Current Topics Seminar: What do number theorists know about homotopy groups?

In homotopy theory, one is often interested in classifying maps between shapes which are "essentially different", i.e. which cannot be continuously deformed into each other. Even in the most simple of cases, such as classifying maps between spheres, this turns out to quickly lead into very deep waters.

While the answers one obtains can appear chaotic at first glance, they contain many subtle patterns and periodicities, or the so-called "music of the spheres". As first discovered by Quillen half a century ago, these phenomena are closely related to number theory, providing a surprising bridge between topology and arithmetic. This talk will be a gentle introduction to this circle of ideas.