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...
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...
