Some cases of the Zilber-Pink conjecture in $Y(1)^n$.

Abstract: The Zilber-Pink conjecture is a far reaching and widely open conjecture in the area of "unlikely intersections" generalizing many previous results in the area, such as the recently established André-Oort conjecture. In the case of curves in $Y(1)^n$, thanks to work of Habegger and Pila, the conjecture has been reduced to the purely arithmetic problem of establishing lower bounds for certain Galois orbits. I will discuss how a method first introduced by Y. André that produces height bounds helps us establish the needed bounds for Galois orbits, and thus cases of Zilber-Pink, for certain curves in $Y(1)^n$.

Mathematics

Audience: researchers in the topic

Greek Algebra & Number Theory Seminar