Holly Krieger

Lecturer, Department of Pure Mathematics and Statistics

Corfield Fellow, Murray Edwards College


I study the arithmetic and algebraic aspects of families of complex dynamical systems.

In preparation

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)


Reduction of dynatomic curves (with J. Doyle, A. Obus, R. Pries, S. Rubenstein-Salzedo, L. West)

To appear in Ergodic Theory and Dynamical Systems.

Bounded height for unlikely intersections in algebraic dynamical systems (with L. DeMarco, D. Ghioca, K. Nguyen, T. Tucker, H. Ye)

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.

Primitive prime divisors in the critical orbit of z^d+c

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.

Research talks

CIRM, Luminy, France -- April 2015.