Oxford Graduate Texts in Mathematics
This book presents the topology of smooth 4-manifolds in an intuitive self-contained way, developed over a number of years by Professor Akbulut. The text is aimed at graduate students and focuses on the teaching and learning of the subject, giving a direct approach to constructions and theorems which are supplemented by exercises to help the reader work through the details not covered in the proofs.
1: 4-manifold handlebodies
2: Building low dimensional manifolds
3: Gluing 4 manifolds along their boundaries
4: Bundles
5: 3-manifolds
6: Operations
7: Lefschetz Fibrations
8: Symplectic Manifolds
9: Exotic 4-manifolds
10: Cork decomposition
11: Covering spaces
12: Complex surfaces
13: Seiberg-Witten invariants
14: Some applications
Published: 14 July 2016 (Estimated)
280 Pages | 100
234x156mm
ISBN: 9780198784869
Series: Progress in Mathematics, Vol. 314
* First Open Access book in the Birkhauser program
* Contains a detailed and easy-to-follow exposition of nilpotent and
homogeneous Lie groups and of homogeneous operators on such
groups
* Features a consistent development of the theory of Sobolev spaces
on graded Lie groups
* Gives a detailed development of the pseudo-differential analysis on
graded Lie groups
* The developed theory is thoroughly illustrated in the case of the
Heisenberg group providing new links with various topics of analysis
in this setting
This book presents a consistent development of the Kohn-Nirenberg type global
quantization theory in the setting of graded nilpotent Lie groups in terms of their
representations. It contains a detailed exposition of related background topics on
homogeneous Lie groups, nilpotent Lie groups, and the analysis of Rockland operators on
graded Lie groups together with their associated Sobolev spaces. For the specific example
of the Heisenberg group the theory is illustrated in detail. In addition, the book features
a brief account of the corresponding quantization theory in the setting of compact Lie
groups.
The monograph is the winner of the 2014 Ferran Sunyer i Balaguer Prize.
1st ed. 2016, XIII, 557 p. 1 illus.
A product of Birkhauser Basel
Printed book
Hardcover
ISBN 978-3-319-29557-2
Series: Progress in Mathematics, Vol. 315
* Presents a unique and up-to-date source on the developments in this
very active and diverse field
* Connects to other current topics: the study of derived categories and
stability conditions, Gromov-Witten theory, and dynamical systems
* Complements related volumes like “The Moduli Space of Curves” and
“Moduli of Abelian Varieties” that have become classics
This book provides an overview of the latest developments concerning the moduli of K3
surfaces. It is aimed at algebraic geometers, but is also of interest to number theorists and
theoretical physicists, and continues the tradition of related volumes like “The Moduli
Space of Curves” and “Moduli of Abelian Varieties,” which originated from conferences on
the islands Texel and Schiermonnikoog and which have become classics.
K3 surfaces and their moduli form a central topic in algebraic geometry and arithmetic
geometry, and have recently attracted a lot of attention from both mathematicians
and theoretical physicists. Advances in this field often result from mixing sophisticated
techniques from algebraic geometry, lattice theory, number theory, and dynamical
systems. The topic has received significant impetus due to recent breakthroughs on
the Tate conjecture, the study of stability conditions and derived categories, and links
with mirror symmetry and string theory. At the same time, the theory of irreducible
holomorphic symplectic varieties, the higher dimensional analogues of K3 surfaces, has
become a mainstream topic in algebraic geometry.
Contributors: S. Boissiere, A. Cattaneo,
I. Dolgachev, V. Gritsenko, B. Hassett, G. Heckman, K. Hulek, S. Katz, A. Klemm, S. Kondo, C.
Liedtke, D. Matsushita, M. Nieper-Wisskirchen, G. Oberdieck, K. Oguiso, R. Pandharipande,
S. Rieken, A. Sarti, I. Shimada, R. P. Thomas, Y. Tschinkel, A. Verra, C. Voisin.
1st ed. 2016, X, 400 p. 39 illus., 3 illus. in
color.
Hardcover
ISBN 978-3-319-29958-7
Series: Contemporary Mathematicians
* Collection of influential papers by respected mathematician and
statistician, Rabi N. Bhattacharya Includes commentaries from
established researchers to enhance accessibility
* Addresses past and present developments and future challenges in
the fields of probability and statistics
This volume presents some of the most influential papers published by Rabi N.
Bhattacharya, along with commentaries from international experts, demonstrating his
knowledge, insight, and influence in the field of probability and its applications. For
more than three decades, Bhattacharya has made significant contributions in areas
ranging from theoretical statistics via analytical probability theory, Markov processes,
and random dynamics to applied topics in statistics, economics, and geophysics. Selected
reprints of Bhattacharya’s papers are divided into three sections: Modes of Approximation,
Large Times for Markov Processes, and Stochastic Foundations in Applied Sciences. The
accompanying articles by the contributing authors not only help to position his work in
the context of other achievements, but also provide a unique assessment of the state of
their individual fields, both historically and for the next generation of researchers.
Rabi N. Bhattacharya: Selected Papers will be a valuable resource for young researchers
entering the diverse areas of study to which Bhattacharya has contributed. Established
researchers will also appreciate this work as an account of both past and present
developments and challenges for the future.
1st ed. 2016, X, 702 p. 1 illus.
Hardcover
ISBN 978-3-319-30188-4
Series: CMS Books in Mathematics
* Introduces reader to recent topics in spaces of measurable functions
* Includes section of problems at the end of each chapter
* Content allows for use with mixed-level classes
* Includes non-standard function spaces, viz. variable exponent
Lebesgue spaces and grand Lebesgue spaces
This book is devoted exclusively to Lebesgue spaces and their direct derived spaces.
Unique in its sole dedication, this book explores Lebesgue spaces, distribution functions
and nonincreasing rearrangement. Moreover, it also deals with weak, Lorentz and the
more recent variable exponent and grand Lebesgue spaces with considerable detail to
the proofs. The book also touches on basic harmonic analysis in the aforementioned
spaces. An appendix is given at the end of the book giving it a self-contained character.
This work is ideal for teachers, graduate students and researchers.
1st ed. 2016, X, 465 p. 13 illus.
Printed book
Hardcover
ISBN 978-3-319-30032-0
Series: Springer Undergraduate Texts in Mathematics and Technology
* Explains the mathematical methods of modern cryptographic design
* Examines both secret key and public key cryptosystems
* Provides undergraduates with advanced topics in algebra
This textbook provides an introduction to the mathematics on which modern cryptology
is based. It covers not only public key cryptography, the glamorous component of modern
cryptology, but also pays considerable attention to secret key cryptography, its workhorse
in practice.
Modern cryptology has been described as the science of the integrity of information,
covering all aspects like confidentiality, authenticity and non-repudiation and also
including the protocols required for achieving these aims. In both theory and practice
it requires notions and constructions from three major disciplines: computer science,
electronic engineering and mathematics. Within mathematics, group theory, the theory of
finite fields, and elementary number theory as well as some topics not normally covered
in courses in algebra, such as the theory of Boolean functions and Shannon theory are
involved. Although essentially self-contained, a degree of mathematical maturity on
the part of the reader is assumed, corresponding to his or her background in computer
science or engineering. Algebra for Cryptologists is a textbook for an introductory course
in cryptography or an upper undergraduate course in algebra, or for self-study in
preparation for postgraduate study in cryptology.
1st ed. 2016, Approx. 310 p. 6 illus.
Printed book
Hardcover
ISBN 978-3-319-30395-6