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Dynamics and Control of Multibody Systems
The study of complex, interconnected mechanical systems with rigid and flexible articulated components is of growing interest to both engineers and mathematicians. Recent work in this area reveals a rich geometry underlying the mathematical models used in this context. In particular, Lie groups of symmetries, reduction, and Poisson structures play a significant role in explicating the qualitative properties of multibody systems. In engineering applications, it is important to exploit the special structures of mechanical systems. For example, certain mechanical problems involving control of interconnected rigid bodies can be formulated as Lie-Poisson systems. The dynamics and control of robot...
Spinor Construction of Vertex Operator Algebras, Triality, and $E^{(1)}_8$
The theory of vertex operator algebras is a remarkably rich new mathematical field which captures the algebraic content of conformal field theory in physics. Ideas leading up to this theory appeared in physics as part of statistical mechanics and string theory. In mathematics, the axiomatic definitions crystallized in the work of Borcherds and in Vertex Operator Algebras and the Monster, by Frenkel, Lepowsky, and Meurman. The structure of monodromies of intertwining operators for modules of vertex operator algebras yield braid group representations and leads to natural generalizations of vertex operator algebras, such as superalgebras and para-algebras. Many examples of vertex operator algeb...
Finite Geometries and Combinatorial Designs
The proceedings of an AMS special session on finite geometries and combinatorial designs. Topics range over finite geometry, combinatorial designs, their automorphism groups and related structures.
Harmonic Analysis and Partial Differential Equations
Illuminates the relationship between harmonic analysis and partial differential equations. This book covers topics such as application of fully nonlinear, uniformly elliptic equations to the Monge Ampere equation; and estimates for Green functions for the purpose of studying Dirichlet problems for operators in non-divergence form.
Combinatorial Group Theory
Eighteen papers presented during a special AMS session designed to draw together researchers in various areas of infinite group theory, especially combinatorial group theory, to share methods and results.
Algebraic $K$-Theory, Commutative Algebra, and Algebraic Geometry
In the mid-1960's, several Italian mathematicians began to study the connections between classical arguments in commutative algebra and algebraic geometry, and the contemporaneous development of algebraic K-theory in the US. These connections were exemplified by the work of Andreotti-Bombieri, Salmon, and Traverso on seminormality, and by Bass-Murthy on the Picard groups of polynomial rings. Interactions proceeded far beyond this initial point to encompass Chow groups of singular varieties, complete intersections, and applications of K-theory to arithmetic and real geometry. This volume contains the proceedings from a US-Italy Joint Summer Seminar, which focused on this circle of ideas. The conference, held in June 1989 in Santa Margherita Ligure, Italy, was supported jointly by the Consiglio Nazionale delle Ricerche and the National Science Foundation. The book contains contributions from some of the leading experts in this area.
Enumerative Algebraic Geometry
1989 marked the 150th anniversary of the birth of the great Danish mathematician Hieronymus George Zeuthen. Zeuthen's name is known to every algebraic geometer because of his discovery of a basic invariant of surfaces. However, he also did fundamental research in intersection theory, enumerative geometry, and the projective geometry of curves and surfaces. Zeuthen's extraordinary devotion to his subject, his characteristic depth, thoroughness, and clarity of thought, and his precise and succinct writing style are truly inspiring. During the past ten years or so, algebraic geometers have reexamined Zeuthen's work, drawing from it inspiration and new directions for development in the field. The 1989 Zeuthen Symposium, held in the summer of 1989 at the Mathematical Institute of the University of Copenhagen, provided a historic opportunity for mathematicians to gather and examine those areas in contemporary mathematical research which have evolved from Zeuthen's fruitful ideas. This volume, containing papers presented during the symposium, as well as others inspired by it, illuminates some currently active areas of research in enumerative algebraic geometry.
Vision Geometry
Since its genesis more than thirty-five years ago, the field of computer vision has been known by various names, including pattern recognitions, image analysis, and image understanding. The central problem of computer vision is obtaining descriptive information by computer analysis of images of a scene. Together with the related fields of image processing and computer graphics, it has become an established discipline at the interface between computer science and electrical engineering. This volume contains fourteen papers presented at the AMS Special Session on Geometry Related to Computer Vision, held in Hoboken, New Jersey in Ooctober 1989. This book makes the results presented at the Spec...
Mathematics of Nonlinear Science
Contains the proceedings of an AMS Special Session on the Mathematics of Nonlinear Science, held in Phoenix in January 1989. The area of research encompasses a large and rapidly growing set of ideas concerning the relationship of mathematics to science, in which the fundamental laws of nature are extended beyond common sense into new areas where the dual aspects of order and chaos abound.
Symbolic Dynamics and its Applications
This volume contains the proceedings of the conference, Symbolic Dynamics and its Applications, held at Yale University in the summer of 1991 in honour of Roy L. Adler on his sixtieth birthday. The conference focused on symbolic dynamics and its applications to other fields, including: ergodic theory, smooth dynamical systems, information theory, automata theory, and statistical mechanics. Featuring a range of contributions from some of the leaders in the field, this volume presents an excellent overview of the subject.
