Complex Analysis, Dynamics and Geometry Seminar

I will discuss joint work with Laura DeMarco and Hexi Ye in which we use dynamical techniques to prove a conjecture of Bogomolov-Fu-Tschinkel asserting a uniform bound on the number of common torsion points of distinct elliptic curves. This bound implies a uniform Manin-Mumford result for a family of curves in their Jacobians. I will explain the application of this strategy to bound the number of common preperiodic points of any two dynamically unrelated maps of the Riemann sphere, and apply them to deduce a uniform bound for common preperiodic points of two unrelated quadratic polynomials. Speaker(s): Holly Krieger (Cambridge)