### 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.

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