Mirzakhani, Maryam
Overview
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
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 threedimensional geometries: hyperbolic geometry and anti de Sitter (AdS) geometry. Given a path of threedimensional 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 halfpipe 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
1 edition published in 2011 in English and held by 1 WorldCat member library worldwide
We introduce a geometric transition between two homogeneous threedimensional geometries: hyperbolic geometry and anti de Sitter (AdS) geometry. Given a path of threedimensional 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 halfpipe 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
Nonsimple 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 selfintersection number. Then, we study the image on a pair of pants of certain sets of complete geodesics, which have restrictions for how the selfintersection number of their subarcs grows with subarc length. We show that such sets have low Hausdorff dimension, and in some cases are nowhere dense
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 selfintersection number. Then, we study the image on a pair of pants of certain sets of complete geodesics, which have restrictions for how the selfintersection 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 MadsenWeiss theorem for discrete surface diffeomorphisms. Similar theorems were proved for punctured 2dimensional 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
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 MadsenWeiss theorem for discrete surface diffeomorphisms. Similar theorems were proved for punctured 2dimensional 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
0 

1  
Kids  General  Special 
Related Identities
 Stanford University Department of Mathematics
 Kerckhoff, Steve Thesis advisor
 Eliashberg, Y. 1946 Thesis advisor
 Church, Thomas (Thomas Franklin) Thesis advisor
 Yang, Tian 1982 Thesis advisor
 Galatius, Søren 1976 Thesis advisor
 Carlsson, G. (Gunnar) 1952 Thesis advisor
 Cohen, Ralph L. 1952 Thesis advisor
 Sapir, Jenya Author
 Danciger, Jeffrey Edward Author
Useful Links
Associated Subjects
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 iranischUSamerikanische 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
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