1st ed. 2017, VII, 419 p. 94 illus., 53 illus. in color.
Printed book
Hardcover
ISBN 978-1-4939-7485-6
Series: Fields Institute Communications, Vol. 80
* Bridges the gap between graduate courses and cutting-edge
research
* Covers a wide range of topics in combinatoric algebraic geometry
* Connects historical sources, computation, explicit examples, and new
results
This volume consolidates selected articles from the 2016 Apprenticeship Program at the
Fields Institute, part of the larger program on Combinatorial Algebraic Geometry that
ran from July through December of 2016. Written primarily by junior mathematicians,
the articles cover a range of topics in combinatorial algebraic geometry including curves,
surfaces, Grassmannians, convexity, abelian varieties, and moduli spaces. This book
bridges the gap between graduate courses and cutting-edge research by connecting
historical sources, computation, explicit examples, and new results.
1st ed. 2017, XII, 511 p. 15 illus., 8 illus. in color.
Printed book
Hardcover
ISBN 978-3-319-65312-9
November 5, 2017
Series: Springer Proceedings in Mathematics & Statistics, Vol. 208
* Dedicated to Valentin Konakov on the occasion of his 70th birthday
* Brings together the latest findings in the area of stochastic analysis
and statistics
* Written by participants of the international conference organised by
the Higher School of Economics (Moscow) in May 2016
* Covers a wide range of topics from limit theorems, Markov processes,
nonparametric methods, acturial science, population dynamics, and
many others
This book brings together the latest findings in the area of stochastic analysis and
statistics. The individual chapters cover a wide range of topics from limit theorems,
Markov processes, nonparametric methods, acturial science, population dynamics, and
many others. The volume is dedicated to Valentin Konakov, head of the International
Laboratory of Stochastic Analysis and its Applications on the occasion of his 70th
birthday. Contributions were prepared by the participants of the international
conference of the international conference “Modern problems of stochastic analysis and
statistics”, held at the Higher School of Economics in Moscow from May 29 - June 2, 2016.
It offers a valuable reference resource for researchers and graduate students interested in
modern stochastics.
1st ed. 2017, XVIII, 582 p. 59 illus., 11 illus. in color.
Printed book
Hardcover
ISBN 978-3-319-69151-0
November 5, 2017
Series: Trends in Mathematics
* Discusses new research areas and results for sequences and number
theory
* Analyzes the relationship of sequence and group theory to theory of
computation and applications of computer science
* Describes combinatorics on words with a variety of theoretical
approaches
This collaborative book presents recent trends on the study of sequences, including
combinatorics on words and symbolic dynamics, and new interdisciplinary links to group
theory and number theory. Other chapters branch out from those areas into subfields
of theoretical computer science, such as complexity theory and theory of automata.
The book is built around four general themes: number theory and sequences, word
combinatorics, normal numbers, and group theory. Those topics are rounded out by
investigations into automatic and regular sequences, tilings and theory of computation,
discrete dynamical systems, ergodic theory, numeration systems, automaton semigroups,
and amenable groups.
This volume is intended for use by graduate students or research mathematicians, as
well as computer scientists who are working in automata theory and formal language
theory. With its organization around unified themes, it would also be appropriate as a
supplemental text for graduate level courses.
1st ed. 2017, VIII, 118 p. 42 illus., 31 illus. in color.
Printed book
Softcover
ISBN 978-3-319-67881-8
November 5, 2017
Series: SpringerBriefs in Mathematics
* Covers the fundamentals of lattices, employing a strongly
geometrical and visual approach and accompanying exercises
* Assumes only a minimum of background knowledge on the part of the reader
* Includes applications like the construction of spherical codes using
lattices and how to obtain lattices using field theory
This book provides a first course on lattices * mathematical objects pertaining to the
realm of discrete geometry, which are of interest to mathematicians for their structure
and, at the same time, are used by electrical and computer engineers working on coding
theory and cryptography. The book presents both fundamental concepts and a wealth of
applications, including coding and transmission over Gaussian channels, techniques for
obtaining lattices from finite prime fields and quadratic fields, constructions of spherical
codes, and hard lattice problems used in cryptography. The topics selected are covered
in a level of detail not usually found in reference books. As the range of applications
of lattices continues to grow, this work will appeal to mathematicians, electrical and
computer engineers, and graduate or advanced undergraduate in these fields.
1st ed. 2017, X, 112 p. 6 illus.
Printed book
Softcover
ISBN 978-3-319-68148-1
Series: SpringerBriefs in Mathematics
This book studies diverse aspects of braid representations via knots and links. Complete
classification results are illustrated for several properties through Xu’s normal 3-braid
form and the Hecke algebra representation theory of link polynomials developed by
Jones. Topological link types are identified within closures of 3-braids which have a
given Alexander or Jones polynomial. Further classifications of knots and links arising
by the closure of 3-braids are given, and new results about 4-braids are part of the work.
Written with knot theorists, topologists,and graduate students in mind, this book features
the identification and analysis of effective techniques for diagrammatic examples with
unexpected properties.
1st ed. 2017, Approx. 575 p.
Printed book
Hardcover
ISBN 978-3-319-69807-6
November 5, 2017
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern
Surveys in Mathematics, Vol. 67
* Offers the first comprehensive treatment of R-boundedness, Banach
space-valued square functions and γ-radonifying operators
* Develops their deep connections with the holomorphic functional
calculus of sectorial and bi-sectorial operators
* Offers a self-contained presentation and complete, detailed proofs of
results in both the core and the background material
This second volume of Analysis in Banach Spaces, Probabilistic Methods and Operator
Theory, is the successor to Volume I, Martingales and Littlewood-Paley Theory. It
presents a thorough study of the fundamental randomisation techniques and the
operator-theoretic aspects of the theory. The first two chapters address the relevant
classical background from the theory of Banach spaces, including notions like type,
cotype, K-convexity and contraction principles. In turn, the next two chapters provide a
detailed treatment of the theory of R-boundedness and Banach space valued square
functions developed over the last 20 years. In the last chapter, this content is applied to
develop the holomorphic functional calculus of sectorial and bi-sectorial operators in
Banach spaces. Given its breadth of coverage, this book will be an invaluable reference to
graduate students and researchers interested in functional analysis, harmonic analysis,
spectral theory, stochastic analysis, and the operator-theoretic approach to deterministic
and stochastic evolution equations.