Book Description
This digital document, covering the life and work of Karen (Keskulla) Uhlenbeck, is an entry from Contemporary Authors, a reference volume published by Thompson Gale. The length of the entry is 1274 words. The page length listed above is based on a typical 300-word page. Although the exact content of each entry from this volume can vary, typical entries include the following information:

• Place and date of birth and death (if deceased)
• Family members
• Education
• Professional associations and honors
• Employment
• Writings, including books and periodicals
• A description of the author's work
• References to further readings about the author

Book Description
Exploring topics from classical and quantum mechanics and field theory, this book is based on lectures presented in the Graduate Summer School at the Regional Geometry Institute in Park City, Utah, in 1991. The chapter by Bryant treats Lie groups and symplectic geometry, examining not only the connection with mechanics but also the application to differential equations and the recent work of the Gromov school. Rabin's discussion of quantum mechanics and field theory is specifically aimed at mathematicians. Alvarez describes the application of supersymmetry to prove the Atiyah-Singer index theorem, touching on ideas that also underlie more complicated applications of supersymmetry. Quinn's account of the topological quantum field theory captures the formal aspects of the path integral and shows how these ideas can influence branches of mathematics which at first glance may not seem connected. Presenting material at a level between that of textbooks and research papers, much of the book would provide excellent material for graduate courses. The book provides an entree into a field that promises to remain exciting and important for years to come. ... Read more

Customer Reviews (1)

Decent survey on "quantum mathematics"
This book has four articles on mathematics in quantum field theory. Some of it is well known and "classical", particularly the article by Bryant on symplectic geometry (however, Bryan does discuss the modernmodern developments by Gromov in the last section). The article by Rabinattempts to do the impossible: try to teach mathematicians the physicsbehind quantum field theory via path integrals. The article by Alvarez onindex theorems summarizes nicely the connections between supersymmetry andindex theory. The last article by Quinn on topological field theory iswritten for the mathematician in mind. It is fascinating mathematics andgives the reader the impression that research in topological field theorywill no doubt continue to grow in importance. Several advances have takenplace since the book was published (1995), so peruse the literature beforebuying it. ... Read more

Book Description
The Surveys in Differential Geometry are supplements to the Journal of Differential Geometry, which are published by International Press. They include significant invited papers combining original research and overviews of the most current research in specific areas of interest to the growing Journal of Differential Geometry community.The survey volumes serve as continuing references, inspirations for new research, and introductions to the variety of topics of interest to differential geometers. These supplements are published annually since 1999.

The theory of integrable systems has been an active area of mathematics for the past thirty years. Different aspects of the subject have fundamental relations with mechanics and dynamics, applied mathematics, algebraic structures, theoretical physics, analysis and spectral theory and geometry. This volume (Vol. 4) is a collection of papers intended to introduce and explain some of the more geometric aspects of integrable systems to the community. ... Read more