This work contains contributions presented at the conference, QMath-8: Mathematical Results in Quantum Mechanics'', held at Universidad Nacional Autonoma de Mexico in December 2001. The articles cover a wide range of mathematical problems and focus on various aspects of quantum mechanics, quantum field theory and nuclear physics. Topics vary from spectral properties of the Schrodinger equation of various quantum systems to the analysis of quantum computation algorithms. The book should be suitable for graduate students and research mathematicians interested in the mathematical aspects of...

This volume presents 19 refereed articles written by participants in the Singapore International Symposium in Topology and Geometry (SISTAG), held July 2-6, 2001, at the National University of Singapore. Rather than being a simple snapshot of the meeting in the form of a proceedings, it serves as a commemorative volume consisting of papers selected to show the diversity and depth of the mathematics presented at SISTAG. The book contains articles on low-dimensional topology, algebraic, differential and symplectic geometry, and algebraic topology. While papers reflect the focus of the...

Our knowledge of objects of algebraic geometry such as moduli of curves, (real) Schubert classes, fundamental groups of complements of hyperplane arrangements, toric varieties, and variation of Hodge structures, has been enhanced by ideas and constructions of quantum field theory, such as mirror symmetry, Gromov-Witten invariants, quantum cohomology, and gravitational descendants. These are some of the themes of this refereed collection of papers, which grew out of the special session, Enumerative Geometry in Physics, held at the AMS meeting in Lowell, MA, USA, April 2000. This session...

This volume outlines the proceedings of the conference on Quadratic Forms and Their Applications held at University College, Dublin. It includes survey articles and research papers ranging from applications in topology and geometry to the algebraic theory of quadratic forms and its history. Various aspects of the use of quadratic forms in algebra, analysis, topology, geometry, and number theory are addressed. Special features include the first published proof of the Conway-Schneeberger Fifteen Theorem on integer-valued quadratic forms and the first English-language biography of Ernst Witt,...

This volume presents the proceedings from the conference on Abelian Groups, Rings, and Modules (AGRAM) held at the University of Western Australia (Perth). Included are articles based on talks given at the conference, as well as a some specially invited papers. The proceedings were dedicated to Professor Laszlo Fuchs. The book includes a tribute and a review of his work by his long-time collaborator, Professor Luigi Salce. Four surveys from leading experts follow Professor Salce's article. They present recent results from active research areas.

Alfred Gray's work covered a great part of differential geometry. In September 2000, an International Congress on Differential Geometry was held in his memory in Bilbao, Spain. Mathematicians from all over the world, representing 24 countries, attended the event. This volume includes major contributions by T. Banchoff, S. Donaldson, H. Ferguson, M. Gromov, N. Hitchin, A. Huckleberry, O. Kowalski, V. Miquel, E. Musso, A. Ros, S. Salamon, L. Vanhecke, P. Wellin and J.A. Wolf.

This volume presents research and expository articles by the participants of the 25th Arkansas Spring Lecture Series on Recent Progress in the Study of Harmonic Measure from a Geometric and Analytic Point of View held at the University of Arkansas, USA. Papers in this volume provide presentations of the problems that are at the forefront of harmonic analysis and partial differential equations. The following topics are featured: the solution of the Kato conjecture, the two bricks problem, new results on Cauchy integrals on non-smooth curves, the Neumann problem for sub-Laplacians, and a...

Because of its many applications to mathematics and mathematical physics, the representation theory of infinite-dimensional Lie and quantized enveloping algebras comprises an important area of current research. This volume includes articles from the proceedings of an international conference, Infinite-Dimensional Lie Theory and Conformal Field Theory, held at the University of Virginia. Many of the contributors to the volume are prominent researchers in the field. This conference provided an opportunity for mathematicians and physicists to interact in an active research area of mutual...

We often think of our natural environment as being composed of very many interacting particles, undergoing individual chaotic motions, of which only very coarse averages are perceptible at scales natural to us.

Algebraic methods and arguments in statistics and probability are well known, from Gauss's least squares principle through Fisher's method of variance decomposition. The relevance of group-theoretic arguments, for example, became evident in the 1980s. Such techniques continue to be of interest, along with other developments, such as the use of graph theory in modelling complex stochastic systems.