Volume 28
Part of Acta Numerica
DATE PUBLISHED: October 2019AVAILABILITY: In stock FORMAT: HardbackISBN: 9781108478687
Acta Numerica is an annual publication containing invited survey papers by leading researchers in numerical mathematics and scientific computing. The papers present overviews of recent developments in their area and provide 'state of the art' techniques and analysis.
The latest issue of the leading review in mathematics as measure by Impact factor
Outstanding contributors provide state-of-art surveys in important topics of contemporary interest
Broad range of fields from data-driven science, to engineering, to computational physics
1. Solving inverse problems using data-driven models Simon Arridge, Peter Maass, Ozan Oktem, and Carola-Bibiane Schonlieb
2. Numerical analysis of hemivariational inequalities in contact mechanics Weimin Han and Mircea Sofonea
3. Derivative-free optimization methods Jeffrey Larson, Matt Menickelly, and Stefan M. Wild
4. Numerical methods for Kohn-Sham density functional theory Lin Lin, Jianfeng Lu, and Lexing Ying
5. Approximation algorithms in combinatorial scientific computing Alex Pothen, S.M. Ferdous, and Fredrik Manne
6. Data assimilation: the Schrodinger perspective Sebastian Reich.
Part of Cambridge Studies in Advanced Mathematics
DATE PUBLISHED: September 2018
AVAILABILITY: In stock FORMAT: Multiple copy packISBN: 9781108697934
This two-volume book provides a self-contained introduction to the theory and application of automorphic forms, using examples to illustrate several critical analytical concepts surrounding and supporting the theory of automorphic forms. The featured critical results, which are proven carefully and in detail, include: discrete decomposition of cuspforms, meromorphic continuation of Eisenstein series, spectral decomposition of pseudo-Eisenstein series, and automorphic Plancherel theorem in Volume 1; and automorphic Green's functions, metrics and topologies on natural function spaces, unbounded operators, vector-valued integrals, vector-valued holomorphic functions, and asymptotics in Volume 2. The book treats three instances, starting with some small unimodular examples, followed by adelic GL2, and finally GLn. With numerous proofs and extensive examples, this classroom-tested introductory text is meant for a second-year or advanced graduate course in automorphic forms, and also as a resource for researchers working in automorphic forms, analytic number theory, and related fields.
Provides an extensive and self-contained treatment of analytical aspects of automorphic forms
Provides a deep exploration of three different examples with varying degrees of complexity and generality, allowing a gradual approach to multi-faceted and highly technical issues
Collects the most important analytical ideas and proofs in the theory of automorphic forms
Volume 1:
1. Four small examples
2. The quotient Z+GL2(k)/GL2(A)
3. SL3(Z), SL5(Z)
4. Invariant differential operators
5. Integration on quotients
6. Action of G on function spaces on G
7. Discrete decomposition of cuspforms
8. Moderate growth functions, theory of the constant term
9. Unbounded operators on Hilbert spaces
10. Discrete decomposition of pseudo-cuspforms
11. Meromorphic continuation of Eisenstein series
12. Global automorphic Sobolev spaces, Green's functions
13. Examples ? topologies on natural function spaces
14. Vector-valued integrals
15. Differentiable vector-valued functions
16. Asymptotic expansions.
Volume 2:
1. Unbounded operators on Hilbert spaces
2. Discrete decomposition of pseudo-cuspforms
3. Meromorphic continuation of Eisenstein series
4. Global automorphic Sobolev spaces, Green's functions
5. Examples ? topologies on natural function spaces
6. Vector-valued integrals
7. Differentiable vector-valued functions
8. Asymptotic expansions.
Part of London Mathematical Society Lecture Note Series
PUBLICATION PLANNED FOR: March 2020A
VAILABILITY: Not yet published - available from March 2020
FORMAT: Paperback ISBN: 9781108790918
Wigner'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.
Contains a brief description of all necessary facts from the basic theory, making the book accessible for graduate students and non-expert researchers
Describes connections between different branches of mathematics, including incidence geometry, graph theory and quantum mechanics
Creates a unified approach by applying geometric methods to preserver problems in quantum mechanics
Introduction
1. Two lattices
2. Geometric transformations of Grassmannians
3. Lattices of closed subspaces
4. Wigner's theorem and its generalizations
5. Compatibility relation
6. Applications
References
Index.
Part of Encyclopedia of Mathematics and its Applications
PUBLICATION PLANNED FOR: May 2020
AVAILABILITY: Not yet published - available from May 2020
FORMAT: HardbackISBN: 9781108489584
Regular polytopes and their symmetry have a long history stretching back two and a half millennia, to the classical regular polygons and polyhedra. Much of modern research focuses on abstract regular polytopes, but significant recent developments have been made on the geometric side, including the exploration of new topics such as realizations and rigidity, which offer a different way of understanding the geometric and combinatorial symmetry of polytopes. This is the first comprehensive account of the modern geometric theory, and includes a wide range of applications, along with new techniques. While the author explores the subject in depth, his elementary approach to traditional areas such as finite reflexion groups makes this book suitable for beginning graduate students as well as more experienced researchers.
Provides the first comprehensive coverage of the modern geometric theory
Uses an elementary approach to topics and collects basic theory in one place, making it suitable for graduate students
Introduces new techniques for the use of researchers
Foreword
Part I. Regular Polytopes:
1. Euclidean space
2. Abstract regular polytopes
3. Realizations of symmetric sets
4. Realizations of polytopes
5. Operations and constructions
6. Rigidity
Part II. Polytopes of Full Rank:
7. Classical regular polytopes
8. Non-classical polytopes
Part III. Polytopes of Nearly Full Rank:
9. General families
10. Three-dimensional apeirohedra
11. Four-dimensional polyhedra
12. Four-dimensional apeirotopes
13. Higher-dimensional cases
Part IV. Miscellaneous Polytopes:
14. Gosset?Elte polytopes
15. Locally toroidal polytopes
16. A family of 4-polytopes
17. Two families of 5-polytopes
Afterword
References
Symbol index
Author index
Subject index.
Volume 1
Part of Cambridge Tracts in Mathematics
PUBLICATION PLANNED FOR: April 2020
AVAILABILITY: Not yet published - available from April 2020
FORMAT: HardbackISBN: 9781108485449
This book shows how operator theory interacts with function theory in one and several variables. The authors develop the theory in detail, leading the reader to the cutting edge of contemporary research. It starts with a treatment of the theory of bounded holomorphic functions on the unit disc. Model theory and the network realization formula are used to solve Nevanlinna-Pick interpolation problems, and the same techniques are shown to work on the bidisc, the symmetrized bidisc, and other domains. The techniques are powerful enough to prove the Julia-Caratheodory theorem on the bidisc, Lempert's theorem on invariant metrics in convex domains, the Oka extension theorem, and to generalize Loewner's matrix monotonicity results to several variables. In Part II, the book gives an introduction to non-commutative function theory, and shows how model theory and the network realization formula can be used to understand functions of non-commuting matrices.
Shows how function theory on the unit disc, properly formulated, can transfer to the bidisc, and other domains in several complex variables
Illustrates the power of network realization formulas, even in the non-commutative setting
Provides a self-contained introduction to non-commutative function theory
Part I. Commutative Theory:
1. The origins of operator-theoretic approaches to function theory
2. Operator analysis on D: model formulas, lurking Isometries, and positivity arguments
3. Further development of models on the disc
4. Operator analysis on D2
5. Caratheodory-Julia theory on the disc and the bidisc
6. Herglotz and Nevanlinna representations in several variables
7. Model theory on the symmetrized bidisc
8. Spectral sets: three case studies
9. Calcular norms
10. Operator monotone functions
Part II. Non-Commutative Theory:
11. Motivation for non-commutative functions
12. Basic properties of non-commutative functions
13. Montel theorems
14. Free holomorphic functions
15. The implicit function theorem
16. Noncommutative functional calculus
Notation.
Part of New Mathematical Monographs
PUBLICATION PLANNED FOR: June 2020
AVAILABILITY: Not yet published - available from June 2020
FORMAT: HardbackISBN: 9781108428095
The theory of unitary group representations began with finite groups, and blossomed in the twentieth century both as a natural abstraction of classical harmonic analysis, and as a tool for understanding various physical phenomena. Combining basic theory and new results, this monograph is a fresh and self-contained exposition of group representations and harmonic analysis on solvable Lie groups. Covering a range of topics from stratification methods for linear solvable actions in a finite-dimensional vector space, to complete proofs of essential elements of Mackey theory and a unified development of the main features of the orbit method for solvable Lie groups, the authors provide both well-known and new examples, with a focus on those relevant to contemporary applications. Clear explanations of the basic theory make this an invaluable reference guide for graduate students as well as researchers.
Concrete and example-based exposition is accessible to advanced graduate students and non-specialists
Contains the first self-contained presentation of the Auslander?Kostant theory
Includes a new layer-wise description of the structure of the orbit space for any finite-dimensional linear solvable action, which has various potential applications
1. Basic theory of solvable Lie algebras and Lie groups
2. Stratification of an orbit space
3. Unitary representations
4. Coadjoint orbits and polarizations
5. Irreducible unitary representations
6. Plancherel formula and related topics
List of notations
Bibliography
Index.
Part of Cambridge Studies in Advanced Mathematics
PUBLICATION PLANNED FOR: May 2020
AVAILABILITY: Not yet published - available from May 2020
FORMAT: HardbackISBN: 9781108489621
Through the fundamental work of Deligne and Lusztig in the 1970s, further developed mainly by Lusztig, the character theory of reductive groups over finite fields has grown into a rich and vast area of mathematics. It incorporates tools and methods from algebraic geometry, topology, combinatorics and computer algebra, and has since evolved substantially. With this book, the authors meet the need for a contemporary treatment, complementing in core areas the well-established books of Carter and Digne?Michel. Focusing on applications in finite group theory, the authors gather previously scattered results and allow the reader to get to grips with the large body of literature available on the subject, covering topics such as regular embeddings, the Jordan decomposition of characters, d-Harish?Chandra theory and Lusztig induction for unipotent characters. Requiring only a modest background in algebraic geometry, this useful reference is suitable for beginning graduate students as well as researchers.
Provides one convenient reference for widely scattered results to help readers to get to grips with the vast range of literature on the subject
Discusses a rapidly evolving area with many applications
Goes beyond earlier treatments and is the first book to treat the subject so comprehensively
1. Reductive groups and Steinberg maps
2. Lusztig's classification of irreducible characters
3. Harish?Chandra theories
4. Unipotent characters
Appendix. Further reading and open questions
References
Index.
Part of Cambridge Tracts in Mathematics
PUBLICATION PLANNED FOR: June 2020
AVAILABILITY: Not yet published - available from June 2020
FORMAT: HardbackISBN: 9781108497404
Intersection theory has played a prominent role in the study of closed symplectic 4-manifolds since Gromov's famous 1985 paper on pseudoholomorphic curves, leading to myriad beautiful rigidity results that are either inaccessible or not true in higher dimensions. Siefring's recent extension of the theory to punctured holomorphic curves allowed similarly important results for contact 3-manifolds and their symplectic fillings. Based on a series of lectures for graduate students in topology, this book begins with an overview of the closed case, and then proceeds to explain the essentials of Siefring's intersection theory and how to use it, and gives some sample applications in low-dimensional symplectic and contact topology. The appendices provide valuable information for researchers, including a concise reference guide on Siefring's theory and a self-contained proof of a weak version of the Micallef?White theorem.
Presents an accessible introduction to the intersection theory of punctured holomorphic curves and its applications
Features self-contained proofs of the similarity principle and positivity of intersections, some of which have not appeared elsewhere in the literature
Includes a 'quick reference' appendix summarizing the main results needed to use the intersection theory in applications
Introduction
1. Closed holomorphic curves in symplectic 4-manifolds
2. Intersections, ruled surfaces and contact boundaries
3. Asymptotics of punctured holomorphic curves
4. Intersection theory for punctured holomorphic curves
5. Symplectic fillings of planar contact 3-manifolds
Appendix A. Properties of pseudoholomorphic curves
Appendix B. Local positivity of intersections
Appendix C. A quick survey of Siefring's intersection theory
References
Index.