I study the arithmetic and algebraic aspects of families of complex dynamical systems.
Arboreal Galois representations for maps with few critical points (with J. Juul, N. Looper, M. Manes, B. Thompson, L. Walton)
A spectral gap of Thurston eigenvalues for unbounded post-critically finite rational maps
Lower bounds on dynamical height pairings (with L. DeMarco and H. Ye)
To appear in Ergodic Theory and Dynamical Systems.
To appear in International Math. Research Notices.
Cohomological conditions on endomorphisms of projective varieties (with P. Reschke)
Bulletin de la SMF (2017) Vol. 145 No. 3, 449 - 468.
The dynamical André-Oort conjecture for unicritical polynomials (with D. Ghioca, K. Nguyen, H. Ye)
Duke Math. J. (2017) Vol. 166 No. 1, 1 - 25.
A case of the dynamical André-Oort conjecture (with D. Ghioca, K. Nguyen)
International Math. Research Notices (2016) Vol. 2016, 738-758.
Uniform boundedness of S-units in arithmetic dynamics (with A. Levin, Z. Scherr, T. Tucker, Y. Yasufuku, M. Zieve)
Pacific Journal of Mathematics (2015) Vol. 274 No. 1, 97-106.
International Math. Research Notices (2013) Vol. 2013, 5498-5525.
Some consequences of Schanuel's conjecture (with C. Cheng, B. Dietel, M. Herblot, J. Huang, D. Marques, J. Mason, M. Mereb, S.R. Wilson)
Journal of Number Theory (2009) No. 6, 1464-1467.
CIRM, Luminy, France -- April 2015.