Presents the first collection of articles consisting entirely of work by the faculty and students at the Higher Mathematics College at the Independent University of Moscow. The 11 contributions cover symmetry groups of regular polyhedra over finite fields, vector bundles on an elliptical curve and Skylanin algebras, Tutte decomposition for graphs and symmetric matrices, and invarians and homology of spaces of knots in arbitrary manifolds. The focus of the text is on quantum groups and low-dimensional topology. No index. Annotation copyrighted by Book News, Inc., Portland, OR.

This book provides an extensive and self-contained presentation of quantum and related invariants of knots and 3-manifolds. Polynomial invariants of knots, such as the Jones and Alexander polynomials, are constructed as quantum invariants, i.e. invariants derived from representations of quantum groups and from the monodromy of solutions to the Knizhnik-Zamolodchikov equation. With the introduction of the Kontsevich invariant and the theory of Vassiliev invariants, the quantum invariants become well-organized. Quantum and perturbative invariants, the LMO invariant, and finite type invariants of 3-manifolds are discussed. The ChernOCoSimons field theory and the WessOCoZuminoOCoWitten model are described as the physical background of the invariants. Contents: Knots and Polynomial Invariants; Braids and Representations of the Braid Groups; Operator Invariants of Tangles via Sliced Diagrams; Ribbon Hopf Algebras and Invariants of Links; Monodromy Representations of the Braid Groups Derived from the KnizhnikOCoZamolodchikov Equation; The Kontsevich Invariant; Vassiliev Invariants; Quantum Invariants of 3-Manifolds; Perturbative Invariants of Knots and 3-Manifolds; The LMO Invariant; Finite Type Invariants of Integral Homology 3-Spheres. Readership: Researchers, lecturers and graduate students in geometry, topology and mathematical physics."

A detailed exposition of the theory with an emphasis on its combinatorial aspects.

These two volumes constitute the Proceedings of the `Conférence Moshé Flato, 1999'. Their spectrum is wide but the various areas covered are, in fact, strongly interwoven by a common denominator, the unique personality and creativity of the scientist in whose honor the Conference was held, and the far-reaching vision that underlies his scientific activity. With these two volumes, the reader will be able to take stock of the present state of the art in a number of subjects at the frontier of current research in mathematics, mathematical physics, and physics. Volume I is prefaced by reminiscences of and tributes to Flato's life and work. It also includes a section on the applications of sciences to insurance and finance, an area which was of interest to Flato before it became fashionable. The bulk of both volumes is on physical mathematics, where the reader will find these ingredients in various combinations, fundamental mathematical developments based on them, and challenging interpretations of physical phenomena. Audience: These volumes will be of interest to researchers and graduate students in a variety of domains, ranging from abstract mathematics to theoretical physics and other applications. Some parts will be accessible to proficient undergraduate students, and even to persons with a minimum of scientific knowledge but enough curiosity.

Devoted to the theory of linear operators in Hilbert spaces and its applications, the subjects covered in this book range from the abstract theory of Toeplitz operators to the analysis of very specific differential operators arising in quantum mechanics, electromagnetism, and the theory of elasticity.

This collection presents new results in algebra, functional analysis, and mathematical physics. In particular, evolution and spectral problems related to small motions of viscoelastic fluid are considered. Specific areas covered in the book include functional equations and functional operator equations from the point of view of the $C*$-algebraic approach, the existence of an isomorphism between certain ideals regarded as Galois modules, spectral problems in singularly perturbed domains, scattering theory, the existence of bounded solutions to the equation $\operatorname{div} u = f$ in a plane domain, and a compactification of a locally compact group. Also given is an historic overview of the mathematical seminars held at St. Petersburg State University. The results, ideas, and methods given in the book will be of interest to a broad range of specialists.

This volume contains papers that originally appeared in Japanese in the journal Sugaku. Ordinarily the papers would appear in the AMS translation of that journal, but to expedite publication, the Society has chosen to publish them as a volume of selected papers. The papers here are in the general area of mathematical analysis as it pertains to free probability theory.