Published: 27 October 2016 (Estimated)
176 Pages
234x156mm
ISBN: 9780198784913
This volume contains a collection of papers based on lectures delivered by distinguished mathematicians at Clay Mathematics Institute events over the past
few years. It is intended to be the first in an occasional series of
volumes of CMI lectures. Although not explicitly linked, the topics in this inaugural volume have a common flavour
and a common appeal to all who are interested in recent developments in geometry. They are intended to be
accessible to all who work in this general area, regardless of their own particular research interests.
1: Two Lectures On The Jones Polynomial and Khovanov Homology, Edward Witten
2: Elementary Knot Theory, Marc Lackenby
3: Cube Complexes, Subgroups of Mapping Class Groups, and Nilpotent Genus, Martin R. Bridson
4: Polyfolds and Fredholm Theory, Helmut Hofer
5: Maps, Sheaves and K3 Surfaces, Rahul Pandharipande
Hardback
ISBN: 9780198794899
Paperback
ISBN: 9780198794905
Published: 15 December 2016 (Estimated)
632 Pages
234x156mm
All chapters have been revised to improve the exposition and to make them more readable, new material has been added in many places, and various
proofs have been tightened up. Copious new references to key papers have been added to the bibliography.
A section on GIT has been added to Chapter 5.
The material on contact geometry in Chapter 3 has been expanded.
Chapter 13 has been completely rewritten and has a new title (Questions of Existence and Uniqueness). It now contains an introduction to existence
and uniqueness problems in symplectic topology, a section an various examples, an overview of Taubes-Seiberg-Witten theory and its applications to
symplectic topology, and a section on symplectic 4-manifolds.
A new Chapter 14 on open problems in the eld has been added.
FOUNDATIONS
1: From classical to modern
2: Linear symplectic geometry
3: Symplectic manifolds
4: Almost complex structures
SYMPLECTIC MANIFOLDS
5: Symplectic group actions
6: Symplectic Fibrations
7: Constructing Symplectic Manifolds
SYMPLECTOMORPHISMS
8: Area-preserving dieomorphisms
9: Generating functions
10: The group of symplectomorphisms
SYMPLECTIC INVARIANTS
11: The Arnold conjecture
12: Symplectic capacities
13: Questions of existence and uniqueness
14: Open problems
A: Smooth Maps
Series: Understanding Complex Systems
2nd ed. 2016, X, 273 p. 119 illus.
Hardcover
ISBN 978-3-319-42495-8
* Offers a concise introduction to the key concepts and control of chaos in dynamical systems
* Explores, in this second edition, the many interfaces of quantum physics and dynamical systems
* Examines the potential role of chaos as control parameter itself in applications
This book offers a short and concise introduction to the many facets of chaos theory.
While the study of chaotic behavior in nonlinear, dynamical systems is a well-established
research field with ramifications in all areas of science, there is a lot to be learnt about how
chaos can be controlled and, under appropriate conditions, can actually be constructive in
the sense of becoming a control parameter for the system under investigation, stochastic
resonance being a prime example.
The present work stresses the latter aspects and, after recalling the paradigm changes
introduced by the concept of chaos, leads the reader skillfully through the basics of chaos
control by detailing the relevant algorithms for both Hamiltonian and dissipative systems,
among others.
The main part of the book is then devoted to the issue of synchronization in chaotic
systems, an introduction to stochastic resonance, and a survey of ratchet models. In this
second, revised and enlarged edition, two more chapters explore the many interfaces
of quantum physics and dynamical systems, examining in turn statistical properties of
energy spectra, quantum ratchets, and dynamical tunneling, among others.
This text is particularly suitable for non-specialist scientists, engineers, and applied
mathematical scientists from related areas, wishing to enter the field quickly and efficiently.
1st ed. 2016, X, 242 p. 64 illus., 47 illus. in color.
Hardcover
ISBN 978-3-319-39443-5
Series: Understanding Complex Systems
* First monograph on this emerging subject matter
* Edited and authored by leading researchers in the field
* Develops novel quantitiative methods for the humanities and social sciences
With an emphasis on exploring measurable aspects of ancient narratives, Maths Meets
Myths sets out to investigate age-old material with new techniques. This book collects,
for the first time, novel quantitative approaches to studying sources from the past, such
as chronicles, epics, folktales, and myths. It contributes significantly to recent efforts in
bringing together natural scientists and humanities scholars in investigations aimed at
achieving greater understanding of our cultural inheritance.
Accordingly, each contribution reports on a modern quantitative approach applicable
to narrative sources from the past, or describes those which would be amenable to such
treatment and why they are important.
This volume is a unique state-of-the-art compendium on an emerging research field which
also addresses anyone with interests in quantitative approaches to humanities.
1st ed. 2016, XII, 266 p. 31 illus.
Softcover
ISBN 978-3-319-42823-9
Series: La Matematica per il 3+2, Vol. 104
* Offers more than 200 problems with detailed solutions, helping the reader to "learn by doing"
* The concise summary of the theory provides an overall view of the subject, highlighting the most important points
* Uses simple and modern language for better readability
This book starts with a concise but rigorous overview of the basic notions of projective
geometry, using straightforward and modern language. The goal is not only to establish
the notation and terminology used, but also to offer the reader a quick survey of the
subject matter. In the second part, the book presents more than 200 solved problems,
for many of which several alternative solutions are provided. The level of difficulty of the
exercises varies considerably: they range from computations to harder problems of a
more theoretical nature, up to some actual complements of the theory. The structure of
the text allows the reader to use the solutions of the exercises both to master the basic
notions and techniques and to further their knowledge of the subject, thus learning some
classical results not covered in the first part of the book. The book addresses the needs of
undergraduate and graduate students in the theoretical and applied sciences, and will
especially benefit those readers with a solid grasp of elementary Linear Algebra.