Contains the proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Integral Geometry and Tomography, held in June 1989 at Humboldt State University in Arcata, California. This book features articles that range over such diverse areas as combinatorics, geometric inequalities, micro-local analysis, group theory, and harmonic analysis.

The topic of integral geometry is not as well known as its counterpart, differential geometry. However, research in integral geometry has indicated that this field may yield as equally deep insights as differential geometry has into the global and local nature of manifolds and the functions on them. In 1984, an AMS-IMS-SIAM joint summer research conference on integral geometry was held at Bowdoin College. This volume consists of papers presented there. The papers range from purely expository to quite technical and represent a good survey of contemporary work in integral geometry. Three major areas are covered: the classical problems of computing geometric invariants by statistical averaging procedures; the circle of ideas concerning the Radon transform, going back to the seminal work of Funck and Radon around 1916-1917; and integral-geometric transforms which are now being used in the study of field equations in mathematical physics. Some of these areas also involve group-representation theoretic problems.

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This book contains the proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Integral Geometry and Tomography, held in June 1989 at Humboldt State University in Arcata, California. The papers collected here represent current research in these two interrelated fields. The articles in pure mathematics range over such diverse areas as combinatorics, geometric inequalities, micro-local analysis, group theory, and harmonic analysis. The interplay between Lie group theory, geometry, harmonic analysis, and Radon transforms is well covered. The papers on tomography reflect current research on X-ray computed tomography, as well as radiation dose planning, radar, and partial differential equations. In addition to describing current research, this book provides a useful perspective on the interplay between the fields. For example, abstract theorems about Radon transforms are used to understand applied mathematics, while applied mathematics motivates some of the results in pure mathematics. Though directed at specialists in the field, the book would also be of interest to others who wish to understand current research in these areas and to witness how they relate to other branches of mathematics.