1st ed. 2019, XVIII, 258 p.
15 illus., 10 illus. in color.
Hardcover
ISBN 978-3-030-34071-1
Series: Trends in Mathematics
The book consists of articles based on the XXXVII Biaowiea Workshop on Geometric Methods
in Physics, 2018. The series of Biaowiea workshops, attended by a community of experts at the
crossroads of mathematics and physics, is a major annual event in the field. This edition of the
workshop featured a special session dedicatedto Professor Daniel Sternheimer on the occasion
of his 80thbirthday. The previously unpublished papers present cutting-edge current research,
typically grounded in geometry and analysis, with applications to classical and quantum
physics. For the past seven years, the Biaowiea Workshops have been complemented by a
School on Geometry and Physics comprising a series ofadvanced lectures for graduate
students and early-career researchers. The book also includes abstracts of the five lecture
series that were given at the seventh school
Due 2020-01-17
1st ed. 2019, X, 454 p. 4illus.
Softcover
ISBN 978-981-15-1727-3
Series :Lecture Notes in Mathematics, 2258
Introduces a new mathematical theory having strong links with several research domains
Opens new research topics with original research results; attracts attention
from researchers and graduate students
Presents in detail the background and the foundation of an Arakelov theory over adelic curves
The purpose of this book is to build the fundament of an Arakelov theory over adelic curves in
order to provide a unified framework for research on arithmetic geometry in several directions.
By adelic curve is meant a field equipped with a family of absolute values parametrized by a
measure space, such that the logarithmic absolute value of each non-zero element of the field
is an integrable function on the measure space. In the literature, such construction has been
discussed in various settings which are apparently transversal to each other. The authors first
formalize the notion of adelic curves and discuss in a systematic way its algebraic covers,
which are important in the study of height theory of algebraic points beyond Weil?Lang’s
height theory. They then establish a theory of adelic vector bundles on adelic curves, which
considerably generalizes the classic geometry of vector bundles or that of Hermitian vector
bundles over an arithmetic curve. They focus on an analogue of the slope theory in the setting
of adelic curves and in particular estimate the minimal slope of tensor product adelic vector
bundles. Finally, by using the adelic vector bundles as a tool, a birational Arakelov geometry for
projective variety over an adelic curve is developed. As an application, a vast generalization of
Nakai?Moishezon’s criterion of positivity is proven in clarifying the arguments of geometric
nature from several fundamental results in the classic geometry of numbers. Assuming basic
knowledge of algebraic geometry and algebraic number theory, the book is almost selfcontained.
It is suitable for researchers in arithmetic geometry as well as graduate students
focusing on these topics for their doctoral theses.
Due 2020-02-15
1st ed. 2020, XX, 438 p.
Hardcover
ISBN 978-3-030-34291-3
Series : Springer Monographs in Mathematics
Nonlinear Oscillations and Global Attractors
Contributes to understanding and predicting global attractors for a special
class of nonautonomous dynamical systems
Author is a leading expert in dynamical systems
Successfully applied to the resolution of different problems in the theory of
linear and non-linear nonautonomous differential equations for more than 50 years
This book emphasizes those topologicalmethods (of dynamical systems) and theories that are
useful in the studyof different classes of nonautonomous evolutionary equations. The content
is developed over six chapters, providinga thorough introduction to the techniques used in the
Chapters III-VI described by Chapter I-II. The author gives asystematic treatment of the basic
mathematical theory and constructive methods for Nonautonomous Dynamics.They show how
these diverse topics are connected to other important parts of mathematics, including Topology,
Functional Analysis and Qualitative Theory of Differential/Difference Equations. Throughout the
book a nice balanceis maintained between rigorous mathematics and applications (ordinary
differential/difference equations, functionaldifferential equations and partial difference
equations). The primary readership includes graduate and PhD studentsand researchers in in
the field of dynamical systems and their applications (control theory, economic dynamics,
mathematical theory of climate, population dynamics, oscillation theory etc).
Due 2020-02-25
1st ed. 2020, XII, 97 p.
Softcover
ISBN 978-3-030-34731-4
Series SpringerBriefs in Mathematics
In measure theory, a familiar representation theorem due to F. Riesz identifies the dual space
Lp(X,L,)* with Lq(X,L,), where 1/p+1/q=1, as long as 1 p<. However, L(X,L,)* cannot be similarly
described, and is instead represented as a class of finitely additive measures. This book
provides a reasonably elementary account of the representation theory of L(X,L,)*, examining
pathologies and paradoxes, and uncovering some surprising consequences. For instance, a
necessary and sufficient condition for a bounded sequence in L(X,L,) to be weakly convergent,
applicable in the one-point compactification of X, is given. With a clear summary of
prerequisites, and illustrated by examples including L(Rn) and the sequence space l, this book
makes possibly unfamiliar material, some of which may be new, accessible to students and
researchers in the mathematical sciences.
Due 2020-02-27
1st ed. 2020, Approx. 350 p.
Hardcover
ISBN 978-3-030-35175-5
Series : Probability Theory and Stochastic Modelling
Presents non-life and life insurance mathematics together with probabilistic
aspects of risk in a single volume at the graduate level
Includes exercises and proposals for further reading in most of its sections
Can potentially replace other textbooks on basic non-life insurance
mathematics and advanced risk management methods in non-life insurance
Provides a reference text for the state-of-the-art of the mathematics of insurance
This textbook provides a broad overview of the present state of insurance mathematics and
some related topics in risk management, financial mathematics and probability. Both non-life
and life aspects are covered. The emphasis is on probability and modeling rather than statistics
and practical implementation. Aimed at the graduate level, pointing in part to current research
topics, it can potentially replace other textbooks on basic non-life insurance mathematics and
advanced risk management methods in non-life insurance. Based on chapters selected
according to the particular topics in mind, the book may serve as a source for introductory
courses to insurance mathematics for non-specialists, advanced courses for actuarial students,
or courses on probabilistic aspects of risk. It will also be useful for practitioners and students
/researchers in related areas such as finance and statistics who wish to get an overview of the
general area of mathematical modeling and analysis in insurance.
Due 2020-02-28
1st ed. 2020, VIII, 229 p.
51 illus., 5 illus. in color.
Hardcover
ISBN 978-3-030-32807-8
Series : Springer Proceedings in Mathematics & Statistics
Presents a unique selection of articles illustrating various aspects of
algebraic combinatorics
Also features a survey, as well as an extensive tutorial
Addresses topics such as association schemes, symmetries of graphs, maps
up to enumeration, and isomorphism problems
This book consists of a selection of peer-reviewed contributions to the Workshop on Algebraic
Graph Theory that took place in Pilsen, Czech Republic in October 2016. Primarily intended for
early career researchers, it presents eight self-contained articles on a selection of topics within
algebraic combinatorics, ranging from association schemes to symmetries of graphs and
isomorphism testing. Algebraic combinatorics is a compelling mathematical discipline based on
the powerful interplay of algebraic and combinatorial methods. Algebraic interpretation of
combinatorial structures (such as symmetry or regularity) has often led to enlightening
discoveries and powerful results, while discrete and combinatorial structures have given rise to
new algebraic structures that have found valuable applications. In addition to these original
research contributions, the reader will find a survey linking numerous threads in algebraic
combinatorics, and an extensive tutorial showcasing the universality of algebraic methods in
the study of combinatorial structures.