Dynamical uniform boundedness and the abc-conjecture
Heilbronn Number Theory Seminar
6th February 2019, 4:00 pm – 5:00 pm
Howard House, 4th Floor Seminar Room
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.