1st ed. 2019, VIII, 154 p. 1
illus.
Printed book
Softcover
ISBN 978-3-658-25337-0
Encoding non-perturbative phenomena in classical observables
Corina Keller studies non-perturbative facets of abelian Chern-Simons theories. This is a
refinement of the entirely perturbative approach to classical Chern-Simons theory via homotopy
factorization algebras of observables that arise from the associated formal moduli problem
describing deformations of flat principal bundles with connections over the spacetime manifold.
The author shows that for theories with abelian group structure, this factorization algebra of
classical observables comes naturally equipped with an action of the gauge group, which
allows to encode non-perturbative effects in the classical observables. About the Author: Corina
Keller currently is a doctoral student in the research group of Prof. Dr. Damien Calaque at the
Universite Montpellier, France. She is mostly interested in the mathematical study of field
theories. Her master’s thesis was supervised by PDDr. Alessandro Valentino and Prof. Dr.
Alberto Cattaneo at Zurich University, Switzerland.
Due 2019-05-15
1st ed. 2019, XI, 104 p.
Printed book
Softcover
ISBN 978-3-030-14500-2
Treatise on the p-Laplace equation
Coverage of a variety of topics
Discussion of open problems
This book in the BCAM SpringerBriefs series is a treatise on the p-Laplace equation. It is based
on lectures by the author that were originally delivered at the Summer School in Jyvaskyla,
Finland, in August 2005 and have since been updated and extended to cover various new
topics, including viscosity solutions and asymptotic mean values. The p-Laplace equation is a
far-reaching generalization of the ordinary Laplace equation, but it is non-linear and
degenerate (p>2) or singular (p<2). Thus it requires advanced methods. Many fascinating
properties of the Laplace equation are, in some modified version, extended to the p-Laplace
equation. Nowadays the theory is almost complete, although some challenging problems
remain opten.
Due 2019-06-06
1st ed. 2019, XIII, 311 p.
Printed book
Softcover
ISBN 978-3-030-14976-5
Provides a pedagogical, self-contained analysis of the theory of convex
optimization and stochastic programming
Offers a synthetical view of many applications such as semidefinite
programming, Markov processes, generalized convexity and optimal transport
Includes a study of algorithmic aspects: dynamic programming, stochastic
dual dynamic programming (in the case of convex Bellman value functions)
and linear decision rules
This textbook provides an introduction to convex duality for optimization problems in Banach
spaces, integration theory, and their application to stochastic programming problems in a static
or dynamic setting. It introduces and analyses the main algorithms for stochastic programs,
while the theoretical aspects are carefully dealt with. The reader is shown how these tools can
be applied to various fields, including approximation theory, semidefinite and second-order
cone programming and linear decision rules. This textbook is recommended for students,
engineers and researchers who are willing to take a rigorous approach to the mathematics
involved in the application of duality theory to optimization with uncertainty.
Due 2019-06-06
1st ed. 2019, XIV, 351 p.
Printed book
Hardcover
ISBN 978-3-030-15451-6
An Algebraic Introduction and Real-World Applications
Exercises in each chapter are real-world application based
Provides solid mathematical preparation for more specialized applied courses
on cryptography/error correction
Presents some of the remarkable strategies for dealing with information in
the computer age and the basic algebraic ideas behind those strategies
Solutions manual is available to instructors who adopt the text for their course
This text presents a careful introduction to methods of cryptology and error correction in wide
use throughout the world and the concepts of abstract algebra and number theory that are
essential for understanding these methods. The objective is to provide a thorough
understanding of RSA, Diffie?Hellman, and Blum?Goldwasser cryptosystems and Hamming and
Reed?Solomon error correction: how they are constructed, how they are made to work
efficiently, and also how they can be attacked. To reach that level of understanding requires
and motivates many ideas found in a first course in abstract algebra?rings, fields, finite
abelian groups, basic theory of numbers, computational number theory, homomorphisms,
ideals, and cosets. Those who complete this book will have gained a solid mathematical
foundation for more specialized applied courses on cryptology or error correction, and should
also be well prepared, both in concepts and in motivation, to pursue more advanced study in
algebra and number theory. This text is suitable for classroom or online use or for
independent study. Aimed at students in mathematics, computer science, and engineering, the
prerequisite includes one or two years of a standard calculus sequence. Ideally the reader will
also take a concurrent course in linear algebra or elementary matrix theory. A solutions
manual for the 400 exercises in the book is available to instructors who adopt the text for
their course.
Due 2019-06-06
1st ed. 2019, XII, 100 p. 8
illus.
Printed book
Softcover
ISBN 978-981-13-7074-8
Is the first exposition of Brakke’s mean curvature flow, a subject that
interests many researchers
Uses accessible language, not highly technical terminology, for all readers
interested in geometric measure theory
Explains recent highly acclaimed research results of the mean curvature flow
This book explains the notion of Brakke’s mean curvature flow and its existence and regularity
theories without assuming familiarity with geometric measure theory. The focus of study is a
time-parameterized family of k-dimensional surfaces in the n-dimensional Euclidean space (1
k<n). The family is the mean curvature flow if the velocity of motion of surfaces is given by the
mean curvature at each point and time. It is one of the simplest and most important geometric
evolution problems with a strong connection to minimal surface theory. In fact, equilibrium of
mean curvature flow corresponds precisely to minimal surface. Brakke’s mean curvature flow
was first introduced in 1978 as a mathematical model describing the motion of grain
boundaries in an annealing pure metal. The grain boundaries move by the mean curvature
flow while retaining singularities such as triple junction points. By using a notion of generalized
surface called a varifold from geometric measure theory which allows the presence of
singularities, Brakke successfully gave it a definition and presented its existence and regularity
theories. Recently, the author provided a complete proof of Brakke’s existence and regularity
theorems, which form the content of the latter half of the book. The regularity theorem is also
a natural generalization of Allard’s regularity theorem, which is a fundamental regularity result
for minimal surfaces and for surfaces with bounded mean curvature. By carefully presenting a
minimal amount of mathematical tools, often only with intuitive explanation, this book serves
as a good starting point for the study of this fascinating object as well as a comprehensive
introduction to other important notions from geometric measure theory.
Due 2019-06-06
1st ed. 2019, Approx. 160 p.
4 illus.
Printed book
Hardcover
ISBN 978-3-030-13157-9
Includes up-to date-surveys on moduli spaces of Kahler-Einstein Fano
varieties
Presents new findings on the existence of minimal models
Offer new connections between classical moduli spaces and tropical ones
This volume is an outcome of the workshop "Moduli of K-stable Varieties", which was held in
Rome, Italy in 2017. The content focuses on the existence problem for canonical Kahler
metrics and links to the algebro-geometric notion of K-stability. The book includes both surveys
on this problem, notably in the case of Fano varieties, and original contributions addressing
this and related problems. The papers in the latter group develop the theory of K-stability;
explore canonical metrics in the Kahler and almost-Kahler settings; offer new insights into the
geometric significance of K-stability; and develop tropical aspects of the moduli space of
curves, the singularity theory necessary for higher dimensional moduli theory, and the
existence of minimal models. Reflecting the advances made in the area in recent years, the
survey articles provide an essential overview of many of the most important findings.The book
is intended for all advanced graduate students and researchers who want to learn about
recent developments in the theory of moduli space, K-stability and Kahler-Einstein metrics.
Due 2019-07-03
1st ed. 2019, Approx. 380 p.
120 illus.
Printed book
Hardcover
ISBN 978-3-030-16030-2
Collection of high-quality, state-of-the-art research and survey articles
Top researchers, including Fields Medal winner like Vaughan Jones
Research in new directions, new tools and methods
This proceedings volume presents a diverse collection of high-quality, state-of-the-art research
and survey articles written by top experts in low-dimensional topology and its applications. The
focal topics include the wide range of historical and contemporary invariants of knots and links
and related topics such as three- and four-dimensional manifolds, braids, virtual knot theory,
quantum invariants, braids, skein modules and knot algebras, link homology, quandles and
their homology; hyperbolic knots and geometric structures of three-dimensional manifolds; the
mechanism of topological surgery in physical processes, knots in Nature in the sense of
physical knots with applications to polymers, DNA enzyme mechanisms, and protein structure
and function. The contents is based on contributions presented at the International Conference
on Knots, Low-Dimensional Topology and Applications ? Knots in Hellas 2016, which was held
at the International Olympic Academy in Greece in July 2016. The goal of the international
conference was to promote the exchange of methods and ideas across disciplines and
generations, from graduate students to senior researchers, and to explore fundamental
research problems in the broad fields of knot theory and low-dimensional topology. This book
will benefit all researchers who wish to take their research in new directions, to learn about
new tools and methods, and to discover relevant and recent literature for future study.
Due 2019-06-15
1st ed. 2019, IX, 138 p.
Printed book
Softcover
ISBN 978-3-030-15674-9
Explores the connections between the classical and representation theoretic
approaches in the study of Siegel modular forms
Illustrates how basic concepts can be applied to solve contemporary
problems in the study of modular forms
Based on lecture notes delivered during a workshop at the Indian Institutes
of Science Education and Research, Pune, India from 2017
This monograph introduces two approaches to studying Siegel modular forms: the classical
approach as holomorphic functions on the Siegel upper half space, and the approach via
representation theory on the symplectic group. By illustrating the interconnections shared by
the two, this book fills an important gap in the existing literature on modular forms. It begins
by establishing the basics of the classical theory of Siegel modular forms, and then details
more advanced topics. After this, much of the basic local representation theory is presented.
Exercises are featured heavily throughout the volume, the solutions of which are helpfully
provided in an appendix. Other topics considered include Hecke theory, Fourier coefficients,
cuspidal automorphic representations, Bessel models, and integral representation. Graduate
students and young researchers will find this volume particularly useful. It will also appeal to
researchers in the area as a reference volume. Some knowledge of GL(2) theory is
recommended, but there are a number of appendices included if the reader is not already
familiar.