Geometry

Download E-books Nonlinear Partial Differential Equations in Geometry and Physics: The 1995 Barrett Lectures PDF

By Ronald Fintushel (auth.), Garth Baker, Alexandre Freire (eds.)

This quantity offers the court cases of a sequence of lectures hosted via the mathematics­ ematics division of The collage of Tennessee, Knoxville, March 22-24, 1995, below the identify "Nonlinear Partial Differential Equations in Geometry and Physics" . whereas the relevance of partial differential equations to difficulties in differen­ tial geometry has been well-known because the early days of the latter topic, the concept that differential equations of differential-geometric starting place should be invaluable within the formula of actual theories is a way more fresh one. maybe the earliest emergence of structures of nonlinear partial differential equations having deep geo­ metric and actual value have been the Einstein equations of basic relativity (1915). a number of easy facets of the preliminary price challenge for the Einstein equa­ tions, reminiscent of life, regularity and balance of options stay best learn components this day. 80 years after Einstein's paintings. a good more moderen improvement is the conclusion that buildings initially the context of types in theoretical physics may well end up to have brought in very important geometric or topological functions. might be its emergence will be traced again to 1954, with the creation of a non-abelian model of Maxwell's equations as a version in elementary-particle physics, via the physicists C.N. Yang and R. turbines. the wealthy geometric constitution ofthe Yang-Mills equations used to be delivered to the eye of mathematicians via paintings of M.F. Atiyah, :"J. Hitchin, I.

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