Geometry Topology And Dynamics Of Character Varieties

Author : William Goldman
Publisher : World Scientific
ISBN 13 : 9814401374
Total Pages : 364 pages
Book Rating : 4.71/5 ( download)

DOWNLOAD NOW!

Download or read book Geometry, Topology and Dynamics of Character Varieties written by William Goldman and published by World Scientific. This book was released on 2012-06-18 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : C. S. Aravinda
Publisher : American Mathematical Soc.
ISBN 13 : 0821898825
Total Pages : 386 pages
Book Rating : 4.26/5 ( download)

DOWNLOAD NOW!

Download or read book Geometry, Groups and Dynamics written by C. S. Aravinda and published by American Mathematical Soc.. This book was released on 2015-05-01 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the ICTS Program: Groups, Geometry and Dynamics, held December 3-16, 2012, at CEMS, Almora, India. The activity was an academic tribute to Ravi S. Kulkarni on his turning seventy. Articles included in this volume, both introductory and advanced surveys, represent the broad area of geometry that encompasses a large portion of group theory (finite or otherwise) and dynamics in its proximity. These areas have been influenced by Kulkarni's ideas and are closely related to his work and contribution.

Author : Javier Aramayona
Publisher : Birkhäuser
ISBN 13 : 3319609408
Total Pages : 149 pages
Book Rating : 4.09/5 ( download)

DOWNLOAD NOW!

Download or read book Algorithmic and Geometric Topics Around Free Groups and Automorphisms written by Javier Aramayona and published by Birkhäuser. This book was released on 2017-11-29 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Omayra Ortega
Publisher : American Mathematical Soc.
ISBN 13 : 1470451301
Total Pages : 184 pages
Book Rating : 4.01/5 ( download)

DOWNLOAD NOW!

Download or read book The Golden Anniversary Celebration of the National Association of Mathematicians written by Omayra Ortega and published by American Mathematical Soc.. This book was released on 2020-12-10 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Mikhail Kapranov
Publisher : Springer Science & Business Media
ISBN 13 : 9783764386085
Total Pages : 742 pages
Book Rating : 4.88/5 ( download)

DOWNLOAD NOW!

Download or read book Geometry and Dynamics of Groups and Spaces written by Mikhail Kapranov and published by Springer Science & Business Media. This book was released on 2008-03-05 with total page 742 pages. Available in PDF, EPUB and Kindle. Book excerpt: Alexander Reznikov (1960-2003) was a brilliant and highly original mathematician. This book presents 18 articles by prominent mathematicians and is dedicated to his memory. In addition it contains an influential, so far unpublished manuscript by Reznikov of book length. The book further provides an extensive survey on Kleinian groups in higher dimensions and some articles centering on Reznikov as a person.

Author : Fei Han
Publisher : World Scientific
ISBN 13 : 9813100567
Total Pages : 220 pages
Book Rating : 4.65/5 ( download)

DOWNLOAD NOW!

Download or read book Geometric Analysis Around Scalar Curvatures written by Fei Han and published by World Scientific. This book was released on 2016-04-18 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Contents:Lectures on the Fourth-Order Q Curvature Equation (Fengbo Hang and Paul C Yang)An Introduction to the Finite and Infinite Dimensional Reduction Methods (Manuel del Pino and Juncheng Wei)Einstein Constraint Equations on Riemannian Manifolds (Quôc Anh Ngô) Readership: Advanced undergraduates, graduate students and researchers interested in the study of conformal geometry and geometric partial differential equations.

Author : Jeffrey Danciger
Publisher : Stanford University
ISBN 13 :
Total Pages : 171 pages
Book Rating : 4.92/5 ( download)

DOWNLOAD NOW!

Download or read book Geometric Transitions written by Jeffrey Danciger and published by Stanford University. This book was released on 2011 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Yu Kiang Leong
Publisher : World Scientific
ISBN 13 : 9811219605
Total Pages : 442 pages
Book Rating : 4.03/5 ( download)

DOWNLOAD NOW!

Download or read book 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 published by World Scientific. This book was released on 2021-06-23 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Heinz Karl Heinrich Siedentop
Publisher : World Scientific
ISBN 13 : 981446015X
Total Pages : 303 pages
Book Rating : 4.56/5 ( download)

DOWNLOAD NOW!

Download or read book Complex Quantum Systems written by Heinz Karl Heinrich Siedentop and published by World Scientific. This book was released on 2013 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Stevo Todorcevic
Publisher : World Scientific
ISBN 13 : 9814571598
Total Pages : 236 pages
Book Rating : 4.93/5 ( download)

DOWNLOAD NOW!

Download or read book Notes on Forcing Axioms written by Stevo Todorcevic and published by World Scientific. This book was released on 2013-12-26 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Contents:Baire Category Theorem and the Baire Category NumbersCoding Sets by the Real NumbersConsequences in Descriptive Set TheoryConsequences in Measure TheoryVariations on the Souslin HypothesisThe S-Spaces and the L-SpacesThe Side-condition MethodIdeal DichotomiesCoherent and Lipschitz TreesApplications to the S-Space Problem and the von Neumann ProblemBiorthogonal SystemsStructure of Compact SpacesRamsey Theory on OrdinalsFive Cofinal TypesFive Linear OrderingsCardinal Arithmetic and mmReflection PrinciplesAppendices:Basic NotionsPreserving Stationary SetsHistorical and Other Comments Readership: Graduate students and researchers in logic, set theory and related fields. Key Features:This is a first systematic exposition of the unified approach for building proper, semi-proper, and stationary preserving forcing notions through the method of using elementary submodels as side conditionsThe books starts from the classical applications of Martin's axioms and ends with some of the most sophisticated applications of the Proper Forcing Axioms. In this way, the reader is led into a natural process of understanding the combinatorics hidden behind the methodKeywords:Set Theory;Forcing Axioms