Maryam Mirzakhani
Early Life and Education
Maryam Mirzakhani was born on May 12, 1977, in Tehran, Iran. She displayed an early aptitude for mathematics and science, excelling in her studies from a young age. Mirzakhani attended the Farzanegan School, part of the National Organization for Development of Exceptional Talents (NODET), which catered to gifted students. Her talent was further recognized when she won gold medals at the International Mathematical Olympiad in 1994 and 1995, achieving a perfect score in the latter year.
Mirzakhani pursued her undergraduate studies at the Sharif University of Technology in Tehran, where she continued to demonstrate her mathematical prowess. She graduated with a Bachelor of Science in Mathematics in 1999. Following her undergraduate education, she moved to the United States to attend Harvard University for her graduate studies. Under the supervision of Curtis T. McMullen, a Fields Medalist himself, she completed her Ph.D. in 2004 with a dissertation on "Simple Geodesics on Hyperbolic Surfaces and the Volume of the Moduli Space of Curves."
Academic Career
After earning her Ph.D., Mirzakhani held a position as a Clay Mathematics Institute Research Fellow and an assistant professor at Princeton University. In 2008, she joined the faculty at Stanford University as a professor of mathematics, where she remained until her untimely death in 2017.
Mirzakhani's research interests were primarily in the fields of hyperbolic geometry, Teichmüller theory, ergodic theory, and symplectic geometry. Her work often involved the study of moduli spaces of Riemann surfaces, which are complex structures that describe all possible shapes of a given surface. This area of mathematics has deep connections to string theory, quantum field theory, and complex dynamics.
Major Contributions
Simple Closed Geodesics
One of Mirzakhani's significant contributions was her work on the asymptotic behavior of the number of simple closed geodesics on hyperbolic surfaces. A geodesic is the shortest path between two points on a surface, and a simple closed geodesic is one that does not intersect itself. Mirzakhani developed a formula to count the number of such geodesics of a given length on a hyperbolic surface, which was a major breakthrough in the field.
Moduli Spaces and Volume Calculations
Mirzakhani's dissertation focused on the volume of moduli spaces of curves. She developed new techniques to calculate these volumes, which have applications in various areas of mathematics and theoretical physics. Her work provided insights into the structure of these spaces and their geometric properties.
Dynamics on Moduli Spaces
In collaboration with Alex Eskin and Amir Mohammadi, Mirzakhani made groundbreaking contributions to the understanding of the dynamics on moduli spaces. Their work on the Eskin-Mirzakhani-Mohammadi theorem provided a comprehensive description of the behavior of SL(2,R) actions on these spaces. This theorem has far-reaching implications in ergodic theory and homogeneous dynamics.
Awards and Honors
Maryam Mirzakhani received numerous awards and honors throughout her career. In 2014, she became the first woman and the first Iranian to be awarded the Fields Medal, often considered the highest honor in mathematics. The Fields Medal recognized her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces.
In addition to the Fields Medal, Mirzakhani received the Blumenthal Award for the Advancement of Research in Pure Mathematics (2009), the Satter Prize from the American Mathematical Society (2013), and was elected to the American Academy of Arts and Sciences (2015) and the National Academy of Sciences (2016).
Personal Life and Legacy
Maryam Mirzakhani was known for her deep curiosity and passion for mathematics. She often described her work as a form of creative art, where she could explore and discover new patterns and structures. Mirzakhani married Jan Vondrák, a Czech theoretical computer scientist, and they had one daughter, Anahita.
Mirzakhani's legacy continues to inspire mathematicians around the world, particularly women and young girls interested in pursuing careers in mathematics and science. Her groundbreaking work and achievements have paved the way for future generations of researchers.