Jorge Buescu / Sofia B.S.D. Castro, Universidade do Porto / A.P.S. Dias, Universidade do Porto / Isabel S. Labouriau, Universidade do Porto (eds.)

Bifurcation, Symmetry and Patterns

Trends in Mathematics
2003. 224 pages. Hardcover
ISBN 3-7643-7020-3
English

This book represents the latest developments on both the theory and applications of bifurcations with symmetry. It includes recent experimental work as well as new approaches to and applications of the theory to other sciences. It shows the range of dissemination of the work of Martin Golubitsky and Ian Stewart and its influence in modern mathematics at the same time as it contains work of young mathematicians in new directions. The range of topics includes mathematical biology, pattern formation, ergodic theory, normal forms, one-dimensional dynamics and symmetric dynamics.

Symmetry-Breaking as an Origin of Species (I. Stewart, T. Elmhirst, J. Cohen) Bifurcation and Planar Pattern Formation for a Liquid Crystal (M. Golubitsky, D. Chillingworth) Patchwork Patterns: Dynamics on Unbounded Domains (P. Ashwin) Persistent Ergodicity and Stably Ergodic SRB Attractors in Equivariant Dynamics (M. Field) Bistability of Vortex Modes in Annular Thermoconvection (D.D. Rusu, W.F. Langford) Secondary Instability of Hexagons: A Bifurcation Analysis of Experimentally Observed Faraday Wave Patterns (A.M. Rucklidge, M. Silber, J. Fineberg)

Table of contents

Foreword by the Editors (-) Organizing Commitee (-) Invited Speakers (-) Invited Lectures (.-) Contributed Papers (-) List of Contributors (-) List of Participants

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V. Balaji / V. Lakshmibai, Northeastern University / V.B. Mehta / K.R. Nagarajan / Kapil Hari Paranjape / P. (Parameswaran) Sankaran / R. Sridharan (eds.)

A Tribute to C.S. Seshadri
A Collection of Articles on Geometry and Representation Theory

Trends in Mathematics
2003. 580 pages. Hardcover
ISBN 3-7643-0444-8
English

C.S. Seshadri turned seventy on the "29th of February", 2002. Some of his friends and students came together on March 1, 2002 to felicitate Seshadri. To mark this occasion, a symposium was held in Chennai, India, where some of his colleagues gave expository talks highlighting Seshadri’s contributions to mathematics.

This volume contains expanded texts of these talks as well as research and expository papers on geometry and representation theory. It will serve as an excellent reference to researchers and students in these areas.

Table of contents

Preface (.-) C.S. Seshadri - A Biographical Sketch (.-) List of Publications of C.S. Seshadri (.-) List of Participants at the Symposium (.-) Excerpts from Birthday Messages (.-) Part I. Mathematical Contributions of C.S. Seshadri. Talks given at the Symposium (.-) Part II. Invited Articles

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Guido Mislin / Alain Valette, Universite de Neuchatel

Proper Group Actions and the Baum-Connes Conjecture

2003. 140 pages. Softcover
ISBN 3-7643-0408-1
English

This book contains a concise introduction to the techniques used to prove the Baum-Connes conjecture.

The Baum-Connes conjecture predicts that the K-homology of the reduced C^*-algebra of a group can be computed as the equivariant K-homology of the classifying space for proper actions. The approach is expository, but it contains proofs of many basic results on topological K-homology and the K-theory of C^*-algebras. It features a detailed introduction to Bredon homology for infinite groups, with applications to K-homology. It also contains a detailed discussion of naturality questions concerning the assembly map, a topic not well documented in the literature.

The book is aimed at advanced graduate students and researchers in the area, leading to current research problems.

Table of contents

Foreword (.-) Equivariant K-Homology of the Classifying Space for Proper Actions (Guido Mislin) (.-) On the Baum-Connes Map for Discrete Groups (Alain Valette)

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Walter Pfeifer

The Lie Algebras su(N), an Introduction

2003. 124 pages. Softcover
ISBN 3-7643-2418-X
English

Lie algebras are efficient tools for analyzing the properties of physical systems. Concrete applications comprise the formulation of symmetries of Hamiltonian systems, the description of atomic, molecular and nuclear spectra, the physics of elementary particles and many others. This work gives an introduction to the properties and the structure of the Lie algebras su(n). First, characteristic quantities such as structure constants, the Killing form and functions of Lie algebras are introduced. The properties of the algebras su(2), su(3) and su(4) are investigated in detail. Geometric models of the representations are developed. A lot of care is taken over the use of the term "multiplet of an algebra".

The book features an elementary (matrix) access to su(N)-algebras, and gives a first insight into Lie algebras. Student readers should be enabled to begin studies on physical su(N)-applications, instructors will profit from the detailed calculations and examples.

Table of contents

Preface .- 1. Lie algebras .- 2. The Lie algebras su(N) .- 3. The Lie algebra su(2) .- 4. The Lie algebra su(3) .- 5. The Lie algebra su(4) .- 6. General properties of the su(N)-algebras .- References .- Index

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Mimmo Iannelli, Universita di Trento / Gunter Lumer (eds.)

Evolution Equations: Applications to Physics, Industry, Life Sciences and Economics
EVEQ2000 Conference in Levico Terme (Trento, Italy), October 30-November 4, 2000

Progress in Non-Linear Differential Equations and Their Applications,Vol.55
2003. 432 pages. Hardcover
ISBN 3-7643-0374-3
English

The international conference on which the book is based brought together many of the world's leading experts, with particular effort on the interaction between established scientists and emerging young promising researchers, as well as on the interaction of pure and applied mathematics.

Among the recent advances treated are new developments in

moving boundary problems
asymptotics in non-linear Volterra equations
Poincare inequality on stratified sets
time operator and Markov processes in physics related advance
behaviour of granular matter
stochastic aspects of the Hamilton-Jacobi-Bellmann equation
very general Paley-Wiener results applied to both classical and generalized functions
Ornstein-Uhlenbeck operators
semigroup approach in economics (pricing theory)
convolution-evolution equation in aeroelasticity
the study of age-structured models All material has been rigorously refereed. The contributions contain much material developed after the conference, continuing research and incorporating additional new results and improvements. In addition, some up-to-date surveys are included.

Table of contents

Preface (.-) 29 refereed contributions