Contemporary Mathematics 1999; 269 pp; softcover Volume: 242 ISBN10: 0821820613 ISBN13: 9780821820612 List Price: US$72 Member Price: US$57.60 Order Code: CONM/242
 This collection of papers by leading researchers gives a broad picture of current research directions in geometric aspects of partial differential equations. Based on lectures presented at a Minisymposium on Spectral Invariants  Heat Equation Approach, held in September 1998 at Roskilde University in Denmark, the book provides both a careful exposition of new perspectives in classical index theory and an introduction to currently active areas of the field. Presented here are new index theorems as well as new calculations of the etainvariant, of the spectral flow, of the Maslov index, of SeibergWitten monopoles, heat kernels, determinants, noncommutative residues, and of the RaySinger torsion. New types of boundary value problems for operators of Dirac type and generalizations to manifolds with cuspidal ends, to noncompact and to infinitedimensional manifolds are also discussed. Throughout the book, the use of advanced analysis methods for gaining geometric insight emerges as a central theme. Aimed at graduate students and researchers, this book would be suitable as a text for an advanced graduate topics course on geometric aspects of partial differential equations and spectral invariants. Readership Graduate students and research mathematicians interested in partial differential equations and global analysis. Table of Contents Part I. Index and small eigenvalues  C. Bär and D. Bleecker  The Dirac operator and the scalar curvature of continuously deformed algebraic varieties
 B. Bojarski  The geometry of the RiemannHilbert problem
 T. Kori  Chiral anomaly and Grassmannian boundary conditions
 G. Rozenblum  The index of cone Mellin operators
Part II. Etainvariants, spectral flows, and SeibergWitten monopoles  B. BoossBavnbek and K. Furutani  Symplectic functional analysis and spectral invariants
 L. I. Nicolaescu  Eta invariants, spectral flows and finite energy SeibergWitten monopoles
Part III. Heat kernels, determinants, torsion  S. Dowker, P. Gilkey, and K. Kirsten  Heat asymptotics with spectral boundary conditions
 P. Gilkey  Heat content asymptotics
 W. Müller and K. Wendland  Extremal Kähler metrics and RaySinger analytic torsion
 E. Schrohe  Noncommutative residues, Dixmier's trace, and heat trace expansions on manifolds with boundary
Part IV. Generalizations  A. Asada  Spectral invariants and geometry of mapping spaces
 J. Brüning and M. Lesch  Spectral theory of boundary value problems for Dirac type operators
 B.W. Schulze and N. Tarkhanov  Ellipticity and parametrices on manifolds with cuspidal edges
 M. Shubin  Classical and quantum completeness for the Schrödinger operators on noncompact manifolds
