Mathematicians, European Congress of Mathematics, and meetings of the American Mathematical Society.

Mirzakhani received numerous accolades including the Fields Medal from the International Mathematical Union for her contributions to geometry and dynamics, the Clay Research Award from the Clay Mathematics Institute, and recognition by bodies such as the National Academy of Sciences and the American Academy of Arts and Sciences. She was awarded prizes including the Blumenthal Award, and invited to present at major venues including the International Congress of Mathematicians and colloquia at Princeton University, Harvard University, Stanford University, Institute for Advanced Study, and Mathematical Sciences Research Institute. Her Fields Medal citation referenced breakthroughs that connected classical results of Gauss, Riemann, and Teichmüller to modern questions posed by researchers from Max Planck Institute for Mathematics and other centers.

As a professor at Princeton University and later Stanford University, Mirzakhani taught courses related to Riemann surfaces, hyperbolic geometry, and dynamical systems, supervising doctoral students who later joined faculties at institutions such as Massachusetts Institute of Technology, University of Chicago, Columbia University, University of California, Berkeley, Yale University, and University of Toronto. She participated in mentorship programs organized by the American Mathematical Society, Association for Women in Mathematics, and outreach initiatives in Iran and the United States, inspiring participants from programs like Math Olympiad training camps and summer schools at Park City Mathematics Institute and Mathematical Sciences Research Institute. Colleagues remember collaborative problem sessions held with visitors from Institut des Hautes Études Scientifiques, CNRS, Max Planck Institute for Mathematics, and Clay Mathematics Institute programs.

Mirzakhani was married to fellow mathematician Jan Vondrák and balanced family life with research and teaching at Stanford University, where she continued collaborations with mathematicians from institutions such as Princeton University, University of Chicago, Harvard University, ETH Zurich, University of Cambridge, and University of Oxford. After her death from cancer, memorials and lectures were organized by Stanford University, Institute for Advanced Study, International Mathematical Union, and the American Mathematical Society; institutions including Sharif University of Technology and Alzahra University recognized her influence on Iranian science. Her legacy endures through continuing research by scholars in Teichmüller theory, hyperbolic geometry, moduli spaces, and dynamical systems, and through prizes, lecture series, and fellowships established in her name by organizations like the International Mathematical Union and academic departments worldwide.

Category:Mathematicians Category:Fields Medal winners Category:Iranian mathematicians