Mirzakhani Research Articles

Recollection of Maryam Mirzakhani's Love for Mathematics: Igniting Female Students' Passion in Mathematics

Many of the famous women mathematicians experienced a spark. Something happened, and a love of mathematics began. This paper is on Maryam Mirzakhani who was the only woman and Iranian to be awarded with the Fields Medal, the most prestigious award in mathematics. Recollecting her love for mathematics may ignite female students' passion in mathematics. Perhaps, through her story, teachers can provide that inspiration. Mathematics teachers can present the beauty of mathematics to the students, helping engage them in a lifelong passion.

Experimental Statistics for Mirzakhani’s Theorem

In her seminal 2008 article, Maryam Mirzakhani showed that the ratio that two topological types of curves occur in is a rational number. In this article, we describe the process by which we obtained experimental evidence that separating and non-separating curves on the surface of genus two occur in the ratio . 1

Stirring biopic of the first woman to win top maths prize

Maryam Mirzakhani, Fields medallist and Iranian national hero, is celebrated in an elegant documentary. Maryam Mirzakhani, Fields medallist and Iranian national hero, is celebrated in an elegant documentary.

The Life of Maryam Mirzakhani

Maryam Mirzakhani is the first and the only female winner of the Fields Medal since its establishment in 1936. She is arguably one of the greatest mathematicians of our generation. This biographical paper outlines her life and work. Her mathematical theorems and noteworthy accomplishments are just as impressive as her determination, imagination, and optimistic outlook on life. Mirzakhani’s success came from her passion, creativity, and playful approach to mathematics. She felt the most rewarding part of mathematics was the enjoyment of understanding or discovering something. Mirzakhani’s work was visual and focused on patterns and ideas rather than on numbers and algorithms. She constructed mathematics in an artistic way, and her goal was to always find truth and beauty in the world. Mirzakhani will forever be an inspiration to anyone who has studied her work and read her story.

Maryam Mirzakhani (1977–2017)

Maryam Mirzakhani (1977–2017)

Maryam Mirzakhani

Maryam Mirzakhani

Maryam Mirzakhani (1977-2017).

Maryam Mirzakhani (1977-2017).

Maryam Mirzakhani (1977-2017).

A profound thinker on the mathematics of abstract surfaces

Maryam Mirzakhani, quantum teleportation and the Great Red Spot.

Maryam Mirzakhani, quantum teleportation and the Great Red Spot.

Maryam Mirzakhani

Maryam Mirzakhani

Maryam Mirzakhani

Maryam Mirzakhani

Maryam Mirzakhani (1977–2017): Her Work and Legacy

Maryam Mirzakhani (1977–2017): Her Work and Legacy

Rank two affine submanifolds in ℋ(2,2) and ℋ(3,1)

We classify all rank two affine manifolds in strata in genus three with two zeros. This confirms a conjecture of Maryam Mirzakhani in these cases. Several technical results are proven for all strata in genus three, with the hope that they may shed light on a complete classification of rank two manifolds in genus three.

The work of Maryam Mirzakhani

The work of Maryam Mirzakhani

Iranian is first woman to nab highest prize in maths

Maryam Mirzakhani is among four young researchers to win Fields Medals, awarded every four years.

The field of definition of affine invariant submanifolds of the moduli space of abelian differentials

The field of definition of an affine invariant submanifold M is the smallest subfield of the reals such that M can be defined in local period coordinates by linear equations with coefficients in this field. We show that the field of definition is equal to the intersection of the holonomy fields of translation surfaces in M, and is a real number field of degree at most the genus. We show that the projection of the tangent bundle of M to absolute cohomology H^1 is simple, and give a direct sum decomposition of H^1. Applications include explicit full measure sets of translation surfaces whose orbit closures are as large as possible, and evidence for finiteness of algebraically primitive Teichm\"uller curves. The proofs use recent results of Artur Avila, Alex Eskin, Maryam Mirzakhani, Amir Mohammadi, and Martin M\"oller.

A Simpler Proof of Mirzakhani’s Simple Curve Asymptotics

Maryam Mirzakhani (in her doctoral dissertation) has proved the author’s conjecture that the number of simple closed curves of length bounded by L on a hyperbolic surface S is asymptotic to a constant times L d , where d is the dimension of the Teichmuller space of S. In this note we clarify and simplify Mirzakhani’s argument.