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. Speaker(s): Nicole Looper (Northwestern)