Author: André Gil HenriquesPublisher: American Mathematical Society
ISBN: 1470455404
Category : Mathematics
Languages : en
Pages : 100
Book Description
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Planar Algebras in Braided Tensor Categories
Author: André Gil HenriquesPublisher: American Mathematical Society
ISBN: 1470455404
Category : Mathematics
Languages : en
Pages : 100
Book Description
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Planar Algebras in Braided Tensor Categories
Author: André Gil HenriquesPublisher:
ISBN: 9781470473488
Category : Algebra
Languages : en
Pages : 0
Book Description
"We generalize Jones' planar algebras by internalising the notion to a pivotal braided tensor category C. To formulate the notion, the planar tangles are now equipped with additional 'anchor lines' which connect the inner circles to the outer circle. We call the resulting notion an anchored planar algebra. If we restrict to the case when C is the category of vector spaces, then we recover the usual notion of a planar algebra."-- Page v.
Mathematical Foundations of Quantum Field Theory and Perturbative String Theory
Author: Hisham SatiPublisher: American Mathematical Soc.
ISBN: 0821851950
Category : Mathematics
Languages : en
Pages : 370
Book Description
Conceptual progress in fundamental theoretical physics is linked with the search for the suitable mathematical structures that model the physical systems. Quantum field theory (QFT) has proven to be a rich source of ideas for mathematics for a long time. However, fundamental questions such as ``What is a QFT?'' did not have satisfactory mathematical answers, especially on spaces with arbitrary topology, fundamental for the formulation of perturbative string theory. This book contains a collection of papers highlighting the mathematical foundations of QFT and its relevance to perturbative string theory as well as the deep techniques that have been emerging in the last few years. The papers are organized under three main chapters: Foundations for Quantum Field Theory, Quantization of Field Theories, and Two-Dimensional Quantum Field Theories. An introduction, written by the editors, provides an overview of the main underlying themes that bind together the papers in the volume.
Congruence Lattices of Ideals in Categories and (Partial) Semigroups
Author: James EastPublisher: American Mathematical Society
ISBN: 1470462699
Category : Mathematics
Languages : en
Pages : 144
Book Description
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Hopf Algebras, Tensor Categories and Related Topics
Author: Nicolás AndruskiewitschPublisher: American Mathematical Soc.
ISBN: 1470456249
Category : Education
Languages : en
Pages : 372
Book Description
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.
Topological Phases of Matter and Quantum Computation
Author: Paul BruillardPublisher: American Mathematical Soc.
ISBN: 1470440741
Category : Education
Languages : en
Pages : 242
Book Description
This volume contains the proceedings of the AMS Special Session on Topological Phases of Matter and Quantum Computation, held from September 24–25, 2016, at Bowdoin College, Brunswick, Maine. Topological quantum computing has exploded in popularity in recent years. Sitting at the triple point between mathematics, physics, and computer science, it has the potential to revolutionize sub-disciplines in these fields. The academic importance of this field has been recognized in physics through the 2016 Nobel Prize. In mathematics, some of the 1990 Fields Medals were awarded for developments in topics that nowadays are fundamental tools for the study of topological quantum computation. Moreover, the practical importance of this discipline has been underscored by recent industry investments. The relative youth of this field combined with a high degree of interest in it makes now an excellent time to get involved. Furthermore, the cross-disciplinary nature of topological quantum computing provides an unprecedented number of opportunities for cross-pollination of mathematics, physics, and computer science. This can be seen in the variety of works contained in this volume. With articles coming from mathematics, physics, and computer science, this volume aims to provide a taste of different sub-disciplines for novices and a wealth of new perspectives for veteran researchers. Regardless of your point of entry into topological quantum computing or your experience level, this volume has something for you.
The Classification of Subfactors with Index at Most $5 frac {1}{4}$
Author: Narjess AfzalyPublisher: American Mathematical Society
ISBN: 1470447126
Category : Mathematics
Languages : en
Pages : 94
Book Description
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Unitarizability in Corank Three for Classical $p$-adic Groups
Author: Marko Tadi?Publisher: American Mathematical Society
ISBN: 1470462834
Category : Mathematics
Languages : en
Pages : 134
Book Description
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The Representation Theory of the Increasing Monoid
Author: Sema GüntürkünPublisher: American Mathematical Society
ISBN: 1470465469
Category : Mathematics
Languages : en
Pages : 148
Book Description
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Spiral Waves: Linear and Nonlinear Theory
Author: Björn SandstedePublisher: American Mathematical Society
ISBN: 1470463091
Category : Mathematics
Languages : en
Pages : 116
Book Description
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