Series: Abel Symposia, Vol. 12
1st ed. 2016, X, 316 p. 10 illus., 2 illus. in
color.
Hardcover
ISBN 978-3-319-39284-4
Like the first Abel Symposium, held in 2004, the Abel Symposium 2015 focused on
operator algebras. It is interesting to see the remarkable advances that have been made
in operator algebras over these years, which strikingly illustrate the vitality of the field. A
total of 26 talks were given at the symposium on a variety of themes, all highlighting the
richness of the subject.
The field of operator algebras was created in the 1930s and was motivated by problems of
quantum mechanics. It has subsequently developed well beyond its initial intended realm
of applications and expanded into such diverse areas of mathematics as representation
theory, dynamical systems, differential geometry, number theory and quantum algebra.
One branch, known as “noncommutative geometry”, has become a powerful tool for
studying phenomena that are beyond the reach of classical analysis.
This volume includes research papers that present new results, surveys that discuss
the development of a specific line of research, and articles that offer a combination of
survey and research. These contributions provide a multifaceted portrait of beautiful
mathematics that both newcomers to the field of operator algebras and seasoned
researchers alike will appreciate.
Series: Trends in Mathematics
1st ed. 2016, Approx. 350 p.
Hardcover
ISBN 978-3-319-39338-4
* Presents authoritative research on Singularity Theory in different
settings
* Provides recent developments in Singularity Theory written by
specialists in the area
This book features state-of-the-art research on singularities in geometry, topology,
foliations and dynamics and provides an overview of the current state of singularity theory
in these settings.
Singularity theory is at the crossroad of various branches of mathematics and science in
general. In recent years there have been remarkable developments, both in the theory
itself and in its relations with other areas.
The contributions in this volume originate from the “Workshop on Singularities in
Geometry, Topology, Foliations and Dynamics”, held in Merida, Mexico, in December
2014, in celebration of Jose Seade’s 60th Birthday.
It is intended for researchers and graduate students interested in singularity theory and its
impact on other fields.
Series: Springer Series in Statistics
1st ed. 2016, XIII, 539 p. 155 illus., 89 illus. in
color.
Hardcover
ISBN 978-3-319-33152-2
* Presents both theory and practical implementation of multivariate
statistical analysis in LISREL
* Illustrates all methods and procedures on numerous examples with
detailed explanations
* Appeals to graduate students as well as researchers from the social,
behavioral and economic sciences
This book traces the theory and methodology of multivariate statistical analysis and shows
how it can be conducted in practice using the LISREL computer program. It presents
not only the typical uses of LISREL, such as confirmatory factor analysis and structural
equation models, but also several other multivariate analysis topics, including regression
(univariate, multivariate, censored, logistic, and probit), generalized linear models,
multilevel analysis, and principal component analysis. It provides numerous examples
from several disciplines and discusses and interprets the results, illustrated with sections
of output from the LISREL program, in the context of the example. The book is intended
for masters and PhD students and researchers in the social, behavioral, economic and
many other sciences who require a basic understanding of multivariate statistical theory
and methods for their analysis of multivariate data. It can also be used as a textbook on
various topics of multivariate statistical analysis.
Series: Advanced Courses in Mathematics - CRM Barcelona
1st ed. 2017, Approx. 190 p.
Softcover
ISBN 978-3-319-34119-4
* Studies invariance and comparison principles for parabolic SPDEs in a
very general framework beyond the classical setting
* Presents an extensive introduction to Levy processes, including the
different constructions
* Provides properties of Feller processes as space inhomogeneous
processes that behave locally like Levy processes
This volume contains the lecture notes of the two courses given by Davar Khoshnevisan
and Rene Schilling, respectively, at the second edition of the Barcelona Summer School
on Stochastic Analysis, held at the Centre de Recerca Matematica (CRM) in Bellaterra
(Barcelona).
The course by Davar Khoshnevisan deals with some problems in the field of stochastic
partial differential equations of parabolic type. More precisely, the main objective is
to establish an Invariance Principle for those equations in a rather general setting, and
also deduce, as an application, comparison-type results. The framework in which these
problems are addressed go beyond the classical setting, in the sense that the driving noise
is assumed to be a multiplicative space-time white noise on a group, and the underlying
elliptic operator corresponds to a generator of a Levy process on that group. This implies
that stochastic integration with respect to the above noise, as well as existence and
uniqueness of solution for the corresponding equation, become relevant on their own.
These aspects are also developed, in parallel with a lot of illustrative examples.
Rene Schilling's notes are an expanded version of his course on Levy and Levytype
processes. Its purpose is two-fold: on the one hand, it extensively presents
some properties of the Levy processes, mainly as Markov processes, and its different
constructions, leading eventually to the celebrated Levy-Ito decomposition. On the other
hand, it identifies the infinitesimal generator of the Levy process as a pseudo-differential
operator whose symbol is the characteristic exponent of the process, allowing to study the
properties of Feller processes as space inhomogeneous processes that behave locally like
Levy processes. The presentation is self-contained, and different chapters are enclosed to
review Markov processes, operator semigroups, random measures, etc.
Series: Advanced Courses in Mathematics - CRM Barcelona
1st ed. 2017, Approx. 150 p.
Softcover
ISBN 978-3-319-33502-5
* Provides a clear introduction to Differential Galois Theory and to
Picard-Vessiot TheoryEstablishes, as a first book, a connection
between Singularities of bi-Hamiltonian systems, stability analysis,
and Poisson pencils
* Shows how to apply the tools used in integrable Hamiltonian systems
to integrable non-Hamiltonian systems, with applications in Control
Theory, economics, and biology
This book contains an elaborated version of the lecture notes given at the Advanced
Course on Geometry and Dynamics of Integrable Systems, held at the CRM in Barcelona.
Native to actual problem-solving problems in mechanics, the topic of Integrable Systems
is currently on the crossroad of different disciplines in pure and applied mathematics, and
it has important interactions with physics. The study of integrable systems has had special
impact and also actively uses methods of Differential Geometry. It is extremely important
in Symplectic Geometry and Hamiltonian Dynamics, and has strong correlations with
Mathematical Physics, Lie Theory and Algebraic Geometry (including Mirror Symmetry).
Therefore, these notes will attract experts from different backgrounds
These notes concentrate on three different aspects of integrable systems: obstructions
to integrability coming from Differential Galois theory, description of singularities of
integrable systems using their relation to bi-Hamiltonian systems, and generalization of
integrable systems to the non-Hamiltonian settings. The three parts are written by top
experts in these fields.