In the field of holomorphic dynamics, we learn that the Lattès maps – the rational functions on ℙ1 that are quotients of maps on elliptic curves – are rather boring. We can understand their dynamics completely. But viewed arithmetically, there are still unanswered questions. I’ll begin the talk with some history of these maps. Then I’ll describe one of the recent questions and how it has led to interesting complex-dynamical questions about other families of maps on ℙ1 and, in turn, new perspectives on the arithmetic side. The new material is a joint project with Myrto Mavraki.
This video is part of the Number Theory Web Seminar series.
