Part of Cambridge IISc Series
Date Published: March 2016
format: Hardback
isbn: 9781107148055
Noncommutative mathematics is a significant new trend of mathematics. Initially motivated by the development of quantum physics, the idea of 'making theory noncommutative' has been extended to many areas of pure and applied mathematics. This book is divided into two parts. The first part provides an introduction to quantum probability, focusing on the notion of independence in quantum probability and on the theory of quantum stochastic processes with independent and stationary increments. The second part provides an introduction to quantum dynamical systems, discussing analogies with fundamental problems studied in classical dynamics. The desire to build an extension of the classical theory provides new, original ways to understand well-known 'commutative' results. On the other hand the richness of the quantum mathematical world presents completely novel phenomena, never encountered in the classical setting. This book will be useful to students and researchers in noncommutative probability, mathematical physics and operator algebras.
Provides an introduction to quantum probability
Presents an introduction to quantum dynamical systems
Discusses analogies with fundamental problems studied in classical dynamics
Part of Cambridge Studies in Advanced Mathematics
Publication planned for: November 2016
available from November 2016
format: Hardback
isbn: 9781107153042
K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi?Yau manifolds from various perspectives in eighteen self-contained chapters. It starts with the basics and guides the reader to recent breakthroughs, such as the proof of the Tate conjecture for K3 surfaces and structural results on Chow groups. Powerful general techniques are introduced to study the many facets of K3 surfaces, including arithmetic, homological, and differential geometric aspects. In this context, the book covers Hodge structures, moduli spaces, periods, derived categories, birational techniques, Chow rings, and deformation theory. Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin?Tate, are discussed in general and for K3 surfaces in particular, and each chapter ends with questions and open problems. Based on lectures at the advanced graduate level, this book is suitable for courses and as a reference for researchers.
Includes many proofs and applies techniques from diverse areas
Suitable for coursework or as a reference for researchers
Provides opportunities for further research
Part of London Mathematical Society Student Texts
Publication planned for: November 2016
format: Hardback
isbn: 9781107149243
format: Paperback
isbn: 9781316603529
Hurwitz theory, the study of analytic functions among Riemann surfaces, is a classical field and active research area in algebraic geometry. The subject's interplay between algebra, geometry, topology and analysis is a beautiful example of the interconnectedness of mathematics. This book introduces students to this increasingly important field, covering key topics such as manifolds, monodromy representations and the Hurwitz potential. Designed for undergraduate study, this classroom-tested text includes over 100 exercises to provide motivation for the reader. Also included are short essays by guest writers on how they use Hurwitz theory in their work, which ranges from string theory to non-Archimedean geometry. Whether used in a course or as a self-contained reference for graduate students, this book will provide an exciting glimpse at mathematics beyond the standard university classes.
A self-contained reference on Hurwitz theory which brings together material dispersed across the literature
Demonstrates connections between complex analysis, algebra, geometry, topology, representation theory and physics
Provides everything a geometer needs to offer a course on Hurwitz theory
Part of London Mathematical Society Lecture Note Series
Publication planned for: January 2017
format: Paperback
isbn: 9781316604403
An accessible and panoramic account of the theory of random walks on groups and graphs, stressing the strong connections of the theory with other branches of mathematics, including geometric and combinatorial group theory, potential analysis, and theoretical computer science. This volume brings together original surveys and research-expository papers from renowned and leading experts, many of whom spoke at the workshop 'Groups, Graphs and Random Walks' celebrating the sixtieth birthday of Wolfgang Woess in Cortona, Italy. Topics include: growth and amenability of groups; Schrodinger operators and symbolic dynamics; ergodic theorems; Thompson's group F; Poisson boundaries; probability theory on buildings and groups of Lie type; structure trees for edge cuts in networks; and mathematical crystallography. In what is currently a fast-growing area of mathematics, this book provides an up-to-date and valuable reference for both researchers and graduate students, from which future research activities will undoubtedly stem.
Emphasizes the strong connections between the theory of random walks on groups and graphs and other branches of mathematics
Provides a valuable and up-to-date reference from which future research activities may stem
Offers a panoramic account of recent developments in the field
Part of London Mathematical Society Lecture Note Series
Publication planned for: November 2016
format: Paperback
isbn: 97811075523
Written by leading experts, this book explores several directions of current research at the interface between dynamics and analytic number theory. Topics include Diophantine approximation, exponential sums, Ramsey theory, ergodic theory and homogeneous dynamics. The origins of this material lie in the 'Dynamics and Analytic Number Theory' Easter School held at Durham University in 2014. Key concepts, cutting-edge results, and modern techniques that play an essential role in contemporary research are presented in a manner accessible to young researchers, including PhD students. This book will also be useful for established mathematicians. The areas discussed include ubiquitous systems and Cantor-type sets in Diophantine approximation, flows on nilmanifolds and their connections with exponential sums, multiple recurrence and Ramsey theory, counting and equidistribution problems in homogeneous dynamics, and applications of thin groups in number theory. Both dynamical and 'classical' approaches towards number theoretical problems are also provided.
Discusses a broad range of topics within analytic number theory, dynamics, and related subjects
Leading experts in the field present current state-of-the-art material
Accessible to young researchers, allowing them insight into cutting-edge research
Part of New Mathematical Monographs
Publication planned for: December 2016
format: Hardback
isbn: 9781107163102
Factorization algebras are local-to-global objects that play a role in classical and quantum field theory which is similar to the role of sheaves in geometry: they conveniently organize complicated information. Their local structure encompasses examples like associative and vertex algebras; in these examples, their global structure encompasses Hochschild homology and conformal blocks. In this first volume, the authors develop the theory of factorization algebras in depth, but with a focus upon examples exhibiting their use in field theory, such as the recovery of a vertex algebra from a chiral conformal field theory and a quantum group from Abelian Chern-Simons theory. Expositions of the relevant background in homological algebra, sheaves and functional analysis are also included, thus making this book ideal for researchers and graduates working at the interface between mathematics and physics.
Systematically develops the local-to-global structure of observables of quantum field theory
Treats several examples in depth, including scalar field theory, chiral conformal field theory, current algebras and a topological gauge theory
Includes an exposition of tools such as operads, cosheaves and homological algebra with topological vector spaces