Caroline Series

Ser Peow Tan

William Mark Goldman

This book aims to describe, for readers uneducated in science, the development of humanity's desire to know and understand the world around us through the various stages of its development to the present, when science is almost universally recognized - at least in the Western world - as the most reliable way of knowing. The book describes the history of the large-scale exploration of the surface of the earth by sea, beginning with the Vikings and the Chinese, and of the unknown interiors of the American and African continents by foot and horseback. After the invention of the telescope, visual exploration of the surfaces of the Moon and Mars were made possible, and finally a visit to the Moon. The book then turns to our legacy from the ancient Greeks of wanting to understand rather than just know, and why the scientific way of understanding is valued. For concreteness, it relates the lives and accomplishments of six great scientists, four from the nineteenth century and two from the twentieth. Finally, the book explains how chemistry came to be seen as the most basic of the sciences, and then how physics became the most fundamental.

Geometry, Topology and Dynamics of Character Varieties

Edward Bierstone

Pierre D. Milman

John J. Millson

The Deformation Theory of Representations of Fundamental Groups of Compact Kähler Manifolds

Semianalytic and Subanalytic Sets

Andy R. Magid

The representations of a finitely generated group in a topological group $G$ form a topological space which is an analytic variety if $G$ is a Lie group, or an algebraic variety if $G$ is an algebraic group. The study of this area draws from and contributes to a wide range of mathematical subjects: algebra, analysis, topology, differential geometry, representation theory, and even mathematical physics. In some cases, the space of representations is the object of the study, in others it is a tool in a program of investigation, and, in many cases, it is both. Most of the papers in this volume are based on talks delivered at the AMS-IMS-SIAM Summer Research Conference on the Geometry of Group Representations, held at the University of Colorado in Boulder in July 1987.The conference was designed to bring together researchers from the diverse areas of mathematics involving spaces of group representations. In keeping with the spirit of the conference, the papers are directed at nonspecialists, but contain technical developments to bring the subject to the current research frontier. Some of the papers include entirely new results. Readers will gain an understanding of the present state of research in the geometry of group representations and their applications.

Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference Held July 5-11, 1987 with Support from the National Science Foundation

Geometry of Group Representations

William Mark Goldman

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