Books in the Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics series

Much of the book is devoted to exploring the wealth of ideas and results generated by thirty years of efforts to extend this result to more general classes of processes, culminating in the recent solution of several key conjectures. A large part of this unique book is devoted to the author's influential work.

This book pioneers a nonlinear Fredholm theory in a general class of spaces called polyfolds.

This monograph provides a systematic treatment of the Brauer group of schemes, from the foundational work of Grothendieck to recent applications in arithmetic and algebraic geometry.

Some years ago a conference on l-adic cohomology in Oberwolfach was held with the aim of reaching an understanding of Deligne's proof of the Weil conjec tures. We intended especially to provide a complete introduction to etale and l-adic cohomology theory including the monodromy theory of Lefschetz pencils.

This second volume of Analysis in Banach Spaces, Probabilistic Methods and Operator Theory, is the successor to Volume I, Martingales and Littlewood-Paley Theory.

The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory.

This book introduces the mathematical methods of theoretical and experimental quantum field theory, emphasizing coordinate-free presentations of the objects in play. Offers examples of classical field theories, discusses renormalization methods and more.

This self-contained introduction treats thin geometries and thick buildings from a diagrammatic perspective, covers polar geometries whose projective planes are Desarguesian and offers a basic reference for study of diagram geometry. Includes many examples.

This book covers the basics of Clifford algebras and spinor modules, with applications to the theory of Lie groups. Topics include Petracci's proof of the Poincare-Birkhoff-Witt theorem, quantized Weil algebras, Duflo's theorem for quadratic Lie algebras and more.

Offering the first comprehensive treatment of this subject in book form, this volume presents the elements of a general theory for flows on three-dimensional compact boundaryless manifolds, encompassing flows with equilibria accumulated by regular orbits.

This book, written by a master of the subject, is primarily devoted to discrete subgroups of finite covolume in semi-simple Lie groups. The author not only proves results in the classical geometry setting, but also obtains theorems of an algebraic nature.

This monograph gives an overview of various classes of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrable systems, gauge theory, and complex geometry. The text includes many exercises and open questions.

This, the fourth edition of Stuwe's book on the calculus of variations, surveys new developments in this exciting field. Recently discovered results for backward bubbling in the heat flow for harmonic maps or surfaces are discussed.

This two volume work on Positivity in Algebraic Geometry contains a contemporary account of a body of work in complex algebraic geometry loosely centered around the theme of positivity.

Neron models were invented by A. This volume of the renowned "Ergebnisse" series provides a detailed demonstration of the construction of Neron models from the point of view of Grothendieck's algebraic geometry.

The classical theory of partial differential equations is rooted in physics, where equations (are assumed to) describe the laws of nature. We deal in this book with a completely different class of partial differential equations (and more general relations) which arise in differential geometry rather than in physics.