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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...

Clear, comprehensible definitions of mathematical terms are not easy to locate, and despite the seemingly close connections between mathematics and other scientific and engineering fields, practical explanations intelligible to those who are not primarily mathematicians are even more difficult to find. The Dictionary of Applied Mathematics for Engineers and Scientists aims to fill that void. It contains authoritative yet accessible definitions of mathematical terms often encountered in other disciplines.

The aim of this CIME Session was to review the state of the art in the recent development of the theory of integrable systems and their relations with quantum groups. The purpose was to gather geometers and mathematical physicists to allow a broader and more complete view of these attractive and rapidly developing fields. The papers contained in this volume have at the same time the character of survey articles and of research papers, since they contain both a survey of current problems and a number of original contributions to the subject.