Nicole Looper

Dynamical uniform boundedness and the abc-conjecture

In 1994, Morton and Silverman formulated what is now known as the Uniform Boundedness Conjecture. A major open problem in arithmetic dynamics, it is a generalization of the theorems of Mazur and Merel on uniform bounds on the rational torsion points on elliptic curves. In this talk, I will discuss a uniform boundedness theorem for unicritical polynomials. I will also discuss the relevant tools from Diophantine geometry and their relation to the abc-conjecture.