One of the most famous – and still not fully understood – objects in mathematics is the Mandelbrot set. It is defined as the set of complex numbers c for which the polynomial fc(z)=z2+c has a connected Julia set. But the Mandelbrot set turns out to be related to many different areas of mathematics. Inspired by recent results in arithmetic geometry, I will describe how the tools of arithmetic intersection theory can be applied in the setting of these complex dynamical systems to give new information about the Mandelbrot set.
This is joint work with Myrto Mavraki.
This video was produced by the Hausdorff Center for Mathematics, and was part of the conference Panorama of Mathematics II.
