Geometry Topology And Dynamics Of Character Varieties
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Geometry Topology And Dynamics Of Character Varieties
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Author : William Mark Goldman
language : en
Publisher: World Scientific
Release Date : 2012
Geometry Topology And Dynamics Of Character Varieties written by William Mark Goldman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
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
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Author : William Goldman
language : en
Publisher: World Scientific
Release Date : 2012-06-18
Geometry Topology And Dynamics Of Character Varieties written by William Goldman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-18 with Mathematics categories.
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.
Algorithmic And Geometric Topics Around Free Groups And Automorphisms
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Author : Javier Aramayona
language : en
Publisher: Birkhäuser
Release Date : 2017-11-29
Algorithmic And Geometric Topics Around Free Groups And Automorphisms written by Javier Aramayona and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-29 with Mathematics categories.
This volume presents the lecture notes from the authors’ three summer courses offered during the program “Automorphisms of Free Groups: Geometry, Topology, and Dynamics,” held at the Centre de Recerca Matemàtica (CRM) in Bellaterra, Spain. The first two chapters present the basic tools needed, from formal language theory (regular and context-free languages, automata, rewriting systems, transducers, etc) and emphasize their connections to group theory, mostly relating to free and virtually-free groups. The material covered is sufficient to present full proofs of many of the existing interesting characterizations of virtually-free groups. In turn, the last chapter comprehensively describes Bonahon’s construction of Thurston’s compactification of Teichmüller space in terms of geodesic currents on surfaces. It also includes several intriguing extensions of the notion of geodesic current to various other, more general settings.
Flexibility Of Group Actions On The Circle
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Author : Sang-hyun Kim
language : en
Publisher: Springer
Release Date : 2019-01-02
Flexibility Of Group Actions On The Circle written by Sang-hyun Kim and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-02 with Mathematics categories.
In this partly expository work, a framework is developed for building exotic circle actions of certain classical groups. The authors give general combination theorems for indiscrete isometry groups of hyperbolic space which apply to Fuchsian and limit groups. An abundance of integer-valued subadditive defect-one quasimorphisms on these groups follow as a corollary. The main classes of groups considered are limit and Fuchsian groups. Limit groups are shown to admit large collections of faithful actions on the circle with disjoint rotation spectra. For Fuchsian groups, further flexibility results are proved and the existence of non-geometric actions of free and surface groups is established. An account is given of the extant notions of semi-conjugacy, showing they are equivalent. This book is suitable for experts interested in flexibility of representations, and for non-experts wanting an introduction to group representations into circle homeomorphism groups.
The Golden Anniversary Celebration Of The National Association Of Mathematicians
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Author : Omayra Ortega
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-12-10
The Golden Anniversary Celebration Of The National Association Of Mathematicians written by Omayra Ortega and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-10 with Education categories.
This volume is put together by the National Association of Mathematicians to commemorate its 50th anniversary. The articles in the book are based on lectures presented at several events at the Joint Mathematics Meeting held from January 16–19, 2019, in Baltimore, Maryland, including the Claytor-Woodard Lecture as well as the NAM David Harold Blackwell Lecture, which was held on August 2, 2019, in Cincinnati, Ohio.
Geometric Analysis Around Scalar Curvatures
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Author : Fei Han
language : en
Publisher: World Scientific
Release Date : 2016-04-18
Geometric Analysis Around Scalar Curvatures written by Fei Han and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-18 with Mathematics categories.
This volume contains three expanded lecture notes from the program Scalar Curvature in Manifold Topology and Conformal Geometry that was held at the Institute for Mathematical Sciences from 1 November to 31 December 2014. The first chapter surveys the recent developments on the fourth-order equations with negative exponent from geometric points of view such as positive mass theorem and uniqueness results. The next chapter deals with the recent important progress on several conjectures such as the existence of non-flat smooth hyper-surfaces and Serrin's over-determined problem. And the final chapter induces a new technique to handle the equation with critical index and the sign change coefficient as well as the negative index term. These topics will be of interest to those studying conformal geometry and geometric partial differential equations.
Geometric Transitions
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Author : Jeffrey Danciger
language : en
Publisher: Stanford University
Release Date : 2011
Geometric Transitions written by Jeffrey Danciger and has been published by Stanford University this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
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.
Art And Practice Of Mathematics The Interviews At The Institute For Mathematical Sciences National University Of Singapore 2010 2020
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Author : Yu Kiang Leong
language : en
Publisher: World Scientific
Release Date : 2021-06-23
Art And Practice Of Mathematics The Interviews At The Institute For Mathematical Sciences National University Of Singapore 2010 2020 written by Yu Kiang Leong and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-23 with Mathematics categories.
This book constitutes the second volume of interviews with prominent mathematicians and mathematical scientists who visited the Institute for Mathematical Sciences, National University of Singapore. First published in the Institute's newsletter Imprints during the period 2010-2020, they offer glimpses of an esoteric universe as viewed and experienced by some of the leading and creative practitioners of the craft of mathematics.The topics covered in this volume are wide-ranging, running from pure mathematics (logic, number theory, algebraic geometry) to applied mathematics (mathematical modeling, fluid dynamics) through probability and statistics, mathematical physics, theoretical computer science and financial mathematics. This eclectic mix of the abstract and the concrete should interest those who are enthralled by the mystique and power of mathematics, whether they are students, researchers or the non-specialists.By briefly tracing the paths traveled by the pioneers of different national backgrounds, the interviews attempt to put a cultural face to an intellectual endeavor that is often perceived as dry and austere by the uninitiated. They should also interest those who are intrigued by the influence of the environment on the creative spirit, and, in particular, those who are interested in the psychology and history of ideas.
Notes On Forcing Axioms
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Author : Stevo Todorcevic
language : en
Publisher: World Scientific
Release Date : 2013-12-26
Notes On Forcing Axioms written by Stevo Todorcevic and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-26 with Mathematics categories.
In the mathematical practice, the Baire category method is a tool for establishing the existence of a rich array of generic structures. However, in mathematics, the Baire category method is also behind a number of fundamental results such as the Open Mapping Theorem or the Banach-Steinhaus Boundedness Principle. This volume brings the Baire category method to another level of sophistication via the internal version of the set-theoretic forcing technique. It is the first systematic account of applications of the higher forcing axioms with the stress on the technique of building forcing notions rather than on the relationship between different forcing axioms or their consistency strengths.
Complex Quantum Systems
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Author : Heinz Karl Heinrich Siedentop
language : en
Publisher: World Scientific
Release Date : 2013
Complex Quantum Systems written by Heinz Karl Heinrich Siedentop and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Science categories.
This volume is based on lectures given during the program Complex Quantum Systems held at the National University of Singapore's Institute for Mathematical Sciences from 17 February to 27 March 2010. It guides the reader through two introductory expositions on large Coulomb systems to five of the most important developments in the field: derivation of mean field equations, derivation of effective Hamiltonians, alternative high precision methods in quantum chemistry, modern many body methods originating from quantum information, and OCo the most complex OCo semirelativistic quantum electrodynamics.These introductions are written by leaders in their fields; amongst them are Volker Bach, Rafael Benguria, Thomas Chen, and Jan Philip Solovej. Together, they fill a gap between current textbooks and the vast modern literature on complex quantum systems.