Phase transitions on one-dimensional symbolic systems
By Tamara Kucherenko
Appears in collection : Diophantine approximation and transcendence / Approximation diophantienne et transcendance
We will present work in progress, joint with Hexi Ye, towards a conjecture of Bogomolov, Fu, and Tschinkel asserting uniform bounds for common torsion points of nonisomorphic elliptic curves. We introduce a general approach towards uniform unlikely intersection bounds based on an adelic height pairing, and discuss the utilization of this approach for uniform bounds on common preperiodic points of dynamical systems, including torsion points of elliptic curves.