Part of Mathematical Sciences Research Institute Publications
Not yet published - available from July 2022
FORMAT: Hardback ISBN: 9781009123297
This comprehensive text focuses on the homotopical technology in use at the forefront of modern algebraic topology. Following on from a standard introductory algebraic topology sequence, it will provide students with a comprehensive background in spectra and structured ring spectra. Each chapter is an extended tutorial by a leader in the field, offering the first really accessible treatment of the modern construction of the stable category in terms of both model categories of point-set diagram spectra and infinity-categories. It is one of the only textbook sources for operadic algebras, structured ring spectra, and Bousfield localization, which are now basic techniques in the field, and the book provides a rare expository treatment of spectral algebraic geometry. Together the contributors ? Emily Riehl, Daniel Dugger, Clark Barwick, Michael A. Mandell, Birgit Richter, Tyler Lawson, and Charles Rezk ? offer a complete, authoritative source to learn the foundations of this vibrant area.
Explains cutting-edge research on the foundations of spectra, stable categories, and structured ring spectra at a level appropriate for graduate students
Chapters are written by some of the most prominent researchers in the area today
Integrated treatment of model categories (point-set models) and infinity-categories (homotopy-coherent models) offers a bridge between the classical literature and modern techniques
1. Introduction Andrew J. Blumberg, Teena Gerhardt, and Michael A. Hill
2. Homotopical categories: from model categories to (∞,1)-categories Emily Riehl
3. Stable categories and spectra via model categories Daniel Dugger
4. Stable homotopy theory via ∞-categories Clark Barwick
5. Operads and operadic algebras in homotopy theory Michael A. Mandell
6. Commutative ring spectra Birgit Richter
7. An introduction to Bousfield localization Tyler Lawson
8. Spectral algebraic geometry Charles Rezk
Bibliography
Index.
Not yet published - available from August 2022
FORMAT: Hardback ISBN: 9781108833271
FORMAT: Paperback ISBN: 9781108978262
Lovers of mathematics, young and old, professional and amateur, will enjoy this book. It is mathematics with fun: a collection of attractive problems that will delight and test readers. Many of the problems are drawn from the large number that have entertained and challenged students, guests and colleagues over the years during afternoon tea. The problems have their roots in many areas of mathematics. They vary greatly in difficulty: some are very easy, but most are far from trivial, and quite a few rather hard. Many provide substantial and surprising results that form the tip of an iceberg, providing an introduction to an important topic. To enjoy and appreciate the problems, readers should browse the book choosing one that looks particularly enticing, and think about it on and off for a while before resorting to the hint or the solution. Follow threads for an enjoyable and enriching journey through mathematics.
Aimed at a broad audience ranging from professional mathematicians to interested amateurs
Introduces many important areas of mathematics via an entertaining mix of problems
Includes over 100 problems, with helpful hints and solutions
Preface
1. Problems
2. Hints
3. Solutions.
Not yet published - available from June 2022
FORMAT: Hardback ISBN: 9781316518953
FORMAT: Paperback ISBN: 9781009001922
This book introduces algebraic number theory through the problem of generalizing 'unique prime factorization' from ordinary integers to more general domains. Solving polynomial equations in integers leads naturally to these domains, but unique prime factorization may be lost in the process. To restore it, we need Dedekind's concept of ideals. However, one still needs the supporting concepts of algebraic number field and algebraic integer, and the supporting theory of rings, vector spaces, and modules. It was left to Emmy Noether to encapsulate the properties of rings that make unique prime factorization possible, in what we now call Dedekind rings. The book develops the theory of these concepts, following their history, motivating each conceptual step by pointing to its origins, and focusing on the goal of unique prime factorization with a minimum of distraction or prerequisites. This makes a self-contained easy-to-read book, short enough for a one-semester course.
Provides a short, self-contained, and readable introduction to the field for beginners, reviewing even basic linear algebra from the viewpoint of number theory
Integrates historical information into the mathematical development, conveying to students where concepts come from and dispelling any mystery around mathematical terms
Includes approximately 300 timely and interesting exercises, testing students' understanding as new concepts occur, but leading to new results
Prerequisites are only a familiarity with the concept of matrices, as well as proofs and abstraction
An ideal main text for a course in algebraic number theory, or as supplementary material for a course in abstract algebra or number theory
Preface
1. Euclidean arithmetic
2. Diophantine arithmetic
3. Quadratic forms
4. Rings and fields
5. Ideals
6. Vector spaces
7. Determinant theory
8. Modules
9. Ideals and prime factorization
References
Index.
Part of Cambridge Studies in Advanced Mathematics
Not yet published - available from July 2022
FORMAT: Hardback ISBN: 9781009232470
This comprehensive introduction to functional analysis covers both the abstract theory and applications to spectral theory, the theory of partial differential equations, and quantum mechanics. It starts with the basic results of the subject and progresses towards a treatment of several advanced topics not commonly found in functional analysis textbooks, including Fredholm theory, form methods, boundary value problems, semigroup theory, trace formulas, and a mathematical treatment of states and observables in quantum mechanics. The book is accessible to graduate students with basic knowledge of topology, real and complex analysis, and measure theory. With carefully written out proofs, more than 300 problems, and appendices covering the prerequisites, this self-contained volume can be used as a text for various courses at the graduate level and as a reference text for researchers in the field.
Presents all proofs in great detail, providing students with an accessible introduction to the field
Offers comprehensive coverage of applications
Includes a number of advanced results with proofs not commonly found in functional analysis textbooks
Part I. Banach Spaces:
1. Banach spaces
2. The classical Banach spaces
3. Hilbert spaces
4. Duality
Part II. Operators on Banach Spaces:
5. Bounded operators
6. Spectral theory
7. Compact operators
Part III. Operators on Hilbert Spaces:
8. Bounded operators on Hilbert spaces
9. The spectral theorem for bounded normal operators
10. The spectral theorem for unbounded normal operators
Part IV. Applications to Partial Differential Equations:
11. Boundary value problems
12. Forms
13. Semigroups of linear operators
Part V. Applications to Quantum Mechanics:
14. Trace class operators
15. States and observables
Appendix A. Zorn's lemma
Appendix B. Tensor products
Appendix C. Topological spaces
Appendix D. Metric spaces
Appendix E. Measure spaces
Appendix F. Integration
Appendix G. Notes
Bibliography
Index.
Part of New Mathematical Monographs
Not yet published - available from July 2022
FORMAT: Hardback ISBN: 9781108831963
The theory of Bruhat?Tits buildings is an important topic in number theory, representation theory, and algebraic geometry. This book, the first in English on the subject, gives a comprehensive account of Bruhat?Tits theory for discretely valued Henselian fields. It can serve both as a reference for researchers in the field and as a thorough introduction for graduate students and early career mathematicians. Part I of the book begins with a review of relevant background material before proceeding to give a complete, detailed, and motivated treatment of the core theory. For more experienced readers looking to learn the essentials for use in their own work, there is also an axiomatic summary of Bruhat?Tits theory that suffices for the main applications. Part II treats modern topics that have become important at the cutting edge of research, while the appendices contain further details on more specialized background material.
A comprehensive up-to-date account including the latest developments unavailable anywhere else in book form
Begins with an extended introduction to the theory, making it suitable for graduate students and other newcomers to the field
Includes a short section giving a summary and overview of the basics, for use by researchers who only need to apply the theory
Introduction
Part I. Background and Review:
1. Affine root systems and abstract buildings
2. Algebraic groups
Part II. Bruhat ?Tits Theory:
3. Examples: Quasi-split groups of rank 1
4. Overview and summary of Bruhat?Tits theory
5. Bruhat, Cartan, and Iwasawa decompositions
6. The apartment
7. The Bruhat?Tits building for a valuation of the root datum
8. Integral models
9. Unramified descent
Part III. Additional Developments:
10. Residue field f of dimension ? 1
11. The buildings of classical groups via lattice chains
12. Component groups of integral models
13. Finite group actions and tamely ramified descent
14. Moy?Prasad filtrations
15. Functorial properties
Part IV. Applications:
16. Classification of maximal unramified tori (d'apres DeBacker)
17. Classification of tamely ramified maximal tori
18. The volume formula
Part V. Appendices: A. Operations on integral models
B. Integral models of tori
C. Integral models of root subgroups
References
Index.
Part of London Mathematical Society Lecture Note Series
Not yet published - available from July 2022
FORMAT: Paperback ISBN: 9781009096225
This volume contains eight survey articles by the invited speakers of the 29th British Combinatorial Conference, held at Lancaster University in July 2022. Each article provides an overview of recent developments in a current hot research topic in combinatorics. These topics span graphs and hypergraphs, Latin squares, linear programming, finite fields, extremal combinatorics, Ramsey theory, graph minors and tropical geometry. The authors are among the world's foremost researchers on their respective topics but their surveys are aimed at nonspecialist readers: they are written clearly with little prior knowledge assumed and with pointers to the wider literature. Taken together these surveys give a snapshot of the research frontier in contemporary combinatorics, making the latest developments accessible to researchers and graduate students in mathematics and theoretical computer science with an interest in combinatorics and helping them to keep abreast of the field.
Includes eight survey articles on current hot topics by leading researchers in combinatorics
Provides a snapshot of the research frontier in the field
Broadly accessible to mathematicians and theoretical computer scientists
Preface Anthony Nixon and Sean Prendiville
1. Fair partitions Noga Alon
2. Hypergraph Turan Problems in \ell_2-norm Jozsef Balogh, Felix Christian Clemen and Bernard Lidicky
3. Circuit imbalance measures and linear programming Farbod Ekbatani, Bento Natura and Laszlo A. Vegh
4. Intersection problems in extremal combinatorics: theorems, techniques and questions old and new David Ellis
5. Finite geometry and extremal graph theory Valentina Pepe
6. Rainbow subgraphs and their applications Alexey Pokrovskiy
7. Explicit bounds for graph minors Paul Wollan
8. Convex and combinatorial tropical geometry Josephine Yu.
Part of London Mathematical Society Lecture Note Series
Not yet published - available from October 2022
FORMAT: Paperback ISBN: 9781009180856
Written in celebration of Miles Reid's 70th birthday, this illuminating volume contains 11 papers by leading mathematicians in and around algebraic geometry, broadly related to the themes and interests of Reid's varied career. Just as in Reid's own scientific output, some of the papers give comprehensive accounts of the state of the art of foundational matters, while others give expositions of subject areas or techniques in concrete terms. Reid has been one of the major expositors of algebraic geometry and a great influence on many in this field ? this book hopes to inspire a new generation of graduate students and researchers in his tradition.
Discusses a broad range of contemporary research and recent advances related to Miles Reid's interests and career
Written by a cross-section of Reid's colleagues and collaborators spanning his career, all leading mathematicians at the forefront of algebraic geometry research
Includes concrete analysis of a foundational case of mirror symmetry, as well as other topics ranging from classical geometry to new classes of variety
Happy Birthday Hamid Abban, Gavin Brown, Alexander Kasprzyk, Shigefumi Mori
1. On stable cohomology of central extensions of elementary abelian groups Fedor Bogomolov, Christian Bohning, Alena Pirutka
2. On projective 3-folds of general type with p_g = 2 Meng Chen, Yong Hu, Matteo Penegini
3. 15-nodal quartic surfaces. Part I: quintic del Pezzo surfaces and congruences of lines in P^3 Igor V. Dolgachev
4. Mori flips, cluster algebras and diptych varieties without unprojection Tom Ducat
5. The mirror of the cubic surface Mark Gross, Paul Hacking, Sean Keel, Bernd Siebert
6. Semi-orthogonal decomposition of a derived category of a 3-fold with an ordinary double point Yujiro Kawamata
7. Duality and normalization, variations on a theme of Serre and Reid Janos Kollar, Hailong Dao
8. Rationality of Q-Fano threefolds of large Fano index Yuri Prokhorov
9. An exceptional locus in the perfect compacti cation of A_g Nicholas Shepherd-Barron, John Armstrong
10. Variation of stable Birational types of Hypersurfaces Evgeny Shinder, Claire Voisin
11. Triangle varieties and surface decomposition of hyper-Kahler manifolds Claire Voisin.
Part of London Mathematical Society Lecture Note Series
Not yet published - available from November 2022
FORMAT: Paperback ISBN: 9781009054850
The Stacks Project Expository Collection (SPEC) compiles expository articles in advanced algebraic geometry, intended to bring graduate students and researchers up to speed on recent developments in the geometry of algebraic spaces and algebraic stacks. The articles in the text make explicit in modern language many results, proofs, and examples that were previously only implicit, incomplete, or expressed in classical terms in the literature. Where applicable this is done by explicitly referring to the Stacks project for preliminary results. Topics include the construction and properties of important moduli problems in algebraic geometry (such as the Deligne?Mumford compactification of the moduli of curves, the Picard functor, or moduli of semistable vector bundles and sheaves), and arithmetic questions for fields and algebraic spaces.
Brings researchers up to speed with recent developments in the geometry of algebraic spaces and algebraic stacks
Presents many classical results using a modern language and using modern techniques
Many steps in proofs usually left implicit or to the reader are backed up with ample references to the Stacks project
List of contributors
Preface
1. Projectivity of the moduli of curves Raymond Cheng, Carl Lian and Takumi Murayama
2. The stack of admissible covers is algebraic Elsa Corniani, Neeraj Deshmukh, Brett Nasserden, Emanuel Reinecke, Nawaz Sultani and Rachel Webb
3. Projectivity of the moduli space of vector bundles on a curve Jarod Alper, Pieter Belmans, Daniel Bragg, Jason Liang and Tuomas Tajakka
4. Boundedness of semistable sheaves Haoyang Guo, Sanal Shivaprasad, Dylan Spence and Yueqiao Wu
5. Theorem of the Base Raymond Cheng, Lena Ji, Matt Larson and Noah Olander
6. Weil restriction for schemes and beyond Lena Ji, Shizhang Li, Patrick McFaddin, Drew Moore and Matthew Stevenson
7. Heights over finitely generated fields Stephen McKean and Soumya Sankar
8. An explicit self-duality Nikolas Kuhn, Devlin Mallory, Vaidehee Thatte and Kirsten Wickelgren
9. Tannakian reconstruction of coalgebroids Yifei Zhao.