Minimal models for rational functions in a dynamical setting

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• Nils Bruin (Simon Fraser University)
• Tuesday 20 February 2018, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Beth Romano.

We consider the following conjecture by Silverman:

For each d>=0 there is a constant C(d) such that for each rational function phi(z) in Q(z) of degree d>=0 and such that phi^2 is not a polynomial, and for any alpha in Q, the orbit

O(phi,alpha)={alpha,phi(alpha),phi(phi(alpha)),...}

contains at most C(d) integers if phi is minimal.

This conjecture is inspired by uniform boundedness conjectures on the number of integral points on elliptic curves in minimal Weierstrass form.

As for elliptic curves, the conjecture is clearly false without a minimality condition. In this talk we will explore a suitable notion of minimality and a way to compute it. See [Nils Bruin, Alexander Molnar. Minimal models for rational functions in a dynamical setting. LMS J . Comput. Math. 15 (2012), 400—417.]

This talk is part of the Number Theory Seminar series.

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