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Geometry Topology And Dynamics Of Character Varieties
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Book Synopsis Geometry, Topology and Dynamics of Character Varieties by : William Goldman
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
Book Synopsis Geometry, Groups and Dynamics by : C. S. Aravinda
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 369 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.
Book Synopsis Algorithmic and Geometric Topics Around Free Groups and Automorphisms by : Javier Aramayona
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.
Book Synopsis The Golden Anniversary Celebration of the National Association of Mathematicians by : Omayra Ortega
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.
Book Synopsis Geometric Analysis Around Scalar Curvatures by : Fei Han
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.
Book Synopsis Geometric Transitions by : Jeffrey Danciger
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.
Book Synopsis Geometry and Dynamics of Groups and Spaces by : Mikhail Kapranov
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.
Book Synopsis Art And Practice Of Mathematics, The: Interviews At The Institute For Mathematical Sciences, National University Of Singapore, 2010-2020 by : Yu Kiang Leong
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.
Book Synopsis Complex Quantum Systems by : Heinz Karl Heinrich Siedentop
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.
Book Synopsis Notes on Forcing Axioms by : Stevo Todorcevic
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
Book Synopsis Infinity and Truth by : Chitat Chong
Download or read book Infinity and Truth written by Chitat Chong and published by World Scientific. This book was released on 2013-11-28 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on the talks given at the Workshop on Infinity and Truth held at the Institute for Mathematical Sciences, National University of Singapore, from 25 to 29 July 2011. The chapters cover topics in mathematical and philosophical logic that examine various aspects of the foundations of mathematics. The theme of the volume focuses on two basic foundational questions: (i) What is the nature of mathematical truth and how does one resolve questions that are formally unsolvable within the Zermelo–Fraenkel Set Theory with the Axiom of Choice, and (ii) Do the discoveries in mathematics provide evidence favoring one philosophical view over others? These issues are discussed from the vantage point of recent progress in foundational studies. The final chapter features questions proposed by the participants of the Workshop that will drive foundational research. The wide range of topics covered here will be of interest to students, researchers and mathematicians concerned with issues in the foundations of mathematics. Contents:Invited Lectures:Absoluteness, Truth, and Quotients (Ilijas Farah)A Multiverse Perspective on the Axiom of Constructiblity (Joel David Hamkins)Hilbert, Bourbaki and the Scorning of Logic (A R D Mathias)Toward Objectivity in Mathematics (Stephen G Simpson)Sort Logic and Foundations of Mathematics (Jouko Väänänen)Reasoning about Constructive Concepts (Nik Weaver)Perfect Infinites and Finite Approximation (Boris Zilber)Special Session:An Objective Justification for Actual Infinity? (Stephen G Simpson)Oracle Questions (Theodore A Slaman and W Hugh Woodin) Readership: Mathematicians, philosophers, scientists, graduate students, academic institutions, and research organizations interested in logic and the philosophy of mathematics. Keywords:Mathematical Logic;Foundations of Mathematics;Philosophy of Mathematics;Mathematical Truth;Infinity;Set Theory;Proof Theory;MultiverseKey Features:All the contributors are world-renownedThe final chapter is written by Theodore A Slaman and W Hugh Woodin, who are two of the leading logicians in the world. They are also the volume editors
Book Synopsis Hyperbolic Knot Theory by : Jessica S. Purcell
Download or read book Hyperbolic Knot Theory written by Jessica S. Purcell and published by American Mathematical Soc.. This book was released on 2020-10-06 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to hyperbolic geometry in dimension three, with motivation and applications arising from knot theory. Hyperbolic geometry was first used as a tool to study knots by Riley and then Thurston in the 1970s. By the 1980s, combining work of Mostow and Prasad with Gordon and Luecke, it was known that a hyperbolic structure on a knot complement in the 3-sphere gives a complete knot invariant. However, it remains a difficult problem to relate the hyperbolic geometry of a knot to other invariants arising from knot theory. In particular, it is difficult to determine hyperbolic geometric information from a knot diagram, which is classically used to describe a knot. This textbook provides background on these problems, and tools to determine hyperbolic information on knots. It also includes results and state-of-the art techniques on hyperbolic geometry and knot theory to date. The book was written to be interactive, with many examples and exercises. Some important results are left to guided exercises. The level is appropriate for graduate students with a basic background in algebraic topology, particularly fundamental groups and covering spaces. Some experience with some differential topology and Riemannian geometry will also be helpful.
Book Synopsis Modular Representation Theory of Finite and p-Adic Groups by : Wee Teck Gan
Download or read book Modular Representation Theory of Finite and p-Adic Groups written by Wee Teck Gan and published by World Scientific. This book was released on 2015-02-13 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an outgrowth of the program Modular Representation Theory of Finite and p-Adic Groups held at the Institute for Mathematical Sciences at National University of Singapore during the period of 1–26 April 2013. It contains research works in the areas of modular representation theory of p-adic groups and finite groups and their related algebras. The aim of this volume is to provide a bridge — where interactions are rare between researchers from these two areas — by highlighting the latest developments, suggesting potential new research problems, and promoting new collaborations. It is perhaps one of the few volumes, if not only, which treats such a juxtaposition of diverse topics, emphasizing their common core at the heart of Lie theory. Contents:Modular Representations of Finite Reductive Groups (Marc Cabanes)ℓ-Modular Representations of p-Adic Groups (ℓ ≠ p) (Vincent Sécherre)p-Modular Representations of p-Adic Groups (Florian Herzig)Representation Theory and Cohomology of Khovanov–Lauda–Rouquier Algebras (Alexander S Kleshchev)Cyclotomic Quiver Hecke Algebras of Type A (Andrew Mathas) Readership: Graduate students and professional mathematicians interested in modular representation theory. Key Features:Contains a survey of modular representation theory of finite groups of Lie type, with a description of recent progress and outstanding conjecturesCovers the modular representation theory of p-adic groups in both defining and non-defining characteristic which is being pursued in the modular Langlands programIntroduces the increasingly popular representation theory of Khovanov–Lauda–Rouquier algebras and the graded representation theory of cyclotomic Hecke algebrasSuitable for graduate students as well as mathematical researchers who desire to learn about representation theory in these areasKeywords:Modular Representation Theory;Reductive Groups;Modular Langlands Program;Khovanov–Lauda–Rouquier Algebras;Cyclotomic Hecke Algebras
Book Synopsis Dynamics, Geometry, Number Theory by : David Fisher
Download or read book Dynamics, Geometry, Number Theory written by David Fisher and published by University of Chicago Press. This book was released on 2022-02-07 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: This definitive synthesis of mathematician Gregory Margulis’s research brings together leading experts to cover the breadth and diversity of disciplines Margulis’s work touches upon. This edited collection highlights the foundations and evolution of research by widely influential Fields Medalist Gregory Margulis. Margulis is unusual in the degree to which his solutions to particular problems have opened new vistas of mathematics; his ideas were central, for example, to developments that led to the recent Fields Medals of Elon Lindenstrauss and Maryam Mirzhakhani. Dynamics, Geometry, Number Theory introduces these areas, their development, their use in current research, and the connections between them. Divided into four broad sections—“Arithmeticity, Superrigidity, Normal Subgroups”; “Discrete Subgroups”; “Expanders, Representations, Spectral Theory”; and “Homogeneous Dynamics”—the chapters have all been written by the foremost experts on each topic with a view to making them accessible both to graduate students and to experts in other parts of mathematics. This was no simple feat: Margulis’s work stands out in part because of its depth, but also because it brings together ideas from different areas of mathematics. Few can be experts in all of these fields, and this diversity of ideas can make it challenging to enter Margulis’s area of research. Dynamics, Geometry, Number Theory provides one remedy to that challenge.
Book Synopsis E-Recursion, Forcing and C*-Algebras by : Chitat Chong
Download or read book E-Recursion, Forcing and C*-Algebras written by Chitat Chong and published by World Scientific. This book was released on 2014-05-28 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the lecture notes of short courses given by three leading experts in mathematical logic at the 2012 Asian Initiative for Infinity Logic Summer School. The major topics cover set-theoretic forcing, higher recursion theory, and applications of set theory to C*-algebra. This volume offers a wide spectrum of ideas and techniques introduced in contemporary research in the field of mathematical logic to students, researchers and mathematicians. Contents:Selected Applications of Logic to Classification Problem for C*-Algebras (Ilijas Farah)Subcomplete Forcing and L-Forcing (Ronald Jensen)E-Recursion (Gerald E Sacks) Readership: Mathematics graduate students, researchers in logic, set theory and related areas. Key Features:These are notes based on short courses given by three leading experts in set theory, recursion theory and their applicationsKeywords:Logic;Set Theory;Forcing;E-recursion;C*-Algebra;Recursion Theory;Computability Theory
Book Synopsis Forcing, Iterated Ultrapowers, and Turing Degrees by : Chitat Chong
Download or read book Forcing, Iterated Ultrapowers, and Turing Degrees written by Chitat Chong and published by World Scientific. This book was released on 2015-07-30 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the lecture notes of short courses given by three leading experts in mathematical logic at the 2010 and 2011 Asian Initiative for Infinity Logic Summer Schools. The major topics covered set theory and recursion theory, with particular emphasis on forcing, inner model theory and Turing degrees, offering a wide overview of ideas and techniques introduced in contemporary research in the field of mathematical logic. Contents:Prikry-Type Forcings and a Forcing with Short Extenders (Moti Gitik)The Turing Degrees: An Introduction (Richard A Shore)An Introduction to Iterated Ultrapowers (John Steel) Readership: Graduate students in mathematics, and researchers in logic, set theory and computability theory. Key Features:These are notes based on short courses given by three leading experts in set theory, recursion theory and their applicationsKeywords:Logic;Set Theory;Forcing;Recursion Theory;Computability Theory;Turing Degrees;C*-algebra
Book Synopsis Slicing the Truth by : Denis R Hirschfeldt
Download or read book Slicing the Truth written by Denis R Hirschfeldt and published by World Scientific. This book was released on 2014-07-18 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a brief and focused introduction to the reverse mathematics and computability theory of combinatorial principles, an area of research which has seen a particular surge of activity in the last few years. It provides an overview of some fundamental ideas and techniques, and enough context to make it possible for students with at least a basic knowledge of computability theory and proof theory to appreciate the exciting advances currently happening in the area, and perhaps make contributions of their own. It adopts a case-study approach, using the study of versions of Ramsey's Theorem (for colorings of tuples of natural numbers) and related principles as illustrations of various aspects of computability theoretic and reverse mathematical analysis. This book contains many exercises and open questions. Contents:Setting Off: An IntroductionGathering Our Tools: Basic Concepts and NotationFinding Our Path: König's Lemma and ComputabilityGauging Our Strength: Reverse MathematicsIn Defense of DisarrayAchieving Consensus: Ramsey's TheoremPreserving Our Power: ConservativityDrawing a Map: Five DiagramsExploring Our Surroundings: The World Below RT22Charging Ahead: Further TopicsLagniappe: A Proof of Liu's Theorem Readership: Graduates and researchers in mathematical logic. Key Features:This book assumes minimal background in mathematical logic and takes the reader all the way to current research in a highly active areaIt is the first detailed introduction to this particular approach to this area of researchThe combination of fully worked out arguments and exercises make this book well suited to self-study by graduate students and other researchers unfamiliar with the areaKeywords:Reverse Mathematics;Computability Theory;Computable Mathematics;Computable Combinatorics
