Diagrammatic Morphisms and Applications
Diagrammatic Morphisms and Applications

Author: David E. Radford

Publisher: American Mathematical Soc.

Published: 2003

Total Pages: 232

ISBN-13: 0821827944

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The technique of diagrammatic morphisms is an important ingredient in comprehending and visualizing certain types of categories with structure. It was widely used in this capacity in many areas of algebra, low-dimensional topology and physics. It was also applied to problems in classical and quantum information processing and logic. This volume contains articles based on talks at the Special Session, ``Diagrammatic Morphisms in Algebra, Category Theory, and Topology'', at the AMS Sectional Meeting in San Francisco. The articles describe recent achievements in several aspects of diagrammatic morphisms and their applications. Some of them contain detailed expositions on various diagrammatic techniques. The introductory article by D. Yetter is a thorough account of the subject in a historical perspective.

Theory and Application of Diagrams
Theory and Application of Diagrams

Author: Michael Anderson

Publisher: Springer

Published: 2003-07-31

Total Pages: 518

ISBN-13: 3540445900

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Diagrams 2000 is dedicated to the memory of Jon Barwise. Diagrams 2000 was the ?rst event in a new interdisciplinary conference series on the Theory and Application of Diagrams. It was held at the University of Edinburgh, Scotland, September 1-3, 2000. Driven by the pervasiveness of diagrams in human communication and by the increasing availability of graphical environments in computerized work, the study of diagrammatic notations is emerging as a research ?eld in its own right. This development has simultaneously taken place in several scienti?c disciplines, including, amongst others: cognitive science, arti?cial intelligence, and computer science. Consequently, a number of di?erent workshop series on this topic have been successfully organized during the last few years: Thinking with Diagrams, Theory of Visual Languages, Reasoning with Diagrammatic Representations, and Formalizing Reasoning with Visual and Diagrammatic Representations. Diagrams are simultaneously complex cognitive phenonema and sophis- cated computational artifacts. So, to be successful and relevant the study of diagrams must as a whole be interdisciplinary in nature. Thus, the workshop series mentioned above decided to merge into Diagrams 2000, as the single - terdisciplinary conference for this exciting new ?eld. It is intended that Diagrams 2000 should become the premier international conference series in this area and provide a forum with su?cient breadth of scope to encompass researchers from all academic areas who are studying the nature of diagrammatic representations and their use by humans and in machines.

Diagrams and Gestures
Diagrams and Gestures

Author: Francesco La Mantia

Publisher: Springer Nature

Published: 2023-09-16

Total Pages: 443

ISBN-13: 3031291115

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Drawing a line, and then another, and another. Go back from the lines to the movements they capture and see gestures in them: not spatial displacements, but modes of knowledge that pass through the exercise of the body. Discovering something new in a gesture: the line that contracts into a point or the point that expands into a zone, perhaps sinking into a hole. Thus experiencing a diagram: a becoming other inscribed in the novelty of the gesture and in the changes of the forms it shapes. This and much more is discussed in the essays gathered in Diagrams and Gestures. Resulting from trans-disciplinary work between mathematicians, philosophers, linguists and semioticians, the volume delivers an up-to-date account of the most valuable research on the connections between gesture and diagram. As one of the most important themes in contemporary thought, the study of these connections poses a challenge for the future: to elaborate a theory that is equal to new and stimulating research methodologies. We call this theory a philosophy of diagrammatic gestures.

Hopf Algebras, Tensor Categories and Related Topics
Hopf Algebras, Tensor Categories and Related Topics

Author: Nicolás Andruskiewitsch

Publisher: American Mathematical Soc.

Published: 2021-07-06

Total Pages: 359

ISBN-13: 1470456249

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The articles highlight the latest advances and further research directions in a variety of subjects related to tensor categories and Hopf algebras. Primary topics discussed in the text include the classification of Hopf algebras, structures and actions of Hopf algebras, algebraic supergroups, representations of quantum groups, quasi-quantum groups, algebras in tensor categories, and the construction method of fusion categories.

An Invitation to Knot Theory
An Invitation to Knot Theory

Author: Heather A. Dye

Publisher: CRC Press

Published: 2018-09-03

Total Pages: 246

ISBN-13: 1315360098

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The Only Undergraduate Textbook to Teach Both Classical and Virtual Knot Theory An Invitation to Knot Theory: Virtual and Classical gives advanced undergraduate students a gentle introduction to the field of virtual knot theory and mathematical research. It provides the foundation for students to research knot theory and read journal articles on their own. Each chapter includes numerous examples, problems, projects, and suggested readings from research papers. The proofs are written as simply as possible using combinatorial approaches, equivalence classes, and linear algebra. The text begins with an introduction to virtual knots and counted invariants. It then covers the normalized f-polynomial (Jones polynomial) and other skein invariants before discussing algebraic invariants, such as the quandle and biquandle. The book concludes with two applications of virtual knots: textiles and quantum computation.

Towards Higher Categories
Towards Higher Categories

Author: John C. Baez

Publisher: Springer Science & Business Media

Published: 2009-09-24

Total Pages: 292

ISBN-13: 1441915362

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The purpose of this book is to give background for those who would like to delve into some higher category theory. It is not a primer on higher category theory itself. It begins with a paper by John Baez and Michael Shulman which explores informally, by analogy and direct connection, how cohomology and other tools of algebraic topology are seen through the eyes of n-category theory. The idea is to give some of the motivations behind this subject. There are then two survey articles, by Julie Bergner and Simona Paoli, about (infinity,1) categories and about the algebraic modelling of homotopy n-types. These are areas that are particularly well understood, and where a fully integrated theory exists. The main focus of the book is on the richness to be found in the theory of bicategories, which gives the essential starting point towards the understanding of higher categorical structures. An article by Stephen Lack gives a thorough, but informal, guide to this theory. A paper by Larry Breen on the theory of gerbes shows how such categorical structures appear in differential geometry. This book is dedicated to Max Kelly, the founder of the Australian school of category theory, and an historical paper by Ross Street describes its development.

Algebraic and Arithmetic Theory of Quadratic Forms
Algebraic and Arithmetic Theory of Quadratic Forms

Author: Ricardo Baeza

Publisher: American Mathematical Soc.

Published: 2004

Total Pages: 364

ISBN-13: 082183441X

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This proceedings volume contains papers presented at the International Conference on the algebraic and arithmetic theory of quadratic forms held in Talca (Chile). The modern theory of quadratic forms has connections with a broad spectrum of mathematical areas including number theory, geometry, and K-theory. This volume contains survey and research articles covering the range of connections among these topics. The survey articles bring readers up-to-date on research and open problems in representation theory of integral quadratic forms, the algebraic theory of finite square class fields, and developments in the theory of Witt groups of triangulated categories. The specialized articles present important developments in both the algebraic and arithmetic theory of quadratic forms, as well as connections to geometry and K-theory. The volume is suitable for graduate students and research mathematicians interested in various aspects of the theory of quadratic forms.

Spectral Theory of Schrodinger Operators
Spectral Theory of Schrodinger Operators

Author: Rafael del Río

Publisher: American Mathematical Soc.

Published: 2004

Total Pages: 264

ISBN-13: 0821832972

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This volume gathers the articles based on a series of lectures from a workshop held at the Institute of Applied Mathematics of the National University of Mexico. The aim of the book is to present to a non-specialized audience the basic tools needed to understand and appreciate new trends of research on Schrodinger operator theory. Topics discussed include various aspects of the spectral theory of differential operators, the theory of self-adjoint operators, finite rank perturbations, spectral properties of random Schrodinger operators, and scattering theory for Schrodinger operators. The material is suitable for graduate students and research mathematicians interested in differential operators, in particular, spectral theory of Schrodinger operators.

Towards a Theory of Geometric Graphs
Towards a Theory of Geometric Graphs

Author: János Pach

Publisher: American Mathematical Soc.

Published: 2004

Total Pages: 300

ISBN-13: 0821834843

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This volume contains a collection of papers on graph theory, with the common theme that all the graph theoretical problems addressed are approached from a geometrical, rather than an abstract point of view. This is no accident; the editor selected these papers not as a comprehensive literature revie