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

Nonlinear Partial Differential Equations in Geometry and Physics: The 1995 Barrett Lectures
ISBN-10
3034888953
ISBN-13
9783034888950
Category
Mathematics
Pages
156
Language
English
Published
2012-12-06
Publisher
Birkhäuser
Authors
Garth Baker, Alexandre Freire

Description

This volume presents the proceedings of a series of lectures hosted by the Math ematics Department of The University of Tennessee, Knoxville, March 22-24, 1995, under the title "Nonlinear Partial Differential Equations in Geometry and Physics" . While the relevance of partial differential equations to problems in differen tial geometry has been recognized since the early days of the latter subject, the idea that differential equations of differential-geometric origin can be useful in the formulation of physical theories is a much more recent one. Perhaps the earliest emergence of systems of nonlinear partial differential equations having deep geo metric and physical importance were the Einstein equations of general relativity (1915). Several basic aspects of the initial value problem for the Einstein equa tions, such as existence, regularity and stability of solutions remain prime research areas today. eighty years after Einstein's work. An even more recent development is the realization that structures originally the context of models in theoretical physics may turn out to have introduced in important geometric or topological applications. Perhaps its emergence can be traced back to 1954, with the introduction of a non-abelian version of Maxwell's equations as a model in elementary-particle physics, by the physicists C.N. Yang and R. Mills. The rich geometric structure ofthe Yang-Mills equations was brought to the attention of mathematicians through work of M.F. Atiyah, :"J. Hitchin, I.

Get the book

Amazon.com
Amazon.com
Search the book
eBay.com
eBay.com
Search the book

Other editions

Similar books