The aim of this book is to present the fundamental concepts and properties of the geodesic flow of a closed Riemannian manifold. The topics covered are close to my research interests. An important goal here is to describe properties of the geodesic flow which do not require curvature assumptions. A typical example of such a property and a central result in this work is Mane's formula that relates the topological entropy of the geodesic flow with the exponential growth rate of the average numbers of geodesic arcs between two points in the manifold. The material here can be reasonably covered...
The aim of this book is to present the fundamental concepts and properties of the geodesic flow of a closed Riemannian manifold. The topics covered ar...
Rigid (analytic) spaces were invented to describe degenerations, reductions, and moduli of algebraic curves and abelian varieties. This work, a revised and greatly expanded new English edition of an earlier French text by the same authors, presents important new developments and applications of the theory of rigid analytic spaces to abelian varieties, "points of rigid spaces," etale cohomology, Drinfeld modular curves, and Monsky-Washnitzer cohomology. The exposition is concise, self-contained, rich in examples and exercises, and will serve as an excellent graduate-level text for the...
Rigid (analytic) spaces were invented to describe degenerations, reductions, and moduli of algebraic curves and abelian varieties. This work, a revise...
This volume Studies in Memory of Issai Schur was conceived as a tribute to Schur's of his tragic end. His impact on great contributions to mathematics and in remembrance of mathematicians Representation Theory alone was so great that a significant number of Researchers (TMR) Network, in the European Community Training and Mobility Orbits, Crystals and Representation Theory, in operation during the period (1997-2002) have been occupied with what has been called Schur theory. Consequently, this volume has the additional purpose of recording some of the significant results of the network. It was...
This volume Studies in Memory of Issai Schur was conceived as a tribute to Schur's of his tragic end. His impact on great contributions to mathematics...
Kac-Moody Lie algebras 9 were introduced in the mid-1960s independently by V. Kac and R. Moody, generalizing the finite-dimensional semisimple Lie alge bras which we refer to as the finite case. The theory has undergone tremendous developments in various directions and connections with diverse areas abound, including mathematical physics, so much so that this theory has become a stan dard tool in mathematics. A detailed treatment of the Lie algebra aspect of the theory can be found in V. Kac's book Kac-90l This self-contained work treats the algebro-geometric and the topological aspects of...
Kac-Moody Lie algebras 9 were introduced in the mid-1960s independently by V. Kac and R. Moody, generalizing the finite-dimensional semisimple Lie alg...
Presents many major differential geometric acheivements in the theory of CR manifolds for the first time in book form
Explains how certain results from analysis are employed in CR geometry
Many examples and explicitly worked-out proofs of main geometric results in the first section of the book making it suitable as a graduate main course or seminar textbook
Provides unproved statements and comments inspiring further study
Presents many major differential geometric acheivements in the theory of CR manifolds for the first time in book form
This research monograph is a systematic exposition of the background, methods, and recent results in the theory of cycle spaces of ?ag domains. Some of the methods are now standard, but many are new. The exposition is carried out from the viewpoint of complex algebraic and differential geometry. Except for certain foundational material, whichisreadilyavailablefromstandardtexts, itisessentiallyself-contained; at points where this is not the case we give extensive references. After developing the background material on complex ?ag manifolds and rep- sentationtheory,...
This research monograph is a systematic exposition of the background, methods, and recent results in the theory of cycle spaces of ?ag domains. Some o...
Invited articles by leading researchers explore various aspects of the parallel worlds of function fields and number fields
Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and t-motives
Aimed at graduate students, mathematicians, and researchers interested in geometry and arithmetic and their connections
Invited articles by leading researchers explore various aspects of the parallel worlds of function fields and number fields
Eisenstein series are an essential ingredient in the spectral theory of automorphic forms and an important tool in the theory of L-functions. They have also been exploited extensively by number theorists for many arithmetic purposes. Bringing together contributions from areas that are not usually interacting with each other, this volume introduces diverse users of Eisenstein series to a variety of important applications. With this juxtaposition of perspectives, the reader obtains deeper insights into the arithmetic of Eisenstein series.
The central theme of the exposition...
Eisenstein series are an essential ingredient in the spectral theory of automorphic forms and an important tool in the theory of L-functio...
This volume uses a unified approach to representation theory and automorphic forms. It collects papers, written by leading mathematicians, that track recent progress in the expanding fields of representation theory and automorphic forms and their association with number theory and differential geometry. Topics include: Automorphic forms and distributions, modular forms, visible-actions, Dirac cohomology, holomorphic forms, harmonic analysis, self-dual representations, and Langlands Functoriality Conjecture, Both graduate students and researchers will find inspiration in this volume.
This volume uses a unified approach to representation theory and automorphic forms. It collects papers, written by leading mathematicians, that tra...
Hideki Omori is widely recognized as one of the world s most creative and original mathematicians. This volume is dedicated to Hideki Omori on the occasion of his retirement from Tokyo University of Science. His retirement was also celebrated in April 2004 with an in?uential conference at the Morito Hall of Tokyo University of Science. Hideki Omori was born in Nishionmiya, Hyogo prefecture, in 1938 and was an undergraduate and graduate student at Tokyo University, where he was awarded his Ph.D degree in 1966 on the study of transformation groups on manifolds 3], which became one of his major...
Hideki Omori is widely recognized as one of the world s most creative and original mathematicians. This volume is dedicated to Hideki Omori on the occ...
