27 citations · 83 across the 13 of their papers we have counts for
14 papers
Bounded geometry for PCF-special subvarieties
Laura DeMarco, Niki Myrto Mavraki, Hexi Ye
For each integer , let denote the moduli space of maps of degree . We study the geometric configurations of subsets of postcriti…
Common preperiodic points for quadratic polynomials
Laura DeMarco, Holly Krieger, Hexi Ye
Let for . We show there exists a uniform bound on the number of points in that can be preperiodic for both a…
Uniform Manin-Mumford for a family of genus 2 curves
Laura DeMarco, Holly Krieger, Hexi Ye
We introduce a general strategy for proving quantitative and uniform bounds on the number of common points of height zero for a pair of inequivalent height functions on $\mathbb{P}…
The Dynamical Manin-Mumford Conjecture and the Dynamical Bogomolov Conjecture for endomorphisms of (P^1)^n
Dragos Ghioca, Khoa D. Nguyen, Hexi Ye
We prove Zhang's Dynamical Manin-Mumford Conjecture and Dynamical Bogomolov Conjecture for dominant endomorphisms of (P^1)^n. We use the equidistribution theorem for points of smal…
Bounded height in families of dynamical systems
Laura DeMarco, Dragos Ghioca, Holly Krieger +3
Let a and b be algebraic numbers such that exactly one of a and b is an algebraic integer, and let f_t(z):=z^2+t be a family of polynomials parametrized by t. We prove that the set…
The Dynamical Andre-Oort Conjecture for cubic polynomials
Dragos Ghioca, Hexi Ye
In the moduli space of degree d polynomials, the special subvarieties are those cut out by critical orbit relations, and then the special points are the post-critically finite poly…