Integration techniques for exterior differential systems I & II. London Mathematical Society -- EPSRC Durham Symposium Geometric and Algebraic Aspects of Integrability. Durham University. July 27, 2016
These two lectures will describe some of the techniques that have been found useful for explicitly finding the integrals of exterior differential systems arising in geometry. These include Darboux’ method and its generalizations, compatible reductions, integrable extensions and Bäcklund transformations, conservation laws, and methods connected with analysis of the characteristic variety. Emphasis will be placed on illustrative examples and computations using the structure equations of Cartan. The first lecture will begin with a brief summary of the basics of exterior differential systems (EDSs) including involutivity, Cartan-Kähler theory, and the characteristic variety. This will be followed by an introduction to EDS formulations of some geometric problems via Cartan’s structure equations, illustrated by examples. The second lecture will focus mainly on examples, including minimal submanifolds, pseudo-holomorphic curves, Willmore geometry, and prescribed curvature problems in Riemannian and Finsler geometry.
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London Mathematical Society -- EPSRC Durham Symposium Geometric and Algebraic Aspects of Integrability
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