Series: Birkhauser Advanced Texts Basler Lehrbucher
2015, XVI, 448 p. 78 illus., 4 illus. in color.
A product of Birkhauser Basel
Printed book
Hardcover
ISBN 978-1-4939-3090-6
Offers a self-contained treatment of progress and problems related
to the Eulerian numbers
Covers a topic that plays an important role in combinatorics, number
theory, and topology
Provides previously-unpublished coverage of gamma-nonnegativity
of a simplicial complex and its results in combinatorial terms
Includes discussion of open problems and directions for future
research, as well as numerous exercises and examples
This text presents the Eulerian numbers in the context of modern enumerative, algebraic,
and geometric combinatorics. The book first studies Eulerian numbers from a purely
combinatorial point of view, then embarks on a tour of how these numbers arise in the
study of hyperplane arrangements, polytopes, and simplicial complexes. Some topics
include a thorough discussion of gamma-nonnegativity and real-rootedness for Eulerian
polynomials, as well as the weak order and the shard intersection order of the symmetric
group.
The book also includes a parallel story of Catalan combinatorics, wherein the Eulerian
numbers are replaced with Narayana numbers. Again there is a progression from
combinatorics to geometry, including discussion of the associahedron and the lattice of
noncrossing partitions.
The final chapters discuss how both the Eulerian and Narayana numbers have analogues
in any finite Coxeter group, with many of the same enumerative and geometric
properties. There are four appendices, which survey more advanced topics, including
some open problems in combinatorial topology.
This textbook will serve a resource for experts in the field as well as for graduate students
and others hoping to learn about these topics for the first time.
Series: Developments in Mathematics, Vol. 42
2015, X, 175 p. 27 illus.
Printed book
Hardcover
ISBN 978-1-4939-3081-4
Presents an exciting playing field for graduate students and
researchers in mathematics, physics, and computer science, to
expand their knowledge in the field of algebraic geometry
Comprehensive treatment brings graduate students and new
researchers to the forefront of the field
Serves as excellent supplementary material for a graduate course on
Grassmannian varieties
This book gives a comprehensive treatment of the Grassmannian varieties and their
Schubert subvarieties, focusing on the geometric and representation-theoretic aspects of
Grassmannian varieties. Research of Grassmannian varieties is centered at the crossroads
of commutative algebra, algebraic geometry, representation theory, and combinatorics.
Therefore, this text uniquely presents an exciting playing field for graduate students
and researchers in mathematics, physics, and computer science, to expand their
knowledge in the field of algebraic geometry. The standard monomial theory (SMT) for
the Grassmannian varieties and their Schubert subvarieties are introduced and the text
presents some important applications of SMT including the Cohen?Macaulay property,
normality, unique factoriality, Gorenstein property, singular loci of Schubert varieties, toric
degenerations of Schubert varieties, and the relationship between Schubert varieties and
classical invariant theory.
This text would serve well as a reference book for a graduate work on Grassmannian
varieties and would be an excellent supplementary text for several courses including
those in geometry of spherical varieties, Schubert varieties, advanced topics in geometric
and differential topology, representation theory of compact and reductive groups, Lie
theory, toric varieties, geometric representation theory, and singularity theory. The reader
should have some familiarity with commutative algebra and algebraic geometry.
Series: Fields Institute Communications, Vol. 76
2015, XVIII, 346 p. 14 illus.
Printed book
Hardcover
ISBN 978-1-4939-3075-3
Contains articles written by prominent scholars who have developed
stochastics for the last forty years
Presents new results and recent research developments in important
topics in both theoretical and applied probability and statistics
Features review articles providing a short history and state of the art
of the field, in an effort to stimulate future research
This book contains articles arising from a conference in honour of mathematicianstatistician
Mikls Csorg on the occasion of his 80th birthday, held in Ottawa in July 2012.
It comprises research papers and overview articles, which provide a substantial glimpse
of the history and state-of-the-art of the field of asymptotic methods in probability and
statistics, written by leading experts.
The volume consists of twenty articles on topics on limit theorems for self-normalized
processes, planar processes, the central limit theorem and laws of large numbers, changepoint
problems, short and long range dependent time series, applied probability and
stochastic processes, and the theory and methods of statistics. It also includes Csorgfs list
of publications during more than 50 years, since 1962.
Series: Research Perspectives CRM Barcelona, Vol. 4
2015, X, 120 p. 26 illus., 14 illus. in color.
A product of Birkhauser Basel
Printed book
Softcover
ISBN 978-3-319-22128-1
The two parts of the present volume contain extended conference abstracts
corresponding to selected talks given by participants at the "Conference on Hamiltonian
Systems and Celestial Mechanics 2014" (HAMSYS2014) (15 abstracts) and at the
"Workshop on Virus Dynamics and Evolution" (12 abstracts), both held at the Centre
de Recerca Matematica (CRM) in Barcelona from June 2nd to 6th, 2014, and from June
23th to 27th, 2014, respectively. Most of them are brief articles, containing preliminary
presentations of new results not yet published in regular research journals. The articles are
the result of a direct collaboration between active researchers in the area after working in
a dynamic and productive atmosphere.
The first part is about Central Configurations, Periodic Orbits and Hamiltonian Systems
with applications to Celestial Mechanics ? a very modern and active field of research.
The second part is dedicated to mathematical methods applied to viral dynamics and
evolution. Mathematical modelling of biological evolution currently attracts the interest
of both mathematicians and biologists. This material offers a variety of new exciting
problems to mathematicians and reasonably inexpensive mathematical methods to
evolutionary biologists. It will be of scientific interest to both communities.
The book is intended for established researchers, as well as for PhD and postdoctoral
students who want to learn more about the latest advances in these highly active areas of
research.
Series: Studies in Universal Logic
2015, X, 390 p. 9 illus.
A product of Birkhauser Basel
Printed book
Softcover
ISBN 978-3-319-22086-4
Presents an original work on the foundations of logic and
mathematics
Covers many topics in logic, mathematics and physics that are
relevant to formal logic and the philosophy of science
Offers a new foundational and critical perspective in constructivist
foundations
The diverse range of topics will be of interest to a broad audience of
scholars
This book offers an original contribution to the foundations of logic and mathematics,
and focuses on the internal logic of mathematical theories, from arithmetic or number
theory to algebraic geometry. Arithmetical logic is the term used to refer to the internal
logic of classical arithmetic, here called Fermat-Kronecker arithmetic, and combines
Fermatfs method of infinite descent with Kroneckerfs general arithmetic of homogeneous
polynomials. The book also includes a treatment of theories in physics and mathematical
physics to underscore the role of arithmetic from a constructivist viewpoint. The scope
of the work intertwines historical, mathematical, logical and philosophical dimensions
in a unified critical perspective; as such, it will appeal to a broad readership from
mathematicians to logicians, to philosophers interested in foundational questions.
Researchers and graduate students in the fields of philosophy and mathematics will
benefit from the authorfs critical approach to the foundations of logic and mathematics.