Series: Progress in Mathematics, Vol. 324
1st ed. 2017, VIII, 364 p.
Hardcover
ISBN 978-3-319-59938-0
* Contains foundational research papers by leading experts in rapidly
developing fields
* Provides new ideas at the interface of algebraic geometry and
mathematical physics
* A tribute to M. Kontsevich in admiration by close colleagues and
friends
This volume is a tribute to Maxim Kontsevich, one of the most original and influential
mathematicians of our time. Maxim's vision has inspired major developments in many
areas of mathematics, ranging all the way from probability theory to motives over finite
fields, and brought forth a paradigm shift at the interface of modern geometry and
mathematical physics. Many of his papers have opened completely new directions of
research and leading to solutions of many classical problems. This book collects papers by
leading experts, working on topics close to Maxim’s heart.
S. Donaldson
A. Goncharov
D. Kaledin
M. Kapranov
A. Kapustin
L. Katzarkov
A. Noll
P. Pandit
S. Pimenov
J.
Series: Lecture Notes in Mathematics, Vol. 2180
1st ed. 2017, X, 230 p. 68 illus., 56 illus. in color.
Softcover
ISBN 978-3-319-60770-2
* Bridges the gap between academic developments in optimization
and control and tools applied in industry
* Presents the state-of-the-art developments in optimization and
control in an attractive and self-contained manner
* Developed by early career researchers, the text exhibits a good
balance between clarity and scientific rigor
Focusing on applications to science and engineering, this book presents the results of the
ITN-FP7 SADCO network’s innovative research in optimization and control in the following
interconnected topics: optimality conditions in optimal control, dynamic programming
approaches to optimal feedback synthesis and reachability analysis, and computational
developments in model predictive control. The novelty of the book resides in the fact that
it has been developed by early career researchers, providing a good balance between
clarity and scientific rigor. Each chapter features an introduction addressed to PhD
students and some original contributions aimed at specialist researchers. Requiring only
a graduate mathematical background, the book is self-contained. It will be of particular
interest to graduate and advanced undergraduate students, industrial practitioners and to
senior scientists wishing to update their knowledge.
Series: Levy Matters, Vol. 2187
1st ed. 2017, X, 360 p. 15 illus.
Softcover
ISBN 978-3-319-60887-7
* All results are illustrated with numerous applications
* Numerous examples of Levy-type processes offer new possibilities to
model irregular phenomena
* Detailed explanations help the reader to get a better understanding
of Levy-type processes
Presenting some recent results on the construction and the moments of Levy-type
processes, the focus of this volume is on a new existence theorem, which is proved using
a parametrix construction. Applications range from heat kernel estimates for a class of
Levy-type processes to existence and uniqueness theorems for Levy-driven stochastic
differential equations with Holder continuous coefficients. Moreover, necessary and
sufficient conditions for the existence of moments of Levy-type processes are studied
and some estimates on moments are derived. Levy-type processes behave locally like
Levy processes but, in contrast to Levy processes, they are not homogeneous in space.
Typical examples are processes with varying index of stability and solutions of Levy-driven
stochastic differential equations.
This is the sixth volume in a subseries of the Lecture Notes in Mathematics called Levy
Matters. Each volume describes a number of important topics in the theory or applications
of Levy processes and pays tribute to the state of the art of this rapidly evolving subject,
with special emphasis on the non-Brownian world.
Series: C.I.M.E. Foundation Subseries, Vol. 2186
1st ed. 2018, X, 290 p. 75 illus., 70 illus. in color.
Softcover
ISBN 978-3-319-61493-9
* Clearly presented, with a particular emphasis on introducing young
students to important research topics
* Features a state-of-the-art description of rapidly developing topics in
nonlinear, nonlocal diffusions and interactions
* Authored by well-known researchers, who have the capacity to single
out some of the most promising topics in stationary and evolutionary
local and nonlocal PDEs
Presenting a selection of topics in the area of nonlocal and nonlinear diffusions, this
book places a particular emphasis on new emerging subjects such as nonlocal operators
in stationary and evolutionary problems and their applications, swarming models and
applications to biology and mathematical physics, and nonlocal variational problems. The
authors are some of the most well-known mathematicians in this innovative field, which
is presently undergoing rapid development. The intended audience includes experts in
elliptic and parabolic equations who are interested in extending their expertise to the
nonlinear setting, as well as Ph.D. or postdoctoral students who want to enter into the
most promising research topics in the field.
Series: Lecture Notes in Mathematics, Vol. 2188
1st ed. 2017, VI, 215 p. 1 illus.
Softcover
ISBN 978-3-319-61598-1
* Offers a new, universal algebraic and lattice-theoretical
approach Provides tools for further work, for example on varieties of
algebras, but also on operator theory Includes many examples and
counterexamples
Adopting a new universal algebraic approach, this book explores and consolidates the link
between Tarski's classical theory of equidecomposability types monoids, abstract measure
theory (in the spirit of Hans Dobbertin's work on monoid-valued measures on Boolean
algebras) and the nonstable K-theory of rings. This is done via the study of a monoid
invariant, defined on Boolean inverse semigroups, called the type monoid. The new
techniques contrast with the currently available topological approaches. Many positive
results, but also many counterexamples, are provided.
Series: Advanced Courses in Mathematics - CRM Barcelona
1st ed. 2017, Approx. 150 p.
Softcover
ISBN 978-3-319-60939-3
* Features a comprehensive introduction to the connections between
formal language theory and group theoryIncludes Thurston's
compactification of Teichmuller space following the point of view of
geodesic currents on surfaces
* Presents specialized research topics in a friendlier way than in a
research article
This volume contains the lecture notes of the three summer courses given by the
authors during the program "Automorphisms of Free Groups: Geometry, Topology, and
Dynamics", held at the Centre de Recerca Matematica (CRM) in Bellaterra (Barcelona).
The first two chapters present the basic tools from formal language theory (regular and
context-free languages, automata, rewriting systems, transducers, etc) and emphasize
their connections to group theory, mostly relating to free and virtually-free groups. The
material covered is enough to present full proofs of many of the existing interesting
characterizations of virtually-free groups.
The last chapter describes, in a comprehensive exposition, Bonahon's construction
of Thurston's compactification of Teichmuller space, in terms of geodesic currents on
surfaces. It also includes several interesting extensions of the notion of geodesic current to
various other more general settings.