Presents an account of lectures delivered at the NSF-CBMS Regional Conference on Singular Integral Operators, held at the University of Montana in the summer of 1989. This title covers developments in the subject related to the Cauchy integral on Lipschitz curves and the T(1) theorem.

The concept of 'wave packet analysis' originates in Carleson's famous proof of almost everywhere convergence of Fourier series of $L^2$ functions. This work emphasizes the classical successes (Carleson's theorem and the Hilbert transform) in the main devel

The last twenty years have seen an active interaction between mathematics and physics. This book is devoted to one of the new areas which deals with mathematical structures related to conformal field theory and its sqs-deformations. In the book, the author discusses the interplay between Knizhnik-Zamolodchikov type equations, the Bethe ansatz method, representation theory, and geometry of multi-dimensional hypergeometric functions. This book aims to provide an introduction to the area and expose different facets of the subject. It contains constructions, discussions of notions, statements of...

Among nonlinear PDEs, dispersive and wave equations form an important class of equations, including the nonlinear Schrodinger equation, nonlinear wave equation, Korteweg de Vries equation, and the wave maps equation. This book offers an introduction to the

This volume contains lectures presented by Hugh L. Montgomery at the NSF-CBMS Regional Conference held at Kansas State University in May 1990. The book focuses on important topics in analytic number theory that involve ideas from harmonic analysis. One particularly valuable aspect of the book is that it collects material that was either unpublished or that had appeared only in the research literature. The book should be a useful resource for harmonic analysts interested in moving into research in analytic number theory. In addition, it is suitable as a textbook in an advanced graduate topics...

Includes an analytic solution to the Busemann-Petty problem, which asks whether bodies with smaller areas of central hyperplane sections necessarily have smaller volume, characterizations of intersection bodies, extremal sections of certain classes of bodi

Although division algebras are a very classical object, this book presents this 'classical' material in a new way, highlighting various approaches and fresh theorems, and illuminating the connections with a variety of areas in mathematics. It is based on lectures on division algebras given at a conference held at Colorado State University.

The geometrical study of differential equations has a long and distinguished history, dating back to the classical investigations of Sophus Lie, Gaston Darboux, and Elie Cartan. These ideas occupy a central position in several areas of pure and applied mathematics, including the theory of completely integrable evolution equations, the calculus of variations, and the study of conservation laws.