Neil Dobbs: Line, spiral, dense

Abstract. Generic analytic curves are dense in the plane. For particular parametrised families of analytic curves, this need not be true (e.g. graphs of complex polynomials), or something stronger could be true (e.g. under the zeta-function, the image of every vertical line in the critical strip is dense). Not many classes of explicit dense curves were known. In an accessible talk with lots of pictures, I will show that exponential of exponential of almost every line in the complex plane is dense in the plane, along with some related results.