Due 2018-01-17
1st ed. 2017, VI, 366 p. 1
illus.
Hardcover
ISBN 978-3-319-69711-6
Series
Contributions in Mathematical and Computational Sciences
Mathematics : Number Theory
This book presents a collection of carefully refereed research articles and lecture notes
stemming from the Conference "Automorphic Forms and L-Functions", held at the University of
Heidelberg in 2016. The theory of automorphic forms and their associated L-functions is one
of the central research areas in modern number theory, linking number theory, arithmetic
geometry, representation theory, and complex analysis in many profound ways. The 19 papers
cover a wide range of topics within the scope of the conference, including automorphic Lfunctions
and their special values, p-adic modular forms, Eisenstein series, Borcherds products,
automorphic periods, and many more.
Due 2018-01-20
1st ed. 2017, XI, 389 p. 119
illus., 100 illus. in color.
Softcover
ISBN 978-3-319-72253-5
Series Universitext
Mathematics : Group Theory and Generalizations
Features more than 250 exercises of varying difficulty including programming tasks
Introduces the key notions from quasi-geometry, such as growth,
hyperbolicity, boundary constructions and amenability
Assumes only a basic background in group theory, metric spaces and pointset topology
Inspired by classical geometry, geometric group theory has in turn provided a variety of
applications to geometry, topology, group theory, number theory and graph theory. This
carefully written textbook provides a rigorous introduction to this rapidly evolving field whose
methods have proven to be powerful tools in neighbouring fields such as geometric topology.
Geometric group theory is the study of finitely generated groups via the geometry of their
associated Cayley graphs. It turns out that the essence of the geometry of such groups is
captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants
include growth types, curvature conditions, boundary constructions, and amenability. This book
covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The
subject is illustrated by many elementary examples, outlooks on applications, as well as an
extensive collection of exercises.
Due 2018-03-23
1st ed. 2018, XVIII, 638 p.
109 illus.
Hardcover
ISBN 978-3-319-71839-2
Series Springer Monographs in Mathematics
Mathematics : Graph Theory
Presents the latest research in the subject area, including significant new
results obtained over recent years
Illustrates various approaches, techniques and algorithms used in digraph theory
Explores structural results as well as algorithms and complexity, including
results on fixed parameter tractability
Collects over 120 open problems and conjectures
This edited volume offers a detailed account on the theory of directed graphs from the
perspective of important classes of digraphs, with each chapter written by experts on the topic.
Outlining fundamental discoveries and new results obtained over recent years, this book
provides a comprehensive overview of the latest research in the field. It covers core new
results on each of the classes discussed, including chapters on tournaments, planar digraphs,
acyclic digraphs, Euler digraphs, graph products, directed width parameters, and algorithms.
Detailed indices ease navigation while more than 120 open problems and conjectures ensure
that readers are immersed in all aspects of the field. Classes of Directed Graphs provides a
valuable reference for graduate students and researchers in computer science, mathematics
and operations research. As digraphs are an important modelling tool in other areas of
research, this book will also be a useful resource to researchers working in bioinformatics,
chemoinformatics, sociology, physics, medicine, etc.
*
Due 2018-01-31
1st ed. 2017, XII, 204 p.
Softcover
ISBN 978-3-319-72178-1
Series Lecture Notes in Mathematics
Mathematics : Dynamical Systems and Ergodic Theory
Contains entirely original results which cannot be found elsewhere in the literature
Treats topics which are now the subject of rapidly developing extensive research
Serves both as a reference and as a source of inspiration for further original work
The focus of this book is on open conformal dynamical systems corresponding to the escape
of a point through an open Euclidean ball. The ultimate goal is to understand the asymptotic
behavior of the escape rate as the radius of the ball tends to zero. In the case of hyperbolic
conformal systems this has been addressed by various authors. The conformal maps
considered in this book are far more general, and the analysis correspondingly more involved.
The asymptotic existence of escape rates is proved and they are calculated in the context of
(finite or infinite) countable alphabets, uniformly contracting conformal graph-directed Markov
systems, and in particular, conformal countable alphabet iterated function systems. These
results have direct applications to interval maps, rational functions and meromorphic
maps. Towards this goal the authors develop, on a purely symbolic level, a theory of singular
perturbations of Perron--Frobenius (transfer) operators associated with countable alphabet
subshifts of finite type and Holder continuous summable potentials. This leads to a fairly full
account of the structure of the corresponding open dynamical systems and their associated
surviving sets.
Due 2018-05-23
1st ed. 2018, Approx. 375 p.
ISBN 978-3-319-72448-5
Series Operator Theory: Advances and Applications
Mathematics : Operator Theory
Presents papers that establish a connection between three related areas in
Operator Theory
Establishes recent research results of some of the most well reputed
researchers in the area
Includes both survey and research papers
This book consists of invited survey articles and research papers in the scientific areas of the
gInternational Workshop on Operator Algebras, Operator Theory and Applications,h which was
held in Lisbon in July 2016. Reflecting recent developments in the field of algebras of
operators, operator theory and matrix theory, it particularly focuses on groupoid algebras and
Fredholm conditions, algebras of approximation sequences, C* algebras of convolution type
operators, index theorems, spectrum and numerical range of operators, extreme
supercharacters of infinite groups, quantum dynamics and operator algebras, and inverse
eigenvalue problems. Establishing bridges between the three related areas of operator
algebras, operator theory, and matrix theory, the book is aimed at researchers, members of the
scientific and graduate students who use results from these areas.