University Lecture Series 2002; 85 pp; softcover Volume: 27 ISBN10: 0821832107 ISBN13: 9780821832103 List Price: US$22 Member Price: US$17.60 Order Code: ULECT/27
 Recent developments in topology and analysis have led to the creation of new lines of investigation in differential geometry. The 2000 Barrett Lectures present the background, context and main techniques of three such lines by means of surveys by leading researchers. The first chapter (by Alice Chang and Paul Yang) introduces new classes of conformal geometric invariants, and then applies powerful techniques in nonlinear differential equations to derive results on compactifications of manifolds and on Yamabetype variational problems for these invariants. This is followed by Karsten Grove's lectures, which focus on the use of isometric group actions and metric geometry techniques to understand new examples and classification results in Riemannian geometry, especially in connection with positive curvature. The chapter written by Jon Wolfson introduces the emerging field of Lagrangian variational problems, which blends in novel ways the structures of symplectic geometry and the techniques of the modern calculus of variations. The lectures provide an updodate overview and an introduction to the research literature in each of their areas. This very readable introduction should prove useful to graduate students and researchers in differential geometry and geometric analysis. Readership Graduate students and research mathematicians interested in geometry and geometric analysis. Table of Contents  S.Y. A. Chang and P. C. Yang  Partial differential equations related to the GaussBonnetChern integrand on 4manifolds
 K. Grove  Geometry of, and via, symmetries
 J. G. Wolfson  Lagrangian cycles and volume
