Series, Caroline
Overview
Works:  38 works in 115 publications in 3 languages and 5,138 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Editor, Author, Other 
Classifications:  QA614.86, 514.742 
Publication Timeline
.
Most widely held works by
Caroline Series
Indra's pearls : the vision of Felix Klein by
David Mumford(
Book
)
25 editions published between 2000 and 2015 in English and held by 527 WorldCat member libraries worldwide
"Felix Klein, one of the great nineteenthcentury geometers, discovered in mathematics an idea prefigured in Buddhist mythology: the heaven of Indra contained a net of pearls, each of which was reflected in its neighbour, so that the whole Universe was mirrored in each pearl. Klein studied infinitely repeated reflections and was led to forms with multiple coexisting symmetries, each simple in itself, but whose interactions produce fractals on the edge of chaos. For a century these images, which were practically impossible to draw by hand, barely existed outside the imagination of mathematicians. However in the 1980s the authors embarked on the first computer exploration of Klein's vision, and in so doing found further extraordinary images of their own. Join the authors on the path from some basic mathemathical ideas to the simple algorithms that create the delicate fractal filigrees, most of which have never appeared in print before. Beginners can learn to understand what the images mean and follow the stepbystep instructions for writing computer programs that generate them. More advanced readers can see how the images relate to ideas that take them to the forefront of research."Jacket
25 editions published between 2000 and 2015 in English and held by 527 WorldCat member libraries worldwide
"Felix Klein, one of the great nineteenthcentury geometers, discovered in mathematics an idea prefigured in Buddhist mythology: the heaven of Indra contained a net of pearls, each of which was reflected in its neighbour, so that the whole Universe was mirrored in each pearl. Klein studied infinitely repeated reflections and was led to forms with multiple coexisting symmetries, each simple in itself, but whose interactions produce fractals on the edge of chaos. For a century these images, which were practically impossible to draw by hand, barely existed outside the imagination of mathematicians. However in the 1980s the authors embarked on the first computer exploration of Klein's vision, and in so doing found further extraordinary images of their own. Join the authors on the path from some basic mathemathical ideas to the simple algorithms that create the delicate fractal filigrees, most of which have never appeared in print before. Beginners can learn to understand what the images mean and follow the stepbystep instructions for writing computer programs that generate them. More advanced readers can see how the images relate to ideas that take them to the forefront of research."Jacket
Ergodic theory, symbolic dynamics, and hyperbolic spaces(
Book
)
11 editions published between 1991 and 1992 in English and Undetermined and held by 315 WorldCat member libraries worldwide
11 editions published between 1991 and 1992 in English and Undetermined and held by 315 WorldCat member libraries worldwide
Kleinian groups and hyperbolic 3manifolds : proceedings of the Warwick Workshop, September 1114, 2001 by Kleinian Groups and Hyperbolic 3Manifolds(
Book
)
11 editions published in 2003 in English and held by 231 WorldCat member libraries worldwide
The subject of Kleinian groups and hyperbolic 3manifolds is currently undergoing explosively fast development, with many old problems and conjectures close to resolution. This volume, proceedings of the Warwick workshop in September 2001, contains expositions of many of these breakthroughs including Minsky's lectures on the first half of the proof of the Ending Lamination Conjecture, the Bers Density Conjecture by Brock and Bromberg, the Tameness Conjecture by Kleineidam and Souto, the state of the art in cone manifolds by Hodgson and Kerckhoff, and the counter example to Thurston's K=2 conjecture by Epstein, Marden and Markovic. It also contains Jorgensen's famous paper 'On pairs of once punctured tori' in print for the first time. The excellent collection of papers here will appeal to graduate students, who will find much here to inspire them, and established researchers who will find this valuable as a snapshot of current research
11 editions published in 2003 in English and held by 231 WorldCat member libraries worldwide
The subject of Kleinian groups and hyperbolic 3manifolds is currently undergoing explosively fast development, with many old problems and conjectures close to resolution. This volume, proceedings of the Warwick workshop in September 2001, contains expositions of many of these breakthroughs including Minsky's lectures on the first half of the proof of the Ending Lamination Conjecture, the Bers Density Conjecture by Brock and Bromberg, the Tameness Conjecture by Kleineidam and Souto, the state of the art in cone manifolds by Hodgson and Kerckhoff, and the counter example to Thurston's K=2 conjecture by Epstein, Marden and Markovic. It also contains Jorgensen's famous paper 'On pairs of once punctured tori' in print for the first time. The excellent collection of papers here will appeal to graduate students, who will find much here to inspire them, and established researchers who will find this valuable as a snapshot of current research
Spaces of Kleinian groups(
Book
)
11 editions published in 2006 in English and held by 225 WorldCat member libraries worldwide
The subject of Kleinian groups and hyperbolic 3manifolds is currently undergoing explosively fast development, the last few years having seen the resolution of many longstanding conjectures. This volume contains important expositions and original work by some of the main contributors on topics such as topology and geometry of 3manifolds, curve complexes, classical AhlforsBers theory, computer explorations and projective structures. Researchers in these and related areas will find much of interest here from the explosion in the area over recent years, including important and original research from leading names in the field
11 editions published in 2006 in English and held by 225 WorldCat member libraries worldwide
The subject of Kleinian groups and hyperbolic 3manifolds is currently undergoing explosively fast development, the last few years having seen the resolution of many longstanding conjectures. This volume contains important expositions and original work by some of the main contributors on topics such as topology and geometry of 3manifolds, curve complexes, classical AhlforsBers theory, computer explorations and projective structures. Researchers in these and related areas will find much of interest here from the explosion in the area over recent years, including important and original research from leading names in the field
Geometry, topology and dynamics of character varieties by William M Goldman(
Book
)
13 editions published between 2011 and 2012 in English and held by 64 WorldCat member libraries worldwide
This volume is based on lectures given at the highly successful threeweek Summer School on Geometry, Topology and Dynamics of Character Varieties held at the National University of Singapore's Institute for Mathematical Sciences in July 2010. Aimed at graduate students in the early stages of research, the edited and refereed articles comprise an excellent introduction to the subject of the program, much of which is otherwise available only in specialized texts. Topics include hyperbolic structures on surfaces and their degenerations, applications of pingpong lemmas in various contexts, intro
13 editions published between 2011 and 2012 in English and held by 64 WorldCat member libraries worldwide
This volume is based on lectures given at the highly successful threeweek Summer School on Geometry, Topology and Dynamics of Character Varieties held at the National University of Singapore's Institute for Mathematical Sciences in July 2010. Aimed at graduate students in the early stages of research, the edited and refereed articles comprise an excellent introduction to the subject of the program, much of which is otherwise available only in specialized texts. Topics include hyperbolic structures on surfaces and their degenerations, applications of pingpong lemmas in various contexts, intro
The Epstein birthday schrift : papers delivered to David Epstein on the occasion of his 60th birthday, 16 May 1997(
Book
)
9 editions published in 1998 in English and Undetermined and held by 35 WorldCat member libraries worldwide
9 editions published in 1998 in English and Undetermined and held by 35 WorldCat member libraries worldwide
Geometry, Topology and Dynamics of Character Varieties by William Goldman(
Book
)
2 editions published in 2012 in English and held by 7 WorldCat member libraries worldwide
2.12. The projective plane associated to a hyperbolic plane2.13. Centerpencils of a hyperbolic triangle; 2.14. Equidistant curves; 2.15. Positions of proper points relative to an ideal point; 2.16. Hyperbolic areas via equivalence of triangles; 2.17. Metric relations of corresponding arcs in concentric horocycles; 3. Isometries of the Hyperbolic Plane; 3.1. Isometries and reections in straight lines; 3.2. Orientation preserving/reversing isometries; 3.3. Rotations; 3.4. Translations; 3.5. Isometries of parabolic type; 3.6. Redundancy of two reflections
2 editions published in 2012 in English and held by 7 WorldCat member libraries worldwide
2.12. The projective plane associated to a hyperbolic plane2.13. Centerpencils of a hyperbolic triangle; 2.14. Equidistant curves; 2.15. Positions of proper points relative to an ideal point; 2.16. Hyperbolic areas via equivalence of triangles; 2.17. Metric relations of corresponding arcs in concentric horocycles; 3. Isometries of the Hyperbolic Plane; 3.1. Isometries and reections in straight lines; 3.2. Orientation preserving/reversing isometries; 3.3. Rotations; 3.4. Translations; 3.5. Isometries of parabolic type; 3.6. Redundancy of two reflections
Indra's pearls the vision of Felix Klein(
)
1 edition published in 2002 in English and held by 5 WorldCat member libraries worldwide
1 edition published in 2002 in English and held by 5 WorldCat member libraries worldwide
Indora no shinju : kurain no yumemita sekai(
Book
)
2 editions published in 2013 in Japanese and held by 3 WorldCat member libraries worldwide
2 editions published in 2013 in Japanese and held by 3 WorldCat member libraries worldwide
Frattali, riflessioni e distorsioni by
Caroline Series(
)
1 edition published in 1992 in Italian and held by 2 WorldCat member libraries worldwide
1 edition published in 1992 in Italian and held by 2 WorldCat member libraries worldwide
Kleinian groups and hyperbolic 3manifolds proceedings of the Warwick Workshop, September 1115, 2001 by Kleinian Groups and Hyperbolic 3Manifolds(
)
2 editions published between 2003 and 2007 in English and held by 2 WorldCat member libraries worldwide
The subject of Kleinian groups and hyperbolic 3manifolds is currently undergoing explosively fast development, with many old problems and conjectures close to resolution. This volume, proceedings of the Warwick workshop in September 2001, contains expositions of many of these breakthroughs including Minsky's lectures on the first half of the proof of the Ending Lamination Conjecture, the Bers Density Conjecture by Brock and Bromberg, the Tameness Conjecture by Kleineidam and Souto, the state of the art in cone manifolds by Hodgson and Kerckhoff, and the counter example to Thurston's K=2 conjecture by Epstein, Marden and Markovic. It also contains Jørgensen's famous paper 'On pairs of once punctured tori' in print for the first time. The excellent collection of papers here will appeal to graduate students, who will find much here to inspire them, and established researchers who will find this valuable as a snapshot of current research
2 editions published between 2003 and 2007 in English and held by 2 WorldCat member libraries worldwide
The subject of Kleinian groups and hyperbolic 3manifolds is currently undergoing explosively fast development, with many old problems and conjectures close to resolution. This volume, proceedings of the Warwick workshop in September 2001, contains expositions of many of these breakthroughs including Minsky's lectures on the first half of the proof of the Ending Lamination Conjecture, the Bers Density Conjecture by Brock and Bromberg, the Tameness Conjecture by Kleineidam and Souto, the state of the art in cone manifolds by Hodgson and Kerckhoff, and the counter example to Thurston's K=2 conjecture by Epstein, Marden and Markovic. It also contains Jørgensen's famous paper 'On pairs of once punctured tori' in print for the first time. The excellent collection of papers here will appeal to graduate students, who will find much here to inspire them, and established researchers who will find this valuable as a snapshot of current research
Simple curves have Hausdorff dimension one by
Joan S Birman(
)
1 edition published in 1983 in English and held by 1 WorldCat member library worldwide
1 edition published in 1983 in English and held by 1 WorldCat member library worldwide
The infinite word problem and limit sets in Fuchsian groups by
Caroline Series(
)
1 edition published in 1980 in English and held by 1 WorldCat member library worldwide
1 edition published in 1980 in English and held by 1 WorldCat member library worldwide
On coding geodesics with continued fractions by
Caroline Series(
)
1 edition published in 1980 in English and held by 1 WorldCat member library worldwide
1 edition published in 1980 in English and held by 1 WorldCat member library worldwide
Geometrical Markov coding of geodisics on surfaces of constant negative curvature by
Caroline Series(
)
1 edition published in 1985 in English and held by 1 WorldCat member library worldwide
1 edition published in 1985 in English and held by 1 WorldCat member library worldwide
Symbolic dynamics for geodesic flows by
Caroline Series(
)
1 edition published in 1979 in English and held by 1 WorldCat member library worldwide
1 edition published in 1979 in English and held by 1 WorldCat member library worldwide
Algebraic linearity for an automorphism of a surface group by Joan S Briman(
)
1 edition published in 1985 in English and held by 1 WorldCat member library worldwide
1 edition published in 1985 in English and held by 1 WorldCat member library worldwide
Women and mathematics across cultures(
Visual
)
1 edition published in 1996 in English and held by 1 WorldCat member library worldwide
1 edition published in 1996 in English and held by 1 WorldCat member library worldwide
Limits of limit sets II : geometrically infinite groups by
Mahan Mj(
Book
)
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
On Kerckhoff minima and pleating loci for quasifuchsian groups by
Caroline Series(
Book
)
1 edition published in 2000 in English and held by 1 WorldCat member library worldwide
1 edition published in 2000 in English and held by 1 WorldCat member library worldwide
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Audience Level
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Kids  General  Special 
Related Identities
 Mumford, David 1937 Other Author
 Wright, David James
 Klein, Felix 18491925
 Indra (Hindu deity)
 Gonick, Larry Illustrator
 Komori, Y. (Yohei) Author Editor
 Markovic, V. (Vladimir) Editor
 Tan, Ser Peow Editor
 Goldman, William Editor
 Bedford, T. Editor
Useful Links
Associated Subjects
Differentiable dynamical systems Differential topology Direct marketing Epstein, D. B. A Ergodic theory Fractals Geometric quantization Geometry Geometry, Differential Geometry, Hyperbolic Group theory Indra (Hindu deity) Klein, Felix, Kleinian groups Lowdimensional topology Mathematical physics Quantum field theory Symbolic dynamics Symmetry Threemanifolds (Topology) Topology Women mathematicians