My main goal is to present a somewhat technical result, joint with Karim Adiprasito and Ehud Hrushovski, about the existence of a family of polynomials whose zeros (at a certain desired family of sets) increase faster than their degree.I will explain the 'local' and 'global' consequences of this result. In the unlikely case I have enough time, I shall attempt to elaborate on the relation to quantifier-free stability in Globally Valued Fields.This will be in some sense complementary to my recent talk in Banff.[-]