Past lectures

Abstract

The course will begin with an introduction to the technique of exterior differential systems and the basic concepts of integral manifolds, involutivity, Cartan-Kähler existence theory, and prolongation. The ideas will be illustrated by means of applications to various problems in geometry and partial differential equations. After this preliminary material, several more advanced applications will be covered, including Cartan's generalization of Lie theory and its application to existence of various geometric objects, including Lie algebroids and groupoids and their appearance in differential geometry. Also, applications to holonomy, various soliton equations, calibration theory, and the calculus of variations will be covered as time permits and interest of the audience directs.