Ser Peow Tan

Complex Fenchel-Nielsen Coordinates for Quasi-Fuchsian Structures

Louis Hsiao Yun Chen

10, Celebrating 10 Years of Mathematical Synergy

William Goldman

Greg McShane

George Stantchev

The automorphisms of a two-generator free group F acting on the space of orientation-preserving isometric actions of F on hyperbolic 3-space defines a dynamical system. Those actions which preserve a hyperbolic plane but not an orientation on that plane is an invariant subsystem, which reduces to an action of a group on by polynomial automorphisms preserving the cubic polynomial and an area form on the level surfaces .

Automorphisms ofTwo-Generator Free Groups and Spaces of Isometric Actions on the Hyperbolic Plane

Caroline Series

William Mark Goldman

This book aims to describe, for readers uneducated in science, the development of humanity's desire to know and understand the world around us through the various stages of its development to the present, when science is almost universally recognized - at least in the Western world - as the most reliable way of knowing. The book describes the history of the large-scale exploration of the surface of the earth by sea, beginning with the Vikings and the Chinese, and of the unknown interiors of the American and African continents by foot and horseback. After the invention of the telescope, visual exploration of the surfaces of the Moon and Mars were made possible, and finally a visit to the Moon. The book then turns to our legacy from the ancient Greeks of wanting to understand rather than just know, and why the scientific way of understanding is valued. For concreteness, it relates the lives and accomplishments of six great scientists, four from the nineteenth century and two from the twentieth. Finally, the book explains how chemistry came to be seen as the most basic of the sciences, and then how physics became the most fundamental.

Geometry, Topology and Dynamics of Character Varieties

This volume is based on lectures given at the highly successful three-week 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 ping-pong lemmas in various contexts, introductions to Lorenzian and complex hyperbolic geometry, and representation varieties of surface groups into PSL(2, ℝ) and other semi-simple Lie groups. This volume will serve as a useful portal to students and researchers in a vibrant and multi-faceted area of mathematics. Sample Chapter(s) Foreword (72 KB) Chapter 1: An Invitation to Elementary Hyperbolic Geometry (708 KB) Contents:An Invitation to Elementary Hyperbolic Geometry (Ying Zhang)Hyperbolic Structures on Surfaces (Javier Aramayona)Degenerations of Hyperbolic Structures on Surfaces (Christopher J Leininger)Ping-Pong Lemmas with Applications to Geometry and Topology (Thomas Koberda)Creating Software for Visualizing Kleinian Groups (Yasushi Yamashita)Traces in Complex Hyperbolic Geometry (John R Parker)Lorentzian Geometry (Todd A Drumm)Connected Components of PGL(2,R)-Representation Spaces of Non-Orientable Surfaces (Frédéric Palesi)Rigidity and Flexibility of Surface Groups in Semisimple Lie Groups (Inkang Kim)Abelian and Non-Abelian Cohomology (Eugene Z Xia) Readership: Graduate students, researchers and professors in mathematical areas such as low-dimensional topology, dynamical systems and hyperbolic geometry. Keywords:Character Varieties;Representation Spaces;Mapping Class Groups;Hyperbolic Geometry;Kleinian GroupsKey Features:Accessible introduction to structures on surfaces, measured foliations and the Thurston compactification of Teichmüller spaceHow to write a python program to draw limit sets and other geometric objects associated with simple Kleinian groupsTwo excellent expository articles by students who attended the program

Ser Peow Tan

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