Krause, H., Universitat Bielfeld,
Ringel, C.M., Universitat Bielfeld,
(Ed.)
Infinite Length Modules
Trends in Mathematics
Approx. 425 pages. Hardcover
ISBN 3-7643-6413-0
English
Due in August 2000
This book is concerned with the role played by modules of infinite length when dealing with problems in the
representation theory of groups and algebras, but also in topology and geometry; it shows the intriguing
interplay between finite and infinite length modules.
The volume presents the invited lectures of a conference devoted to "Infinite Length Modules", held at Bielefeld in September 1998, which brought together experts from quite different schools in order to survey
surprising relations between algebra, topology and geometry. Some additional reports have been included in order to establish a unified picture. The collection of articles, written by well-known experts from all parts of the world, is conceived as a sort of handbook which provides an easy access to the present state of knowledge and its aim is to stimulate further development.
Schwartz, L.
A Mathematician Grappling with His Century
Approx. 472 pages. Softcover
ISBN 3-7643-6052-6
English
Due in August 2000
Laurent Schwartz is one of the most remarkable intellects of the 20th century. His discovery of distributions, one of the most beautiful theories in mathematics, earned him a 1950 Fields Medal. Beyond this formidable achievement, his love for science and for teaching led him to think deeply and lecture broadly to the general public on the significance of science and mathematics to the well-being of the world. At the same
time, his commitment to the social good, even at the expense of his beloved research, proved a moral compass throughout his life. The fight for human rights and his major role in the battle against the wars in Algeria and Vietnam were typical of matters close to his heart. The story of his life in the context of
his century provides for future generations an inspiring testimonial from an extraordinary mathematician and thinker.
"Laurent Schwartz is a strategist of ideas, within mathematics and without. He is a great communicator who has drawn huge audiences and conveyed to them the fragrance of research, or the joy of teaching,
or the value of freedom. His is a mind whose company is never dull. He belongs to the great libertarian tradition of France. And his book has the very French characteristic of giving serious consideration to the life of the intellect. No man's life can be encompassed in one telling, yet the spirit of the man and his
times are well caught in his autobiography." K. Chandrasekharan, Notices of the AMS
Andre Y., Universite Pierre et Marie Curie, Paris, France,
Baldassari, F., Universita di Padova, Italy
Da Rham Cohomology of Differential Modules on Algebraic Varieties
Progress in Mathematics vol. 189
Approx. 224 pages. Hardcover
ISBN 3-7643-6348-7
English
Due in August 2000
The book offers a systematic treatment of the theory of differential modules on algebraic varieties over a field of characteristic 0. Its final purpose is to give a proof of a conjecture of Baldassarri comparing the algebraic and p-adic analytic De Rham cohomologies of such a module.
Along the way, the authors present a purely algebraic treatment of the theory of regularity and irregularity in several variables, give original elementary proofs of the main results on De Rham cohomology of differential
modules, and then develop a new approach to the classical algebraic/analytic comparison theorems (concerning regular modules) which unifies the complex and p-adic situations and avoids resolution of
singularities.
The main results should be of interest to arithmetic-algebraic geometers. The methods should be of interest to specialists of D-modules. On the other hand, the greater part of the book can be used as an
introduction to the subject and should be accessible to non-specialists and graduate students with a background in algebraic geometry.
Essen van den, A., University of Nijmegen, The Netherlands
Polynomial Automorphisms and the Jacobian Conjecture
Progress in Mathematics vol.190
Approx. 344 pages. Hardcover
ISBN 3-7643-6350-9
English
Due in August 2000
Motivated by some notorious open problems, such as the Jacobian conjecture and the tame generators
problem, the subject of polynomial automorphisms has become a rapidly growing field of interest. This book, the first in the field, collects many of the results scattered throughout the literature.
It introduces the reader to a fascinating subject and brings him to the forefront of research in this area. Some of the topics treated are invertibility criteria, face polynomials, the tame generators problem,
the cancellation problem, exotic spaces, DNA for polynomial automorphisms, the Abhyankar-Moh theorem, stabilization methods, dynamical systems, the Markus-Yamabe conjecture, group actions, Hilbert's 14th problem, various linearization problems and the Jacobian conjecture. The work is essentially self-contained and aimed at the level of beginning graduate students. Exercises are included at the end of each section. At the end of the book there are appendices to cover used material from algebra, algebraic geometry, D-modules and Grobner basis theory. A long list of 'strong' examples and an extensive bibliography
conclude the book.
Gardy, D., Mokkadem, A., Universite de Versailles-St-Quentin,
(Ed.)
Mathematics and Computer Science
Algorithms, Trees, Combinatorics and Probabilities
Trends in Mathematics
Approx. 320 pages. Hardcover
ISBN 3-7643-6430-0
English
Due in September 2000
This is the first book where mathematics and computer science are directly confronted and joined to tackle intricate problems in computer science with deep mathematical approaches.
It contains a collection of refereed papers presented at the Colloquium on Mathematics and Computer Science held at the University of Versailles-St-Quentin on September 18-20, 2000. The colloquium was a meeting place for researchers in mathematics and computer science and thus an important opportunity to exchange ideas and points of view, and to present new approaches and new results in the common areas such as algorithms analysis, trees, combinatorics, optimization, performance evaluation and probabilities.
The book is intended for a large public in applied mathematics, discrete mathematics and computer science, including researchers, teachers, graduate students and engineers. It provides an overview of the current
questions in computer science and related modern mathematical methods. The range of applications is very wide and reaches beyond computer science.