Due 2020-01-03
1st ed. 2019, Approx. 265 p.
Printed book
Hardcover
ISBN 978-3-030-29122-8
First book on quasimodular forms
Presents all of the necessary basic materials on quasimodular forms and their
relation to pseudodifferential operators, making the book accessible also to non-specialists
Contains a nice selection of applications of the theory to a variety of other areas
This book explores various properties of quasimodular forms, especially their connections with
Jacobi-like forms and automorphic pseudodifferential operators. The material that is essential
to the subject is presented in sufficientdetail, including necessary background on
pseudodifferential operators, Lie algebras, etc.,to make it accessible also to non-specialists. The
book also covers a sufficiently broad range or illustrations of how the main themes of the
book have occurred in various partsof mathematics to make it attractive to a wider audience.
The book is intended for researchers and graduate students in number theory
Due 2019-12-11
1st ed. 2019, XL, 406 p.
Printed book
Hardcover
ISBN 978-3-030-33241-9
Provides a complete theory of triangulated rational mixed motives satisfying
Grothendieck’s six operations, including the state of the art for integral coefficients
Gives a systematic, self-contained, account of Grothendieck’s six functor formalism
Includes a modern presentation of descent theory with applications to Ktheory
Explains the close relationship between mixed Weil cohomologies and coefficient systems
The primary aim of this monograph is to achieve part of Beilinson’s program on mixed motives
using Voevodsky’s theories of A1-homotopy and motivic complexes. Historically, this book is the
first to give a complete construction of a triangulated category of mixed motives with rational
coefficients satisfying the full Grothendieck six functors formalism as well as fulfilling Beilinson’
s program, in particular the interpretation of rational higher Chow groups as extension groups.
Apart from Voevodsky’s entire work and Grothendieck’s SGA4, our main sources are Gabber’s
work on etale cohomology and Ayoub’s solution to Voevodsky’s cross functors theory. We also
thoroughly develop the theory of motivic complexes with integral coefficients over general
bases, along the lines of Suslin and Voevodsky. Besides this achievement, this volume provides
a complete toolkit for the study of systems of coefficients satisfying Grothendieck’ six functors
formalism, including Grothendieck-Verdier duality. It gives a systematic account of
cohomological descent theory with an emphasis on h-descent. It formalizes morphisms of
coefficient systems with a view towards realization functors and comparison results. The latter
allows to understand the polymorphic nature of rational mixed motives. They can be
characterized by one of the following properties: existence of transfers, universality of rational
algebraic K-theory, h-descent, etale descent, orientation theory. This monograph is a
longstanding research work of the two authors. The first three parts are written in a selfcontained
manner and could be accessible to graduate students with a background in
algebraic geometry and homotopy theory
Due 2020-01-10
1st ed. 2019, X, 476 p. 55
illus., 18 illus. in color.
Printed book
Hardcover
ISBN 978-3-030-32067-6
Brings under one roof results previously scattered in many research papers
published during the past 50 years since the origin of the three-dimensional
theory of quasiconformal and quasiregular mappings
Contains an extensive set of exercises, including solutions
Can be used as learning material/collateral reading for several courses
This book is an introduction to the theory of quasiconformal and quasiregular mappings in the
euclidean n-dimensional space, (where n is greater than 2). There are many ways to develop
this theory as the literature shows. The authors' approach is based on the use of metrics, in
particular conformally invariant metrics, which will have a key role throughout the whole book.
The intended readership consists of mathematicians from beginning graduate students to
researchers. The prerequisite requirements are modest: only some familiarity with basic ideas
of real and complex analysis is expected.
1st ed. 2019, XVIII, 109 p.
53 illus., 1 illus. in color.
Printed book
Hardcover
ISBN 978-3-030-28920-1
Details ordinal combinatorics of large sets tailored for independence results
Presents various proofs of Godel incompleteness theorems
Offers an approach towards independence results by model-theoretic methods
This book presents a detailed treatment of ordinal combinatorics of large sets tailored for
independence results. It uses model theoretic and combinatorial methods to obtain results in
proof theory, such as incompleteness theorems or a description of the provably total functions
of a theory. In the first chapter, the authors first discusses ordinal combinatorics of finite sets
in the style of Ketonen and Solovay. This provides a background for an analysis of subsystems
of Peano Arithmetic as well as for combinatorial independence results. Next, the volume
examines a variety of proofs of Godel's incompleteness theorems. The presented proofs differ
strongly in nature. They show various aspects of incompleteness phenomena. In additon,
coverage introduces some classical methods like the arithmetized completeness theorem,
satisfaction predicates or partial satisfaction classes. It also applies them in many contexts. The
fourth chapter defines the method of indicators for obtaining independence results. It shows
what amount of transfinite induction we have in fragments of Peano arithmetic. Then, it
usescombinatorics of large sets of the first chapter to show independence results. The last
chapter considers nonstandard satisfaction classes. It presents some of the classical theorems
related to them. In particular, it covers the results by S. Smith on definability in the language
with a satisfaction class and on models without a satisfaction class.Overall, the book's content
lies on the border between combinatorics, proof theory, and model theory of arithmetic. It
offers readers a distinctive approach towards independence results by model-theoretic methods.
Due 2019-12-02
1st ed. 2020, Approx. 400 p. 42 illus. in color.
Printed book
Hardcover
ISBN 978-3-030-33142-9
Provides student-friendly explanations with ample examples and exercises throughout
Includes chapters on Hilbert space operators, Fourier analysis, and probability measures
Prepares students for further graduate studies by promoting a deep understanding of key concepts
This open access textbook welcomes students into the fundamental theory of measure,
integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations
for further study by promoting a deep understanding of key results. Content is carefully
curated to suit a single course, or two-semester sequence of courses, creating a versatile entry
point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief
review of Riemann integration and its deficiencies, the text begins by immersing students in the
concepts of measure and integration. Lebesgue measure and abstract measures are developed
together, with each providing key insight into the main ideas of the other approach. Lebesgue
integration links into results such as the Lebesgue Differentiation Theorem. The development
of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach
spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn?Banach
Theorem, Holder’s Inequality, and the Riesz Representation Theorem. An in-depth study of
linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value
Decomposition for compact operators, with an optional interlude in real and complex
measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an
invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a
taste of probability. Extensively class tested at multiple universities and written by an awardwinning
mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for
students at the start of their journey into graduate mathematics.