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Categorification in Geometry Topology and Physics

Categorification in Geometry  Topology  and Physics Author Anna Beliakova
ISBN-10 9781470428211
Release 2017-02-21
Pages 267
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The emergent mathematical philosophy of categorification is reshaping our view of modern mathematics by uncovering a hidden layer of structure in mathematics, revealing richer and more robust structures capable of describing more complex phenomena. Categorification is a powerful tool for relating various branches of mathematics and exploiting the commonalities between fields. It provides a language emphasizing essential features and allowing precise relationships between vastly different fields. This volume focuses on the role categorification plays in geometry, topology, and physics. These articles illustrate many important trends for the field including geometric representation theory, homotopical methods in link homology, interactions between higher representation theory and gauge theory, and double affine Hecke algebra approaches to link homology. The companion volume (Contemporary Mathematics, Volume 683) is devoted to categorification and higher representation theory.

Differential Geometry and Topology

Differential Geometry and Topology Author A.T. Fomenko
ISBN-10 9780306109959
Release 1987-05-31
Pages 344
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Differential Geometry and Topology has been writing in one form or another for most of life. You can find so many inspiration from Differential Geometry and Topology also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Differential Geometry and Topology book for free.

Compact Riemann Surfaces

Compact Riemann Surfaces Author Jürgen Jost
ISBN-10 9783662034460
Release 2013-04-17
Pages 295
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This book is novel in its broad perspective on Riemann surfaces: the text systematically explores the connection with other fields of mathematics. The book can serve as an introduction to contemporary mathematics as a whole, as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. The book is unique among textbooks on Riemann surfaces in its inclusion of an introduction to Teichmüller theory. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation.

Geometric Topology Recent Developments

Geometric Topology  Recent Developments Author Jeff Cheeger
ISBN-10 9783540466512
Release 2006-11-17
Pages 200
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Geometric Topology Recent Developments has been writing in one form or another for most of life. You can find so many inspiration from Geometric Topology Recent Developments also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Geometric Topology Recent Developments book for free.

Algebraic and Geometric Combinatorics

Algebraic and Geometric Combinatorics Author Christos A. Athanasiadis
ISBN-10 9780821840801
Release 2006
Pages 324
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This volume contains original research and survey articles stemming from the Euroconference ""Algebraic and Geometric Combinatorics"". The papers discuss a wide range of problems that illustrate interactions of combinatorics with other branches of mathematics, such as commutative algebra, algebraic geometry, convex and discrete geometry, enumerative geometry, and topology of complexes and partially ordered sets. Among the topics covered are combinatorics of polytopes, lattice polytopes, triangulations and subdivisions, Cohen-Macaulay cell complexes, monomial ideals, geometry of toric surfaces, groupoids in combinatorics, Kazhdan-Lusztig combinatorics, and graph colorings. This book is aimed at researchers and graduate students interested in various aspects of modern combinatorial theories.

The Influence of Solomon Lefschetz in Geometry and Topology

The Influence of Solomon Lefschetz in Geometry and Topology Author Ernesto Lupercio
ISBN-10 9780821894941
Release 2014-08-05
Pages 226
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The influence of Solomon Lefschetz (1884-1972) in geometry and topology 40 years after his death has been very profound. Lefschetz's influence in Mexican mathematics has been even greater. In this volume, celebrating 50 years of mathematics at Cinvestav-México, many of the fields of geometry and topology are represented by some of the leaders of their respective fields. This volume opens with Michael Atiyah reminiscing about his encounters with Lefschetz and México. Topics covered in this volume include symplectic flexibility, Chern-Simons theory and the theory of classical theta functions, toric topology, the Beilinson conjecture for finite-dimensional associative algebras, partial monoids and Dold-Thom functors, the weak b-principle, orbit configuration spaces, equivariant extensions of differential forms for noncompact Lie groups, dynamical systems and categories, and the Nahm pole boundary condition.

Geometry Topology and Mathematical Physics

Geometry  Topology  and Mathematical Physics Author V. M. Buchstaber
ISBN-10 0821836137
Release 2004
Pages 324
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This volume contains a selection of papers based on presentations given at the S. P. Novikov seminar held at the Steklov Mathematical Institute in Moscow. Topics and speakers were chosen by the well-known expert, S. P. Novikov, one of the leading mathematicians of the twentieth century. His diverse interests are the tradition of the seminar and are reflected in the topics presented in the book. The book begins with Novikov's paper analyzing the position of mathematics and theoretical physics at the beginning of the new millennium. Following is an interview with Novikov published in the Newsletter of the European Mathematical Society presenting the genesis of many of his ideas and his scientific school. The remaining articles address topics in geometry, topology, and mathematical physics. The volume is suitable for graduate students and researchers interested in the corresponding areas of mathematics and physics.

Topics in Contemporary Mathematical Physics

Topics in Contemporary Mathematical Physics Author Kai S Lam
ISBN-10 9789814667821
Release 2015-09-17
Pages 852
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This new (second) edition contains a general treatment of quantum field theory (QFT) in a simple scalar field setting in addition to the modern material on the applications of differential geometry and topology, group theory, and the theory of linear operators to physics found in the first edition. All these are introduced without assuming more background on the part of the reader than a good foundation in undergraduate (junior) level mathematical physics. The new material entirely focuses on an introduction to quantum field theory, emphasizing the Feynman path (functional integral) approach to QFT and the renormalization group. With respect to the latter, the focus is on an introduction of its application to critical phenomena in statistical physics, following the outgrowth of the Callan–Symanzik equation originally developed in the context of high energy physics, and the seminal contributions of Kenneth Wilson. One of the overriding aims of the new material is also to draw students' attention to the deep connections between high energy physics and statistical mechanics. The unavoidable technical aspects are explained with a minimum of prerequisite material and jargon, and conceptual understanding is always given prominence before mastery of technical details, but the importance of the latter is never underestimated. Derivational details and motivational discussions are provided in abundance in order to ensure continuity of reading, and to avoid trying the readers' patience.

Geometry and Topology Down Under

Geometry and Topology Down Under Author Craig D. Hodgson
ISBN-10 9780821884805
Release 2013-08-23
Pages 369
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This book contains the proceedings of the conference Geometry & Topology Down Under, held July 11-22, 2011, at the University of Melbourne, Parkville, Australia, in honour of Hyam Rubinstein. The main topic of the book is low-dimensional geometry and topology. It includes both survey articles based on courses presented at the conferences and research articles devoted to important questions in low-dimensional geometry. Together, these contributions show how methods from different fields of mathematics contribute to the study of 3-manifolds and Gromov hyperbolic groups. It also contains a list of favorite problems by Hyam Rubinstein.

Elements of Point Set Topology

Elements of Point Set Topology Author John D. Baum
ISBN-10 9780486668260
Release 1964
Pages 150
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Topology continues to be a topic of prime importance in contemporary mathematics, but until the publication of this book there were few if any introductions to topology for undergraduates. This book remedied that need by offering a carefully thought-out, graduated approach to point set topology at the undergraduate level. To make the book as accessible as possible, the author approaches topology from a geometric and axiomatic standpoint; geometric, because most students come to the subject with a good deal of geometry behind them, enabling them to use their geometric intuition; axiomatic, because it parallels the student's experience with modern algebra, and keeps the book in harmony with current trends in mathematics. After a discussion of such preliminary topics as the algebra of sets, Euler-Venn diagrams and infinite sets, the author takes up basic definitions and theorems regarding topological spaces (Chapter 1). The second chapter deals with continuous functions (mappings) and homeomorphisms, followed by two chapters on special types of topological spaces (varieties of compactness and varieties of connectedness). Chapter 5 covers metric spaces. Since basic point set topology serves as a foundation not only for functional analysis but also for more advanced work in point set topology and algebraic topology, the author has included topics aimed at students with interests other than analysis. Moreover, Dr. Baum has supplied quite detailed proofs in the beginning to help students approaching this type of axiomatic mathematics for the first time. Similarly, in the first part of the book problems are elementary, but they become progressively more difficult toward the end of the book. References have been supplied to suggest further reading to the interested student.

Surveys in Contemporary Mathematics

Surveys in Contemporary Mathematics Author Nicholas Young
ISBN-10 9780521705646
Release 2008
Pages 361
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A collection of articles showcasing the achievements of young Russian researchers in combinatorial and algebraic geometry and topology.

Topology of Algebraic Varieties and Singularities

Topology of Algebraic Varieties and Singularities Author Anatoly Libgober
ISBN-10 9780821848906
Release 2011
Pages 467
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This volume contains invited expository and research papers from the conference Topology of Algebraic Varieties, in honor of Anatoly Libgober's 60th birthday, held June 22-26, 2009, in Jaca, Spain. The volume contains four parts corresponding to the four main focal points of the conference: algebraic geometry and fundamental groups, braids and knots, hyperplane arrangements, and singularities. Together, the papers provide an overview of the current status of a broad range of topological questions in Algebraic Geometry.

Symplectic Geometry

Symplectic Geometry Author A.T. Fomenko
ISBN-10 2881249019
Release 1995-11-30
Pages 484
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Symplectic Geometry has been writing in one form or another for most of life. You can find so many inspiration from Symplectic Geometry also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Symplectic Geometry book for free.

Contemporary Trends in Algebraic Geometry and Algebraic Topology

Contemporary Trends in Algebraic Geometry and Algebraic Topology Author Shiing-Shen Chern
ISBN-10 9789814488518
Release 2002-08-02
Pages 276
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The Wei-Liang Chow and Kuo-Tsai Chen Memorial Conference was proposed and held by Prof S S Chern in Nankai Institute of Mathematics. It was devoted to memorializing those two outstanding and original Chinese mathematicians who had made significant contributions to algebraic geometry and algebraic topology, respectively. It also provided a forum for leading mathematicians to expound and discuss their views on new ideas in these fields, as well as trends in 21st Century mathematics. About 100 mathematicians participated in the conference, including Sir Michael Atiyah, Jacob Palis, Phillip Griffiths, David Eisenbud, Philippe Tondeur, Yujiro Kawamata, Tian Gang, etc. This invaluable volume contains the selected papers presented at the conference. The topics include canonical maps of Gorenstein 3-folds, fundamental groups of algebraic curves, Chen's interated integrals, algebraic fiber spaces, and others. Contents:Mathematics in the 20th Century (M Atiyah)The Φ4 of Minimal Gorenstein 3-Folds of General Type (M Chen)Morphisms of Curves and the Fundamental Group (M Cushman)Iterated Integrals and Algebraic Cycles: Examples and Prospects (R Hain)Chen's Interated Integrals and Algebraic Cycles (B Harris)On Algebraic Fiber Spaces (Y Kawamata)Local Holomorphic Isometric Embeddings Arising from Correspondences in the Rank-1 Case (N Mok)Multiple Polylogarithms: Analytic Continuation, Monodromy, and Variations of Mixed Hodge Structures (J Zhao)Deformation Types of Real and Complex Manifolds (F Catanese)Wei-Liang Chow, 1911–1995 (S S Chern)Comments on Chow's Work (S Lang)The Life and Work of Kuo-Tsai Chen (R Hain & Ph Tondeur) Readership: Graduate students and researchers in geometry and topology. Keywords:

Geometry and Topology Aarhus

Geometry and Topology  Aarhus Author Karsten Grove
ISBN-10 9780821821589
Release 2000
Pages 393
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This volume includes both survey and research articles on major advances and future developments in geometry and topology. Papers include those presented as part of the 5th Aarhus Conference - a meeting of international participants held in connection with ICM Berlin in 1998 - and related papers on the subject. This collection of papers is aptly published in the Contemporary Mathematics series, as the works represent the state of research and address areas of future development in the area of manifold theory and geometry. The survey articles in particular would serve well as supplemental resources in related graduate courses.

Geometric Topology

Geometric Topology Author Cameron Gordon
ISBN-10 9780821851821
Release 1994
Pages 246
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This volume contains the refereed proceedings of the conference.

Topological and Algebraic Geometry Methods in Contemporary Mathematical Physics

Topological and Algebraic Geometry Methods in Contemporary Mathematical Physics Author B. A. Dubrovin
ISBN-10 OCLC:780426182
Release 2004
Pages 139
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Topological and Algebraic Geometry Methods in Contemporary Mathematical Physics has been writing in one form or another for most of life. You can find so many inspiration from Topological and Algebraic Geometry Methods in Contemporary Mathematical Physics also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Topological and Algebraic Geometry Methods in Contemporary Mathematical Physics book for free.