Due 2018-09-21
1st ed. 2018, VIII, 322 p.
55 illus., 4 illus. in color.
Hardcover
ISBN 978-3-319-95347-2
Series
Graduate Texts in Mathematics
Presents a thorough study of binomial ideals and their applications, working
from the basics through to current research
Offers an accessible introduction to the area for combinatorialists and
statisticians, building only on the basics of commutative algebra.
Explores the new research area of algebraic statistics and its relation to toric
ideals and their Grobner bases
This textbook provides an introduction to the combinatorial and statistical aspects of
commutative algebra with an emphasis on binomial ideals. In addition to thorough coverage of
the basic concepts and theory, it explores current trends, results, and applications of binomial
ideals to other areas of mathematics. The book begins with a brief, self-contained overview of
the modern theory of Grobner bases and the necessary algebraic and homological concepts
from commutative algebra. Binomials and binomial ideals are then considered in detail, along
with a short introduction to convex polytopes. Chapters in the remainder of the text can be
read independently and explore specific aspects of the theory of binomial ideals, including
edge rings and edge polytopes, join-meet ideals of finite lattices, binomial edge ideals, ideals
generated by 2-minors, and binomial ideals arising from statistics. Each chapter concludes with
a set of exercises and a list of related topics and results that will complement and offer a
better understanding of the material presented. Binomial Ideals is suitable for graduate
students in courses on commutative algebra, algebraic combinatorics, and statistics.
Additionally, researchers interested in any of these areas but familiar with only the basic facts
of commutative algebra will find it to be a valuable resource.
Due 2018-09-07
1st ed. 2018, X, 286 p. 56
illus., 50 illus. in color.
Softcover
ISBN 978-3-319-94910-9
Series
C.I.M.E. Foundation Subseries
Contains a multi-perspective exposition of the use of splines in the numerical
treatment of PDEs
Covers mathematical foundations, numerical paradigms, and
implementational issues
Collects contributions from internationally renowned experts in the field
This book takes readers on a multi-perspective tour through state-of-the-art mathematical
developments related to the numerical treatment of PDEs based on splines, and in particular
isogeometric methods. A wide variety of research topics are covered, ranging from
approximation theory to structured numerical linear algebra. More precisely, the book provides
(i) a self-contained introduction to B-splines, with special focus on approximation and
hierarchical refinement, (ii) a broad survey of numerical schemes for control problems based
on B-splines and B-spline-type wavelets, (iii) an exhaustive description of methods for
computing and analyzing the spectral distribution of discretization matrices, and (iv) a detailed
overview of the mathematical and implementational aspects of isogeometric analysis. The text
is the outcome of a C.I.M.E. summer school held in Cetraro (Italy), July 2017, featuring four
prominent lecturers with different theoretical and application perspectives. The book may serve
both as a reference and an entry point into further research.
Due 2018-09-16
1st ed. 2018, X, 190 p. 32
illus., 4 illus. in color.
Softcover
ISBN 978-3-319-95185-0
Series
C.I.M.E. Foundation Subseries
Provides an excellent, up-to-date and friendly introduction to the hot topics in
the study of PDEs
Will attract potential readers from several areas of mathematics
Presents numerous open problems that are discussed in some detail
The aim of this book is to present different aspects of the deep interplay between Partial
Differential Equations and Geometry. It gives an overview of some of the themes of recent
research in the field and their mutual links, describing the main underlying ideas, and providing
up-to-date references. Collecting together the lecture notes of the five mini-courses given at
the CIME Summer School held in Cetraro (Cosenza, Italy) in the week of June 19?23, 2017,
the volume presents a friendly introduction to a broad spectrum of up-to-date and hot topics
in the study of PDEs, describing the state-of-the-art in the subject. It also gives further details
on the main ideas of the proofs, their technical difficulties, and their possible extension to other
contexts. Aiming to be a primary source for researchers in the field, the book will attract
potential readers from several areas of mathematics.
Due 2018-10-14
1st ed. 2018, VIII, 100 p.
Softcover
ISBN 978-3-319-95039-6
Series :Lecture Notes in Mathematics
The first book presenting a systematic study of the Sovolev/BV capacity
theory in the Gaussian setting
Provides fundamental material for a cross-disciplinary field
Provides interesting applications in the geometry of Gaussian space
This monograph develops the Gaussian functional capacity theory with applications to
restricting the Gaussian Campanato/Sobolev/BV space. Included in the text is a new geometric
characterization of the Gaussian 1-capacity and the Gaussian Poincare 1-inequality. Applications
to function spaces and geometric measures are also presented. This book will be of use to
researchers who specialize in potential theory, elliptic differential equations, functional analysis,
probability, and geometric measure theory.
Due 2018-10-15
1st ed. 2018, XII, 218 p.
Softcover
ISBN 978-3-319-98269-4
Series : Universitext
Contains an application of quivers to the Harish-Chandra modules for SL(2)
Focuses on representations of finite groups
Includes expositions of the theory of representations of quivers along with
substatial material on continuous groups
Introduces more advanced topics, such as representations of quantum
groups and representations over non-Archimedean local fields, in an
elementary way that is accessible to students
This text covers a variety of topics in representation theory and is intended for graduate
students and more advanced researchers who are interested in the field. The book begins with
classical representation theory of finite groups over complex numbers and ends with results on
representation theory of quivers. The text includes in particular infinite-dimensional unitary
representations for abelian groups, Heisenberg groups and SL(2), and representation theory of
finite-dimensional algebras. The last chapter is devoted to some applications of quivers,
including Harish-Chandra modules for SL(2). Ample examples are provided and some are
revisited with a different approach when new methods are introduced, leading to deeper
results. Exercises are spread throughout each chapter. Prerequisites include an advanced
course in linear algebra that covers Jordan normal forms and tensor products as well as basic
results on groups and rings.