WorldCat Identities

Mirzakhani, Maryam

Works: 4 works in 6 publications in 1 language and 7 library holdings
Roles: Author, Thesis advisor
Publication Timeline
Most widely held works by Maryam Mirzakhani
Simple geodesics on hyperbolic surfaces and the volume of the moduli space of curves by Maryam Mirzakhani( )

3 editions published in 2004 in English and held by 4 WorldCat member libraries worldwide

Geometric transitions : from hyperbolic to Ads geometry by Jeffrey Edward Danciger( )

1 edition published in 2011 in English and held by 1 WorldCat member library worldwide

We introduce a geometric transition between two homogeneous three-dimensional geometries: hyperbolic geometry and anti de Sitter (AdS) geometry. Given a path of three-dimensional hyperbolic structures that collapse down onto a hyperbolic plane, we describe a method for constructing a natural continuation of this path into AdS structures. In particular, when hyperbolic cone manifolds collapse, the AdS manifolds generated on the "other side" of the transition have tachyon singularities. The method involves the study of a new transitional geometry called half-pipe geometry. We also discuss combinatorial/algebraic tools for constructing transitions using ideal tetrahedra. Using these tools we prove that transitions can always be constructed when the underlying manifold is a punctured torus bundle
Non-simple geodesics on surfaces by Jenya Sapir( )

1 edition published in 2014 in English and held by 1 WorldCat member library worldwide

In this thesis, we study geodesics on pairs of pants, and then generalize our results to all surfaces. We get bounds on the number of closed geodesics in a hyperbolic surface given certain upper bounds on both length and self-intersection number. Then, we study the image on a pair of pants of certain sets of complete geodesics, which have restrictions for how the self-intersection number of their subarcs grows with subarc length. We show that such sets have low Hausdorff dimension, and in some cases are nowhere dense
Stable moduli of flat manifold bundles by Sam Nariman( )

1 edition published in 2015 in English and held by 1 WorldCat member library worldwide

Flat manifold bundles (i.e. manifold bundles with foliations transverse to the fibers) are classified by homotopy classes of maps to the classifying space of diffeomorphisms made discrete. In my thesis, I studied the homology of the classifying spaces of discrete diffeomorphisms for certain type of manifolds including surfaces, higher dimensional analogue of surfaces and disks with punctures. I established homological stability of discrete surface diffeomorphisms and discrete symplectic diffeomorphisms which was conjectured by Morita. To study the stable homology of these family of groups, I described an infinite loop space related to the Haefliger space whose homology is the same as group homology of discrete surface diffeomorphisms in the stable range which is the analogous of the Madsen-Weiss theorem for discrete surface diffeomorphisms. Similar theorems were proved for punctured 2-dimensional disk and higher dimensional analogue of surfaces. I utilized these new techniques of studying discrete diffeomorphism groups to obtain interesting applications to the characteristic classes of flat surface bundles and foliated bordism groups of codimension 2 foliations
Audience Level
Audience Level
  Kids General Special  
Audience level: 0.87 (from 0.81 for Non-simple ... to 0.92 for Simple geo ...)

Alternative Names
Maria Mirzakhani

Marjam Mirzachani

Marjam Mirzaĥani

Marjama Mīrzāhāni

Maryam Mirzachaniová

Maryam Mirzajani matemática iraní

Maryam Mirzakhani iráni matematikus

Maryam Mirzakhani Iranian mathematician

Maryam Mirzakhani iranisch-US-amerikanische Mathematikerin

Maryam Mirzakhani iransk matematiker

Maryam Mirzakhani matemàtica iraniana

Maryam Mirzakhani matematiciană iraniană

Maryam Mirzakhani mathématicienne iranienne

Maryam Mirzakhani wiskundige uit Iran

Meryem Mirzahani

Məryəm Mirzəxani

Мариам Мирзахани

Мариам Мирзахани иранска математичка

Мариам Мирзахани иранский и американский математик, специализирующаяся на геометрии Лобачевского, теории Тейхмюллера, эргодической теории, симплектической геометрии

Марям Мирзохонӣ

Мар'ям Мірзахані

Марјам Мирзахани

Мәриәм Мирзәхәни

Մարիամ Միրզախանի

מרים מירזחאני מתמטיקאית איראנית

مريم ميرزاخاني

مریم مرزاخانی

مریەم میرزاخانی

मरियम मिर्ज़ाख़ानी

মরিয়ম মির্জাখানি Mathematician

ਮਰਿਯਮ ਮਿਰਜ਼ਾਖਾਨੀ

மரியாம் மீர்சாக்கானி

మరియం మిర్జాఖనీ

മറിയം മിർസാഖാനി

მარიამ მირზახანი

마리암 미르자카니

マリアム・ミルザハニ Mathematician

瑪麗安·米爾札哈尼 Mathematician

玛丽安·米尔札哈尼 伊朗数学家,首位女性费尔兹奖得主