WorldCat Identities

Mirzakhani, Maryam

Works: 3 works in 4 publications in 1 language and 5 library holdings
Roles: Author, Thesis advisor
Publication Timeline
Publications about  Maryam Mirzakhani Publications about Maryam Mirzakhani
Publications by  Maryam Mirzakhani Publications by Maryam Mirzakhani
Most widely held works by Maryam Mirzakhani
Simple geodesics on hyperbolic surfaces and the volume of the moduli space of curves by Maryam Mirzakhani ( Book )
2 editions published in 2004 in English and held by 3 WorldCat member libraries worldwide
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
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
Audience Level
Audience Level
  Kids General Special  
Audience level: 0.79 (from 0.47 for Geometric ... to 1.00 for Simple geo ...)
English (4)