Lam,K.et al(eds.)

Cryptography and Computational Number Theory

(Progress in Computer Science and Applied Logic vol.20)

The fields of cryptography and computational number theory have recently witnessed a rapid development, which was the subject of the CCNT workshop in Singapore in Nov. 1999. Its aim was to stimulate further research in information and computer security as well as the design and implementation of number theoretic cryptosystems and other related areas. Another achievement of the meeting was the collaboration of mathematicians, computer scientists, practical cryptographers and engineers in academia, industry and government. The present volume comprises a selection of refereed papers originating-from this event, presenting either a survey of some area or original and new results. They concern many different aspects of the field such as theory, techniques, applications and practical experience. It provides a state-of-the-art report on some number theoretical issues of significance to cryptography.

3-7643-6510-2

FabeI, C.

Moduli of Abelian Varieties

(Progress in Mathematics,vol.195)

Abelian varieties and their moduli are a central topic of increasing importance in today's: mathematics. Applications range from a algebraic geometry and number theory to mathematical physics. The present collection of 17 refereed articles originates from the third "Texel Conference" 1999, Leading experts discuss and study the structure of the moduli spaces of abelian varieties and related spaces, giving an excellent view of the state of the art in this field. The book will appeal to pure mathematicians, especially algebraic geometers and number theorists, but will also be relevant for researchers in mathematical physics.

3-7643-6517-X

Gil,J.et al (eds.)

Approaches to Singular Analysis

(Operator Theory : Advances and Applications,vol.125)

The purpose of this publication is to present, in one book, various approaches to analytic problems that arise in the context of singular spaces. It is based on the workshop "Approaches to Singular Analysis" which was held at the Humboldt University Berlin in April 1999. The book contains articles by workshop participants as well as invited contributions. The former are expanded versions of talks given at the workshop; they offer introductions to various pseudodifferential calculi and discussions of relations between them. In addition, a limited number of invited papers from mathematicians who have made significant contributions to this field are included.

3-7643-6518-8

Barndorff-Nielsen,O. et al (eds.)

Levy Processes

In the past, representatives of the Levy class were considered most useful for applications to either Brownian motion or the Poisson process. Nowadays, the need for modeling jumps, bursts, extremes and other irregular behavior of phenomena in nature and society has led to a renaissance of the theory of general Levy processes. Researchers and practitioners in physics, meteorology, statistics, insurance and finance have rediscovered the simplicity of Levy processes and their enormous flexibility in modeling tails, dependence and path behavior. A Levy process is a continuous-time analogue of a random walk, and as such, is at the cradle of modern theories of stochastic processes. Martingales, Markov processes, and diffusions are extensions and generalizations of these processes. In the past, representatives of the Levy class were considered most useful for applications to either Brownian motion or the Poisson process. Nowadays the need for modeling jumps, bursts, extremes and other irregular behavior of phenomena in nature and society has led to a renaissance of the theory of general Levy processes.

3-7643-4167-X

Koike Kazuhiko

Combinatorial Methods in Representation Theory

(Advanced Studies in Pure Mathematics,vol.28)

This field, which is developed by the interactions of Combinatorics and Representation Theory, is old and new. From the origin of the representation theory (A. Young, I. Schur, H. Weyl etc.), the study of the representations of specific groups and algebras inevitably incurred the combinatorial problems to be conquered. From the viewpoints of combinatorics, the combinatorial objects or structure occurring in this manner have interesting properties and beautiful symmetries in their own right. Since representation theory has strong wings, such as cohomology theory, harmonic analysis and algebraic geometry, it can fly up to the higher sky without any help of combinatorics. But if we stick to the down-to-earth calculations, which we believe to be essential in mathematics, we need to study their combinatorial aspects.

4-314-10141-5

Brasselet,J./Suwa, T.

Singularities - Sapporo 1998

(Advanced Studies in Pure Mathematics,vol.29)

The international symposium on "Singularities in Geometry and Topology" took place at Hokkaido University, Sapporo, July 6 - 10, 1998. There Were sixty-eight participants, mostly from Japan and France but also from other countries including China, Mexico, Poland, Spain and USA. There were twenty-two lectures, whose main topics are singularities of curves, Characteristic classes of singular varieties, D-modules, motives, resolution of singularities, Milnor fibration, Enriques diagrams, Hilbert schemes and log-canonical singularities.

4-314-10143-1