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Abstract: Jet schemes are fancy new tools for describing
various things in algebraic geometry, but their origins are fairly
simple. Basically a jet is a way of approximating something; 1-jets
tell us about derivatives and tangent vectors, 2-jets talk about
second derivatives, and so on. In this talk, I'll introduce some
language from algebraic geometry in order to define a few types of
jets, and use them with a little bit of intersection theory to derive
a nice classical result - the number of inflection points on a plane
curve. I'll also talk a bit about why these fancy new tools are of
current interest.
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