ISBN: 978-1-4704-5133-2
Series, Volume: Mathematical Surveys and Monographs, Volume 241
Published: 18 September 2019; Copyright Year: 2019;
Pages: approximately 404; Hardcover;
Itemcode: SURV/241
Analysis
Supplementary Text
Graduate students and researchers interested in C* -algebras.
The construction of a C* -algebra from a locally compact groupoid is an important
generalization of the group C* -algebra construction and of the transformation group C* -algebra
construction. Since their introduction in 1980, groupoid C ? -algebras have been intensively
studied with diverse applications, including graph algebras, classification theory, variations on
the Baum-Connes conjecture, and noncommutative geometry. This book provides a detailed
introduction to this vast subject and is suitable for graduate students or any researcher who
wants to use groupoid C*-algebras in their work. The main focus is to equip the reader with
modern versions of the basic technical tools used in the subject, which will allow the reader to
understand fundamental results and make contributions to various areas in the subject. Thus,
in addition to covering the basic properties and construction of groupoid C* -algebras, the
focus is to give a modern treatment of some of the major developments in the subject in recent
years, including the Equivalence Theorem and the Disintegration Theorem. Also covered are
the complicated subjects of amenability of groupoids and simplicity results.
The book is reasonably self-contained and accessible to graduate students with a good background
in operator algebras.
ISBN: 978-1-4704-5015-1
Series, Volume: Mathematical Surveys and Monographs, Volume 242
Published: 18 September 2019; Copyright Year: 2019;
Pages: approximately 312; Hardcover;
Itemcode: SURV/242
Algebra and Algebraic Geometry
Number Theory
Graduate students and researchers interested in new developments in algebraic
geometry and algebraic number theory.
Introduced by Peter Scholze in 2011, perfectoid spaces are a bridge between geometry
in characteristic 0 and characteristic p , and have been used to solve many important
problems, including cases of the weight-monodromy conjecture and the association of Galois
representations to torsion classes in cohomology. In recognition of the transformative impact
perfectoid spaces have had on the field of arithmetic geometry, Scholze was awarded a Fields
Medal in 2018.
This book, originating from a series of lectures given at the 2017 Arizona Winter School on
perfectoid spaces, provides a broad introduction to the subject. After an introduction with
insight into the history and future of the subject by Peter Scholze, Jared Weinstein gives a userfriendly
and utilitarian account of the theory of adic spaces. Kiran Kedlaya further develops the
foundational material, studies vector bundles on Fargues?Fontaine curves, and introduces diamonds
and shtukas over them with a view toward the local Langlands correspondence. Bhargav
Bhatt explains the application of perfectoid spaces to comparison isomorphisms in p -adic
Hodge theory. Finally, Ana Caraiani explains the application of perfectoid spaces to the construction
of Galois representations associated to torsion classes in the cohomology of locally
symmetric spaces for the general linear group.
This book will be an invaluable asset for any graduate student or researcher interested in the
theory of perfectoid spaces and their applications.
ISBN: 978-1-4704-4333-7
Series, Volume: Contemporary Mathematics, Volume 735
Published: 25 September 2019; Copyright Year: 2019;
Pages: 259; Softcover;
Itemcode: CONM/735
Analysis
Graduate students and research mathematicians interested in complex geometry and
complex analysis.
This volume contains contributions from speakers at the 2015?2018 joint Johns
Hopkins University and University of Maryland Complex Geometry Seminar. It begins with a
survey article on recent developments in pluripotential theory and its applications to Kahler?
Einstein metrics and continues with articles devoted to various aspects of the theory of complex
manifolds and functions on such manifolds.
ISBN: 978-1-4704-5055-7
Series, Volume: Pure and Applied Undergraduate Texts, Volume 40
Published: 10 October 2019; Copyright Year: 2019;
Pages: 323; Hardcover;
Itemcode: AMSTEXT/40
Applications
Discrete Mathematics and Combinatorics
Number Theory
Probability and Statistics
Undergraduate students interested in cryptography.
This book provides a compact course in modern cryptography. The mathematical
foundations in algebra, number theory and probability are presented with a focus on their
cryptographic applications. The text provides rigorous definitions and follows the provable
security approach. The most relevant cryptographic schemes are covered, including block
ciphers, stream ciphers, hash functions, message authentication codes, public-key encryption,
key establishment, digital signatures and elliptic curves. The current developments in postquantum
cryptography are also explored, with separate chapters on quantum computing,
lattice-based and code-based cryptosystems.
Many examples, figures and exercises, as well as SageMath (Python) computer code, help the
reader to understand the concepts and applications of modern cryptography. A special focus is
on algebraic structures, which are used in many cryptographic constructions and also in postquantum
systems. The essential mathematics and the modern approach to cryptography and
security prepare the reader for more advanced studies.
The text requires only a first-year course in mathematics (calculus and linear algebra) and is
also accessible to computer scientists and engineers. This book is suitable as a textbook for
undergraduate and graduate courses in cryptography as well as for self-study.
ISBN: 978-1-4704-5081-6
Series, Volume: Graduate Studies in Mathematics, Volume 201
Published: 16 October 2019; Copyright Year: 2019;
Pages: approximately 363; Hardcover;
Itemcode: GSM/201
Differential Equations
Mathematical Physics
Supplementary Text
Graduate students and researchers interested in nonlinear differential equations and,
in particular, in mathematical aspects of general relativity.
Many problems in general relativity are essentially geometric in nature, in the sense
that they can be understood in terms of Riemannian geometry and partial differential equations.
This book is centered around the study of mass in general relativity using the techniques
of geometric analysis. Specifically, it provides a comprehensive treatment of the positive mass
theorem and closely related results, such as the Penrose inequality, drawing on a variety of
tools used in this area of research, including minimal hypersurfaces, conformal geometry,
inverse mean curvature flow, conformal flow, spinors and the Dirac operator, marginally outer
trapped surfaces, and density theorems. This is the first time these topics have been gathered
into a single place and presented with an advanced graduate student audience in mind; several
dozen exercises are also included.
The main prerequisite for this book is a working understanding of Riemannian geometry and
basic knowledge of elliptic linear partial differential equations, with only minimal prior knowledge
of physics required. The second part of the book includes a short crash course on general
relativity, which provides background for the study of asymptotically flat initial data sets satisfying
the dominant energy condition.
ISBN: 978-3-03719-197-2
Series, Volume: EMS Series of Congress Reports, Volume 15
Bibliographic Information: Published: 15 July 2019; Copyright
Year: 2019; Pages: 433; Hardcover; List Price: US$108; Itemcode:
EMSSCR/15
Algebra and Algebraic Geometry
Analysis
Number Theory
Specialists working in both pure and applied mathematics.
This book is a collection of survey articles about spectral structures
and the application
of topological methods bridging different mathematical disciplines, from pure to applied.
The topics are based on work done in the Collaborative Research Centre (SFB) 701.
Notable examples are non-crossing partitions, which connect representation theory, braid
groups, non-commutative probability, as well as spectral distributions of random matrices.
The local distributions of such spectra are universal and also represent the local distribution of
zeros of L-functions in number theory.
An overarching method is the use of zeta functions in the asymptotic counting of sublattices,
group representations, etc. Further examples connecting probability, analysis, dynamical systems,
and geometry are generating operators of deterministic or stochastic processes, stochastic
differential equations, and fractals, relating them to the local geometry of such spaces and the
convergence to stable and semi-stable states.
Information for our distributors: Distributed within the Americas by the American
Mathematical Society. All commerical channel discounts apply.
ISBN: 978-2-85629-904-3
Series, Volume: Asterisque, Number 410
Published: 15 June 2019; Copyright Year: 2019;
Pages: 180; Softcover;
Itemcode: AST/410
Analysis
Graduate students and research mathematicians.
The strong regularity program was initiated by Jean-Christophe Yoccoz during
his
first lecture at College de France. As explained in the first article of this volume, this program
aims to show the abundance of dynamics displaying a non-uniformly hyperbolic attractor. It
proposes a topological and combinatorial definition of such mappings using the formalism of
puzzle pieces. Their combinatorics make it possible to deduce the desired analytical properties.
In 1997, this method enabled Jean-Chritophe Yoccoz to give an alternative proof of the
Jakobson theorem: the existence of a set of positive Lebesgue measure of parameters a such
that the map x šl x2 + a has an attractor which is non-uniformly hyperbolic. This proof is the
second article of this volume.
In the third article, this method is generalized in dimension 2 by Pierre Berger to show the
following theorem. For every C 2 -perturbation of the family of maps (x, y ) šl (x2 + a , 0),
there exists a parameter set of positive Lebesgue measure at which these maps display a nonuniformly
hyperbolic attractor. This gives, in particular, an alternative proof of the Benedicks-
Carleson Theorem.
Information for our distributors: A publication of the Societe Mathematique de France,
Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other
countries should be sent to the SMF. AMS individual members receive a 10% discount and
members of the SMF receive a 30% discount from list. No other discounts apply.