Part of London Mathematical Society Lecture Note Series
PUBLICATION PLANNED FOR: April 2020
AVAILABILITY: Not yet published - available from April 2020
FORMAT: Multiple copy pack
ISBN: 9781108785495
Created as a celebration of mathematical pioneer Emma Previato, this comprehensive book highlights the connections between algebraic geometry and integrable systems, differential equations, mathematical physics, and many other areas. The authors, many of whom have been at the forefront of research into these topics for the last decades, have all been influenced by Previato's research, as her collaborators, students, or colleagues. The diverse articles in the book demonstrate the wide scope of Previato's work and the inclusion of several survey and introductory articles makes the text accessible to graduate students and non-experts, as well as researchers. The work is split into two volumes, with the first covering a wide range of areas related to integrable systems, and the second focusing on algebraic geometry and its applications.
PUBLICATION PLANNED FOR: April 2020
AVAILABILITY: Not yet published - available from April 2020
FORMAT: Hardback
ISBN: 9780521899642
This accessible text covers key results in functional analysis that are essential for further study in the calculus of variations, analysis, dynamical systems, and the theory of partial differential equations. The treatment of Hilbert spaces covers the topics required to prove the Hilbert?Schmidt theorem, including orthonormal bases, the Riesz representation theorem, and the basics of spectral theory. The material on Banach spaces and their duals includes the Hahn?Banach theorem, the Krein?Milman theorem, and results based on the Baire category theorem, before culminating in a proof of sequential weak compactness in reflexive spaces. Arguments are presented in detail, and more than 200 fully-worked exercises are included to provide practice applying techniques and ideas beyond the major theorems. Familiarity with the basic theory of vector spaces and point-set topology is assumed, but knowledge of measure theory is not required, making this book ideal for upper undergraduate-level and beginning graduate-level courses.
'This excellent introduction to functional analysis brings the reader at a gentle pace from a rudimentary acquaintance with analysis to a command of the subject sufficient, for example, to start a rigorous study of partial differential equations. The choice and order of topics are very well thought-out, and there is a fine balance between general results and concrete examples and applications.' Charles Fefferman, Princeton University, New Jersey
Part of London Mathematical Society Student Texts
PUBLICATION PLANNED FOR: May 2020
AVAILABILITY: Not yet published - available from May 2020
FORMAT: Hardback
ISBN: 9781108479011
Based on the author's university lecture courses, this book presents the many facets of one of the most important open problems in operator algebra theory. Central to this book is the proof of the equivalence of the various forms of the problem, including forms involving C*-algebra tensor products and free groups, ultraproducts of von Neumann algebras, and quantum information theory. The reader is guided through a number of results (some of them previously unpublished) revolving around tensor products of C*-algebras and operator spaces, which are reminiscent of Grothendieck's famous Banach space theory work. The detailed style of the book and the inclusion of background information make it easily accessible for beginning researchers, Ph.D. students, and non-specialists alike.
Part of Cambridge Studies in Advanced Mathematics
PUBLICATION PLANNED FOR: May 2020
AVAILABILITY: Not yet published - available from May 2020
FORMAT: Hardback
ISBN: 9781108482783
The beginning graduate student in homotopy theory is confronted with a vast literature on spectra that is scattered across books, articles and decades. There is much folklore but very few easy entry points. This comprehensive introduction to stable homotopy theory changes that. It presents the foundations of the subject together in one place for the first time, from the motivating phenomena to the modern theory, at a level suitable for those with only a first course in algebraic topology. Starting from stable homotopy groups and (co)homology theories, the authors study the most important categories of spectra and the stable homotopy category, before moving on to computational aspects and more advanced topics such as monoidal structures, localisations and chromatic homotopy theory. An appendix containing the essential facts on model categories, and the many examples and suggestions for further reading make this is a friendly introduction to an often daunting subject.
Introduction
1. Basics of stable homotopy theory
2. Sequential spectra and the stable homotopy category
3. The suspension and loop functors
4. Triangulated categories
5. Modern categories of spectra
6. Monoidal structures
7. Left Bousfield localisation
Appendix. Model categories
References
Index.
Part of Cambridge Studies in Advanced Mathematics
PUBLICATION PLANNED FOR: May 2020
AVAILABILITY: Not yet published - available from May 2020
FORMAT: Hardback
ISBN: 9781108486897
The Bellman function, a powerful tool originating in control theory, can be used successfully in a large class of difficult harmonic analysis problems and has produced some notable results over the last 30 years. This book by two leading experts is the first devoted to the Bellman function method and its applications to various topics in probability and harmonic analysis. Beginning with basic concepts, the theory is introduced step-by-step starting with many examples of gradually increasing sophistication, culminating with Calderon?Zygmund operators and end-point estimates. All necessary techniques are explained in generality, making this book accessible to readers without specialized training in non-linear PDEs or stochastic optimal control. Graduate students and researchers in harmonic analysis, PDEs, functional analysis, and probability will find this to be an incisive reference, and can use it as the basis of a graduate course.
'I first encountered Bellman functions about 35 years ago when advising engineers striving to minimize the expenditure of diamond chips in silicon grinding. Fifteen years later I was amused to learn that Nazarov, Treil, and Volberg successfully applied similar ideas to a variety of problems in harmonic analysis. Together with Vasyunin (and other analysts), they developed these techniques into a powerful tool which is carefully explained in the present book. The book is written on a level accessible to graduate students and I recommend it to everyone who wishes to join the Bellman functions club.' Mikhail Sodin, Tel Aviv University
Introduction
1. Examples of Bellman functions
2. What you always wanted to know about Stochastic Optimal Control, but were afraid to ask
3. Conformal martingales models. Stochastic and classical Ahlfors-Beurling operators
4. Dyadic models. Application of Bellman technique to upper estimates of singular integrals
5. Application of Bellman technique to the end-point estimates of singular integrals.