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Author: Mark Pankov
Publisher: Cambridge University Press
Published: 2020-01-16
Total Pages: 154
ISBN-13: 1108790917
DOWNLOAD EBOOKAn accessible introduction to the geometric approach to Wigner's theorem and its role in quantum mechanics.
Author: Mark Pankov
Publisher: Cambridge University Press
Published: 2020-01-16
Total Pages: 155
ISBN-13: 1108848397
DOWNLOAD EBOOKWigner's theorem is a fundamental part of the mathematical formulation of quantum mechanics. The theorem characterizes unitary and anti-unitary operators as symmetries of quantum mechanical systems, and is a key result when relating preserver problems to quantum mechanics. At the heart of this book is a geometric approach to Wigner-type theorems, unifying both classical and more recent results. Readers are initiated in a wide range of topics from geometric transformations of Grassmannians to lattices of closed subspaces, before moving on to a discussion of applications. An introduction to all the key aspects of the basic theory is included as are plenty of examples, making this book a useful resource for beginning graduate students and non-experts, as well as a helpful reference for specialist researchers.
Author: David Jordan
Publisher: Cambridge University Press
Published: 2023-08-17
Total Pages: 407
ISBN-13: 1009097350
DOWNLOAD EBOOKExpanding upon the material delivered during the LMS Autumn Algebra School 2020, this volume reflects the fruitful connections between different aspects of representation theory. Each survey article addresses a specific subject from a modern angle, beginning with an exploration of the representation theory of associative algebras, followed by the coverage of important developments in Lie theory in the past two decades, before the final sections introduce the reader to three strikingly different aspects of group theory. Written at a level suitable for graduate students and researchers in related fields, this book provides pure mathematicians with a springboard into the vast and growing literature in each area.
Author: Aurelian Gheondea
Publisher: Cambridge University Press
Published: 2022-07-28
Total Pages: 511
ISBN-13: 1108969038
DOWNLOAD EBOOKPresents a modern, readable introduction to spaces with indefinite inner product and their operator theory.
Author: Vladimir Dotsenko
Publisher: Cambridge University Press
Published: 2023-08-31
Total Pages: 187
ISBN-13: 1108965644
DOWNLOAD EBOOKCovering an exceptional range of topics, this text provides a unique overview of the Maurer-Cartan methods in algebra, geometry, topology, and mathematical physics. It offers a new conceptual treatment of the twisting procedure, guiding the reader through various versions with the help of plentiful motivating examples for graduate students as well as researchers. Topics covered include a novel approach to the twisting procedure for operads leading to Kontsevich graph homology and a description of the twisting procedure for (homotopy) associative algebras or (homotopy) Lie algebras using the biggest deformation gauge group ever considered. The book concludes with concise surveys of recent applications in areas including higher category theory and deformation theory.
Author: Jeffrey Shallit
Publisher: Cambridge University Press
Published: 2022-09-30
Total Pages: 376
ISBN-13: 1108786979
DOWNLOAD EBOOKAutomatic sequences are sequences over a finite alphabet generated by a finite-state machine. This book presents a novel viewpoint on automatic sequences, and more generally on combinatorics on words, by introducing a decision method through which many new results in combinatorics and number theory can be automatically proved or disproved with little or no human intervention. This approach to proving theorems is extremely powerful, allowing long and error-prone case-based arguments to be replaced by simple computations. Readers will learn how to phrase their desired results in first-order logic, using free software to automate the computation process. Results that normally require multipage proofs can emerge in milliseconds, allowing users to engage with mathematical questions that would otherwise be difficult to solve. With more than 150 exercises included, this text is an ideal resource for researchers, graduate students, and advanced undergraduates studying combinatorics, sequences, and number theory.
Author: Caterina Campagnolo
Publisher: Cambridge University Press
Published: 2022-11-30
Total Pages: 171
ISBN-13: 100918329X
DOWNLOAD EBOOKAn overview of bounded cohomology and simplicial volume covering the basics of the subject and recent research directions.
Author: Alexander A. Ivanov
Publisher: Cambridge University Press
Published: 2023-08-17
Total Pages: 584
ISBN-13: 1009338056
DOWNLOAD EBOOKCovering, arguably, one of the most attractive and mysterious mathematical objects, the Monster group, this text strives to provide an insightful introduction and the discusses the current state of the field. The Monster group is related to many areas of mathematics, as well as physics, from number theory to string theory. This book cuts through the complex nature of the field, highlighting some of the mysteries and intricate relationships involved. Containing many meaningful examples and a manual introduction to the computer package GAP, it provides the opportunity and resources for readers to start their own calculations. Some 20 experts here share their expertise spanning this exciting field, and the resulting volume is ideal for researchers and graduate students working in Combinatorial Algebra, Group theory and related areas.
Author: Felix Fischer
Publisher: Cambridge University Press
Published: 2024-06-13
Total Pages: 305
ISBN-13: 1009490532
DOWNLOAD EBOOKThis volume contains surveys of current research directions in combinatorics written by leading researchers in their fields.
Author: R. A. Bailey
Publisher: Cambridge University Press
Published: 2024-05-30
Total Pages: 452
ISBN-13: 1009465945
DOWNLOAD EBOOKThis collection of four short courses looks at group representations, graph spectra, statistical optimality, and symbolic dynamics, highlighting their common roots in linear algebra. It leads students from the very beginnings in linear algebra to high-level applications: representations of finite groups, leading to probability models and harmonic analysis; eigenvalues of growing graphs from quantum probability techniques; statistical optimality of designs from Laplacian eigenvalues of graphs; and symbolic dynamics, applying matrix stability and K-theory. An invaluable resource for researchers and beginning Ph.D. students, this book includes copious exercises, notes, and references.
