Athanase Papadopoulos - Böcker

This is a collection of surveys on important mathematical ideas, their origin, their evolution and their impact in current research. The authors are mathematicians who are leading experts in their fields. The book is addressed to all mathematicians, from undergraduate students to senior researchers, regardless of the specialty.

This is a collection of surveys on important mathematical ideas, their origin, their evolution and their impact in current research. The authors are mathematicians who are leading experts in their fields. The book is addressed to all mathematicians, from undergraduate students to senior researchers, regardless of the specialty.

At the same time, it is a tribute to Thurston, one of the greatest geometers of all time, whose work extended over many fields in mathematics and who had a unique way of perceiving forms and patterns, and of communicating and writing mathematics.

At the same time, it is a tribute to Thurston, one of the greatest geometers of all time, whose work extended over many fields in mathematics and who had a unique way of perceiving forms and patterns, and of communicating and writing mathematics.

The volume consists of a set of surveys on geometry in the broad sense. The goal is to present a certain number of research topics in a non-technical and appealing manner.The topics surveyed include spherical geometry, the geometry of finite-dimensional normed spaces, metric geometry (Bishop—Gromov type inequalities in Gromov-hyperbolic spaces), convexity theory and inequalities involving volumes and mixed volumes of convex bodies, 4-dimensional topology, Teichmüller spaces and mapping class groups actions, translation surfaces and their dynamics, and complex higher-dimensional geometry.Several chapters are based on lectures given by their authors to middle-advanced level students and young researchers. The whole book is intended to be an introduction to current research trends in geometry.

The purpose of this volume and of the other volumes in the same series is to provide a collection of surveys that allows the reader to learn the important aspects of William Thurston’s heritage. Thurston’s ideas have altered the course of twentieth century mathematics, and they continue to have a significant influence on succeeding generations of mathematicians. The topics covered in the present volume include com-plex hyperbolic Kleinian groups, Möbius structures, hyperbolic ends, cone 3-manifolds, Thurston’s norm, surgeries in representation varieties, triangulations, spaces of polygo-nal decompositions and of singular flat structures on surfaces, combination theorems in the theories of Kleinian groups, hyperbolic groups and holomorphic dynamics, the dynamics and iteration of rational maps, automatic groups, and the combinatorics of right-angled Artin groups.

The purpose of this volume and of the other volumes in the same series is to provide a collection of surveys that allows the reader to learn the important aspects of William Thurston’s heritage. Thurston’s ideas have altered the course of twentieth century mathematics, and they continue to have a significant influence on succeeding generations of mathematicians. The topics covered in the present volume include com-plex hyperbolic Kleinian groups, Möbius structures, hyperbolic ends, cone 3-manifolds, Thurston’s norm, surgeries in representation varieties, triangulations, spaces of polygo-nal decompositions and of singular flat structures on surfaces, combination theorems in the theories of Kleinian groups, hyperbolic groups and holomorphic dynamics, the dynamics and iteration of rational maps, automatic groups, and the combinatorics of right-angled Artin groups.

This volume presents the beautiful memoirs of Euler, Lagrange and Lambert on geography, translated into English and put into perspective through explanatory and historical essays as well as commentaries and mathematical notes.

This volume presents the beautiful memoirs of Euler, Lagrange and Lambert on geography, translated into English and put into perspective through explanatory and historical essays as well as commentaries and mathematical notes. These works had a major impact on the development of the differential geometry of surfaces and they deserve to be studied, not only as historical documents, but most of all as a rich source of ideas.

William Thurston’s ideas have altered the course of twentieth century mathematics, and they continue to have a significant influence on succeeding generations of mathematicians.

William Thurston’s ideas have altered the course of twentieth century mathematics, and they continue to have a significant influence on succeeding generations of mathematicians.

The book is the second volume of a collection which consists of surveys that focus on important topics in geometry which are at the heart of current research. The topics in the present volume include the conformal and the metric geometry of surfaces, Teichmüller spaces, immersed surfaces of prescribed extrinsic curvature in 3-dimensional manifolds, symplectic geometry, the metric theory of Grassmann spaces, homogeneous metric spaces, polytopes, the higher-dimensional Gauss–Bonnet formula, isoperimetry in finitely generated groups and Coxeter groups.Each chapter is intended for graduate students and researchers. Several chapters are based on lectures given by their authors to middle-advanced level students and young researchers. The whole book is intended to be an introduction to important topics in geometry.

The special topics addressed in this volume include hyperbolic geometry, 3-manifolds, complex and symplectic geometry, differential topology, combinatorial group theory, piecewise-linear topology, algebraic geometry, knots and links, homotopy theory, braid groups, phylogenetics, the history of geometry, and the philosophy of mathematics.

This volume is the first English edition, with commentaries and introductory material, of the writings on spherical geometry by Leonhard Euler, Joseph-Louis Lagrange and Johann Heinrich Lambert. The book is divided into two parts. The first part contains essays related the works by Euler, Lagrange and Lambert on spherical geometry. The goal of these essays is to include these works in the appropriate mathematical, historical and philosophical contexts. The second part of the volume is devoted to the English translations of the original memoirs, originally written in Latin, French and German. These translations are new and they are done by mathematicians who are involved in the subjects of the memoirs. Footnotes by the editors and the translators are appended to the translations.The book is addressed to students and researchers in geometry. It constitutes an invaluable reference in mathematics, and also in the history and philosophy of mathematics.

Despite its importance in the history of Ancient science, Menelaus’ Spherics is still by and large unknown. This treatise, which lies at the foundation of spherical geometry, is lost in Greek but has been preserved in its Arabic versions. The reader will find here, for the first time edited and translated into English, the essentials of this tradition, namely: a fragment of an early Arabic translation and the first Arabic redaction of the Spherics composed by al-Māhānī /al-Harawī, together with a historical and mathematical study of Menelaus’ treatise. With this book, a new and important part of the Greek and Arabic legacy to the history of mathematics comes to light. This book will be an indispensable acquisition for any reader interested in the history of Ancient geometry and science and, more generally, in Greek and Arabic science and culture.

This book explores the work of Bernhard Riemann and its impact on mathematics, philosophy and physics. It features contributions from a range of fields, historical expositions, and selected research articles that were motivated by Riemann’s ideas and demonstrate their timelessness. The editors are convinced of the tremendous value of going into Riemann’s work in depth, investigating his original ideas, integrating them into a broader perspective, and establishing ties with modern science and philosophy. Accordingly, the contributors to this volume are mathematicians, physicists, philosophers and historians of science. The book offers a unique resource for students and researchers in the fields of mathematics, physics and philosophy, historians of science, and more generally to a wide range of readers interested in the history of ideas.

This is a two-volume collection presenting the selected works of Herbert Busemann, one of the leading geometers of the twentieth century and one of the main founders of metric geometry, convexity theory and convexity in metric spaces.

This is a two-volume collection presenting the selected works of Herbert Busemann, one of the leading geometers of the twentieth century and one of the main founders of metric geometry, convexity theory and convexity in metric spaces. Busemann also did substantial work (probably the most important) on Hilbert’s Problem IV. These collected works include Busemann’s most important published articles on these topics.  Volume I of the collection features Busemann’s papers on the foundations of geodesic spaces and on the metric geometry of Finsler spaces.   Volume II includes Busemann’s papers on convexity and integral geometry, on Hilbert’s Problem IV, and other papers on miscellaneous subjects. Each volume offers biographical documents and introductory essays on Busemann’s work, documents from his correspondence and introductory essays written by leading specialists on Busemann’s work. They are a valuable resource for researchers in synthetic and metric geometry, convexity theory and the foundations of geometry.

This book explores the work of Bernhard Riemann and its impact on mathematics, philosophy and physics. The book offers a unique resource for students and researchers in the fields of mathematics, physics and philosophy, historians of science, and more generally to a wide range of readers interested in the history of ideas.

The book is an introduction of Gromov's theory of hyperbolic spaces and hyperbolic groups. It contains complete proofs of some basic theorems which are due to Gromov, and emphasizes some important developments on isoperimetric inequalities, automatic groups, and the metric structure on the boundary of a hyperbolic space.