Research

My mathematical interests lie in arithmetic dynamics and arithmetic geometry.  Links to preprints of the articles I've written may be found below. 

Publications and Preprints:

• Arakelov-Green's functions for dynamical systems on projective varieties. pdf

• Local heights on abelian varieties and integral torsion points, with R. de Jong and F. Shokrieh. In progress

• A dynamical Shafarevich theorem for endomorphisms of projective space, with J. Juul, H. Krieger, and N.M. Mavraki. To appear in Proceedings of the AMS. pdf

• A uniform quantitative Manin-Mumford theorem for curves over function fields, with J. Silverman and R. Wilms. pdf

• A Lehmer-type height lower bound for abelian surfaces over function fields, with J.H. Silverman. To appear in Transactions of the AMS. pdf

• A Bogomolov property for the canonical height of maps with superattracting periodic points. pdf

• The Uniform Boundedness and Dynamical Lang Conjectures for polynomials. pdf

• Dynamical uniform boundedness and the abc-conjecture. Inventiones Mathematicae 225(3): 1-44 (2021) pdf

• Arboreal representations for rational maps with few critical points, with J. Juul, H. Krieger, M. Manes, B. Thompson, and L. Walton.  In Research Directions in Number Theory, Association for Women in Mathematics Series, vol. 19, 133-151.

• The abc-Conjecture implies uniform bounds on dynamical Zsigmondy sets. Transactions of the AMS 373 (2020): 4627-4647 pdf

• A lower bound on the canonical height for polynomials. Math. Annalen 373 (2019): 1057-1074. pdf

• Dynamical Galois groups of trinomials and Odoni's Conjecture. Bulletin of the LMS 51(2): 278-292 (2019). pdf

• Galois groups of iterates of some unicritical polynomials, with M. Bush and W. Hindes. Acta Arithmetica 181 (2017): 57-73. pdf