Picturing Differential Forms
Texts on ordinary differential equations typically present the picture of a vector field in the plane. At a zero of a vector field something interesting happens; eigenvalues indicate the nearby behavior of the vector field. This talk presents the corresponding story for differential forms in the plane. There is a simple and useful picture of a differential form, but it is quite different from that for a vector field. There are also numerical invariants at a zero of a differential form, but they belong to quite another chapter of linear algebra. Nevertheless, they have an interesting practical interpretation.