Author: Simone GuttPublisher: Cambridge University Press
ISBN: 9780521615051
Category : Mathematics
Languages : en
Pages : 380
Book Description
An accessible introduction to Poisson geometry suitable for graduate students.
Poisson Geometry, Deformation Quantisation and Group Representations
Author: Simone GuttPublisher: Cambridge University Press
ISBN: 9780521615051
Category : Mathematics
Languages : en
Pages : 380
Book Description
An accessible introduction to Poisson geometry suitable for graduate students.
Deformation Quantization for Actions of $R^d$
Author: Marc Aristide RieffelPublisher: American Mathematical Soc.
ISBN: 0821825755
Category : Mathematics
Languages : en
Pages : 110
Book Description
This work describes a general construction of a deformation quantization for any Poisson bracket on a manifold which comes from an action of R ]d on that manifold. These deformation quantizations are strict, in the sense that the deformed product of any two functions is again a function and that there are corresponding involutions and operator norms. Many of the techniques involved are adapted from the theory of pseudo-differential operators. The construction is shown to have many favorable properties. A number of specific examples are described, ranging from basic ones such as quantum disks, quantum tori, and quantum spheres, to aspects of quantum groups.
Poisson Geometry in Mathematics and Physics
Author: Giuseppe DitoPublisher: American Mathematical Soc.
ISBN: 0821844237
Category : Mathematics
Languages : en
Pages : 330
Book Description
This volume is a collection of articles by speakers at the Poisson 2006 conference. The program for Poisson 2006 was an overlap of topics that included deformation quantization, generalized complex structures, differentiable stacks, normal forms, and group-valued moment maps and reduction.
Poisson Structures
Author: Camille Laurent-GengouxPublisher: Springer Science & Business Media
ISBN: 3642310907
Category : Mathematics
Languages : en
Pages : 470
Book Description
Poisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory. In each one of these contexts, it turns out that the Poisson structure is not a theoretical artifact, but a key element which, unsolicited, comes along with the problem that is investigated, and its delicate properties are decisive for the solution to the problem in nearly all cases. Poisson Structures is the first book that offers a comprehensive introduction to the theory, as well as an overview of the different aspects of Poisson structures. The first part covers solid foundations, the central part consists of a detailed exposition of the different known types of Poisson structures and of the (usually mathematical) contexts in which they appear, and the final part is devoted to the two main applications of Poisson structures (integrable systems and deformation quantization). The clear structure of the book makes it adequate for readers who come across Poisson structures in their research or for graduate students or advanced researchers who are interested in an introduction to the many facets and applications of Poisson structures.
Reversibility in Dynamics and Group Theory
Author: Anthony G. O'FarrellPublisher: Cambridge University Press
ISBN: 1316195767
Category : Mathematics
Languages : en
Pages : 295
Book Description
Reversibility is a thread woven through many branches of mathematics. It arises in dynamics, in systems that admit a time-reversal symmetry, and in group theory where the reversible group elements are those that are conjugate to their inverses. However, the lack of a lingua franca for discussing reversibility means that researchers who encounter the concept may be unaware of related work in other fields. This text is the first to make reversibility the focus of attention. The authors fix standard notation and terminology, establish the basic common principles, and illustrate the impact of reversibility in such diverse areas as group theory, differential and analytic geometry, number theory, complex analysis and approximation theory. As well as showing connections between different fields, the authors' viewpoint reveals many open questions, making this book ideal for graduate students and researchers. The exposition is accessible to readers at the advanced undergraduate level and above.
Recent Advances in Algebraic Geometry
Author: Christopher D. HaconPublisher: Cambridge University Press
ISBN: 131619583X
Category : Mathematics
Languages : en
Pages : 451
Book Description
Contemporary research in algebraic geometry is the focus of this collection, which presents articles on modern aspects of the subject. The list of topics covered is a roll-call of some of the most important and active themes in this thriving area of mathematics: the reader will find articles on birational geometry, vanishing theorems, complex geometry and Hodge theory, free resolutions and syzygies, derived categories, invariant theory, moduli spaces, and related topics, all written by leading experts. The articles, which have an expository flavour, present an overall picture of current research in algebraic geometry, making this book essential for researchers and graduate students. This volume is the outcome of the conference Recent Advances in Algebraic Geometry, held in Ann Arbor, Michigan, to honour Rob Lazarsfeld's many contributions to the subject on the occasion of his 60th birthday.
A Celebration of Algebraic Geometry
Author: Brendan HassettPublisher: American Mathematical Soc.
ISBN: 0821889834
Category : Mathematics
Languages : en
Pages : 614
Book Description
This volume resulted from the conference A Celebration of Algebraic Geometry, which was held at Harvard University from August 25-28, 2011, in honor of Joe Harris' 60th birthday. Harris is famous around the world for his lively textbooks and enthusiastic teaching, as well as for his seminal research contributions. The articles are written in this spirit: clear, original, engaging, enlivened by examples, and accessible to young mathematicians. The articles in this volume focus on the moduli space of curves and more general varieties, commutative algebra, invariant theory, enumerative geometry both classical and modern, rationally connected and Fano varieties, Hodge theory and abelian varieties, and Calabi-Yau and hyperkähler manifolds. Taken together, they present a comprehensive view of the long frontier of current knowledge in algebraic geometry. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
Nonlinear Poisson Brackets
Author: Mikhail Vladimirovich KarasevPublisher: American Mathematical Soc.
ISBN: 9780821845967
Category : Mathematics
Languages : en
Pages : 384
Book Description
This book deals with two old mathematical problems. The first is the problem of constructing an analog of a Lie group for general nonlinear Poisson brackets. The second is the quantization problem for such brackets in the semiclassical approximation (which is the problem of exact quantization for the simplest classes of brackets). These problems are progressively coming to the fore in the modern theory of differential equations and quantum theory, since the approach based on constructions of algebras and Lie groups seems, in a certain sense, to be exhausted. The authors' main goal is to describe in detail the new objects that appear in the solution of these problems. Many ideas of algebra, modern differential geometry, algebraic topology, and operator theory are synthesized here. The authors prove all statements in detail, thus making the book accessible to graduate students.
Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry: Volume 2
Author: Raf CluckersPublisher: Cambridge University Press
ISBN: 1139501739
Category : Mathematics
Languages : en
Pages : 263
Book Description
The development of Maxim Kontsevich's initial ideas on motivic integration has unexpectedly influenced many other areas of mathematics, ranging from the Langlands program over harmonic analysis, to non-Archimedean analysis, singularity theory and birational geometry. This book assembles the different theories of motivic integration and their applications for the first time, allowing readers to compare different approaches and assess their individual strengths. All of the necessary background is provided to make the book accessible to graduate students and researchers from algebraic geometry, model theory and number theory. Applications in several areas are included so that readers can see motivic integration at work in other domains. In a rapidly-evolving area of research this book will prove invaluable. This second volume discusses various applications of non-Archimedean geometry, model theory and motivic integration and the interactions between these domains.
The Maximal Subgroups of the Low-Dimensional Finite Classical Groups
Author: John N. BrayPublisher: Cambridge University Press
ISBN: 0521138604
Category : Mathematics
Languages : en
Pages : 453
Book Description
Classifies the maximal subgroups of the finite groups of Lie type up to dimension 12, using theoretical and computational methods.