Algebraic geometry for the jet set

Zack Treisman
Department of Mathematics, University of Washington

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.