Series: Contemporary Mathematicians
2015, XII, 806 p.
Hardcover
ISBN 978-3-319-18798-3
* Presents Nigel Kalton's most influential articles
* Features comments by a panel of leading experts
* Makes some unpublished work available for the first time
* Provides a useful guide to contemporary analysis
This is the second part of a two volume anthology comprising a selection of 49 articles
that illustrate the depth, breadth and scope of Nigel Kalton’s research. Each article is
accompanied by comments from an expert on the respective topic, which serve to
situate the article in its proper context, to successfully link past, present and hopefully
future developments of the theory, and to help readers grasp the extent of Kalton’s
accomplishments. Kalton’s work represents a bridge to the mathematics of tomorrow, and
this book will help readers to cross it.
Nigel Kalton (1946-2010) was an extraordinary mathematician who made major
contributions to an amazingly diverse range of fields over the course of his career.
2015, XIII, 349 p. 25 illus.
Hardcover
ISBN 978-3-319-19044-0
* Introduces the fundamental tools of differential topology
* Ideally suited as a textbook for an orientation course for advancedlevel
research students or for independent study
* Presents a number of epochal discoveries in the field of manifolds
This book presents a systematic and comprehensive account of the theory of
differentiable manifolds and provides the necessary background for the use of
fundamental differential topology tools. The text includes, in particular, the earlier
works of Stephen Smale, for which he was awarded the Fields Medal. Explicitly, the
topics covered are Thom transversality, Morse theory, theory of handle presentation, hcobordism
theorem, and the generalised Poincare conjecture. The material is the outcome
of lectures and seminars on various aspects of differentiable manifolds and differential
topology given over the years at the Indian Statistical Institute in Calcutta, and at other
universities throughout India.
The book will appeal to graduate students and researchers interested in these topics. An
elementary knowledge of linear algebra, general topology, multivariate calculus, analysis,
and algebraic topology is recommended.
Series: SpringerBriefs in Mathematics
2015, VII, 128 p. 15 illus., 6 illus. in color.
Softcover
ISBN 978-3-319-19760-9
* Studies concrete examples in detail, to illustrate a wide variety of methods
* Begins from basic material, introducing mixed-type problems in different applications
* Provides a grand view of mixed-type equations, from basic materials
to recent progress and emerging applications
This text is a concise introduction to the partial differential equations which change
from elliptic to hyperbolic type across a smooth hypersurface of their domain. These are
becoming increasingly important in diverse sub-fields of both applied mathematics and
engineering, for example:
* The heating of fusion plasmas by electromagnetic waves
* The behaviour of light near a caustic
* Extremal surfaces in the space of special relativity
* The formation of rapids; transonic and multiphase fluid flow
* The dynamics of certain models for elastic structures
* The shape of industrial surfaces such as windshields and airfoils
* Pathologies of traffic flow
* Harmonic fields in extended projective space
They also arise in models for the early universe, for cosmic acceleration, and for possible
violation of causality in the interiors of certain compact stars. Within the past 25 years,
they have become central to the isometric embedding of Riemannian manifolds and the
prescription of Gauss curvature for surfaces: topics in pure mathematics which themselves
have important applications.
Series: Abel Symposia, Vol. 10
2015, X, 264 p. 6 illus., 2 illus. in color.
Hardcover
ISBN 978-3-319-20336-2
This book focuses on complex geometry and covers highly active topics centered around
geometric problems in several complex variables and complex dynamics, written by some
of the world’s leading experts in their respective fields.
This book features research and expository contributions from the 2013 Abel Symposium,
held at the Norwegian University of Science and Technology Trondheim on July 2-5, 2013.
The purpose of the symposium was to present the state of the art on the topics, and to
discuss future research directions.
Series: Lecture Notes in Mathematics, Vol. 2147
2016, Approx. 355 p.
Softcover
ISBN 978-3-319-20546-5
* Studies topics that are somewhat ignored in the existent literature on
properads
* Contains important results, especially concerning the combinatorics
of graphs and graphs substitution
* Analyses technical and conceptual difficulties in an easy-to-read
manner
The topic of this book sits at the interface of the theory of higher categories (in the guise
of (∞,1)-categories) and the theory of properads. Properads are devices more general than
operads, and enable one to encode bialgebraic, rather than just (co)algebraic, structures.
The text extends both the Joyal-Lurie approach to higher categories and the Cisinski-
Moerdijk-Weiss approach to higher operads, and provides a foundation for a broad
study of the homotopy theory of properads. This work also serves as a complete guide
to the generalised graphs which are pervasive in the study of operads and properads. A
preliminary list of potential applications and extensions comprises the final chapter.
Infinity Properads and Infinity Wheeled Properads is written for mathematicians in the fields
of topology, algebra, category theory, and related areas. It is written roughly at the second
year graduate level, and assumes a basic knowledge of category theory.