In Exterior Differential Systems, the authors present the results of their ongoing development of a theory of the geometry of differential equations, focusing especially on Lagrangians and Poincare-Cartan forms. They also cover certain aspects of the theory of exterior differential systems, which provides the language and techniques for the entire study, because it plays a central role in uncovering geometric properties of differential equations, the method of equivalence is particularly emphasized. In addition, the authors discuss conformally invariant systems at length, including results on...
In Exterior Differential Systems, the authors present the results of their ongoing development of a theory of the geometry of differential equations, ...
Changes in algebraic geometry have made the subject increasingly inaccessible to all but specialists in the field. This comprehensive, self-contained monograph presents some of the main, general results of the theory accompanied by, and with emphasis on, their applications to the study of interesting examples and to the development of computational tools. The effective utilization of the techniques of elementary complex analysis and topology synthesize the classical and the modern into a cohesive presentation.
Changes in algebraic geometry have made the subject increasingly inaccessible to all but specialists in the field. This comprehensive, self-contained ...
This book presents an overview of recent developments in the area of localization for quasi-periodic lattice Schrodinger operators and the theory of quasi-periodicity in Hamiltonian evolution equations. The physical motivation of these models extends back to the works of Rudolph Peierls and Douglas R. Hofstadter, and the models themselves have been a focus of mathematical research for two decades. Jean Bourgain here sets forth the results and techniques that have been discovered in the last few years. He puts special emphasis on so-called "non-perturbative" methods and the important role...
This book presents an overview of recent developments in the area of localization for quasi-periodic lattice Schrodinger operators and the theory o...
Containing four parts such as Analytic Geometry, Algebraic Geometry, Variations of Hodge Structures, and Differential Systems that are organized according to the subject matter, this title provides the reader with a panoramic view of important and exciting mathematics during the second half of the 20th century.
Containing four parts such as Analytic Geometry, Algebraic Geometry, Variations of Hodge Structures, and Differential Systems that are organized accor...
Covers analytic geometry, algebraic geometry, variations of Hodge Structures, and differential systems. This book also provides the reader with a panoramic view of important and exciting mathematics during the second half of the 20th century.
Covers analytic geometry, algebraic geometry, variations of Hodge Structures, and differential systems. This book also provides the reader with a pano...
Containing four parts such as Analytic Geometry, Algebraic Geometry, Variations of Hodge Structures, and Differential Systems that are organized according to the subject matter, this title provides the reader with a panoramic view of important and exciting mathematics during the second half of the 20th century.
Containing four parts such as Analytic Geometry, Algebraic Geometry, Variations of Hodge Structures, and Differential Systems that are organized accor...
This book differs from a number of recent books on this subject in that it combines analytic and geometric methods at the outset, so that the reader can grasp the basic results of the subject. Although such modern techniques of sheaf theory, cohomology, and commutative algebra are not covered here, the book provides a solid foundation to proceed to more advanced texts in general algebraic geometry, complex manifolds, and Riemann surfaces, as well as algebraic curves. Containing numerous exercises this book would make an excellent introductory text.
This book differs from a number of recent books on this subject in that it combines analytic and geometric methods at the outset, so that the reader c...
This completely revised and corrected version of the well-known Florence notes circulated by the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an in-depth look at differential forms and de Tham s theorem on simplicial complexes. In addition, Sullivan s results on computing the rational homotopy type from forms is presented.
New to the Second Edition:
*Fully-revised appendices including an expanded discussion of the Hirsch...
This completely revised and corrected version of the well-known Florence notes circulated by the authors together with E. Friedlander examines basi...
