Strasbourg master class on geometry with contributions by N. A'Campo and A. Papadopoulos; F. Dal'Bo; F. Herrlich; Ph. Korablev and S. Matveev; G. Link; J. Marché; C. Petronio; V. Schroeder

This book contains carefully revised and expanded versions of eight courses that were presented at the University of Strasbourg, during two geometry master classes, in 2008 and 2009. The aim of the master classes was to give to fifth-year students and PhD students in mathematics the opportunity to learn new topics that lead directly to the current research in geometry and topology. The courses were held by leading experts. The subjects treated include hyperbolic geometry, three-manifold topology, representation theory of fundamental groups of surfaces and of three-manifolds, dynamics on the hyperbolic plane with applications to number theory, Riemann surfaces, Teichmüller theory, Lie groups and asymptotic geometry. The text is addressed to students and mathematicians who wish to learn the subject. It can also be used as a reference book and as a textbook for short courses on geometry. This book contains carefully revised and expanded versions of eight courses that were presented at the University of Strasbourg during two geometry master classes in 2008 and 2009. The aim of the master classes was to give fifth-year students and Ph.D. students in mathematics the opportunity to learn new topics that lead directly to the current research in geometry and topology. The courses were taught by leading experts. The subjects treated include hyperbolic geometry, three-manifold topology, representation theory of fundamental groups of surfaces and of three-manifolds, dynamics on the hyperbolic plane with applications to number theory, Riemann surfaces, Teichmller theory, Lie groups, and asymptotic geometry. The text is aimed at graduate students and research mathematicians. It can also be used as a reference book and as a textbook for short courses on geometry. A publication of the European Mathematical Society. Distributed within the Americas by the American Mathematical Society. In 2008 and 2009, two weeks of intensive courses were given at the University of Strasbourg to allow graduate and PhD students of mathematics to learn new topics that lead directly to the current research in geometry and topology, and to meet students from other universities and exchange ideas for future involvement in research--the technical term is schmoozing. The topics are non-Euclidean geometry, crossroads between hyperbolic geometry and number theory; origamis in Teichmüller space; 3-manifold topology; globally symmetric spaces; the geometry of the representation spaces in SU(2); the algorithmic construction and recognition of hyperbolic 3-manifolds, links, and graphs; and asymptotic geometry. No index is provided. Distributed in the US by American Mathematical Society. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com) This book contains carefully revised and expanded versions of eight courses that were presented at the University of Strasbourg, during two geometry master classes, in 2008 and 2009. The aim of the master classes was to give to fifth-year students and PhD students in mathematics the opportunity to learn new topics that lead directly to the current research in geometry and topology. The courses were held by leading experts. The subjects treated include hyperbolic geormetry, three-manifold topology, representation theory of fundamental groups of surfaces and of three-manifolds, dynamics on the hyperbolic plane with applications to number theory, Riemann surfaces, Teichmullër theory, Lie groups and asymptotic geometry Notes on non-Euclidean geometry / Norbert A'Campo and Athanase Papadopoulos Crossroads between hyperbolic geometry and number theory / Françoise Dal'Bo Introduction to origamis in Teichmüller space / Frank Herrlich Five lectures on 3-manifold topology / Philipp Korablev and Sergey Mateev An introduction to globally symmetric spaces / Gabriele Link Geometry of the representation spaces in SU(2) / Julien Marché Algorithmic construction and recognition of hyperbolic 3-manifolds, links, and graphs / Carlo Petronio An introduction to asymptotic geometry / Viktor Schroeder.