All ebooks in the collection "Progress in Mathematics" - Birkhäuser

From Geometry to Quantum Mechanics

Yoshiaki Maeda , Peter Michor , Takushiro Ochiai , Akira Yoshioka

Hideki Omori is widely recognized as one of the world’s most creative and original mathematicians. This volume is dedicated toHideki Omori on the occasion of his retirement from Tokyo University of Science. His retirement was also celebrated in April 2004 with an...

Rigorous Quantum Field Theory

Anne Boutet De Monvel , Detlev Buchholz , Daniel Iagolnitzer , Ugo Moschella

Jacques Bros has greatly advanced our present understanding of rigorous quantum field theory through numerous fundamental contributions. The impact of his work is also visible in several articles in this book. Quantum fields are considered as genuine mathematical...

Number Fields and Function Fields – Two Parallel Worlds

Bjj Moonen , René Schoof , Gerard B. M. Van Der Geer

Ever since the analogy between number fields and function fields was discovered, it has been a source of inspiration for new ideas, and a long history has not in any way detracted from the appeal of the subject. As a deeper understanding of this analogy could have...

The Fourfold Way in Real Analysis

André Unterberger

The Algebra of Secondary Cohomology Operations

Hans-Joachim Baues

The algebra of primary cohomology operations computed by the well-known Steenrod algebra is one of the most powerful tools of algebraic topology. This book computes the algebra of secondary cohomology operations which enriches the structure of the Steenrod algebra in a...

Infinite Groups: Geometric, Combinatorial and Dynamical Aspects

Laurent Bartholdi , Tullio Ceccherini-Silberstein , Tatiana Smirnova-Nagnibeda , Andrzej Zuk

This book offers a panorama of recent advances in the theory of infinite groups. It contains survey papers contributed by leading specialists in group theory and other areas of mathematics. Topics include amenable groups, Kaehler groups, automorphism groups of rooted...

Perturbation Methods and Semilinear Elliptic Problems on R^n

Antonio Ambrosetti , Andrea Malchiodi

Several important problems arising in Physics, Di?erential Geometry and other n topics lead to consider semilinear variational elliptic equations on R and a great deal of work has been devoted to their study. From the mathematical point of view, the main interest relies...

On the Topology of Isolated Singularities in Analytic Spaces

José Seade

Lie Theory

Jean-Philippe Anker , Bent Orsted

Lie Theory: Unitary Representations and Compactifications of Symmetric Spaces, a self-contained work by A. Borel, L. Ji and T. Kobayashi, focuses on two fundamental questions in the theory of semisimpleLie groups: the geometry of Riemannian symmetric spaces and their...

Lie Theory

Jean-Philippe Anker , Bent Orsted

Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics. Three independent, self-contained volumes, under the general title of Lie Theory, feature survey work...

Poisson Structures and Their Normal Forms

Jean-Paul Dufour , Nguyen Tien Zung

Poisson manifolds play a fundamental role in Hamiltonian dynamics, where they serve as phase spaces. They also arise naturally in other mathematical problems, and form a bridge from the "commutative world" to the "noncommutative world". The aim of this book is twofold:...