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Recent Developments in Integrable Systems and Related Topics of Mathematical Physics
This volume, whose contributors include leading researchers in their field, covers a wide range of topics surrounding Integrable Systems, from theoretical developments to applications. Comprising a unique collection of research articles and surveys, the book aims to serve as a bridge between the various areas of Mathematics related to Integrable Systems and Mathematical Physics. Recommended for postgraduate students and early career researchers who aim to acquire knowledge in this area in preparation for further research, this book is also suitable for established researchers aiming to get up to speed with recent developments in the area, and may very well be used as a guide for further study.
Discrete Systems and Integrability
A first introduction to the theory of discrete integrable systems at a level suitable for students and non-experts.
Symmetries and Integrability of Difference Equations
This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations. Difference equations are playing an increasingly important role in the natural sciences. Indeed, many phenomena are inherently discrete and thus naturally described by difference equations. More fundamentally, in subatomic physics, space-time may actually be discrete. Differential equations would then just be approximations of more basic discrete ones. Moreover, when using differential equations to analyze continuous processes, it is often necessary to resort to numerical methods. This always involves a discretization of the diffe...
Algebraic Structures In Integrability: Foreword By Victor Kac
Relationships of the theory of integrable systems with various branches of mathematics are extremely deep and diverse. On the other hand, the most fundamental exactly integrable systems often have applications in theoretical physics. Therefore, many mathematicians and physicists are interested in integrable models.The book is intelligible to graduate and PhD students and can serve as an introduction to separate sections of the theory of classical integrable systems for scientists with algebraic inclinations. For the young, the book can serve as a starting point in the study of various aspects of integrability, while professional algebraists will be able to use some examples of algebraic stru...
Soliton Theory and Its Applications
Soliton theory is an important branch of applied mathematics and mathematical physics. An active and productive field of research, it has important applications in fluid mechanics, nonlinear optics, classical and quantum fields theories etc. This book presents a broad view of soliton theory. It gives an expository survey of the most basic ideas and methods, such as physical background, inverse scattering, Backlünd transformations, finite-dimensional completely integrable systems, symmetry, Kac-moody algebra, solitons and differential geometry, numerical analysis for nonlinear waves, and gravitational solitons. Besides the essential points of the theory, several applications are sketched and some recent developments, partly by the authors and their collaborators, are presented.
History of Greek Cinema
The book is a detailed historical survey of Greek cinema from its very beginning (1905) until today (2010).
Toric Topology
This book is about toric topology, a new area of mathematics that emerged at the end of the 1990s on the border of equivariant topology, algebraic and symplectic geometry, combinatorics, and commutative algebra. It has quickly grown into a very active area with many links to other areas of mathematics, and continues to attract experts from different fields. The key players in toric topology are moment-angle manifolds, a class of manifolds with torus actions defined in combinatorial terms. Construction of moment-angle manifolds relates to combinatorial geometry and algebraic geometry of toric varieties via the notion of a quasitoric manifold. Discovery of remarkable geometric structures on mo...
Symmetries and Integrability of Difference Equations
A comprehensive introduction to the subject suitable for graduate students and researchers. This book is also an up-to-date survey of the current state of the art and thus will serve as a valuable reference for specialists in the field.
Tabula Plena
Edited by Bryony Roberts, a collaboration of the Oslo School of Architecture and Design and Columbia University's Graduate School of Architecture, Planning, and Preservation In contrast to tabula rasa urbanism, this book considers strategies for tabula plena -- urban sites that are full of existing buildings of multiple time periods. Such dense sites prompt designers to work between the fields of architecture, historic preservation, and urban planning, developing methods for collaborative authorship and interlocking architectural forms. The book grew from a collaboration between the Oslo School of Architecture and Design and Columbia University's Graduate School of Architecture, Planning and Preservation on the planning of the government quarter in Oslo. Emerging from this process, the book asks larger questions about how we practice, teach, and theorise engagement with existing architecture on an urban scale. It contains a compilation of short essays addressing theoretical questions, a sampling of design projects offering different July formal strategies for architectural design, and a series of discussions about pedagogical strategies. 149 images
