Contemporary Mathematics, Volume: 742
2020; 217 pp; Softcover
MSC: Primary 14; 32; 57; 58;
Print ISBN: 978-1-4704-4792-2
This volume contains the proceedings of the conference A Panorama on Singular Varieties, celebrating the 70th birthday of Le Dong Trang, held from February 7-10, 2017, at the University of Seville, IMUS, Seville, Spain.
The articles cover a wide range of topics in the study of singularities and should be of great value to graduate students and research faculty who have a basic background in the theory of singularities.
Graduate students and researchers interested in algebraic and analytic geometry and singularities.
Part of London Mathematical Society Lecture Note Series
Not yet published - available from July 2020
FORMAT: PaperbackI SBN: 9781108703390
The amount of mathematics invented for number-theoretic reasons is impressive. It includes much of complex analysis, the re-foundation of algebraic geometry on commutative algebra, group cohomology, homological algebra, and the theory of motives. Zeta and L-functions sit at the meeting point of all these theories and have played a profound role in shaping the evolution of number theory. This book presents a big picture of zeta and L-functions and the complex theories surrounding them, combining standard material with results and perspectives that are not made explicit elsewhere in the literature. Particular attention is paid to the development of the ideas surrounding zeta and L-functions, using quotes from original sources and comments throughout the book, pointing the reader towards the relevant history. Based on an advanced course given at Jussieu in 2013, it is an ideal introduction for graduate students and researchers to this fascinating story.
Introduction
1. The Riemann zeta function
2. The zeta function of a Z-scheme of finite type
3. The Weil Conjectures
4. L-functions from number theory
5. L-functions from geometry
6. Motives
Appendix A. Karoubian and monoidal categories
Appendix B. Triangulated categories, derived categories, and perfect complexes
Appendix C. List of exercises
Bibliography
Index.
Part of Cambridge Studies in Advanced Mathematics
Not yet published - available from August 2020
FORMAT: Hardback SBN: 9781108491068
Index theory studies the solutions to differential equations on geometric spaces, their relation to the underlying geometry and topology, and applications to physics. If the space of solutions is infinite dimensional, it becomes necessary to generalise the classical Fredholm index using tools from the K-theory of operator algebras. This leads to higher index theory, a rapidly developing subject with connections to noncommutative geometry, large-scale geometry, manifold topology and geometry, and operator algebras. Aimed at geometers, topologists and operator algebraists, this book takes a friendly and concrete approach to this exciting theory, focusing on the main conjectures in the area and their applications outside of it. A well-balanced combination of detailed introductory material (with exercises), cutting-edge developments and references to the wider literature make this a valuable guide to this active area for graduate students and experts alike.
Introduction
Part I. Background:
1. C*-algebras
2. K-theory for C*-algebras
3. Motivation: positive scalar curvature on tori
Part II. Roe Algebras, Localisation Algebras, and Assembly:
4. Geometric modules
5. Roe algebras
6. Localisation algebras and K-homology
7. Assembly maps and the Baum ?Connes conjecture
Part III. Differential Operators:
8. Elliptic operators and K-homology
9. Products and Poincare duality
10. Applications to algebra, geometry, and topology
Part IV. Higher Index Theory and Assembly:
11. Almost constant bundles
12. Higher index theory for coarsely embeddable spaces
13. Counterexamples
Appendix A. Topological spaces, group actions, and coarse geometry
Appendix B. Categories of topological spaces and homology theories
Appendix C. Unitary representations
Appendix D. Unbounded operators
Appendix E. Gradings
References
Index of symbols
Subject index.
Part of Encyclopedia of Mathematics and its Applications
Not yet published - available from September 2020
FORMAT: Hardback ISBN: 9781107154254
The relatively young theory of structured dependence between stochastic processes has many real-life applications in areas including finance, insurance, seismology, neuroscience, and genetics. With this monograph, the first to be devoted to the modeling of structured dependence between random processes, the authors not only meet the demand for a solid theoretical account but also develop a stochastic processes counterpart of the classical copula theory that exists for finite-dimensional random variables. Presenting both the technical aspects and the applications of the theory, this is a valuable reference for researchers and practitioners in the field, as well as for graduate students in pure and applied mathematics programs. Numerous theoretical examples are included, alongside examples of both current and potential applications, aimed at helping those who need to model structured dependence between dynamic random phenomena.
1. Introduction
Part I. Consistencies:
2. Strong Markov Consistency of Multivariate Markov Families and of Multivariate Markov Processes
3. Consistency of Finite Multivariate Markov Chains
4. Consistency of Finite Multivariate Conditional Markov Chains
5. Consistency of Multivariate Special Semimartingales
Part II. Structures:
6.Strong Markov Family Structures
7. Markov Chain Structures
8. Conditional Markov Chain Structures
9. Special Semimartingale Structures
Part III. Further Developments:
10. Archimedean Survival Processes, their Markov Consistency, and ASP Structures
11. Generalized Multivariate Hawkes Processes: Hawkes Consistency and Hawkes Structures
Part IV. Applications of Stochastic Structures:
12. Applications of Stochastic Structures
Appendix A. Stochastic Analysis: Selected Concepts and Results Used in this Book
Appendix B. Markov Processes and Markov Families
Appendix C. Finite Markov Chains: Auxiliary Technical Framework
Appendix D. Crash Course on Conditional Markov Chains and on Doubly Stochastic Markov Chains
Appendix E. Evolution Systems of Linear Operators, Semigroups of Linear Operators and Their Generator Systems
Appendix F. Martingale Problem: Some New Results Needed in This Book
Appendix G. Function Spaces and Pseudo Differential Operators: Selected Concepts, De finitions and Results Used in this Book
References
Notation Index
Subject Index.
Part of London Mathematical Society Lecture Note Series
Not yet published - available from August 2020
FORMAT: PaperbackISBN: 9781108713184
The interplay of geometry, spectral theory and stochastics has a long and fruitful history, and is the driving force behind many developments in modern mathematics. Bringing together contributions from a 2017 conference at the University of Potsdam, this volume focuses on global effects of local properties. Exploring the similarities and differences between the discrete and the continuous settings is of great interest to both researchers and graduate students in geometric analysis. The range of survey articles presented in this volume give an expository overview of various topics, including curvature, the effects of geometry on the spectrum, geometric group theory, and spectral theory of Laplacian and Schrodinger operators. Also included are shorter articles focusing on specific techniques and problems, allowing the reader to get to the heart of several key topics.
1. Infinite planar graphs with nonnegative combinatorial curvature Bobo Hua and Yanhui Su
2. Curvature calculations for antitrees David Cushing, Shiping Liu, Florentin Munch and Norbert Peyerimho
3. Gromov-Lawson tunnels with estimates Jozef Dodziuk
4. Norm convergence of the resolvent for wild perturbations Colette Anne and Olaf Post
5. Manifolds with Ricci curvature in the Kato class: heat kernel bounds and applications Peter Stollmann and Christian Rose
6. Multiple boundary representations of ă ? harmonic functions on trees Massimo A. Picardello and Wolfgang Woess
7. Internal DLA on Sierpinski gasket graphs Joe P. Chen, Wilfried Huss, Ecaterina Sava-Huss and Alexander Teplyaev
8. Universal lower bounds for Laplacians on weighted graphs Daniel Lenz and Peter Stollmann 9. On Hardy inequalities on graphs and manifolds Matthias Keller, Yehuda Pinchover and Felix Pogorzelski
10. Neumann domains on manifolds and graphs Lior Alon, Michael Bersudsky, Sebastian Egger and Rami Band
11. On the existence and uniqueness of self-adjoint realizations of discrete (magnetic) Schrodinger operators Marcel Schmidt
12. Box spaces: geometry of finite quotients Ana Khukhro and Alain Valette
13. Ramanujan graphs and digraphs Ori Parzanchevski
14. From partial differential equations to groups Tsuyoshi Kato, Satoshi Tsujimoto and Andrzej ?uk
15. Spectral properties of limit-periodic operators David Damanik and Jake Fillman
16. Uniform existence of the IDS on lattices and groups Christoph Schumacher, Fabian Schwarzenberger and Ivan Veselic.
Part of New Mathematical Monographs
Not yet published - available from November 2020
FORMAT: Hardback ISBN: 9781107150744
Intersection homology is a version of homology theory that extends Poincare duality and its applications to stratified spaces, such as singular varieties. This is the first comprehensive expository book-length introduction to intersection homology from the viewpoint of singular and piecewise-linear chains. Recent breakthroughs have made this approach viable by providing intersection homology and cohomology versions of all the standard tools in the homology tool box, making the subject readily accessible to graduate students and researchers in topology as well as researchers from other fields. This text includes both new research material and new proofs of previously-known results in intersection homology, as well as treatments of many classical topics in algebraic and manifold topology. Written in a detailed but expository style, this book is suitable as an introduction to intersection homology or as a thorough reference.
Contains brand new research and results, bringing the reader right up to date
Works as a reference for classical material, including detailed descriptions that are difficult to find elsewhere
Provides a self-contained introduction to less standard background material, serving as a one-stop shop for the reader
Preface
Notations and conventions
1. Introduction
2. Stratified spaces
3. Intersection homology
4. Basic properties of singular and PL intersection homology
5. Mayer?Vietoris arguments and further properties of intersection homology
6. Non-GM intersection homology
7. Intersection cohomology and products
8. Poincare duality
9. Witt spaces and IP spaces
10. Suggestions for further reading
Appendix A. Algebra
Appendix B. An introduction to simplicial and PL topology
References
Glossary of symbols
Index.