Title: A lower bound on the canonical height for polynomials
Speaker: Nicole Looper
Speaker Info: Northwestern University
Brief Description:
Special Note:
Abstract:
The canonical height associated to a rational function defined over a number field measures arithmetic information about the forward orbits of points under that function. Silverman conjectured that given any number field K and degree d at least 2, there is a uniform lower bound on the canonical heights associated to degree d rational functions defined over K, evaluated at points of K having infinite forward orbit. I will discuss a proof of such a lower bound across large families of polynomials. I will also discuss related questions, both in the setting of elliptic curves and that of dynamical systems.Date: Monday, January 22, 2018