Date Published: January 2019
format: Paperback
isbn: 9781316634790
This compact guide presents the key features of general relativity, to support and supplement the presentation in mainstream, more comprehensive undergraduate textbooks, or as a re-cap of essentials for graduate students pursuing more advanced studies. It helps students plot a careful path to understanding the core ideas and basics of differential geometry, as applied to general relativity, without overwhelming them. While the guide doesn't shy away from necessary technicalities, it emphasises the essential simplicity of the main physical arguments. Presuming a familiarity with special relativity (with a brief account in an appendix), it describes how general covariance and the equivalence principle motivate Einstein's theory of gravitation. It then introduces differential geometry and the covariant derivative as the mathematical technology which allows us to understand Einstein's equations of general relativity. The book is supported by numerous worked exampled and problems, and important applications of general relativity are described in an appendix.
Preface
1. Introduction
2. Vectors, tensors and functions
3. Manifolds, vectors and differentiation
4. Energy, momentum and Einstein's equations
Appendix A. Special relativity ? a brief introduction
Appendix B. Solutions to Einstein's equations
Appendix C. Notation
Bibliography
Index.
Part of Cambridge Tracts in Mathematics
Publication planned for: June 2019
format: Hardback
This study of Schrodinger equations with power-type nonlinearity provides a great deal of insight into other dispersive partial differential equations and geometric partial differential equations. It presents important proofs, using tools from harmonic analysis, microlocal analysis, functional analysis, and topology. This includes a new proof of Keel?Tao endpoint Strichartz estimates, and a new proof of Bourgain's result for radial, energy-critical NLS. It also provides a detailed presentation of scattering results for energy-critical and mass-critical equations. This book is suitable as the basis for a one-semester course, and serves as a useful introduction to nonlinear Schrodinger equations for those with a background in harmonic analysis, functional analysis, and partial differential equations.
Preface
1. A first look at the mass-critical problem
2. The cubic NLS in dimensions three and four
3. The energy-critical problem in higher dimensions
4. The mass-critical NLS problem in higher dimensions
5. Low dimensional well-posedness results
References
Index.
Part of London Mathematical Society Lecture Note Series
Publication planned for: June 2019
format: Paperback
isbn: 9781108728744
Every four years leading researchers gather to survey the latest developments in all aspects of group theory. Initially held in St Andrews, these meetings have become the premier forum for group theory across the whole of the UK. Since 1981, the proceedings of 'Groups St Andrews' have provided a regular snapshot of the state-of-the-art in group theory and helped to shape the direction of research in the field. This volume contains papers from the 2017 meeting held in Birmingham. It includes expository articles from the invited speakers, and further surveys contributed by the participants. Topics include: generation of finite simple groups, block theory, fusion systems, algebraic groups, one-relator groups, geometric group theory, and Beauville groups.
Part of Cambridge Monographs on Mathematical Physics
Publication planned for: August 2019
format: Hardback
isbn: 9781108483681
The past decade has seen unprecedented developments in the understanding of relativistic fluid dynamics in and out of equilibrium, with connections to astrophysics, cosmology, string theory, quantum information, nuclear physics and condensed matter physics. Romatschke and Romatschke offer a powerful new framework for fluid dynamics, exploring its connections to kinetic theory, gauge/gravity duality and thermal quantum field theory. Numerical algorithms to solve the equations of motion of relativistic dissipative fluid dynamics as well as applications to various systems are discussed. In particular, the book contains a comprehensive review of the theory background necessary to apply fluid dynamics to simulate relativistic nuclear collisions, including comparisons of fluid simulation results to experimental data for relativistic lead-lead, proton-lead and proton-proton collisions at the Large Hadron Collider (LHC). The book is an excellent resource for students and researchers working in nuclear physics, astrophysics, cosmology, quantum many-body systems and string theory.
Preface
1. Outline, notation, preliminaries
2. Modern theory of fluid dynamics
3. Microscopic theory background
4. Simulating relativistic nuclear collisions
5. Comparison to experimental data
6. Summary and conclusions
Appendices
References
Index.
Publication planned for: July 2019
format: Hardback
isbn: 9781108424912
Classical logic is concerned, loosely, with the behaviour of truths. Epistemic logic similarly is about the behaviour of known or believed truths. Justification logic is a theory of reasoning that enables the tracking of evidence for statements and therefore provides a logical framework for the reliability of assertions. This book, the first in the area, is a systematic account of the subject, progressing from modal logic through to the establishment of an arithmetic interpretation of intuitionistic logic. The presentation is mathematically rigorous but in a style that will appeal to readers from a wide variety of areas to which the theory applies. These include mathematical logic, artificial intelligence, computer science, philosophical logic and epistemology, linguistics, and game theory.
Introduction:
1. Why justification logic?
2. The basics of justification logic
3. The ontology of justifcations
4. Fitting models
5. Sequents and tableaus
6. Realization - how it began
7. Realization - generalized
8. The range of realization
9. Arithmetical completeness and BHK semantics
10. Quantifiers in justification logic
11. Going past modal logic.
availability: Not yet published - available from July 2019