Research Publications 12. Geometry of PCF parameters in spaces of quadratic polynomials (with Laura DeMarco) Algebra and Number Theory, to appear 11. On the dynamical Bogomolov conjecture for families of split rational maps (with Harry Schmidt) Duke Mathematical Journal, to appear 10. A dynamical Shafarevich theorem for endomorphisms of projective space (with Jamie Juul, Holly Krieger and Nicole Looper) Proceedings of the AMS, to appear 9. Elliptic surfaces and intersections of adelic R-divisors (with Laura DeMarco) Journal of the European Mathematical Society, 26 (2024), no. 10, 3639–3684. 8. Dynamics on P^1: preperiodic points and pairwise stability (with Laura DeMarco) Compositio Mathematica, volume 160 (2024), no. 2, 356–387. 7. Height coincidences in products of the projective line (with Harry Schmidt and Robert Wilms) Mathematische Zeitschrift, volume 304, issue 2 (2023) 6. Quasi-adelic measures and equidistribution on P^1 (with Hexi Ye) Ergodic Theory and Dynamical Systems, 43 (2023), no. 8, 2732–2779. 5. Variation of Canonical Height for Fatou points on P^1 (with Laura DeMarco) Journal für die reine und angewandte Mathematik (Crelle), 795 (2023), 183–220. 4. Variation of canonical height and equidistribution (with Laura DeMarco) American Journal of Mathematics, 2020, vol. 142, no. 2, 443-473. 3. Algebraic approximations to linear combinations of powers: an extension of results by Mahler and Corvaja-Zannier (with Avinash Kulkarni and Khoa Nguyen) Transactions of the AMS, 2019, vol. 371, 3787-3804. 2. Impossible intersections in a Weierstrass family of elliptic curves Journal of Number Theory, Volume 169 (2016) 21-40 . 1. Variation of the canonical height in a family of rational maps (with Dragos Ghioca) New York Journal of Mathematics, Volume 19 (2013) 873-907. Preprints 16. The geometry of preperiodic points in families of maps on P^N (with Laura DeMarco) 15. Bounded geometry for PCF-special subvarieties (with Laura DeMarco and Hexi Ye) 14. Multiplier spectrum of maps on P^1: theorems of Ji-Xie and Ji-Xie-Zhang (with Laura DeMarco) 13. Arithmetic dynamics of random polynomials (with Pierre Le Boudec)