Abstract:

While the theory of partial differential equations contains a few theorems with sweeping generality, it consists much more of results on restricted classes of intrinsically interesting equations. For this reason one keeps returning to a small collection of prototypical equations to ask new questions. I intend this talk to be a very informal introduction to the sort of questions one asks about PDE, but in the tradition of Time Magazine I have selected the one equation which I think has been most influential in the 20th century as its centerpiece. Opposing views from the audience are welcome.