Nonlinear Partial Differential Equations in Geometry and Physics: The 1995 Barrett Lectures

The subject of nonlinear partial differential equations is experiencing a period of intense activity in the study of systems underlying basic theories in geometry, topology and physics. These mathematical models share the property of being derived from variational principles. Understanding the structure of critical configurations and the dynamics of the corresponding evolution problems is of fundamental importance for the development of the physical theories and their applications. This volume contains survey lectures in four different areas, delivered by leading resarchers at the 1995 Barrett Lectures held at The University of Tennessee: nonlinear hyperbolic systems arising in field theory and relativity (S. Klainerman); harmonic maps from Minkowski spacetime (M. Struwe); dynamics of vortices in the Ginzburg-Landau model of superconductivity (F.-H. Lin); the Seiberg-Witten equations and their application to problems in four-dimensional topology (R. Fintushel). Most of this material has not previously been available in survey form. These lectures provide an up-to-date overview and an introduction to the research literature in each of these areas, which should prove useful to researchers and graduate students in mathematical physics, partial differential equations, differential geometry and topology.

"All the essays are on the topmost professional level and are highly recommended to researchers and especially to young specialists in mathematical physics, PDE, differential geometry and topology, because they illustrate brilliantly the recent tendency in the theory of nonlinear PDE...namely the realization that structures originally introduced in the context of mathematical models in theoretical physics may turn out to have important applications in topology and (differential) geometry."

--Mathematica Bohemica