### Uniform Manin-Mumford in genus 2

Heilbronn Number Theory Seminar

6th March 2019, 4:00 pm – 5:00 pm

Howard House, 4th Floor Seminar Room

I will discuss joint work with Laura DeMarco and Hexi Ye in which we use dynamically-inspired techniques towards a conjecture of Bogomolov-Fu-Tschinkel asserting a uniform bound on the number of common torsion points of distinct elliptic curves. I will explain our strategy, which has general application to proving uniform bounds in unlikely intersections, and how this theorem implies the first uniform bound on the number of torsion images in their Jacobians for a two-dimensional family of genus 2 curves. No dynamical background will be assumed.

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