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Author: James Lepowsky
Publisher: Cambridge University Press
ISBN: 0521106648
Category : Mathematics
Languages : en
Pages : 415
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Book Description
This volume examines the impact of the 'Monstrous Moonshine' paper on mathematics and theoretical physics.
Author: James Lepowsky
Publisher: Cambridge University Press
ISBN: 0521106648
Category : Mathematics
Languages : en
Pages : 415
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Book Description
This volume examines the impact of the 'Monstrous Moonshine' paper on mathematics and theoretical physics.
Author: Mark Hagen
Publisher: Cambridge University Press
ISBN: 1108577350
Category : Mathematics
Languages : en
Pages : 242
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Book Description
Since the notion was introduced by Gromov in the 1980s, hyperbolicity of groups and spaces has played a significant role in geometric group theory; hyperbolic groups have good geometric properties that allow us to prove strong results. However, many classes of interest in our exploration of the universe of finitely generated groups contain examples that are not hyperbolic. Thus we wish to go 'beyond hyperbolicity' to find good generalisations that nevertheless permit similarly strong results. This book is the ideal resource for researchers wishing to contribute to this rich and active field. The first two parts are devoted to mini-courses and expository articles on coarse median spaces, semihyperbolicity, acylindrical hyperbolicity, Morse boundaries, and hierarchical hyperbolicity. These serve as an introduction for students and a reference for experts. The topics of the surveys (and more) re-appear in the research articles that make up Part III, presenting the latest results beyond hyperbolicity.
Author: Blake C. Stacey
Publisher: Springer Nature
ISBN: 3030761045
Category : Science
Languages : en
Pages : 119
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Book Description
This book focuses on the Symmetric Informationally Complete quantum measurements (SICs) in dimensions 2 and 3, along with one set of SICs in dimension 8. These objects stand out in ways that have earned them the moniker of "sporadic SICs". By some standards, they are more approachable than the other known SICs, while by others they are simply atypical. The author forays into quantum information theory using them as examples, and the author explores their connections with other exceptional objects like the Leech lattice and integral octonions. The sporadic SICs take readers from the classification of finite simple groups to Bell's theorem and the discovery that "hidden variables" cannot explain away quantum uncertainty. While no one department teaches every subject to which the sporadic SICs pertain, the topic is approachable without too much background knowledge. The book includes exercises suitable for an elective at the graduate or advanced undergraduate level.
Author: Maria Gorelik
Publisher: Springer Science & Business
ISBN: 3319029525
Category : Mathematics
Languages : en
Pages : 281
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Book Description
The volume is the outcome of the conference "Lie superalgebras," which was held at the Istituto Nazionale di Alta Matematica, in 2012. The conference gathered many specialists in the subject, and the talks held provided comprehensive insights into the newest trends in research on Lie superalgebras (and related topics like vertex algebras, representation theory and supergeometry). The book contains contributions of many leading esperts in the field and provides a complete account of the newest trends in research on Lie Superalgebras.
Author: Bernhard Heim
Publisher: Springer
ISBN: 3319113526
Category : Mathematics
Languages : en
Pages : 250
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Book Description
This edited volume presents a collection of carefully refereed articles covering the latest advances in Automorphic Forms and Number Theory, that were primarily developed from presentations given at the 2012 “International Conference on Automorphic Forms and Number Theory,” held in Muscat, Sultanate of Oman. The present volume includes original research as well as some surveys and outlines of research altogether providing a contemporary snapshot on the latest activities in the field and covering the topics of: Borcherds products Congruences and Codes Jacobi forms Siegel and Hermitian modular forms Special values of L-series Recently, the Sultanate of Oman became a member of the International Mathematical Society. In view of this development, the conference provided the platform for scientific exchange and collaboration between scientists of different countries from all over the world. In particular, an opportunity was established for a close exchange between scientists and students of Germany, Oman, and Japan. The conference was hosted by the Sultan Qaboos University and the German University of Technology in Oman.
Author: Yang-Hui He
Publisher: Springer Nature
ISBN: 3030775623
Category : Mathematics
Languages : en
Pages : 214
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Book Description
Can artificial intelligence learn mathematics? The question is at the heart of this original monograph bringing together theoretical physics, modern geometry, and data science. The study of Calabi–Yau manifolds lies at an exciting intersection between physics and mathematics. Recently, there has been much activity in applying machine learning to solve otherwise intractable problems, to conjecture new formulae, or to understand the underlying structure of mathematics. In this book, insights from string and quantum field theory are combined with powerful techniques from complex and algebraic geometry, then translated into algorithms with the ultimate aim of deriving new information about Calabi–Yau manifolds. While the motivation comes from mathematical physics, the techniques are purely mathematical and the theme is that of explicit calculations. The reader is guided through the theory and provided with explicit computer code in standard software such as SageMath, Python and Mathematica to gain hands-on experience in applications of artificial intelligence to geometry. Driven by data and written in an informal style, The Calabi–Yau Landscape makes cutting-edge topics in mathematical physics, geometry and machine learning readily accessible to graduate students and beyond. The overriding ambition is to introduce some modern mathematics to the physicist, some modern physics to the mathematician, and machine learning to both.
Author: Alexei Skorobogatov
Publisher: Cambridge University Press
ISBN: 1107616123
Category : Mathematics
Languages : en
Pages : 470
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Book Description
Lecture notes and research articles on the use of torsors and étale homotopy in algebraic and arithmetic geometry.
Author: Joppe Bos
Publisher:
ISBN: 1108848427
Category : Language Arts & Disciplines
Languages : en
Pages : 402
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Book Description
The area of computational cryptography is dedicated to the development of effective methods in algorithmic number theory that improve implementation of cryptosystems or further their cryptanalysis. This book is a tribute to Arjen K. Lenstra, one of the key contributors to the field, on the occasion of his 65th birthday, covering his best-known scientific achievements in the field. Students and security engineers will appreciate this no-nonsense introduction to the hard mathematical problems used in cryptography and on which cybersecurity is built, as well as the overview of recent advances on how to solve these problems from both theoretical and practical applied perspectives. Beginning with polynomials, the book moves on to the celebrated Lenstra-Lenstra-Lovász lattice reduction algorithm, and then progresses to integer factorization and the impact of these methods to the selection of strong cryptographic keys for usage in widely used standards.
Author: Bangming Deng
Publisher: Cambridge University Press
ISBN: 1139789937
Category : Mathematics
Languages : en
Pages : 217
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Book Description
The theory of Schur–Weyl duality has had a profound influence over many areas of algebra and combinatorics. This text is original in two respects: it discusses affine q-Schur algebras and presents an algebraic, as opposed to geometric, approach to affine quantum Schur–Weyl theory. To begin, various algebraic structures are discussed, including double Ringel–Hall algebras of cyclic quivers and their quantum loop algebra interpretation. The rest of the book investigates the affine quantum Schur–Weyl duality on three levels. This includes the affine quantum Schur–Weyl reciprocity, the bridging role of affine q-Schur algebras between representations of the quantum loop algebras and those of the corresponding affine Hecke algebras, presentation of affine quantum Schur algebras and the realisation conjecture for the double Ringel–Hall algebra with a proof of the classical case. This text is ideal for researchers in algebra and graduate students who want to master Ringel–Hall algebras and Schur–Weyl duality.
Author: Cheryl E. Praeger
Publisher: Cambridge University Press
ISBN: 131699905X
Category : Mathematics
Languages : en
Pages : 338
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Book Description
Permutation groups, their fundamental theory and applications are discussed in this introductory book. It focuses on those groups that are most useful for studying symmetric structures such as graphs, codes and designs. Modern treatments of the O'Nan–Scott theory are presented not only for primitive permutation groups but also for the larger families of quasiprimitive and innately transitive groups, including several classes of infinite permutation groups. Their precision is sharpened by the introduction of a cartesian decomposition concept. This facilitates reduction arguments for primitive groups analogous to those, using orbits and partitions, that reduce problems about general permutation groups to primitive groups. The results are particularly powerful for finite groups, where the finite simple group classification is invoked. Applications are given in algebra and combinatorics to group actions that preserve cartesian product structures. Students and researchers with an interest in mathematical symmetry will find the book enjoyable and useful.
