Arithmetic dynamics of random polynomials

We begin with an introduction to arithmetic dynamics and heights attached to rational maps. We then introduce a dynamical version of Lang’s conjecture concerning the minimal canonical height of non-torsion rational points in elliptic curves (due to Silverman) as well as a conjectural analogue of Mazur/Merel’s theorem on uniform bounds of rational torsion points in elliptic curves (due to Morton-Silverman). It is likely that the two conjectures are harder in the dynamical setting due to the lack of structure coming from a group law. We describe joint work with Pierre Le Boudec in which we establish statistical versions of these conjectures for polynomial maps.

Zoom: https://harvard.zoom.us/j/99334398740

Password: The order of the permutation group on 9 elements.