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Friday, October 10, 2014

**Abstract:** Jet bundles are a convenient framework for studying PDE's from a geometric perspective. We will introduce the notion of a jet bundle, incorporating examples along the way, and explicitly see how sections of a jet bundle can give rise to PDE's. We'll then survey some of the applications of jet theory. In particular, we'll explore the relationship between sections of the first jet bundle and connections on a fiber bundle, introduce the notion of an h-principle, and, time permitting, discuss some singularity theory. For the sake of time, there will be no proofs. Our discussion will center around some intriguing examples that will motivate why the theory of jet bundles is useful.