Thanks to Colleagues: Acknowledgment to mathematical colleagues and PhD advisors Rami Takloo-Bighash and Laura DeMarco, along with others like Anton Zorich, Kurt McMullen, and Alex Wright, for inspiration and insights on Maryam's work.
Lecture Hosts: Gratitude to Gresham College and the London Mathematical Society for hosting the talk.
Focus: Discussion on Maryam Mirzakhani's contributions, her mathematical legacy, and why her work is both impressive and compelling.
Background on Maryam Mirzakhani
Early Life: Born in Tehran in 1977, educated in a prestigious school in Tehran.
Mathematical Talent: Recognized early for talent, participated in the International Mathematical Olympiad, earning two gold medals.
Cultural Context: Despite Iran's gender-segregated education, opportunities for women in science existed and were utilized by Maryam.
Maryam's Mathematical Work
Geometry and Dynamics
Riemann Surfaces: Focus on the intersection of geometry and dynamics; Riemann surfaces have geometrical and dynamical properties.
Geodesics: The study of closed geodesics on surfaces and their significance in understanding surface geometry.
PhD Work and Contributions
Counting Geodesics: Pioneering work in counting simple closed geodesics on hyperbolic surfaces.
Methodology and Results: Used grouping techniques to understand the density and distribution of geodesics, leading to significant theorems about their growth.
Moduli Spaces
Definition: Moduli space as a map correlating points to mathematical objects; importance in understanding deformation and classification of geometries.
Translation Surfaces: Explored translation surfaces which arise from billiard table dynamics and have applications in geometry and number theory.
Major Results
Eskin-Mirzakhani-Mohammadi: Collaboration leading to a comprehensive understanding of orbits in moduli spaces, proving they are defined by simple polynomial equations.
Applications and Analogies
Illumination Problem
Concept: Whether a light source can illuminate all parts of a room covered in mirrors.
Rational Polygons: Work shows only finitely many inaccessible points in rational polygonal billiard tables.
Blocking Problem
Description: Can one block paths from point A to B using finitely many obstacles?
Personal Life and Legacy
Personal Challenges: Diagnosed with breast cancer; despite treatment, succumbed at age 40.
Awards and Recognition: First woman to win the Fields Medal, recognized for her groundbreaking contributions.
Influence and Tributes: Inspired initiatives like the International Women in Maths Day and scholarships to promote women in mathematics.
Conclusion
Documentary Recommendation: A documentary capturing her life and legacy, providing another perspective on her impact.
Speaker's Work: Brief insight into the talk's speaker's own work in complex dynamics and its relation to Maryam's field.
Acknowledgments: Thanks to participants and organizers for the event.